1

CERTIFICATE

This is to certify that the project report entitled “Finite Element Analysis of Flat Plate & Beam

Supported Slab” for the award of the degree of B.sc in civil engineering, is a bona fide record

of the research work done by them under my supervision. The project has not been submitted

earlier either to this university or elsewhere for the fulfillment of the requirement of any

course.

MD. TARIKUL ISLAM

SUPERVISOR, PROJECT AND THESIS

SR. LECTURER AND COURSE COORDINATOR

DEPARTMENT OF CIVIL ENGINEERING.

UNIVERSITY OF INFORMATION TECHNOLOGY AND SCIENCES

2

DECLARATION

We declare that this dissertation has not been previously accepted in substance

for any degree and is not being submitted in candidature for any degree. We

state that this dissertation is the result of our own independent

work/investigation, except where otherwise stated.

We hereby give consent for any dissertation, if accepted, to be available for

photocopying and understand that any reference to or quotation from my thesis

will receive an acknowledgement.

Md. Imran Hossain

ID: 12310177

Md. Ruhul Amin

ID: 12410196

Md. Dider-E-Alam

ID: 11510086

Md. Tarikul Islam

3

Course Code: CE 490

Course Title: Project

Project On

Finite Element Analysis of Flat Plate & Beam Supported

Slab

Written by

Md. Imran Hossain(12310177)

Student,Dept. of Civil Engineering, UITS

Md. Ruhul Amin (12410196)

Student,Dept. of Civil Engineering, UITS

Md. Dider-E-Alam (11510086)

Student,Dept. of Civil Engineering, UITS

4

To the memory of our honorable teacher

Md. Tarikul Islam

Lecturer, Dept. of Civil Engineering, UITS

Submission Date:

5

Acknowledgement

At first all praises belong to the Almighty, the most Merciful, the most

Beneficent to men and His action, which provides us the chance to conduct this

study.

We express our gratitude to Md. Tarikul Islam, lecturer, department of

civil Engineering, UITS for his guidance, advice and encouragement towards the

successful completion of the study.

We express our thanks to the fellow students of Department of Civil Engineering

for their active help and advice.

Finally, I like to thank all of them who wished my well and inspired us for the

completion of the study.

6

Table of Contents

Chapter 1 Introduction

1.1 General ………………………………………………………………………………………………13

1.2 Slab System ………………………………………………………………………………………..14

1.3 Objective of the Study ……………………………………………………………………….15

Chapter 2 Literature Review

2.1 General ………………………………………………………………………………………………16

2.2 Classification of Slab……………………………………………………………………………17

2.3 Concrete slab floors…………………………………………………………………………….17

2.4 Different types…………….…………………………………………………….……………..…17

2.4.1 Slab on grounds…..……………………………………………………………………………17

2.4.2 Suspended Slab.....................................................................................18

2.4.3 Precast slab…….....................................................................................18

2.5 Types of Slab…………………………….………………….………………………………………18

2.6 Load path/Framing possibilities of Slab………..………………………………………21

2.6.1Two load path options……………………………………………………………………….22

2.7 Behavior of one way slab…………..…………………………………………………………23

2.8 Behavior of two slab…..………………..………………………………………………………24

2.9 One way Slabs…….....................................................................................24

2.10 Two way Slabs……..................................................................................29

2.10.1 Two way column Supported slab (Flat plate)……….………………….........29

2.11 Slab analysis method……………................................................................33

2.11.1 Direct design method…….…................................................................33

2.11.2 Equivalent frame method…................................................................34

2.11.3 Finite element method………………………...............................................35

2.11.3.1 Introduction..................…................................................................35

7

2.11.3.2 What is FE and why use it? ...............................................................35

2.11.3.3 History...........................…................................................................36

2.11.3.4 When to FE analysis………………………................................................36

2.11.3.5 Advantages……………………................................................................37

2.11.3.6 Disadvantages……………………………….................................................37

2.11.3.7 Finite Element Software…………………...............................................37

2.11.4 Staad.Pro……………….…………................................................................38

2.11.4.1 Introduction……………………...............................................................38

2.11.4.2 About Staad Pro……….……................................................................39

2.11.4.3. Features of Staad Pro……………………….............................................40

2.11.4.4 Techniques for slab design using FEA by Staad.Pro….......................41

2.11.4.4.1 Design using average stress resultants…………….…….....................42

2.11.4.4.2 Computation of design moments using bending moment...........47

2.11.4.5 Design……………………………………….....................................................48

2.11.4.6 Conclusion……………….……................................................................49

Chapter 3 Design Methodology

3.1 General ………………………………………………………………………………………………50

3.2 Plan of Flat plate & Beam supported slab……………………………………………51

3.3 Flat Plate design…….……………………………………………………………………………52

3.4 Basic data for the Structures……………………………………………………………….52

3.5 Design Procedure by Staad.pro…………………………………………………………...52

3.6 Analysis of a plate...............................................................................…...64

3.7 Viewing the output file for flat plate .................................................…...65

3.8 Post processing…………………………………………………………………………………...65

3.9 Staad pro. Output file for beam supported slab……………………………….…...74

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Chapter 4 Results & Discussions

4.1 General ……………………………………………………………………………….………………75

4.2 Mesh analysis…..…….……………………………………………………………………………76

4.2.1 Summary of Flat Plat & Beam Supported Slab (25x25 Mesh)…………….76

4.2.2 Summary of Flat Plat & Beam Supported Slab (50x50 Mesh)……………..79

4.3 Stress Analysis....................................................................................…...82

4.3.1 Summary of Stress for Flat Plat & Beam Supported Slab................…...82

4.4 Displacement analysis........................................................................…...85

4.4.1 Summary of displacement for Flat Plate & Beam Supported Slab...…...85

Chapter 5 Conclusion & Recommendation

5.1 Conclusion ….………………………………………………………………………………………98

5.2 Recommendation.….……………………………………………………………………………98

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List of Figures

Fig. 2.1 Suspended slab ............................................................................................................ 18

Fig. 2.2 One way slab without beam & with beam slab .......................................................... 19

Fig. 2.3 Two way slab & grid slab ............................................................................................ 19

Fig. 2.4 Flat plate slab & flat slab ............................................................................................. 19

Fig. 2.5 Three dimensional view of one way slab, two way slab ............................................. 20

Fig.2.6 Three dimensional view of flat plate and flat slab ....................................................... 20

Fig. 2.7 One way slab load path ............................................................................................... 22

Fig. 2.8 Two way slab load path ............................................................................................... 23

Fig. 2.9 Behavior of one way slab ............................................................................................ 23

Fig. 2.10 Behavior of two way slab .......................................................................................... 24

Fig. 2.11 Flat plate short & long direction ............................................................................... 30

Fig. 2.12 Effective beam of flat plate ....................................................................................... 30

Fig. 2.13 Critical moment section ............................................................................................ 31

Fig. 2.14 Moment variation along a span ................................................................................ 32

Fig. 2.15 Moment variation across the width of critical section ............................................. 32

Fig. 2.16 portion of the slab to include with beam ................................................................. 33

Fig. 2.17 Element stress resultants at a node .......................................................................... 43

Fig. 2.18 X-direction strip selection based on Mxx contour plan ............................................ 46

Fig. 2.19 Average Bending Moment Resultants at each node along cut ................................. 48

Fig. 3.1 Plan of flat plate & beam supported slab ................................................................... 51

Fig. 3.2 Starting page of Staad pro ........................................................................................... 52

Fig. 3.3 Selected plane in Staad pro. ........................................................................................ 53

Fig. 3.4 Plate selected .............................................................................................................. 54

Fig. 3.5 Grid settings ................................................................................................................ 55

Fig. 3.6 Mesh settings page...................................................................................................... 56

Fig. 3.7 Thickness settings ........................................................................................................ 56

Fig. 3.8 Assign to Plate ............................................................................................................. 57

Fig. 3.9 Same plate thickness ................................................................................................... 57

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Fig. 3.10 Support reaction ........................................................................................................ 58

Fig. 3.11 Assigned support ....................................................................................................... 58

Fig. 3.12 Load case ................................................................................................................... 59

Fig. 3.13 Load definition........................................................................................................... 59

Fig. 3.14 Self weight ................................................................................................................. 60

Fig. 3.15 pressure on Plate ....................................................................................................... 60

Fig. 3.16 Flat slab whole structure ........................................................................................... 61

Fig. 3.17 Load of partition wall ................................................................................................ 61

Fig. 3.18 Load combination ...................................................................................................... 62

Fig. 3.19 Load combination ...................................................................................................... 62

Fig. 3.20 Analysis ...................................................................................................................... 63

Fig. 3.21 Analysis Structure ...................................................................................................... 63

Fig. 3.22 Analysis/ Print ............................................................................................................ 64

Fig. 3.23 View output file ......................................................................................................... 64

Fig. 3.24 Viewing stress values in a tabular form .................................................................... 66

Fig. 3.25 Plate center stress table ............................................................................................ 66

Fig. 3.26 Stress contour............................................................................................................ 68

Fig. 3.27 Stress contour............................................................................................................ 68

Fig. 3.28 Flat slab ...................................................................................................................... 69

Fig. 3.29 Plate edge length & area ........................................................................................... 70

Fig. 3.30 Plate Stress ................................................................................................................ 70

Fig. 3.31 Plate Force ................................................................................................................. 71

Fig. 3.32 Plate Force ................................................................................................................ 71

Fig. 3.33 Plate Force tabular form ........................................................................................... 72

Fig. 3.34 Moment value diagram ............................................................................................. 73

Fig. 3.35 Force & Moment table ............................................................................................. 73

Fig. 3.36 Force & Moment table ............................................................................................. 74

Fig. 4.1 Mesh analysis for flat plate 25*25 ............................................................................. 78

Fig. 4.2 Mesh analysis for beam slab 25*25 ........................................................................... 78

Fig. 4.3 Mesh analysis for beam slab 50*50 ............................................................................ 81

Fig. 4.3 Mesh analysis forflat plate 50*50 ............................................................................... 81

Fig. 4.5 Graph for Maximum Moment ..................................................................................... 84

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Fig. 4.6 Displacement 25*25 & 50*50 ..................................................................................... 87

Fig. 4.7 Displacement beam supported slab 25*25 ................................................................. 87

Fig. 4.8 Displacement flat plate 25*25 .................................................................................... 88

Fig. 4.9 Displacement beam supported slab 50*50 ................................................................. 88

Fig. 4.10 Displacement flat plate 50*50 .................................................................................. 89

List of Tables

Table 2.1 Area of bars in slab ................................................................................................... 26

Table 2.2 Minimum thickness of one way slab ........................................................................ 27

Table 2.3 Flexure resistance factor ......................................................................................... 28

Table 4.1 Plate center Stress Mesh(25x25) ............................................................................. 76

Table 4.2 Beam supported slab center Stress Mesh(25x25) ................................................... 77

Table 4.3 Plate center Stress Mesh(50x50) ............................................................................. 79

Table 4.4 Beam supported slab center Stress Mesh(50x50) ................................................... 80

Table 4.5 Center principal Stress for flat plate Mesh(25x25) .................................................. 82

Table 4.6 Center principal Stress for beam supported slab Mesh(25x25) .............................. 82

Table 4.7 Center principal Stress for flat plate Mesh(50x50) .................................................. 83

Table 4.8 Center principal Stress for beam supported slab Mesh(50x50) .............................. 83

Table 4.9 Node displacement for flat plate(25x25) ................................................................. 85

Table 4.10 Node displacement for beam supported slab(25x25) ........................................... 85

Table 4.11 Node displacement for flat plate(50x50) ............................................................... 86

Table 4.12 Node displacement for beam supported slab(50x50) ........................................... 86

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Abstract

In this study, flat plate and beam supported slab were analyzed and evaluated

using the Finite Element Method (FEM) modeling software STAAD Pro, with

different mesh size. For comparison of the moment, displacement, steel

requirement, an estimation of the flat plate and beam supported slab in

different mesh size was done. The basic design of the residential building

includes six (6) inch slabs thickness for beam supported slab and 9 inch slabs

thickness for flat plate. It is design by using F35 grade concrete & Me415 steel.

Firstly 3696 sqft (56x66) flat plate and beam supported slab were analyzed with

mesh size 25x25.Then same size flat plate and beam supported slab were

analyzed with mesh size 50x50.

From analysis, maximum moment of the flat plate is 57.8% & 79.2% higher than

beam supported slab with respective mesh size 25X25 and 50X50. Maximum

node displacement of the flat plate is 10% more than beam supported slab when

mesh size is 25X25. But Maximum node displacement of the flat plate is 9.8%

less than beam supported slab when mesh size is 50X50. Furthermore, analysis

shows an increase of 16% reinforcement & 15% concrete for flat plate than

beam supported slab.

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Chapter 1

Introduction

1.1 General

A slab is a structural element whose thickness is small compared to its own length and width.

Slabs are usually used in floor and roof construction. According to the way loads are

transferred to the supporting beams and columns, slabs are classified into two types; one-

way and two-way.

Concrete slab in some cases may be carried out directly by columns without the use of beams

or girders. Such slabs are described as flat plates and are commonly used where spans are not

large and loads not particularly heavy. Flat slab construction is also beamless but incorporates

a thickened slab region in the vicinity of the column and employs flared column tops. Both

are devices to reduce stresses due shear and negative bending around the columns. They are

referred as drop panels and column capitals respectively. Closely related to the flat plate slab

is the two-way joist, also known as grid or waffle slab.

In many domestic and industrial buildings a thick concrete slab, supported on foundations or

directly on the subsoil, is used to construct the ground floor of a building. These can either be

"ground-bearing" or "suspended" slabs. In high rise buildings and skyscrapers, thinner, pre-

cast concrete slabs are slung between the steel frames to form the floors and ceilings on each

level.

1.2 Slab System

The scope of this study was limited to reinforced concrete flat plate systems. Flat plate

systems are a subset of the two-way slab family, meaning that the system deforms in two

directions. Flat plate systems are reinforced concrete slabs of uniform thickness that transfer

loads directly to supporting columns, and are distinguished from other two way systems by

the lack of beams, column capitals, and drop panels. Flat plate systems have several

14

advantages over other slab systems. The absence of beams, capitals, and drop panels allow

for economical formwork and simple reinforcement layouts, leading to fast construction.

Architecturally, flat plates are advantageous in that smaller overall story heights can be

achieved due to the reduced floor structure depth required, and the locations of columns

and walls are not restricted by the location of beams. Flat plates can be constructed as thin

as 5 inches. In fact, gamble estimates that in areas where height restrictions are critical, the

use of flat plates enable an additional floor.

The floor system of a structure can take many forms such as in situ solid slab, ribbed slab or

pre-cast units. Slabs may span in one direction or in two directions and they may be supported

on monolithic concrete beam, steel beams, walls or directly by the structure’s columns.

Continuous slab should in principle be designed to withstand the most unfavorable

arrangements of loads, in the same manner as beams. Because there are greater

opportunities for redistribution of loads in slabs, analysis may however often be simplified by

the use of a single load case. Bending moment coefficient based on this simplified method

are provided for slabs which span in one direction with approximately equal spans, and also

for flat slabs.

For approximately every 10 floors in a structure, as compared to a general two- way system

with the same clear story heights. The savings in height ultimately lead to economic savings

in many areas, including mechanical systems, foundations, and non-structural components

such as cladding. Another benefit of flat plate systems is good performance under fire

conditions, due to the lack of sharp corners susceptible to spelling. Often the limiting factor

in the selection of flat plate systems as a design solution is the difficulty in shear and

moment transfer at the column connections. Indeed this difficulty often necessitates the

inclusion of drop panels or column capitals. As such, the choice to use a flat plate system is

often determined based on the span length and loading. According to the Port- land Cement

Association, for live loads of approximately 50 pounds per square foot (psf), a span length

of 15 to 30 feet is economical, and for live loads of 100 psf or more, a span length of 15 to

30 feet is economical. Based on economy of construction as well as the loading limitations

described above, flat plate systems are well suited for use in multi-story and high-rise

15

reinforced concrete hotels, apartments, hospitals, and light office spaces, and are perhaps the

most commonly used slab system for these types of structures today.

1.3 Objective of the Study

The objectives of design comparison of both type analysis are as follows

1. To study the FEM systematically for the solution of complex problems

2. To study FEM for minimum understanding to use software for practical design and

analysis problems

3. To analyze RCC flat plate & beam supported slab by finite element method using

software STAAD Pro.

4. To design RCC flat plate & beam supported slab by finite element method using

software STAAD Pro.

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Chapter 2

Literature Review

2.1 General

Common practice of design and construction is to support the slabs by beams and support

the beams by columns. This may be called as beam-slab construction. The beams reduce the

available net clear ceiling height. Hence in warehouses, offices and public halls sometimes

beams are avoided and slabs are directly supported by columns. This types of construction is

aesthetically appealing also. These slabs which are directly supported by columns are called

Flat Slabs.

Flat-slab building structures possesses major advantages over traditional slab-beam-column

structures because of the free design of space, shorter construction time, architectural

functional and economical aspects. Because of the absence of deep beams and shear walls,

flat-slab structural system is significantly more flexible for lateral loads then traditional RC

frame system and that make the system more vulnerable under seismic events.

The system consists of columns resting directly on floor slabs for which sufficient strength and

ductility should be provided to enable sustaining of large inelastic deformations without

failure. The absence of beams, i.e., the transferring of their role to the floor RC structure which

gains in height and density of reinforcement in the parts of the hidden beams, the bearing

capacity of the structural system, the plate-column and plate-wall connection, all the

advantages and disadvantages of the system have been tested through long years of

analytical and experimental investigations. For the last 20 to 30 years, the investigations have

been directed toward definition of the actual bearing capacity, deformability and stability of

these structural systems designed and constructed in seismically active regions.

The economy of flat plate buildings has lead to their wide spread utilization throughout the

world. Conventionally flat-plate structure is generally used for lightly loaded structures such

as apartments, hotels, and office buildings with relatively short spans, typically less than 6m.

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2.2 Classification of Slabs

Slabs are classified based on many aspects

1. Based of shape: Square, rectangular, circular and polygonal in shape.

2. Based on type of support: Slab supported on walls, Slab supported on beams, slab

supported on columns (Flat slabs).

3. Based on support or boundary condition: Simply supported, Cantilever slab,

overhanging slab, Fixed or Continues slab.

4. Based on use: Roof slab, Floor slab, Foundation slab, Water tank slab.

5. Basis of cross section or sectional configuration: Ribbed slab /Grid slab, Solid slab, Filler

slab, folded plate.

6. Basis of spanning directions:

one way slab – Spanning in one direction

two way slab _ Spanning in two direction

In general, rectangular one way and two way slabs are very common and are discussed in

detail.

2.3 Concrete Slab Floors

Concrete slab floors come in many forms and can be used to provide great thermal comfort

and lifestyle advantages. Slabs can be on-ground, suspended, or a mix of both. They can be

insulated, both underneath and on the edges. Conventional concrete has high embodied

energy. It has been the most common material used in slabs but several new materials are

available with dramatically reduced ecological impact.

2.4 Different Types

Some types of concrete slabs may be more suitable to a particular site and climate zone

than others.

2.4.1 Slab-on-ground

Slab-on-ground is the most common and has two variants: conventional slabs with deep

excavated beams and waffle pod slabs, which sit near ground level and have a grid of

expanded polystyrene foam pods as void formers creating a maze of beams in between.

Conventional slabs can be insulated beneath the broad floor panels.

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2.4.2 Suspended slab

Suspended slabs are formed and poured in situ, with either removable or ‘lost’ non-load

bearing formwork, or permanent formwork which forms part of the reinforcement.

Fig.2.1 Suspended slab

2.4.3 Precast slab

Precast slabs are manufactured off site and craned into place, either in finished form or with

an additional thin pour of concrete over the top. They can be made from conventional or

post-tensioned reinforced concrete, or from autoclaved aerated concrete (AAC).

2.5 Types of Slabs

There are different types of slab

i. One way slab

ii. Two way slab

iii. Flat plate

iv. Flat slab

v. Grid or waffle slab

19

Fig. 2.2 One way slab without Beam &with beam

Fig. 2.3 Two way slab & Grid slab

Fig. 2.4 Flat plate slab & Flat slab

20

Fig. 2.5 Three dimensional view of one way slab, two way slab

Fig.2.6 Three dimensional view of flat plate and flat slab

21

2.6 Load Path / Framing Possibilities of Slab

Let’s use a simple example

For our discussion. Column spacing 8 m c-c .We can first assume that

we’ll have major girders running in one direction in our one-way system. If we span between

girders with our slab, then we have a load path, but if the spans are too long. We will need to

shorten up the span with additional beams. But we need

22

Fig. 2.7 One way slab load path

to support the load from these new beams, so we will need additional supporting members.

Now let’s go back through with a slightly different load path. We again assume that we’ll have

major girders running in one direction in our one-way system this time, let’s think about

shortening up the slab span by running beams into our girders.

Our one-way slab will transfer our load to the beams.

2.6.1 Two Load Path options

Consideration:-

o Look for a “natural” load path

o Identify which column lines are best suited to having

major framing members (i.e. girders)

o Assume walls are not there for structural support, but

consider that the may help you in construction (forming)

23

Fig. 2.8 Two way slab load path

2.7 Behavior of One Way Slab

When a slab is supported only on two parallel apposite edges, it spans only in the direction

perpendicular to two supporting edges. Such a slab is called one way slab. Also, if the slab is

supported on all four edges and the ratio of longer span (lb) to shorter span (la) i.e. lb/la>

2practically the slab spans across the shorter span. Such a slabs are also designed as one way

slabs. In this case, the main reinforcement is provided along the spanning direction to resist

one way bending.

Fig. 2.9 Behavior of one way slab

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2.8 Behavior of Two Way Slab

A rectangular slab supported on four edge supports, which bends in two orthogonal

directions and deflects in the form of dish or a saucer is called two way slabs. For a two way

slab the ratio of lb/la shall be ≤ 2.0 (Ref. 7).

Fig. 2.10 Behavior of two way slab

2.9 One-Way Slabs

Reinforced concrete slabs are large flat plates that are supported by reinforced

concrete beams, walls, or columns; by masonry walls; by structural steel beams or

columns; or by the ground. If they are supported on two opposite sides only, they are

referred to as one-way slabs because the bending is in one direction only—that is,

perpendicular to the supported edges.

Actually, if a rectangular slab is supported on all four sides, but the long side is two or

more times as long as the short side, the slab will, for all practical purposes, act as a

25

one-way slab, with bending primarily occurring in the short direction. Such slabs are

designed as one-way slabs.

A one-way slab is assumed to be a rectangular beam with a large ratio of width to

depth. Normally, a 12-in.-wide piece of such a slab is designed as a beam the slab being

assumed to consist of a series of such beams side by side.

Normally, a beam will tend to expand laterally somewhat as it bends, but this tendency

to expand by each of the 12-in. strips is resisted by the adjacent 12-in.-wide strips,

which tend to expand also.

In other words, Poisson’s ratio is assumed to be zero. Actually, the lateral

expansion tendency results in a very slight stiffening of the beam strips, which is

neglected in the design procedure used here.

the reinforcing for flexure is placed

Perpendicular to these supports—that

is, parallel to the long direction of the

12-in.-wide beams. This flexural

reinforcing may not be spaced farther

on center than three times the slab

Thickness, or 18 in., according to the

ACI Code (7.6.5). Of course, there will

be some reinforcing placed in the

other direction to resist shrinkage and

temperature stresses. Fig.3.1 unit strip basis for flexural design

The thickness required for a particular one-way slab depends on the bending, the

deflection, and shear requirements. As described in Section 4.2, the ACI Code (9.5.2.1)

provides certain span/depth limitations for concrete flexural members where

deflections are not calculated. Because of the quantities of concrete involved in floor

slabs, their depths are rounded off to closer values than are used for beam depths.

Slab thicknesses are usually rounded off to the nearest 1/4 in. on the high side for

slabs of 6 in. or less in thickness and to the nearest 1/2 in. on the high side for slabs

thicker than 6 in.

26

As concrete hardens, it shrinks. In addition, temperature changes occur that cause

expansion and contraction of the concrete. When cooling occurs, the shrinkage effect

and the shortening due to cooling add together. It is states that shrinkage and

temperature reinforcement must be provided in a direction perpendicular to the main

reinforcement for one-way slabs. (For two-way slabs, reinforcement is provided in

both directions for bending.)

The code states that for Grade 40 or 50 deformed bars, the minimum percentage of

this steel is 0.002 times the gross cross-sectional area of the slab. Notice that the gross

cross-sectional area is bh (where h is the slab thickness).

Shrinkage and temperature reinforcement may not be spaced farther apart than five

times the slab thickness, or 18 in. When Grade 60 deformed bars or welded wire fabric

is used, the minimum area is 0.0018bh. For slabs with fy >60,000 psi, the minimum

value is (0.0018 × 60,000)/fy ≥ 0.0014.

Table: 2.1 Area of bars in slab

Areas of steel are often determined for 1-ft widths of reinforced concrete slabs, footings, and

walls. A table of areas of bars in slabs such Table 3.1 is very useful in such cases for selecting

the specific bars to be used. A brief explanation of the preparation of this table is provided

here.

27

Table: 2.2 Minimum thickness of one way slab

The designers of reinforced concrete structures must be very careful to comply with building

code requirements for fire resistance. If the applicable code requires a certain fire resistance

rating for floor systems, that requirement may very well cause the designer to use thicker

slabs than might otherwise be required to meet the ACI strength design requirements. In

other words, the designer of a building should study carefully the fire resistance provisions of

the governing building code before proceeding with the design (Ref. 1).

28

Table-2.3 Flexure resistance factor

29

2.10 Two-Way Slabs

Two-way slabs bend under load into dish-shaped surfaces, so there is bending in both

principal directions. As a result, they must be reinforced in both directions by layers of bars

that are perpendicular to each other.

the design of two-way slabs is generally based on empirical moment coefficients, which,

although they might not accurately predict stress variations, result in slabs with satisfactory

overall safety factors. In other words, if too much reinforcing is placed in one part of a slab

and too little somewhere else, the resulting slab behavior will probably still be satisfactory.

The total amount of reinforcement in a slab seems more important than its exact placement.

Designers may design slabs on the basis of numerical solutions, yield-line analysis, or other

theoretical methods, provided that it can be clearly demonstrated that they have met all the

necessary safety and service ability criteria required by the ACI Code.

2.10.1 Two-Way Column Supported Slab (Flat Plate)

When two slabs are supported by relatively shallow, flexible beams, or column line beams are

omitted altogether, as for flat plates, flat slabs, or two way joist systems, then a number of

new considerations are introduced. Fig.3.3 shows that a portion of a floor system in which a

rectangular slab panel is supported by relatively shallow beams on four sides. The beams in

turn, are carried by columns at the intersections of their centerlines. If a surface load q is

applied, that load is shared between imaginary slab strips la in the short direction and lb in the

long direction. The portion of the load that is carried by the long strips lb is delivered to the

beams B1spanning in the short direction of the panel. The portion carried by the beams B1

plus that carried directly in the short direction by the slab strips la sums up to 100% of the

load applied to the panel. Similarly the short direction slab strips la deliver a part of the long

direction by the slabs, includes 100% of the applied load.

30

Fig. 2.11 Flat plate short & long direction

A similar situation is obtained in the flat plate floor shown in fig.3.4. In this case beams are

omitted. However, broad strips of the slab centered on the columns lines in each direction

serve the same function as the beams of fig. 3.3, for this also the full load must be carried in

each direction. The presence of drop panels or column capitals in the double hatched zone

near the columns doesn’t modify this this requirement of statistics.

Fig. 2.12 Effective beam of flat plate

Fig. 3.5 shows a flat plate floor supported by columns at A, B, C and D. Fig. 3.6 shows the

moment diagram for the of span l1. In this direction the slab may be considered as a broad,

flat beam of width l2. Accordingly the load per foot of span is ql2. In any span of continuous

beam, the sum of the mid span positive moment and the average of the negative moments

31

at adjacent supports is equal to the mid span positive moment of a corresponding simply

supported beam. In terms of the slab, the requirement of statics may be written,

1

2(𝑀𝑎𝑏 +𝑀𝑐𝑑) + 𝑀𝑒𝑓 =

1

8𝑞𝑙2𝑙1

2

A similar requirements exists in the perpendicular direction, leading to relation

1

2(𝑀𝑎𝑐 +𝑀𝑏𝑑) + 𝑀𝑔ℎ =

1

8𝑞𝑙1𝑙1

2

The proportion of the total static moment that exists at each critical section can be found

from an elastic analysis that considers the relative span length in adjacent panels, the loading

pattern, and the relative stiffness of the supporting beams, if any, and that of the columns.

Fig. 2.13 Critical moment section

32

Fig. 2.14 Moment variation along a span

The moments across the width of critical sections such as AB or Ef are not constant but vary

as shown in fig. 3.7. The exact variation depends on the presence or absence of beams on the

column lines, the existence of drop panels and column capitals, as well as on the intensity of

the load. For design purposes it is convenient to divide each panel as shown in fig. 3.7 into

column strips, having a width of one-fourth of the panel width, on each side of the column

centerlines, and middle strips in the one-half panel width between two column strips.

Fig. 2.15 Moment variation across the width of critical section

In either case the typical panel is divided, for purposes of design, into column strips and

middle strips (Ref. 1). A column strips as define as a strip of slab having a width on each side

of the column centerline equal to the one-fourth the smaller of the panel dimensions l1& l2.

Such a strip includes column-lines beams, if present. A middle strip is a design bounded by

33

two column strips. In all cases, l1 is defined as the span in the direction of moment analysis

and l2 as the span in lateral direction measured center to center of the support. In the cases

of monolithic construction, beams are defined to include that part of the slab on each side of

the beam extending a distance equal to the projection of the beam above or below the slab

hw (whichever is greater) but not greater than 4 times the slab thickness Fig. 3.8.

Fig.2.16 Portion of the slab to include with beam

The ACI Code (13.5.1.1) specifies two methods for designing two-way slabs for gravity loads.

These are the direct design method and the equivalent frame method.

2.11 Slab Analysis Method

According to the design procedure recommended by ACI code, all types of two way slabs can

be designed by following methods-

1. Direct Design Method

2. Equivalent Frame Method

3. Finite Element Method

4. Strip Method

5. Yield line Method

2.11.1 Direct Design Method

Direct Design Method (DDM) For slab systems with or without beams loaded only by gravity

loads and having a fairly regular layout meeting the following conditions

For the moment coefficients determined by the direct design method to be applicable. The

following limitations must be met, unless a theoretical analysis shows that the strength

furnished after the appropriate capacity reduction or φ factors are applied is sufficient to

34

support the anticipated loads and provided that all serviceability conditions, such as

deflection limitations, are met-

1. There must be at least three continuous spans in each direction.

2. The panels must be rectangular, with the length of the longer side of any panel not

being more than two times the length of its shorter side lengths being measured c to

c of supports.

3. Span lengths of successive spans in each direction may not differ in length by more

than one-third of the longer span.

4. Columns may not be offset by more than 10% of the span length in the direction of

the offset from either axis between center lines of successive columns.

5. The unfactored live load must not be more than two times the unfactored dead load.

All loads must be the result of gravity and must be uniformly distributed over an entire

panel.

6. If a panel is supported on all sides by beams, the relative stiffness of those beams in

the two perpendicular directions, as measured by the following expression, shall not

be less than 0.2 or greater than 5.0. (Ref. 3)

𝛼𝑓1𝑙22

𝛼𝑓2𝑙12

The terms l1 and l2 were shown in Fig

2.11.2 Equivalent Frame Method

1. Equivalent frame method is described is ACI 13.7

2. It is a general method for design of two way column supported slab systems, without

the restrictions of the direct design method.

3. However, the method is only applicable in case of gravity loads and all general

provision for two way slabs, except those of ACI 13.6 are also applied in this method

4. The three dimensional slab systems are first divided into two dimensional design

frames by cutting at the panel centerlines

5. The removal of the torsion links between various design frames makes this method

conservative in nature.

6. The longitudinal distribution moments for these frames is carried out by performing

actual is 2-D frame analysis

7. Firstly, equivalent column stiffness is to be calculated unsupported edge of the slab

and torsion member

8. Secondly, the variation of moment of inertia of horizontal member along its length

between the column centerlines is to be considered

9. Thirdly, the variation of moment of inertia of the column between the centerlines of

horizontal column must be considered

35

10. The horizontal member is the equivalent frame consisting of slab, beams and drop

panel is termed Slab-Beam

2.11.3 Finite Element Method

2.11.3.1 Introduction

The relative cost of computer hardware and software has reduced significantly over recent

years and many engineers now have access to powerful software such as finite element (FE)

analysis packages. However, there is no single source of clear advice on how to correctly

analysis and design using this type of software. This guide seeks to introduce FE methods,

explain how concrete can be successfully modelled and how to interpret the results. It will

also highlight the benefits, some of the common pitfalls and give guidance on best practice.

2.11.3.2 What is FE and Why Use it?

Finite element analysis is a powerful computer method of analysis that can be used to obtain

solutions to a wide range of one- two- and three-dimensional structural problems involving

the use of ordinary or partial differential equations. For the majority of structural applications

the displacement FE method is used, where displacements are treated as unknown variables

to be solved by a series of algebraic equations. Each member within the structure to be

analyzed is broken into elements that have a finite size. For a2D surface such as a flat slab,

these elements are either triangular or quadrilateral and are connected at nodes, which

generally occur at the corners of the elements, thus creating a ‘mesh. Parameters and

analytical functions describe the behavior of each element and are then used to generate a

set of algebraic equations describing the displacements at each node, which can then be

solved.

The elements have a finite size and therefore the solution to these equations is approximate;

the smaller the element the closer the approximation is to the true solution.

36

2.11.3.3 History

FE methods generate numerous complex equations that are too complicated to be solved by

hand; hence FE analysis was of interest only to academics and mathematicians until

computers became available in the 1950s. FE methods were first applied to the design of the

fuselage of jet aircraft, but soon it was civil and structural engineers who saw the potential

for the design of complex structures. The first application to plate structures was by R J

Melosh in 1961

Initially, the use of FE required the designer to define the location of every node for each

element by hand and then the data were entered as code that could be understood by a

computer program written to solve the stiffness matrix. Nowadays this is often known as the

‘solver’. The output was produced as text data only. Many different solvers were developed,

often by academic institutes. During the 1980s and 1990s graphical user interfaces were

developed, which created the coded input files for the solver and then give graphical

representation of the results. The user interface that creates the input files for the solver is

often known as the pre-processor and the results are manipulated and presented using a

post-processor. This has considerably simplified the process of creating the model and

interpreting the results. During the late 1990s and early 2000s the software was enhanced to

carry out design as well as analysis. Initially the software post-processors would only calculate

areas of reinforcing steel required, but more recently the ability to carry out deflection

calculations using cracked section properties has been included in some software.

2.11.3.4 When to FE Analysis?

A common myth is that FE will return lower bending moments and deflections than would be

obtained using traditional methods. Thesis a false assumption as, unless previous techniques

were overly conservative, it is unlikely that a different method of analysis would give more

favorable results. In fact a comparative study carried out by Jones and Morrison

demonstrated that using FE methods for a rectangular grid gives similar results to other

analysis methods including yield line and equivalent frame analysis. Therefore, for simple

structures, there is no benefit in using FE analysis, and hand methods or specialized software

are probably more time-efficient. FE analysis is particularly useful when the slab has a

37

complex geometry, large openings or for unusual loading situations. It may also be useful

where an estimate of deflection is required.

2.11.3.5 Advantages

1. It assists in the design of slabs with complex geometry where other methods require

conservative assumptions to be made.

2. It can be used to assess the forces around large openings.

3. It can be used to estimate deflections where other methods are time-consuming,

particularly for complex geometry. this is provided that the advice on deflection

calculations later in this guide is followed.

4. It can be used for unusual loading conditions e.g. transfer slabs.

5. The model can be updated should changes occur to the design of the structure.

6. Computer processing speeds are increasing; reducing the time for analysis

2.11.3.6 Disadvantages

1. The model can take time to set-up, although the latest generation of software has

speeded up this process considerably.

2. The redistribution of moments is not easily achieved.

3. There is a steep learning curve for new users and the modelling assumptions must be

understood.

4. Human errors can occur when creating the model; these can be difficult to locate

during checking.

5. Design using FE requires engineering judgment and a feel for the behavior of concrete.

2.11.3.7 Finite Elements Softwares

This is a list of software packages that implement the finite element method for solving partial

differential equations or aid in the pre- and post-processing of finite element models.

1. ADINA: finite element software for structural, fluid, heat transfer, electromagnetic,

and multi physics problems, including fluid-structure interaction and thermo-

mechanical coupling

38

2. Autodesk Robot structural analysis: BIM software for FEM structural analysis,

including international design codes.

3. ALGOR: USA software from Autodesk. (Renamed to Simulation Multi physics.)

4. Computers and Structures: Berkeley, California-based producers of SAP2000, CSi

Bridge, ETABS, SAFE, PERFORM-3D.

5. Extreme Loading for Structures: Software made by Applied Science International for

non-linear dynamic structural analysis, progressive collapse, blast, seismic, impact and

other loading.

6. FEDEM: FEDEM is a simulation software for mechanical multi body systems

7. GTSTRUDL, INTEGRAPH System: Structural Design and Analysis Language FEM System

developed by MIT and GATECH, used in Energy and Offshore structural designs

8. Midas Gen: Korea Structural engineering famous software

9. Ing+ Microfe: Russia civil/structural engineering common software

10. MultiMech: Multiscale Structural Finite Element Analysis

11. Risa 3d: USA Structural engineering common software

12. S-FRAME: Software for civil and structural engineers

13. SCAD office: Russia civil/structural engineering common software

14. STARK ES: Russia civil/structural engineering common software

15. VisualFEA, Korean software for structural and geotechnical analysis

16. STAAD pro: USA Structural engineering common software

2.11.4 STAAD.Pro

2.11.4.1 General

STAAD.Pro is a structural analysis design program software. It includes a state of the art user

interface, visualization tools and international design codes. It is used for 3D model

generation, analysis and multi-material design. The commercial version of STAAD.Pro

supports several steel, concrete and timber design codes. It is one of the software applications

created to help structural engineers to automate their tasks and to remove the tedious and

long procedures of the manual methods. STAAD.Pro was originally developed by Research

Engineers International in Yorba Linda, CA. In late 2005, Research Engineer International was

bought by Bentley Systems.

39

2.11.4.2 About STAAD.Pro

Staad.pro is the world leading Structural analysis Design software. Incorporating design codes

for 15 different countries. Most comprehensive and universal. A comprehensive integrated

FEA and design solution, including a state of the art user interface, visualization tools and

integrated design codes. Capable of analyzing a structure exposed to dynamic response, soil

structure interaction or wind, earthquake and moving loads.

STAAD.Pro is a general purpose structural analysis and design program with applications

primarily in the building industry - commercial buildings, bridges and highway structures,

industrial structures, chemical plant structures, dams, retaining walls, turbine foundations,

culverts and other embedded structures, etc. The program hence consists of the following

task.

1. Graphical model generation utilities as well as text editor based commands

for creating the mathematical model. Beam and column members are

represented using lines. Walls, slabs and panel type entities are

represented using triangular and quadrilateral finite elements. Solid blocks

are represented using brick elements. These utilities allow the user to

create the geometry, assign properties, orient cross sections as desired,

assign materials like steel, concrete, timber, aluminum, specify supports,

apply loads explicitly as well as have the program generate loads, design

parameters etc.

2. Analysis engines for performing linear elastic and p-delta analysis, finite

element analysis, frequency extraction, and dynamic response (spectrum,

time history, steady state, etc.).

3. Design engines for code checking and optimization of steel, aluminum and

timber members. Reinforcement calculations for concrete beams, columns,

slabs and shear walls. Design of shear and moment connections for steel

members.

4. Result viewing, result verification and report generation tools for examining

displacement diagrams, bending moment and shear force diagrams, beam,

plate and solid stress contours, etc.

40

5. Peripheral tools for activities like import and export of data from and to

other widely accepted formats, links with other popular softwares for niche

areas like reinforced and prestressed concrete slab design, footing design,

steel connection design, etc.

6. A library of exposed functions called Open STAAD which allows users to

access STAAD.Pro’s internal functions and routines as well as its graphical

commands to tap into STAAD’s database and link input and output data to

third-party software written using languages like C, C++, VB, VBA,

FORTRAN, Java, Delphi, etc. Thus, Open STAAD allows users to link in-house

or third-party applications with STAAD.Pro.

2.11.4.3 Features of STAAD.Pro

Analysis

o The STAAD analysis engine has 2D and 3D capabilities for solving problems

containing beams, plate elements and 8 node bricks.

o A wide range of support conditions, load types and various other

member/element specification are available for combination with these

features.

Postprocessor – Space Frame

o Logical page control layout

o Dynamic Query Function

o Combine view ports to display various results

o Pictures of results for inclusion in output report

o Graphs of bending moments, Shear etc. for individual members

o Graphics interactive with Results tables

o Combine load diagrams with results

o Mode shapes/ Natural frequency results, time history plots

41

Steel Design

o Database of section sizes for a variety of countries e.g United Kingdom, USA,

French, German, European etc.

o Specify Composite action for design

o User specified design parameters

o Automatic iterative design to least weight algorithm, automatically updates

analysis model and re-analysis

o Design fixed groups, e.g isolated beams and columns

Concrete Design

o Design concrete for beams/columns/slabs

o IS 456, BS8110, BS8007, India, French, German, Spanish, Russian etc. design

codes

o Reinforcement details shown on beam/column

o Contours of Reinforcement available for finite element slabs

o Tabular results available

o From continuous members from analysis elements

o Individual groups and briefs

o Combine concrete and steel design in one run

2.11.4.4 Techniques for Slab Design Using FEA Results by Staad.Pro

Assuming that adequate care has been applied in the modeling of the flat plate system &

beam supported slab system, there are two conventional methods for design based on the

results of finite element analysis, each of which are presented and evaluated below. These

two methods are:

1. Design using average stress resultants

2. Design using element forces

42

2.11.4.4.1 Design Using Average Stress Resultants

Computation of Element Stress Resultants

Element stress resultants are the computed stress components per unit width located at a

node of a finite element. For a plate bending analysis, the primary element stress resultants

of interest are the bending stress resultants, which are the bending moments per unit width

evaluated at each node of the element, and the shear stress resultants, which are the shear

forces per unit width evaluated at each node. Element stresses can be computed in many

locations throughout the element, including the centroid, Gaussian quadrature integration

points, and at the nodes.

Stresses computed at the integration points are generally considered to be the most accurate.

These results are of little use to engineers, however, because the physical locations of the

Gauss points are unknown to the user. A common solution to this problem is to extrapolate

the stresses to the nodes, a more useful location for the user.

Element stresses can also be computed directly at the nodes by evaluating the strain-

displacement relation at the nodes instead of the integration points, and then applying the

material constitutive relation. The element stress resultants can be understood as the

integration of the stress field over the thickness of the element, t. The following equations

show the theoretical formulation of the element stress resultants at a typical node

43

Fig.2.17 Element Stress Resultants at a Node

Here, the z-axis is the direction perpendicular to the plane of the elements. A common point

of misinterpretation on the part of the engineer concerns the coordinate system of the results

of Equation 3.1. Mxx refers to a bending moment on the x-face of a small volume of the

element dV at a particular node, due to stress in the x-direction. Note that Mxx is not a

bending moment about the x-axis. Myy refers to a bending moment on the y-face of a small

volume of the element dV at a particular node, due to stress in the y-direction. Mxy refers to

a torsional moment on both the x- and y-faces of a small volume of the element dV at a

particular node, due to the shear stress at the particular node. Figure 2.17 presents a visual

representation of this concept. The units of each of the bending moment resultants are force-

length/length. An easy way to remember the naming convention when applying these results

in design is to say that Mxx is used to compute the reinforcing bars required in the x-direction,

and Myy is used to compute the reinforcing bars required in the y-direction. In implemented

finite element analysis codes, element stress resultants are seldom computed by integrating

the stress field because the moment-curvature relations can be directly applied to the strain

field. For a Kirchoff element, the moment resultants can be computed directly using this

equation

44

In this above Equation w is the normal displacement, ν is Poisson’s Ratio, and D is known as

the flexural rigidity and is given by Equation 3.4

The shear resultants cannot be directly evaluated using the Kirchoff formulation, however.

Instead, these results are computed by evaluating the equilibrium of the element. Thus, Qx

and Qy can be computed using Equation 3.5

For the Kirchoff element, the accuracy of Qx and Qy will generally be less than that of the

bending stress resultants because, as shown in Equation 3.5, an additional derivative is

required to compute this response quantity. For Mindlin elements, the bending moment

resultants are computed using the exact formulation as that for the Kirchoff element.

However, because the Mindlin element has the ability to represent transverse shear strain

through the element thickness, the shear resultants can be computed directly from the strain

field. Equation 3.6 shows the formulation of element stress resultants for a Mindlin element.

In this above Equation G is the shear modulus, ψx and ψy refer to the rotation of the mid-

surface normal at the node, and k accounts for the parabolic variation of transverse shear

stress in the z-direction. Generally, k = 5/6 for an assumed homogenous plate.

45

Once element stress resultants have been computed at each node of each element in

the structure, there is no guarantee that for nodes with multiple elements connected, the

element stresses computed at the node from contributing elements will be identical. This is

because the finite element method only guarantees compatibility of the displacements and

rotations at the nodes. Thus, if four elements are connected to a single node, it is likely

that four different states of stress have been computed at that node from each element. As

the finite element solution converges, these results should approach each other, but even

in a converged solution, there is no guarantee that these results will all lie within a small

tolerance. If these results vary by more than an order of magnitude, further investigation

is required as to the source of the discrepancy.

Another important consideration in the computation of element stresses is that there is

no guarantee that equilibrium is satisfied. Since stresses are only computed at the nodes, if

an engineer wishes to consider the equilibrium of a single element, or the entire structure for

that matter, the stresses must be interpolated between nodes. The physical distribution of

stress will seldom be accurately predicted by such an interpolation procedure. This does not

mean that the solution is altogether invalid, but rather that the engineer must understand

that the applied technique is an approximate one, and that the resulting design should be

critically evaluated.

Once the average element bending moment resultants have been computed for each node

in the structure, the engineer must reduce this information to something useful for design.

The first step is to divide the finite element mesh into strips, similar to those in either direct

design or the equivalent frame method, which will bound the basic cross-sections, or cuts,

to be designed. This is most easily accomplished by generating contour plots of the three

bending moment resultants. Contour plots are useful because they provide an overview of

the distribution of moment in the slab, making it easy to see not only the areas of high

concentration, but also the inflection points where the moment changes from positive to

negative. An example of selecting strip locations based on a bending resultant contour plot

is shown in Figure 3.4. “Narrow” strips should be used in areas with a high stress gradient,

whereas “wider” strips can be used in areas with little variation in moment. What

constitutes “narrow” or “wide” is subjective and can only be determined with experience

46

and expertise in modeling. One applicable guideline is that the width of a strip should

always be narrower than the dimensions of the adjacent bays. Another critical guideline is

that a strip should never represent a change in sign of bending moment across a cross-section

to be designed. If the moment changes signs across the cross-section, the cross-section is

too wide and must be reduced.

Fig. 2.18 X-Direction Strip Selection Based on Mxx Contour Plot

Once an adequate layout of strips has been determined, there are two methodologies for

determining the design moments for a particular cross-section of a strip, or cut. A cut

represents a free body upon which a resultant moment is computed for design. One

methodology for computing this design moment is to average the results of each node along

the cut. This method assumes it is possible at some locations along the cut that the capacity

provided by the reinforcement will be exceeded, but that when this occurs, these areas will

crack and thus the moments will redistribute to areas that were over-reinforced initially.

The second methodology is to design a whole cut for the maximum effect present on that

cut. In this method, it is likely that more reinforcement will be provided than necessary,

leading to an uneconomical design as well as a decrease in ductility of the section. In this

study, the first methodology is applied: design based on average results along the cut.

47

2.11.4.4.2 Computation of Design Moments Using Bending Moment

Resultants

The actual computation of design moments using bending moment resultants is attributed to

Wood and Armer. At a particular node to be designed, the slab must be reinforced in the x-

and y-directions to resist bending about both x- and y-axes. The capacity to be resisted by

bars in the x-direction is Mrx, and the capacity to be resisted by bars in the y-direction is Mry.

Initially, Mrx appears to be the same as Mxx, and Mry the same as Myy. However, this neglects

the effect of the computed torsional resultant Mxy. From Figure 3.3, it is readily apparent that

as dA becomes very small, Mxy acts simultaneously with both Mxx and Myy. Because the

shear stress, τxy, in the slab acts effectively without sign, the effect of Mxy is to always

increase the magnitude of moment to be designed. Based on these concepts, reinforcement

at the bottom of the slab in both directions must be designed to provide positive bending

moment resistance of

If the required positive moment capacity computed using either of these equations is

negative, the capacity for that component should be set equal to zero. Subsequently,

reinforcement at the top of the slab in both directions must be designed to provide negative

bending moment resistance of

If the required negative moment capacity computed using either of these equations is

positive, the capacity for that component should be set equal to zero.

Using the procedure set, the resultant design moment across the section can be determined.

An example cut is shown in Figure 3.5 to illustrate computation of the resultant moment for

the design of reinforcement in the x-direction. The average bending resultants at each node,

Mrx,1 through Mrx,n, are computed using Equations 3.7 and 3.8, where n refers to the

number of nodes along the cross-sectional cut. The total resultant moment acting on the cut,

MB, is then computed as

48

Fig. 2.19 Average Bending Moment Resultants at Each Node along Cut

In this equation, the average moment resultants from each node, Mrx,i, are averaged and

then multiplied by the width of the cut to compute the entire resultant moment acting on the

cross-section [29]. Once the resultant design moment has been computed, flexural

reinforcement is designed according to ACI 318 as explained in Section 2.1. The resultant

bending moment for the design of reinforcement in the y-direction is similarly computed

using Equation 3.9 by replacing Mrx,i with Mry,i.

2.11.4.5 Design

1. After analysis a structure has to be designed to carry loads acting on it considering a

certain factor of safety .

2. In India United Kingdom, USA, French, German, European structures are designed by

using their codes for both concrete and steel structures.

49

3. The design in STAAD.Pro supports over 70 international codes and over 20 U.S. codes

in 7 languages.

4. After designing the structure it is again analyzed and results of analysis for each beam

and column is shown in the output file

2.11.4.6 Conclusion

Staad pro is widely used by most of the organization for their construction needs.

Unfortunately, well skilled staad pro engineers are very hard to search.

If we believe in the prediction of the industry experts then those students who

will be getting trained on staad pro in the current and upcoming two years will

have bright and successful career ahead in the real estate and construction

domain

By attending this training in STAAD.Pro we were able to learn various features of

STAAD.Pro which will be very helpful in the near future

50

Chapter 3

Design Methodology

3.1 General

STAAD or (STAAD.Pro) is a structural analysis and design computer program originally

developed by Research Engineers International at Yorba Linda, CA in year 1997. In late 2005,

Research Engineers International was bought by Bentley Systems.

An older version called Staad-III for windows is used by Iowa State University for educational

purposes for civil and structural engineers. Initially it was used for DOS-Window system.

Design any type of structure and share your synchronized model data with confidence

among entire design team, using STAAD Pro. Ensure on time and on budget completion of

steel, concrete, timber, aluminum, and cold-formed steel projects, regardless of complexity.

This software can confidently design structures anywhere in the world using over 80

international codes, reducing to learn multiple software applications. Thanks to the flexible

modeling environment and advanced features such as dynamic change revisions and

management

o Lower total cost of ownership: Design any type of structure including culverts,

petrochemical plants, tunnels, bridges, and piles

o Increase design productivity: Streamline your workflows to reduce duplication of

effort and eliminate errors

o Reduce project costs and delays: Provide accurate and economical designs to your

clients and quickly turnaround change requests

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3.2 Plan of Flat Plate & Beam Supported Slab

Fig. 3.1 plan of the flat plat & beam supported slab

52

3.3 Flat Plate Design

The structure for this project is a slab fixed along two edges. We will model it using 25

quadrilateral (4-noded) plate elements. The structure and the mathematical model are shown

in the figures below. It is subjected to self weight, pressure loads and temperature loads. Our

goal is to create the model, assign all required input, perform the analysis, and go through

the results.

3.4 Basic Data for the Structure

3.5 Design Procedure by Staad Pro.

Starting the program 1. Select the STAAD Pro. icon from the STAAD Pro. V8i program group

found in the Windows Start menu. The STAAD Pro. window opens to the start screen. Figure2-

259:TheSTAAD.Prowindowdisplayingthestartscreen

Fig.3.2 starting page of Staad Pro.

Attribute Data Element

properties Slab is 9” thick

Material Constants

E, Density, Poisson, Alpha – Default values for concrete

Primary Loads LL=40 Psi , PW= 50Psi, FF=25Psi,

Combination Loads

1.4DL+ 1.7LL

Analysis Type Linear Elastic

53

Creating a new structure In the New dialog, we provide some crucial initial data necessary

for building the model. 1. Select File > New or select New Project under Project Tasks.

Fig.3.3 Selected Plane

The structure type is defined as either Space, Plane, Floor, or Truss:

Space the structure, the loading or both, cause the structure to deform in all 3 global axes (X,

Y and Z).

Plane the geometry, loading and deformation are restricted to the global X-Y plane only

Floor a structure whose geometry is confined to the X-Z plane. Truss the structure carries

loading by pure axial action. Truss members are deemed incapable of carrying shear, bending

and torsion.

2. Select Space.

3. Select Meter as the length unit and Kilo Newton as the force unit.

Hints: The units can be changed later if necessary, at any stage of the model

creation.

4. Specify the File Name as Plates Tutorial and specify a Location where the STAAD input

file will be located on your computer or network.

You can directly type a file path or click […] to open the Browse by Folder dialog, which

is used to select a location using a Windows file tree. After specifying the above input,

click Next.

The next page of the wizard, Where do you want to go? opens

5. Set the Add Plate check box

54

Fig.3.4 Plate selected

Add Beam, Add Plate, or Add Solid

Respectively, the tools selected for you used in constructing beams, plates, or solids

when the GUI opens.

Open Structure Wizard

Provides access to a library of structural templates which the program comes

equipped with. Those template models can be extracted and modified parametrically to

arrive at our model geometry or some of its parts.

Open STAAD Editor

Used to be create a model using the STAAD command language in the STAAD editor.

All these options are also available from the menus and dialogs of the GUI, even after we

dismiss this dialog.

5. Click Finish. The dialog will be dismissed and the STAAD.Pro graphical environment

will be displayed.

Elements of the STAAD.Pro screen

The STAAD.Pro main window is the primary screen from where the model generation

process takes place. It is important to familiarize ourselves with the components of that

window before we embark on creating the RC Frame of this manual explains the

components of that window in details.

55

Building the STAAD.Pro model

We are now ready to start building the model geometry. The steps and, wherever possible,

the corresponding STAAD.Pro commands (the instructions which get written in the STAAD

input file) are described in the following sections

Creating the Plates - Method 1

Steps: The Grid Settings

1. We selected the Add Plate option earlier to enable us to add plates to create the

structure. This initiates a grid in the main drawing area as shown below. The directions

of the global axes (X, Y, Z) are represented in the icon in the

Fig.3.5 grid settings

2. Lower left hand corner of the drawing area. (Note that we could initiate this grid by

selecting the Geometry > Snap/Grid Node > Plate menu option also.)

It is worth paying attention to the fact that when we chose the Add Plate option in section

3.4, the page control Geometry | Plate page is automatically selected.

As we click at the start node the second time, the following dialog opens. Select the

Quadrilateral Meshing option and click OK.

56

Fig. 3.6 Mesh setting page

The Select Meshing Parameters dialog (as we saw earlier in Method 3), comes up. Notice that

this time however, the data for the four corners is automatically filled in. The program used

the coordinates of the four nodes we selected to define A, B, C, and D. Provide the Bias and

the Divisions of the model as shown in the figure below. Click Apply.

As we click Apply, our model will appear in the drawing area as the one shown below.

Press the ESC key to exit the mesh generating mode.

Fig.3.7 Thickness settings

At this point, the Properties dialog will look as shown below.

The structure will now look as shown below.

57

Fig.3.8Assign to plate

Click anywhere in the drawing area to un-highlight the selected entities. We do this only as a

safety precaution. When an entity is highlighted, clicking on any Assign option is liable to

cause an undesired attribute to be assigned to that entity.

Fig.3.9 same plate thickness

1. In either case, the Supports dialog opens as shown in the next figure.

2. For easy identification of the nodes where we wish to place the supports,

toggle the display of the Node Numbers on.

3. Since we already know that nodes 1, 2, 5, 7, 4 and 10 are to be associated

58

with the Fixed support, using the Nodes Cursor , select these nodes.

4. Then, click Create in the Supports dialog as shown below.

Fig. 3.10 support reaction

Note: It is important to understand that the Assign button is active because of what we did

in step 4 earlier. Had we not selected the nodes before reaching this point, this option

would not have been active.

After the supports have been assigned, the structure will look like the one shown below.

Fig.3.11 Assigned Support

Load Cases Notice that the pressure load value listed in the beginning of this tutorial is in KN

and meter units. Rather than convert that value to the current input units, we will conform

to those units. The current input units, which we last set while specifying THICKNESS was

CENTIMETER. We have to change the force unit to Kilogram and the length units to Meter. To

change the units, as before, select the Input Units tool from the top toolbar, or select the

Tools > Set Current input Unit menu option from the top menu bar. In the Set Current input

59

Units dialog that comes up, specify the length units as Meter and the force units as Kilogram.

Window titled “Load” appears on the right-hand side of the screen. To initiate the first load

case, highlight Load Case Details and click Add.

Fig. 3.12 Load case

Load Definition the newly created load case will now appear under the Load Cases Details in

the Load dialog.

Fig. 3.13 Load definition

In the Add New Load Items dialog, select the Self weight Load option under the Self weight

item. Specify the Direction as Y, and the Factor as -1.0 the negative number signifies that the

self-weight load acts opposite to the positive direction of the global axis (Y in this case) along

which it is applied. Click Add. The self-weight load is applicable to every member of the

structure, and cannot be applied on a selected list of members.

60

Fig. 3.14 Self Weight

Next, let us initiate the creation of the second load case which is a pressure load on the

elements. To do this, highlight Load Case Details in the Add New Load Cases dialog, once

again, we are not associating the load case we are about to create with any code based

Loading Type and so, leave that box as none. Specify the Title of the second load case as

External Pressure Load and click Add.

Fig. 3.15 Pressure on plate

Since the pressure load is to be applied on all the elements of the model, the easiest way to

do that is to set the Assignment Method to Assign to View. Then, click Assign in the Load

dialog as shown below.

61

Fig.3.16 Flat slab whole structure

Click Define Commands in the data area on the right hand side of the screen. The

Analysis/Print Commands dialog opens.

Fig. 3.17 load of partition wall

Next, let us create the third load case which is a temperature load. The initiation of a new

load case is best done using the procedure explained in step 7. In the dialog that comes up,

let us specify the Title of the third load case as Temperature Load and click Add.

62

Fig. 3.18 Load combination

Next, in the Define Combinations box, select load case 1 from the left side list box and click

[>]. Repeat this with load case 2 also. Load cases 1 and 2 will appear in the right side list

box as shown in the figure below. (These data indicate that we are adding the two load cases

with a multiplication factor of 1.0 and that the load combination results would be obtained

by algebraic summation of the results for individual load cases.) Finally, click Add.

Fig. 3.19 Load combination

To initiate and define load case 5 as a load combination, as before, enter the Load No: as 102 and the Title as Case 1 + Case 3.

Next, repeat step 2 except for selecting load cases 1 and 3 instead of cases 1 and 2.

63

Fig. 3.20 Analysis

Thus, load 102 is also created. If we change our mind about the composition of any existing

combination case, we can select the case we want to alter, and make the necessary changes

in terms of the constituent cases or their factors.

Fig. 3.21 Analysis Structure

64

Hint:Remember to save your work by either selecting File > Save, the Save tool, or pressing

CTRL+S.

Fig. 3.22 Analysis/print

Click Define Commands in the data area on the right hand side of the screen. The

Analysis/Print Commands dialog opens.

3.6 Analysis of a plate

Fig. 3.23 View output file

65

At the end of these calculations, two activities take place. a) A Done button becomes active

b) three options become available at the bottom left corner of this information window.

The View Output File option allows us to view the output file created by STAAD. The output

file contains the numerical results produced in response to the various input commands we

specified during the model generation process. It also tells us whether any errors were

encountered, and if so, whether the analysis and design was successfully completed or not.

Section 3.10 (also, see section 1.9) offers additional details on viewing and understanding the

contents of the output file. The Go to Post Processing Mode option allows us to go to graphical

part of the program known as the Post-processor. This is where one can extensively verify the

results, view the results graphically, plot result diagrams, produce reports, etc. Section 3.11

explains the Post processing mode in greater detail. The Stay in Modelling Mode lets us

continue to be in the Model generation mode of the program (the one we currently are in) in

case we wish to make further changes to our model.

3.7 Viewing the output file

During the analysis stage, an output file containing results, warnings and messages associated

with errors if any in the output, is produced. This file has the extension .anl and may be viewed

using the output viewer. See Appendix A

3.8 Post-Processing

If there are no errors in the input, the analysis is successfully completed. The extensive

facilities of the Post-processing mode can then be used to view the results graphically and

numerically assess the suitability of the structure from the standpoint of safety, serviceability

and efficiency create customized reports and plots the procedure for entering the post

processing mode is explained in section of this manual. Node results such as displacements

and support reactions are available for all models. The methods explained in the first two

tutorials – see sections– may be used to explore these. If beams are present in the model,

beam results will be available too For this example, we will look at the support reactions. We

do not have any beams in our model, so no results will be available for this type of entity. For

plates, the results available are stresses, and “unit width” moments. There are several

different methods for viewing these results, as explained in the next few sections.

66

Viewing stress values in a tabular form

1. Select View > Tables or Right-click in the View window and select Tables from the pop-up

menu. The Tables dialog opens.

Fig.3.24 Viewing stress values in a tabular form

2. Select Plate Center Stress and click OK. The Plate Center Stress table opens.

Fig. 3.25 The Plate Center Stress table

The table has the following tabs:

Shear, Membrane and Bending

These terms are explained in Section 1.6.1 of the STAAD Technical Reference Manual. The

individual values for each plate for each selected load case are displayed.

67

This tab contains the maximum for each of the 8 values listed in the Shear, Membrane and

Bending tab.

Principal and Von Mises

These terms too are explained in Section 1.6.1 of the STAAD Technical Reference Manual. The

individual values for each plate for each selected load case are displayed, for the top and

bottom surfaces of the elements.

Summary

This tab contains the maximum for each of the 8 values listed in the Principal and Von Mises

tab. Global Moments This tab provides the moments about the global X, Y and Z axes at the

center of each element.

Stress Contours

Stress contours are a color-based plot of the variation of stress or moment across the surface

of the slab or a selected portion of it. There are 2 ways to switch on stress contour plots:

1. Select either

The Plate | Contour page

Select Results > Plate Stress Contour.

The Diagrams dialog opens

2. From the Stress type field, select the specific type of stress for which you want the

contour drawn.

3. From the Load Case selection box, select the load case number.

Stress values are known exactly only at the plate centroid locations. Everywhere else,

they are calculated by linear interpolation between the center point stress values of

adjacent plates. The Enhanced type contour chooses a larger number of points

compared to the Normal type contour in determining the stress variation.

4. View Stress Index will display a small table consisting of the numerical range of values

from smallest to largest which are represented in the plot. Let us set the following:

68

Fig.3.26 stress contour

Load case – 102

Stress Type – Von Mis Top

Contour Type – Normal Fill

Index based on Center Stress

View Stress Index

Re-Index for new view

Fig.3.27 stress contour

69

Fig.3.28 Flat slab

The following diagram will be displayed. We can keep changing the settings and click on

apply to see all the various possible results in the above facility.

Viewing plate results using element query

Element Query is a facility where several results for a specific element can be viewed at the

same time from a single dialog. Let us explore this facility for element 4.

1. Select the Plate Cursor tool.

2. Double-click on element

or

Select element 4 and then select Tools > Query > Plate.

The Plate dialog opens.

The various tabs of the query box enable one to view various types of information such as the

plate geometry, property constants, stresses, etc., for various load cases, as well as print those

values.

Some example tabs of this dialog.

70

Fig. 3.29 plate edge length & area

Fig. 3.30 plate stress

Producing an onscreen report

Occasionally, we will come across a need to obtain results conforming to certain restrictions,

such as, say, the resultant node displacements for a few selected nodes, for a few selected

load cases, sorted in the order from low to high, with the values reported in a tabular form.

The facility which enables us to obtain such customized on-screen results is the Report

menu on top of the screen.

Let us produce a report consisting of the plate principal stresses, for all plates, sorted in the

order from Low to High of the Principal Maximum Stress (SMAX) for load combined.

71

1. Select all the plates using the Plates Cursor.

2. Select Report > Plate Results > Principal Stresses.

Fig.3.31 Plate force

3. Select the Loading tab.

4. Select load cases COMBINED in the Available list and click [>] to add them to the Selected

list.

5. Select the Sorting tab. Choose SMAX under the Sort by Plate Stress category and select

List from Low to High as the Set Sorting Order

Fig. 3.32 Plate force

6. (Optional) If you wish to save this report for future use, select the Report tab, provide a

title for the report, and set the Save ID check box.

7. Click OK.

72

The following figure shows the table of maximum principal stress with SMAX values sorted

from Low to High.

Fig. 3.33 Plate force

8. To print this table, right-click anywhere within the table and select Print from the pop-up

menu.

Select the print option to get a hardcopy of the report.

To transfer the contents of this table to a Microsoft Excel file

1. Click at the top left corner of the table with the left mouse button. The entire table will

become highlighted.

2. Right click and select Copy from the pop-up menu.

3. Open an Excel worksheet, click at the desired cell and Paste the contents.

Viewing Support Reactions

Since supports are located at nodes of the structure, results of this type are available along

with other node results such as displacements.

1. Select the Node | Reactions page on the left side of the screen.

The six values — namely, the three forces along global X, Y and Z, and the three moments Mx,

My and Mz, in the global axis system — are displayed in a box for each support node.

Display of one or more of the six terms of each support node may be toggled off in the

following manner.

1. Select Results > View Value…. The Annotation dialog opens.

2. Select the Reactions tab. clear the Global X and Global Z check boxes in the direct

category.

73

3. Click Annotate and then Close. The drawing will now contain only the remaining 4

terms (see figure below).

Fig. 3.34 moment value diagram

The table on the right side of the screen contains the reaction values for all supports for all

selected load cases

Fig. 3.35 Force & Moment table

This table can also be displayed from any mode by clicking on the View menu, choosing Tables,

and switching on Support Reactions.

74

The method explained in section 3.11.3 may be used to change the units in which these values

are displayed. The summary tab contains the maximum value for each of the 6 degrees of

freedom along with the load case number responsible for it.

Fig. 3.36 Force & Moment table

This brings us to the conclusion of this tutorial. Additional help on using plates is available in

Examples 9, 10 and 18 in the Examples Manual

3.9 Staad Pro. Output File for Beam supported slab

See Appendix B

75

Chapter 4

Results & Discussions

4.1 General

The forces and displacements developed of the flat plate and beam supported slab of the

structure are got from the analysis with different mesh size. These results obtained from the

analysis have been discussed details in this chapter. Further these results have been used for

the understanding of the behavior of the structure between the beam supported slab and flat

plate under the effects of vertical loads.

In this part of the document analysis and results for Mesh analysis results, moment analysis,

displacement analysis, and stress analysis are discussed.

Results

From moment analysis results it can be observed that the flat plate is higher than

beam supported slab with respectively mesh size 25X25 and 50X50. At 25x25 mesh

size, the maximum moment of the flat plate is 57.8% more than that of the beam

supported slab and 50X50 mesh size, the maximum moment of the flat plate is 79.2%

more than that of the beam supported slab.

From node displacement analysis results it can be observed that of the flat plate is

more than beam supported slab when mesh size 25X25. But Maximum node

displacement of the flat plate is less than beam supported when mesh size 50X50.

Finally it can be observed that, the node displacement of the flat plate will decrease

as the mesh size increases.

Flat plate slab is thicker and more heavily reinforced than slabs with beams and

girders. Almost16% more reinforcement are used for flat plate structure than beam

supported structure.

Almost 15% more concrete are used for flat plate structure than beam supported

structure

76

4.2 Mesh Analysis

4.2.1 Summary of Flat Plat & Beam Supported Slab (25x25 Mesh)

Summary of table for flat plate center stress mesh analysis (25x25)

Qx Qy Sx Sy Sxy Mx My Mxy

(psi) (psi) (psi) (psi) (psi) (lb-in/in) (lb

-in/in) (lb

-in/in)

Max Qx 1106 5:1.4DL+1.7LL 386.067 -333.62 0 0 0 -26.3E 3 -32.1E 3 2.26E 3

Min Qx 1694 5:1.4DL+1.7LL -276.73 -168.68 0 0 0 -22.9E 3 -18.5E 3 -12.3E 3

Max Qy 3336 5:1.4DL+1.7LL 386.067 333.617 0 0 0 -26.3E 3 -32.1E 3 -2.26E 3

Min Qy 1106 5:1.4DL+1.7LL 386.067 -333.62 0 0 0 -26.3E 3 -32.1E 3 2.26E 3

Max Sx 35 1:SW 0 0 0 0 0 0 0 0

Min Sx 35 1:SW 0 0 0 0 0 0 0 0

Max Sy 35 1:SW 0 0 0 0 0 0 0 0

Min Sy 35 1:SW 0 0 0 0 0 0 0 0

Max Sxy 35 1:SW 0 0 0 0 0 0 0 0

Min Sxy 35 1:SW 0 0 0 0 0 0 0 0

Max Mx 53 5:1.4DL+1.7LL 4.274 3.329 0 0 0 7.84E 3 240.746 247.187

Min Mx 1106 5:1.4DL+1.7LL 386.067 -333.62 0 0 0 -26.3E 3 -32.1E 3 2.26E 3

Max My 295 5:1.4DL+1.7LL 3.435 3.749 0 0 0 280.821 8.08E 3 215.592

Min My 1106 5:1.4DL+1.7LL 386.067 -333.62 0 0 0 -26.3E 3 -32.1E 3 2.26E 3

Max Mxy 3294 5:1.4DL+1.7LL 195.325 -194.42 0 0 0 -22.3E 3 -21.7E 3 18E 3

Min Mxy 35 5:1.4DL+1.7LL 195.326 194.421 0 0 0 -22.3E 3 -21.7E 3 -18E 3

Summary of Plate Centre Stress (Mesh 25x25)BendingShear Membrane

Plate L/C

Table 4.1 Plate center stress mesh (25x25)

77

Summary of table for beam supported slab center stress mesh analysis (25x25)

Qx Qy Sx Sy Sxy Mx My Mxy

(psi) (psi) (psi) (psi) (psi) (lb-in/in) (lb-in/in) (lb-in/in)

Max Qx 1106 5:1.4DL+1.7LL 67.855 -53.82 0 0 0 -7.14E 3 -7.09E 3 280.971

Min Qx 600 5:1.4DL+1.7LL -60.277 -22.921 0 0 0 -5.03E 3 -6.04E 3 -1.05E 3

Max Qy 2264 5:1.4DL+1.7LL -35.309 56.207 0 0 0 -6.23E 3 -3.34E 3 643.449

Min Qy 2767 5:1.4DL+1.7LL -35.364 -56.02 0 0 0 -6.23E 3 -3.34E 3 -643.34

Max Sx 35 1:SW 0.158 0.124 0 0 0 -2.329 -1.978 0.045

Min Sx 35 1:SW 0.158 0.124 0 0 0 -2.329 -1.978 0.045

Max Sy 35 1:SW 0.158 0.124 0 0 0 -2.329 -1.978 0.045

Min Sy 35 1:SW 0.158 0.124 0 0 0 -2.329 -1.978 0.045

Max Sxy 35 1:SW 0.158 0.124 0 0 0 -2.329 -1.978 0.045

Min Sxy 35 1:SW 0.158 0.124 0 0 0 -2.329 -1.978 0.045

Max Mx 1479 5:1.4DL+1.7LL 0.114 -3.662 0 0 0 3.06E 3 2.35E 3 -9.111

Min Mx 3336 5:1.4DL+1.7LL 67.798 54.026 0 0 0 -7.14E 3 -7.09E 3 -281.15

Max My 306 5:1.4DL+1.7LL -1.616 0.609 0 0 0 2.95E 3 3.09E 3 0.194

Min My 3336 5:1.4DL+1.7LL 67.798 54.026 0 0 0 -7.14E 3 -7.09E 3 -281.15Max Mxy 3294 5:1.4DL+1.7LL 32.303 -32.607 0 0 0 -4.21E 3 -3.88E 3 2.06E 3

Min Mxy 35 5:1.4DL+1.7LL 32.255 32.837 0 0 0 -4.21E 3 -3.88E 3 -2.06E 3

Summary of Beam Supported Slab Centre Stress (Mesh 25x25)Shear Membrane Bending

Plate L/C

Table 4.2 Beam supported slab mesh (25x25)

78

Fig. 4.1 mesh analysis for flat plate 25*25

Fig.4.2 mesh analysis for beam slab 25*25

79

4.2.2 Summary of Flat Plat & Beam Supported Slab (50x50 Mesh)

Summary of the table for flat plate center stress mesh analysis (50x50)

Qx Qy Sx Sy Sxy Mx My Mxy

(psi) (psi) (psi) (psi) (psi) (lb-in/in) (lb

-in/in) (lb

-in/in)

Max Qx 15964 5:1.4DL+1.7LL 1.45E 3 1.44E 3 0 0 0 -75.9E 3 -101E 3 -23.5E 3

Min Qx 18612 5:1.4DL+1.7LL -1.16E 3 580.744 0 0 0 -83.9E 3 -54.6E 3 49.7E 3

Max Qy 15964 5:1.4DL+1.7LL 1.45E 3 1.44E 3 0 0 0 -75.9E 3 -101E 3 -23.5E 3

Min Qy 5278 5:1.4DL+1.7LL 1.45E 3 -1.44E 3 0 0 0 -75.9E 3 -100E 3 23.5E 3

Max Sx 35 1:SW 229.542 221.578 0 0 0 -25.7E 3 -24.2E 3 -20.3E 3

Min Sx 35 1:SW 229.542 221.578 0 0 0 -25.7E 3 -24.2E 3 -20.3E 3

Max Sy 35 1:SW 229.542 221.578 0 0 0 -25.7E 3 -24.2E 3 -20.3E 3

Min Sy 35 1:SW 229.542 221.578 0 0 0 -25.7E 3 -24.2E 3 -20.3E 3

Max Sxy 35 1:SW 229.542 221.578 0 0 0 -25.7E 3 -24.2E 3 -20.3E 3

Min Sxy 35 1:SW 229.542 221.578 0 0 0 -25.7E 3 -24.2E 3 -20.3E 3

Max Mx 15908 5:1.4DL+1.7LL 13.395 -4.637 0 0 0 14.8E 3 153.206 -343.22

Min Mx 15866 5:1.4DL+1.7LL 748.514 -751.26 0 0 0 -84E 3 -82.2E 3 67.4E 3

Max My 14618 5:1.4DL+1.7LL 4.877 -7.466 0 0 0 182.009 15.4E 3 -207.14

Min My 15964 5:1.4DL+1.7LL 1.45E 3 1.44E 3 0 0 0 -75.9E 3 -101E 3 -23.5E 3

Max Mxy 15866 5:1.4DL+1.7LL 748.514 -751.26 0 0 0 -84E 3 -82.2E 3 67.4E 3

Min Mxy 13270 5:1.4DL+1.7LL 717.718 743.501 0 0 0 -81.1E 3 -81.6E 3 -66.1E 3

Summary of Plate Centre Stress (Mesh 50x50)BendingShear Membrane

Plate L/C

Table 4.3 Plate center stress mesh (50x50)

80

Summary of the table for beam supported slab center stress mesh analysis (50x50)

Qx Qy Sx Sy Sxy Mx My Mxy(psi) (psi) (psi) (psi) (psi) (lb-in/in) (lb-in/in) (lb-in/in)

Max Qx 15964 5:1.4DL+1.7LL 150.871 139.753 0 0 0 -13E 3 -13.2E 3 -816.65

Min Qx 16014 5:1.4DL+1.7LL -127.58 119.207 0 0 0 -12.1E 3 -12.3E 3 712.992

Max Qy 15964 5:1.4DL+1.7LL 150.871 139.753 0 0 0 -13E 3 -13.2E 3 -816.65

Min Qy 5278 5:1.4DL+1.7LL 150.87 -139.75 0 0 0 -13E 3 -13.2E 3 816.645

Max Sx 35 1:SW 22.818 21.946 0 0 0 -2.38E 3 -2.18E 3 -952.28

Min Sx 35 1:SW 22.818 21.946 0 0 0 -2.38E 3 -2.18E 3 -952.28

Max Sy 35 1:SW 22.818 21.946 0 0 0 -2.38E 3 -2.18E 3 -952.28

Min Sy 35 1:SW 22.818 21.946 0 0 0 -2.38E 3 -2.18E 3 -952.28

Max Sxy 35 1:SW 22.818 21.946 0 0 0 -2.38E 3 -2.18E 3 -952.28

Min Sxy 35 1:SW 22.818 21.946 0 0 0 -2.38E 3 -2.18E 3 -952.28

Max Mx 7185 5:1.4DL+1.7LL -0.366 -8.323 0 0 0 4.73E 3 2.67E 3 17.811Min Mx 5278 5:1.4DL+1.7LL 150.87 -139.75 0 0 0 -13E 3 -13.2E 3 816.645

Max My 1355 5:1.4DL+1.7LL -0.881 0.386 0 0 0 4.67E 3 4.7E 3 4.519

Min My 5278 5:1.4DL+1.7LL 150.87 -139.75 0 0 0 -13E 3 -13.2E 3 816.645

Max Mxy 15866 5:1.4DL+1.7LL 75.04 -72.25 0 0 0 -8.17E 3 -7.51E 3 3.66E 3

Min Mxy 35 5:1.4DL+1.7LL 75.04 72.251 0 0 0 -8.17E 3 -7.51E 3 -3.66E 3

Summary of Beam Supported Slab Centre Stress (Mesh 50x50)Shear Membrane Bending

Plate L/C

Table 4.4 Beam supported slab mesh (50x50)

81

Fig.4.3 mesh analysis for beam slab 50*50

Fig. 4.4 mesh analysis for flat plate 50*50

82

4.3 Stress Analysis

4.3.1 Summary of Stress for Flat Plat & Beam Supported Slab

Summary of the table for flat plate stress analysis (25x25 mesh)

Top Bottom Top Bottom Top Bottom

(psi) (psi) (psi) (psi) (psi) (psi)

Max (t) 1106 1.4DL+1.7LL -1.89E 3 2.44E 3 2.21E 3 2.21E 3 2.44E 3 2.44E 3

Max (b) 35 1.4DL+1.7LL -297.1 2.96E 3 2.82E 3 2.82E 3 2.96E 3 2.96E 3

Max VM (t) 35 1.4DL+1.7LL -297.1 2.96E 3 2.82E 3 2.82E 3 2.96E 3 2.96E 3

Max VM (b) 35 1.4DL+1.7LL -297.1 2.96E 3 2.82E 3 2.82E 3 2.96E 3 2.96E 3

Tresca (t) 35 1.4DL+1.7LL -297.1 2.96E 3 2.82E 3 2.82E 3 2.96E 3 2.96E 3

Tresca (b) 35 1.4DL+1.7LL -297.1 2.96E 3 2.82E 3 2.82E 3 2.96E 3 2.96E 3

Summary of Centre Principal Stress for Flat Plate(Mesh 25x25)TrescaVon MisPrincipal

Plate L/C

Table 4.5 Centre principal stress for flat plate (25x25 mesh)

Summary of the table for beam supported slab stress analysis (25x25 mesh)

Plate L/C Top Bottom Top Bottom Top Bottom

(psi) (psi) (psi) (psi) (psi) (psi)

Max (t) 3336 1.4DL+1.7LL -1.14E 3 1.23E 3 1.19E 3 1.19E 3 1.23E 3 1.23E 3

Max (b) 3336 1.4DL+1.7LL -1.14E 3 1.23E 3 1.19E 3 1.19E 3 1.23E 3 1.23E 3

Max VM (t) 3336 1.4DL+1.7LL -1.14E 3 1.23E 3 1.19E 3 1.19E 3 1.23E 3 1.23E 3

Max VM (b) 3336 1.4DL+1.7LL -1.14E 3 1.23E 3 1.19E 3 1.19E 3 1.23E 3 1.23E 3

Tresca (t) 3336 1.4DL+1.7LL -1.14E 3 1.23E 3 1.19E 3 1.19E 3 1.23E 3 1.23E 3

Tresca (b) 3336 1.4DL+1.7LL -1.14E 3 1.23E 3 1.19E 3 1.19E 3 1.23E 3 1.23E 3

Summary of Centre Principal Stress for Beam supported Slab(Mesh 25x25)Principal Von Mis Tresca

Table 4.6 Centre principal stress for beam supported slab (25x25 mesh)

83

Summary of the table for flat plate stress analysis (50x50 mesh)

Top Bottom Top Bottom Top Bottom

(psi) (psi) (psi) (psi) (psi) (psi)

Max (t) 15964 5:1.4DL+1.7LL -4.58E 3 8.51E 3 7.37E 3 7.37E 3 8.51E 3 8.51E 3

Max (b) 15866 5:1.4DL+1.7LL -1.16E 3 11.2E 3 10.6E 3 10.6E 3 11.2E 3 11.2E 3

Max VM (t) 15866 5:1.4DL+1.7LL -1.16E 3 11.2E 3 10.6E 3 10.6E 3 11.2E 3 11.2E 3

Max VM (b) 15866 5:1.4DL+1.7LL -1.16E 3 11.2E 3 10.6E 3 10.6E 3 11.2E 3 11.2E 3

Tresca (t) 15866 5:1.4DL+1.7LL -1.16E 3 11.2E 3 10.6E 3 10.6E 3 11.2E 3 11.2E 3

Tresca (b) 15866 5:1.4DL+1.7LL -1.16E 3 11.2E 3 10.6E 3 10.6E 3 11.2E 3 11.2E 3

Summary of Centre Principal Stress for Flat Plate(Mesh 50x50)Principal Von Mis Tresca

Plate L/C

Table 4.7 Centre principal stress for flat plate (50x50 mesh)

Summary of the table for beam supported slab stress analysis (50x50 mesh)

Top Bottom Top Bottom Top Bottom

(psi) (psi) (psi) (psi) (psi) (psi)

Max (t) 5278 5:1.4DL+1.7LL -2.05E 3 2.32E 3 2.2E 3 2.2E 3 2.32E 3 2.32E 3

Max (b) 5278 5:1.4DL+1.7LL -2.05E 3 2.32E 3 2.2E 3 2.2E 3 2.32E 3 2.32E 3

Max VM (t) 5278 5:1.4DL+1.7LL -2.05E 3 2.32E 3 2.2E 3 2.2E 3 2.32E 3 2.32E 3

Max VM (b) 5278 5:1.4DL+1.7LL -2.05E 3 2.32E 3 2.2E 3 2.2E 3 2.32E 3 2.32E 3

Tresca (t) 5278 5:1.4DL+1.7LL -2.05E 3 2.32E 3 2.2E 3 2.2E 3 2.32E 3 2.32E 3

Tresca (b) 5278 5:1.4DL+1.7LL -2.05E 3 2.32E 3 2.2E 3 2.2E 3 2.32E 3 2.32E 3

Summary of Centre Principal Stress for Beam supported Slab(Mesh 50x50)Principal Von Mis Tresca

Plate L/C

Table 4.8 Centre principal stress for beam supported slab (50x50 mesh)

84

1190

22002820

10600

0

2000

4000

6000

8000

10000

12000

Mesh 25x25 Mesh 50x50

Mom

ent v

alue

(psi

)

Beam supported slab Flat plate

Fig.4.5 Graph for Maximum moment

85

4.4 Displacement Analysis

4.4.1 Summary of displacement for Flat Plate & Beam Supported Slab

Summary of the table for flat plate node displacement analysis (25x25 mesh)

X Y Z Resultant rX rY rZ

(in) (in) (in) (in) (rad) (rad) (rad)

Max X 1 1:SW 0 0 0 0 0 0 0

Min X 1 1:SW 0 0 0 0 0 0 0

Max Y 1597 5:1.4DL+1.7LL 0 0.013 0 0.013 0 0 -0.002

Min Y 278 5:1.4DL+1.7LL 0 -0.355 0 0.355 0 0 0

Max Z 1 1:SW 0 0 0 0 0 0 0

Min Z 1 1:SW 0 0 0 0 0 0 0

Max rX 58 5:1.4DL+1.7LL 0 -0.002 0 0.002 0.003 0 0.001

Min rX 3061 5:1.4DL+1.7LL 0 -0.002 0 0.002 -0.003 0 0.001

Max rY 1 1:SW 0 0 0 0 0 0 0

Min rY 1 1:SW 0 0 0 0 0 0 0

Max rZ 1528 5:1.4DL+1.7LL 0 -0.002 0 0.002 -0.001 0 0.003Min rZ 22 5:1.4DL+1.7LL 0 -0.079 0 0.079 0.002 0 -0.003

Max Rst 278 5:1.4DL+1.7LL 0 -0.355 0 0.355 0 0 0

Node L/C

Summary of Node Displacement for Flat Plate(Mesh 25x25)

Table 4.9 node displacement for flat plate (25x25)

Summary of the table for beam supported slab node displacement analysis (25x25 mesh)

X Y Z Resultant rX rY rZ

(in) (in) (in) (in) (rad) (rad) (rad)

Max X 1 1:SW 0 0 0 0 0 0 0

Min X 1 1:SW 0 0 0 0 0 0 0

Max Y 1 1:SW 0 0 0 0 0 0 0

Min Y 2799 5:1.4DL+1.7LL 0 -0.394 0 0.394 0 0 0

Max Z 1 1:SW 0 0 0 0 0 0 0

Min Z 1 1:SW 0 0 0 0 0 0 0

Max rX 72 5:1.4DL+1.7LL 0 -0.217 0 0.217 0.003 0 0

Min rX 3006 5:1.4DL+1.7LL 0 -0.217 0 0.217 -0.003 0 0

Max rY 1 1:SW 0 0 0 0 0 0 0

Min rY 1 1:SW 0 0 0 0 0 0 0

Max rZ 1327 5:1.4DL+1.7LL 0 -0.211 0 0.211 0 0 0.003

Min rZ 271 5:1.4DL+1.7LL 0 -0.222 0 0.222 0 0 -0.003

Max Rst 2799 5:1.4DL+1.7LL 0 -0.394 0 0.394 0 0 0

Summary of Node Displacement for Beam Supported Slab(Mesh 25x25)

Node L/C

Table 4.10 Node displacement for beam supported slab (25x25)

86

Summary of the table for flat plate node displacement analysis (50x50 mesh)

X Y Z

Resultan

t rX rY rZ

(in) (in) (in) (in) (rad) (rad) (rad)

Max X 1 1:SW 0 0 0 0 0 0 0

Min X 1 1:SW 0 0 0 0 0 0 0

Max Y 9700 5:1.4DL+1.7LL 0 0.039 0 0.039 0 0 -0.003

Min Y 14104 5:1.4DL+1.7LL 0 -0.689 0 0.689 0 0 0

Max Z 1 1:SW 0 0 0 0 0 0 0

Min Z 1 1:SW 0 0 0 0 0 0 0

Max rX 269 5:1.4DL+1.7LL 0 -0.108 0 0.108 0.006 0 0.001

Min rX 15151 5:1.4DL+1.7LL 0 -0.108 0 0.108 -0.006 0 0.001

Max rY 1 1:SW 0 0 0 0 0 0 0

Min rY 1 1:SW 0 0 0 0 0 0 0

Max rZ 17898 5:1.4DL+1.7LL 0 -0.113 0 0.113 0.002 0 0.005

Min rZ 15309 5:1.4DL+1.7LL 0 -0.118 0 0.118 -0.005 0 -0.005

Max Rst 14104 5:1.4DL+1.7LL 0 -0.689 0 0.689 0 0 0

Node L/C

Summary of Node Displacement for Flat Plate(Mesh 50x50)

Table 4.11 node displacement for flat plate (50x50)

Summary of the table for beam supported slab node displacement analysis (50x50 mesh)

X Y ZResultan

trX rY rZ

(in) (in) (in) (in) (rad) (rad) (rad)

Max X 1 1:SW 0 0 0 0 0 0 0

Min X 1 1:SW 0 0 0 0 0 0 0

Max Y 1 1:SW 0 0 0 0 0 0 0

Min Y 1315 5:1.4DL+1.7LL 0 -0.62 0 0.62 0 0 0

Max Z 1 1:SW 0 0 0 0 0 0 0

Min Z 1 1:SW 0 0 0 0 0 0 0

Max rX 574 5:1.4DL+1.7LL 0 -0.151 0 0.151 0.004 0 0.001

Min rX 14844 5:1.4DL+1.7LL 0 -0.151 0 0.151 -0.004 0 0.001

Max rY 1 1:SW 0 0 0 0 0 0 0

Min rY 1 1:SW 0 0 0 0 0 0 0

Max rZ 7600 5:1.4DL+1.7LL 0 -0.188 0 0.188 -0.002 0 0.005

Min rZ 7570 5:1.4DL+1.7LL 0 -0.176 0 0.176 -0.002 0 -0.005

Max Rst 1315 5:1.4DL+1.7LL 0 -0.62 0 0.62 0 0 0

Summary of Node Displacement for Beam Supported Slab(Mesh 50x50)

Node L/C

Table 4.12 node displacement for beam supported slab (50x50)

87

0.62

0.394

0.689

0.355

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Mesh 50x50 Mesh 25x25

Nod

e D

ispl

acem

ent (

inch

)

beam supported slub Flat Plate

Fig 4.6 Displacement 25*25 & 50*50

Fig.4.7 Displacement beam supported slab 25*25

88

Fig.4.8 Displacement flat plate 25*25

Fig. 4.9 Displacement beam supported slab 50*50

.

89

Fig. 4.10 Displacement flat plate 50*50

90

4.5 Cost Estimation

Steel=45000 TK/tone

Cement =400 TK/bag

Stone= 165 TK/cft

Sand=35 TK/cft

1) Estimate of Floor Beam:

a) Beam supported slab

Fig: 4.11 Reinforcement detailing of floor Beam

91

Fig. 4.12 Reinforcement detailing of beam supported slab

92

No. of bar Unit

#5 ft

#3 ft

#5 ft

#3 ft

Tons

Tons

Tons

Tk

Bag

Tk

cft

Tk

cft

Tk

Tk

Total cost 69960

Total cost for Beam 215605.12

Total cost 9170

Stone

Total Stone 424

Total cost 41600

Sand

Total Sand 262

Total cost of steel 94875.12

Cement

Total Cement 104

Steel weight for #3 1.50072

Steel weight for #4 0.607616

Total weight of steel 2.108336

Total steel length 3120

Total steel length 3232

Main bar length 1568 1552

Stirrup Length 1512 1720

Estimation for Beam Steel

Type of bar Long Short

Table. 4.13 Estimation for beam

93

No. of bar Unit

#3 ft

#3 ft

#4 ft

#3 ft

#4 ft

Tons

Tons

Tons

Tk

Bag

Tk

cft

Tk

cft

Tk

Tk

Tk754603.99

538998.87

Sand

Stone27825

Total Stone

Total cost

1589

262185

Total cost for slab

Total Beam supported slab

Total cost

Total steel length

Short

3739

0

2928

Type of bar

8100

Estimation for Beam Supported Slab

Main bar length

Extra top

Extra top

SteelLong

3053

1308

1538

Cement

4466

1.5228

1.210286

2.733086

122988.87

Total steel length

Steel weight for #3

Steel weight for #4

Total weight of steel

Total cost of steel

Total Cement

Total cost

315

126000

795Total Sand

Table. 4.14 Estimation for beam supported slab

For one story Beam Supported Slab total cost=754603.99 TK

For eight story =(754603.99 *8) TK

= 6036831.92 TK

94

Fig 4.13 Reinforcement Detailing of Flat plate

95

b) Flat plate structure

No. of bar Unit

#4 ft

#4 ft

#4 ft

#4 ft

Tons

Tk

Bag

Tk

cft

Tk

cft

Tk

TkTotal cost for Flat Plate 936463.6

12376 12624

Stone

Total Stone 2383

Total cost 393195

Sand

Total Sand 1191.96

Total cost 41718.6

Cement

Total Cement 472

Total cost 188800

Total weight of steel 6.95

Total cost of steel 312750

Total

Total steel length 25000

Main bar length 6648 7144

Extra top 5728 5480

Estimation for Flat PlateSteel

Type of bar Long Short

Table.4.15 Estimation for flat plate

For one story Flat Plate Slab total cost=936463.6TK

For Eight Story =(936463.6*8) TK

=7491708.8 TK

96

Fig: 4.14 Reinforcement of all Grade beam and Slab of all structures

Fig: 4.15 Cement, Sand & Brick chips of all floors on Slab of all structures

0

50000

100000

150000

200000

250000

300000

350000

Slab Grade beam

To

tal c

ost

(tk

)Influence of Reinforcement of Beam supported Slab & Flat plate Slab

With Grade Beam

Beam Supported slab

Flat Plate

0

5000

10000

15000

20000

25000

cement sand stone

Qu

an

tity

(ft3

)

Influence of Cement, Sand & Stone of Beam supported structure and Flat plate

structure on all Slab

Flat Plate Slab

Beam Supported Slab

97

Discussions

The forces and displacements developed of the flat plate and beam supported slab of the

structure are got from the analysis with different mesh size. These results obtained from the

analysis have been discussed details in this chapter.

More reinforcement and concrete are used for flat plate than beam supported slab.

Maximum moment of the flat plate is higher than beam supported slab with mesh size

25X25 and 50X50 respectively.

Maximum node displacement of the flat plate is more than beam supported slab when

mesh size 25X25. But Maximum node displacement of the flat plate is less than beam

supported slab when mesh size 50X50. More reinforcement and concrete are used for

flat plate than beam supported slab.

Finally observed that, when the increase of mesh size than the node displacement of

the flat plate is decreased.

98

Chapter 5

Conclusion & Recommendation

5.1 Conclusion

After performing analysis of the structures as well as the comparative study of beam

supported structure and flat plate structure, we gathered knowledge that:

a) When mesh size is 25x25 the maximum moment of the flat plate is 57.8% higher than

beam supported slab and at mesh size is 50x50, the maximum moment of the flat

plate is 79.2% higher than beam supported slab

b) When mesh size is 25x25, the maximum displacement of the flat plate is 10% more

than beam supported slab but at mesh size 50x50, the maximum displacement of the

flat plate is 9.8% less than the beam supported slab.

c) Flat plate slab is thicker and more heavily reinforced than slabs with beams and

girders. Almost16% more reinforcement are used for flat plate structure than beam

supported structure.

d) Almost 15% more concrete are used for flat plate structure than beam supported

structure.

e) And finally increased the cost of flat plate structure about 19% than beam supported

structure.

f) So from economic point of view, beam supported structure is more economical than

flat plate structure .But from aesthetic point of view, flat plate structure is better.

5.2 Recommendation

For further study in this field, the following recommendations are put forward:

For further study estimation of cost of footing, stair, overhead tank and lift core are

required.

Cost analysis for finishing work & upper design are required for better result.

In the further study, soil test reports nearer projects of that area should have been

collected and used in foundation design for the proposed project.

This research work has been conducted on slab of a Eight storied residential building

but it can be conducted on all the components of the building as well as for other high

and low rise buildings.

For analysis STAAD Pro. design software was used, so it may be checked by other

reliable software’s

99

References

[1]Arthur H. Nelson, David Darwin & Charles W. Dolan “Design of Concrete

Structures” 14th Edition, pp. 424-492 McGraw-Hill Book Co., 2010, ISBN:0073293490

[2]P.C Varghese a book of “Advanced Reinforced Concrete Design”, 2005 by PHI Learning

Private Limited, New Delhi, ISBN-978-81-203-2787-0

[3]American Concrete Institute, “ACI 318-08, Building Code Requirements for

Structural Concrete and Commentary”, January (2008)

[4]M.L Gambhir a book of “Fundamental of Reinforced Concrete Design”, 2006 by PHI

Learning Private Limited, New Delhi, ISBN-978-81-203-3048-1

[5]RANGAN, B.V, “Prediction of Long-Term Deflections of Flat Plates and

Slabs”, Journal of the American Concrete Institute,Vol.73,April 1976,pp.223-

226.

[6] Brotchie, J. F. and Russell, J. J., “Flat Plate Structures: Elastic-Plastic Analysis, “Journal of

the American Concrete Institute, vol. 61, pp. 959–996, August

1964.

[7]Bangladesh National Building Code BNBC-2006. Housing and building Research Institute.

Darussalam, Mirpur, Dhaka-1218 and Bangladesh standard and

Testing Institution. 16/a Tejgaon Industrial Area, Dhaka 1208.ISBN 984-30-

0086-2, 1993

.

100

Appendix

Frequently Used Notation

Av = Area of shear reinforcement within a distance.

b0 = perimeter of the critical section.

b1 = Width of the critical section measured in the direction of the span for which

moments are determined.

b2 = Width of the critical section measured in the direction perpendicular to b1

c1 = Size of rectangular or equivalent rectangular column, capital or bracket measured in the

direction of the span for which moments are being determined.

c2 = Size of rectangular or equivalent rectangular column, capital or bracket measured

transverse to the direction of the span for which moments are being determined.

C = cross-sectional constant to define torsional properties.

d = distance from extreme compression fiber to the centroid of longitudinal tension

reinforcement, (For circular sections, d need not be less than the distance

from extreme compression fiber to centroid of tension reinforcement in opposite

half of member).

f’c = specified compressive strength of concrete.

f

y = specified yield strength of reinforcement.

h = overall thickness of member.

hv = total depth of shear head cross-section.

Is = moment of inertia about centroid axis of gross section of slab.

Kb = flexural stiffness of slab, moment per unit rotation.

KC = flexural stiffness of column, moment per unit rotation

Ks = flexural stiffness of slab, moment per unit rotation.

K1 = torsional stiffness of torsional member, moment per unit rotation.

105

L1 = length of span in direction that moments are being determined measured

center of supports.

L2 = length of span transverse to l1, measured center to center of supports.

ln = length of clear span in direction that moments are being determined, measured face to

face of supports.

M0 = total factored static moment.

MP = required plastic moment strength of shear head cross-section.

Mu = factored moment at section.

Mv = moment resistance contributed by shear head reinforcement.

101

Vc = nominal shear strength provided by concrete.

Vs = nominal shear strength provided by shear reinforcement.

Vu = factored shear force at section.

wd = factored dead load per unit area.

wl = factored live load per unit area.

wu = factored load per unit area.

x = shorter overall dimension of rectangular part of cross-section.

y = longer overall dimension of rectangular part of cross-section.

α = ratio of flexural stiffness of beam section to flexural stiffness of a width of

slab bounded laterally by center lines of adjacent panels (if any) on each side of

the beam=ECBIB/ECSIS.

α3 = constant used to compute Vc in in slabs and footings.

α1 = α in direction of l1

α2 = α in direction of l2

β = ratio of clear spans in spans in long to short direction of two-way slabs.

ϒf = fraction of unbalanced moment transferred by flexure at slab-column

Table- Bar area

102

103

Appendix A

Output File for Flat Plate

WARNING : IT IS ADVISABLE TO ANALYZE THIS STRUCTURE

USING THE COMMAND STAAD SPACE INSTEAD OF STAAD PLANE.

37. ELEMENT LOAD

38. 8 10 12 14 16 18 TO 21 23 25 TO 28 30 32 TO 35 37 39 41 43 45 46 PR GY -40

39. LOAD 2 LOADTYPE DEAD TITLE SW

40. SELFWEIGHT Y -1 LIST ALL

41. LOAD 3 LOADTYPE DEAD TITLE PW

42. ELEMENT LOAD

43. 8 10 12 14 16 18 TO 21 23 25 TO 28 30 32 TO 35 37 39 41 43 45 46 PR GY -50

44. LOAD 4 LOADTYPE DEAD TITLE FF

45. ELEMENT LOAD

46. 8 10 12 14 16 18 TO 21 23 25 TO 28 30 32 TO 35 37 39 41 43 45 46 PR GY -25

47. LOAD COMB 5 1.4DL+1.7LL

48. 1 1.7 2 1.4 3 1.4 4 1.4

49. PERFORM ANALYSIS PRINT STATICS CHECK

P R O B L E M S T A T I S T I C S

-----------------------------------

NUMBER OF JOINTS 36 NUMBER OF MEMBERS 0

NUMBER OF PLATES 25 NUMBER OF SOLIDS 0

NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 4

SOLVER USED IS THE IN-CORE ADVANCED SOLVER

104

TOTAL PRIMARY LOAD CASES = 4, TOTAL DEGREES OF FREEDOM = 96

STAAD PLANE -- PAGE NO. 3

STATIC LOAD/REACTION/EQUILIBRIUM SUMMARY FOR CASE NO. 1

LOADTYPE LIVE REDUCIBLE TITLE LL

CENTER OF FORCE BASED ON Y FORCES ONLY (FEET).

(FORCES IN NON-GLOBAL DIRECTIONS WILL INVALIDATE RESULTS)

X = 0.100000003E+02

Y = 0.000000000E+00

Z = 0.110000001E+02

TOTAL APPLIED LOAD

1

***TOTAL APPLIED LOAD ( POUN FEET ) SUMMARY (LOADING 1 )

SUMMATION FORCE-X = 0.00

SUMMATION FORCE-Y = -17600.00

SUMMATION FORCE-Z = 0.00

SUMMATION OF MOMENTS AROUND THE ORIGIN-

MX= 193599.99 MY= 0.00 MZ= -175999.99

TOTAL REACTION LOAD

1

***TOTAL REACTION LOAD( POUN FEET ) SUMMARY (LOADING 1 )

SUMMATION FORCE-X = 0.00

SUMMATION FORCE-Y = 17600.00

SUMMATION FORCE-Z = 0.00

SUMMATION OF MOMENTS AROUND THE ORIGIN-

MX= -193599.99 MY= 0.00 MZ= 175999.99

MAXIMUM DISPLACEMENTS ( INCH /RADIANS) (LOADING 1)

MAXIMUMS AT NODE

X = 0.00000E+00 0

Y = -2.79677E-02 16

105

Z = 0.00000E+00 0

RX= 0.00000E+00 0

RY= 0.00000E+00 0

RZ= -3.83955E-04 5

STATIC LOAD/REACTION/EQUILIBRIUM SUMMARY FOR CASE NO. 2

LOADTYPE DEAD TITLE SW

CENTER OF FORCE BASED ON Y FORCES ONLY (FEET).

(FORCES IN NON-GLOBAL DIRECTIONS WILL INVALIDATE RESULTS)

X = 0.100000003E+02

Y = 0.000000000E+00

Z = 0.110000001E+02

STAAD PLANE -- PAGE NO. 4

TOTAL APPLIED LOAD

2

***TOTAL APPLIED LOAD ( POUN FEET ) SUMMARY (LOADING 2 )

SUMMATION FORCE-X = 0.00

SUMMATION FORCE-Y = -49610.88

SUMMATION FORCE-Z = 0.00

SUMMATION OF MOMENTS AROUND THE ORIGIN-

MX= 545719.65 MY= 0.00 MZ= -496108.77

TOTAL REACTION LOAD

2

***TOTAL REACTION LOAD( POUN FEET ) SUMMARY (LOADING 2 )

SUMMATION FORCE-X = 0.00

SUMMATION FORCE-Y = 49610.88

SUMMATION FORCE-Z = 0.00

SUMMATION OF MOMENTS AROUND THE ORIGIN-

MX= -545719.65 MY= 0.00 MZ= 496108.77

MAXIMUM DISPLACEMENTS ( INCH /RADIANS) (LOADING 2)

106

MAXIMUMS AT NODE

X = 0.00000E+00 0

Y = -7.88353E-02 26

Z = 0.00000E+00 0

RX= 0.00000E+00 0

RY= 0.00000E+00 0

RZ= -1.08229E-03 5

STATIC LOAD/REACTION/EQUILIBRIUM SUMMARY FOR CASE NO. 3

LOADTYPE DEAD TITLE PW

CENTER OF FORCE BASED ON Y FORCES ONLY (FEET).

(FORCES IN NON-GLOBAL DIRECTIONS WILL INVALIDATE RESULTS)

X = 0.100000003E+02

Y = 0.000000000E+00

Z = 0.110000001E+02

TOTAL APPLIED LOAD

3

***TOTAL APPLIED LOAD ( POUN FEET ) SUMMARY (LOADING 3 )

SUMMATION FORCE-X = 0.00

SUMMATION FORCE-Y = -22000.00

SUMMATION FORCE-Z = 0.00

SUMMATION OF MOMENTS AROUND THE ORIGIN-

MX= 241999.99 MY= 0.00 MZ= -219999.99

TOTAL REACTION LOAD

3

***TOTAL REACTION LOAD( POUN FEET ) SUMMARY (LOADING 3 )

SUMMATION FORCE-X = 0.00

SUMMATION FORCE-Y = 22000.00

SUMMATION FORCE-Z = 0.00

STAAD PLANE -- PAGE NO. 5

107

SUMMATION OF MOMENTS AROUND THE ORIGIN-

MX= -241999.99 MY= 0.00 MZ= 219999.99

MAXIMUM DISPLACEMENTS ( INCH /RADIANS) (LOADING 3)

MAXIMUMS AT NODE

X = 0.00000E+00 0

Y = -3.49596E-02 26

Z = 0.00000E+00 0

RX= 0.00000E+00 0

RY= 0.00000E+00 0

RZ= -4.79943E-04 5

STATIC LOAD/REACTION/EQUILIBRIUM SUMMARY FOR CASE NO. 4

LOADTYPE DEAD TITLE FF

CENTER OF FORCE BASED ON Y FORCES ONLY (FEET).

(FORCES IN NON-GLOBAL DIRECTIONS WILL INVALIDATE RESULTS)

X = 0.100000003E+02

Y = 0.000000000E+00

Z = 0.110000001E+02

TOTAL APPLIED LOAD

4

***TOTAL APPLIED LOAD ( POUN FEET ) SUMMARY (LOADING 4 )

SUMMATION FORCE-X = 0.00

SUMMATION FORCE-Y = -11000.00

SUMMATION FORCE-Z = 0.00

SUMMATION OF MOMENTS AROUND THE ORIGIN-

MX= 121000.00 MY= 0.00 MZ= -110000.00

TOTAL REACTION LOAD

4

***TOTAL REACTION LOAD( POUN FEET ) SUMMARY (LOADING 4 )

SUMMATION FORCE-X = 0.00

SUMMATION FORCE-Y = 11000.00

108

SUMMATION FORCE-Z = 0.00

SUMMATION OF MOMENTS AROUND THE ORIGIN-

MX= -121000.00 MY= 0.00 MZ= 110000.00

MAXIMUM DISPLACEMENTS ( INCH /RADIANS) (LOADING 4)

MAXIMUMS AT NODE

X = 0.00000E+00 0

Y = -1.74798E-02 26

Z = 0.00000E+00 0

RX= 0.00000E+00 0

RY= 0.00000E+00 0

RZ= -2.39972E-04 5

************ END OF DATA FROM INTERNAL STORAGE ************

STAAD PLANE -- PAGE NO. 6

50. PRINT ELEMENT FORCE LIST ALL

ELEMENT FORCE ALL

STAAD PLANE -- PAGE NO. 7

ELEMENT FORCES FORCE,LENGTH UNITS= POUN FEET

-------------

**NOTE- IF A COMBINATION INCLUDES A DYNAMIC CASE OR IS AN SRSS OR ABS

COMBINATION

THEN RESULTS CANNOT BE COMPUTED PROPERLY.

GLOBAL CORNER FORCES

JOINT FX FY FZ MX MY MZ

ELE.NO. 8 FOR LOAD CASE 1

1 0.0000E+00 4.2240E+03 0.0000E+00 -6.5171E+03 0.0000E+00 9.1771E+03

5 0.0000E+00 -7.2598E+02 0.0000E+00 -2.5934E+03 0.0000E+00 6.3392E+02

6 0.0000E+00 -2.7618E+03 0.0000E+00 -4.6447E+03 0.0000E+00 2.7218E+03

7 0.0000E+00 -7.3623E+02 0.0000E+00 -1.5910E+03 0.0000E+00 1.4592E+03

ELE.NO. 8 FOR LOAD CASE 2

1 0.0000E+00 1.1907E+04 0.0000E+00 -1.8370E+04 0.0000E+00 2.5869E+04

109

5 0.0000E+00 -2.0464E+03 0.0000E+00 -7.3102E+03 0.0000E+00 1.7869E+03

6 0.0000E+00 -7.7849E+03 0.0000E+00 -1.3092E+04 0.0000E+00 7.6721E+03

7 0.0000E+00 -2.0753E+03 0.0000E+00 -4.4848E+03 0.0000E+00 4.1133E+03

ELE.NO. 8 FOR LOAD CASE 3

1 0.0000E+00 5.2800E+03 0.0000E+00 -8.1464E+03 0.0000E+00 1.1471E+04

5 0.0000E+00 -9.0748E+02 0.0000E+00 -3.2417E+03 0.0000E+00 7.9240E+02

6 0.0000E+00 -3.4522E+03 0.0000E+00 -5.8058E+03 0.0000E+00 3.4022E+03

7 0.0000E+00 -9.2028E+02 0.0000E+00 -1.9888E+03 0.0000E+00 1.8240E+03

ELE.NO. 8 FOR LOAD CASE 4

1 0.0000E+00 2.6400E+03 0.0000E+00 -4.0732E+03 0.0000E+00 5.7357E+03

5 0.0000E+00 -4.5374E+02 0.0000E+00 -1.6209E+03 0.0000E+00 3.9620E+02

6 0.0000E+00 -1.7261E+03 0.0000E+00 -2.9029E+03 0.0000E+00 1.7011E+03

7 0.0000E+00 -4.6014E+02 0.0000E+00 -9.9440E+02 0.0000E+00 9.1202E+02

ELE.NO. 8 FOR LOAD CASE 5

1 0.0000E+00 3.4938E+04 0.0000E+00 -5.3905E+04 0.0000E+00 7.5907E+04

5 0.0000E+00 -6.0048E+03 0.0000E+00 -2.1451E+04 0.0000E+00 5.2433E+03

6 0.0000E+00 -2.2844E+04 0.0000E+00 -3.8418E+04 0.0000E+00 2.2513E+04

7 0.0000E+00 -6.0896E+03 0.0000E+00 -1.3160E+04 0.0000E+00 1.2070E+04

ELE.NO. 10 FOR LOAD CASE 1

5 0.0000E+00 3.7398E+02 0.0000E+00 -1.1514E+03 0.0000E+00 -6.3392E+02

8 0.0000E+00 -7.8505E+02 0.0000E+00 -1.6591E+03 0.0000E+00 -8.2014E+02

9 0.0000E+00 -6.0219E+02 0.0000E+00 -1.4905E+03 0.0000E+00 9.7169E+02

6 0.0000E+00 1.0133E+03 0.0000E+00 -1.8029E+03 0.0000E+00 -1.1619E+03

ELE.NO. 10 FOR LOAD CASE 2

5 0.0000E+00 1.0542E+03 0.0000E+00 -3.2457E+03 0.0000E+00 -1.7869E+03

8 0.0000E+00 -2.2129E+03 0.0000E+00 -4.6766E+03 0.0000E+00 -2.3118E+03

9 0.0000E+00 -1.6975E+03 0.0000E+00 -4.2015E+03 0.0000E+00 2.7390E+03

6 0.0000E+00 2.8562E+03 0.0000E+00 -5.0819E+03 0.0000E+00 -3.2752E+03

ELE.NO. 10 FOR LOAD CASE 3

110

5 0.0000E+00 4.6748E+02 0.0000E+00 -1.4393E+03 0.0000E+00 -7.9240E+02

8 0.0000E+00 -9.8132E+02 0.0000E+00 -2.0738E+03 0.0000E+00 -1.0252E+03

9 0.0000E+00 -7.5274E+02 0.0000E+00 -1.8632E+03 0.0000E+00 1.2146E+03

6 0.0000E+00 1.2666E+03 0.0000E+00 -2.2536E+03 0.0000E+00 -1.4524E+03

ELE.NO. 10 FOR LOAD CASE 4

5 0.0000E+00 2.3374E+02 0.0000E+00 -7.1964E+02 0.0000E+00 -3.9620E+02

8 0.0000E+00 -4.9066E+02 0.0000E+00 -1.0369E+03 0.0000E+00 -5.1259E+02

9 0.0000E+00 -3.7637E+02 0.0000E+00 -9.3159E+02 0.0000E+00 6.0731E+02

6 0.0000E+00 6.3329E+02 0.0000E+00 -1.1268E+03 0.0000E+00 -7.2620E+02

ELE.NO. 10 FOR LOAD CASE 5

5 0.0000E+00 3.0933E+03 0.0000E+00 -9.5239E+03 0.0000E+00 -5.2433E+03

8 0.0000E+00 -6.4934E+03 0.0000E+00 -1.3723E+04 0.0000E+00 -6.7837E+03

9 0.0000E+00 -4.9809E+03 0.0000E+00 -1.2329E+04 0.0000E+00 8.0372E+03

6 0.0000E+00 8.3810E+03 0.0000E+00 -1.4912E+04 0.0000E+00 -9.6106E+03

STAAD PLANE -- PAGE NO. 8

ELEMENT FORCES FORCE,LENGTH UNITS= POUN FEET

--------------

GLOBAL CORNER FORCES

JOINT FX FY FZ MX MY MZ

ELE.NO. 12 FOR LOAD CASE 1

8 0.0000E+00 4.3305E+02 0.0000E+00 -4.2480E+02 0.0000E+00 8.2014E+02

10 0.0000E+00 4.3305E+02 0.0000E+00 4.2480E+02 0.0000E+00 8.2014E+02

11 0.0000E+00 -4.3305E+02 0.0000E+00 -4.3900E+02 0.0000E+00 9.1208E+02

9 0.0000E+00 -4.3305E+02 0.0000E+00 4.3900E+02 0.0000E+00 9.1208E+02

ELE.NO. 12 FOR LOAD CASE 2

111

8 0.0000E+00 1.2207E+03 0.0000E+00 -1.1974E+03 0.0000E+00 2.3118E+03

10 0.0000E+00 1.2207E+03 0.0000E+00 1.1974E+03 0.0000E+00 2.3118E+03

11 0.0000E+00 -1.2207E+03 0.0000E+00 -1.2375E+03 0.0000E+00 2.5710E+03

9 0.0000E+00 -1.2207E+03 0.0000E+00 1.2375E+03 0.0000E+00 2.5710E+03

ELE.NO. 12 FOR LOAD CASE 3

8 0.0000E+00 5.4132E+02 0.0000E+00 -5.3099E+02 0.0000E+00 1.0252E+03

10 0.0000E+00 5.4132E+02 0.0000E+00 5.3099E+02 0.0000E+00 1.0252E+03

11 0.0000E+00 -5.4132E+02 0.0000E+00 -5.4875E+02 0.0000E+00 1.1401E+03

9 0.0000E+00 -5.4132E+02 0.0000E+00 5.4875E+02 0.0000E+00 1.1401E+03

ELE.NO. 12 FOR LOAD CASE 4

8 0.0000E+00 2.7066E+02 0.0000E+00 -2.6550E+02 0.0000E+00 5.1259E+02

10 0.0000E+00 2.7066E+02 0.0000E+00 2.6550E+02 0.0000E+00 5.1259E+02

11 0.0000E+00 -2.7066E+02 0.0000E+00 -2.7438E+02 0.0000E+00 5.7005E+02

9 0.0000E+00 -2.7066E+02 0.0000E+00 2.7438E+02 0.0000E+00 5.7005E+02

ELE.NO. 12 FOR LOAD CASE 5

8 0.0000E+00 3.5819E+03 0.0000E+00 -3.5136E+03 0.0000E+00 6.7836E+03

10 0.0000E+00 3.5819E+03 0.0000E+00 3.5136E+03 0.0000E+00 6.7836E+03

11 0.0000E+00 -3.5819E+03 0.0000E+00 -3.6311E+03 0.0000E+00 7.5441E+03

9 0.0000E+00 -3.5819E+03 0.0000E+00 3.6311E+03 0.0000E+00 7.5441E+03

ELE.NO. 14 FOR LOAD CASE 1

10 0.0000E+00 -7.8505E+02 0.0000E+00 1.6591E+03 0.0000E+00 -8.2014E+02

12 0.0000E+00 3.7398E+02 0.0000E+00 1.1514E+03 0.0000E+00 -6.3392E+02

13 0.0000E+00 1.0133E+03 0.0000E+00 1.8029E+03 0.0000E+00 -1.1619E+03

11 0.0000E+00 -6.0219E+02 0.0000E+00 1.4905E+03 0.0000E+00 9.7169E+02

ELE.NO. 14 FOR LOAD CASE 2

10 0.0000E+00 -2.2129E+03 0.0000E+00 4.6766E+03 0.0000E+00 -2.3118E+03

12 0.0000E+00 1.0542E+03 0.0000E+00 3.2457E+03 0.0000E+00 -1.7869E+03

13 0.0000E+00 2.8562E+03 0.0000E+00 5.0819E+03 0.0000E+00 -3.2752E+03

11 0.0000E+00 -1.6975E+03 0.0000E+00 4.2015E+03 0.0000E+00 2.7390E+03

112

ELE.NO. 14 FOR LOAD CASE 3

10 0.0000E+00 -9.8132E+02 0.0000E+00 2.0738E+03 0.0000E+00 -1.0252E+03

12 0.0000E+00 4.6748E+02 0.0000E+00 1.4393E+03 0.0000E+00 -7.9240E+02

13 0.0000E+00 1.2666E+03 0.0000E+00 2.2536E+03 0.0000E+00 -1.4524E+03

11 0.0000E+00 -7.5274E+02 0.0000E+00 1.8632E+03 0.0000E+00 1.2146E+03

ELE.NO. 14 FOR LOAD CASE 4

10 0.0000E+00 -4.9066E+02 0.0000E+00 1.0369E+03 0.0000E+00 -5.1259E+02

12 0.0000E+00 2.3374E+02 0.0000E+00 7.1964E+02 0.0000E+00 -3.9620E+02

13 0.0000E+00 6.3329E+02 0.0000E+00 1.1268E+03 0.0000E+00 -7.2620E+02

11 0.0000E+00 -3.7637E+02 0.0000E+00 9.3159E+02 0.0000E+00 6.0731E+02

ELE.NO. 14 FOR LOAD CASE 5

10 0.0000E+00 -6.4934E+03 0.0000E+00 1.3723E+04 0.0000E+00 -6.7837E+03

12 0.0000E+00 3.0933E+03 0.0000E+00 9.5239E+03 0.0000E+00 -5.2433E+03

13 0.0000E+00 8.3810E+03 0.0000E+00 1.4912E+04 0.0000E+00 -9.6106E+03

11 0.0000E+00 -4.9809E+03 0.0000E+00 1.2329E+04 0.0000E+00 8.0372E+03

STAAD PLANE -- PAGE NO. 9

ELEMENT FORCES FORCE,LENGTH UNITS= POUN FEET

--------------

GLOBAL CORNER FORCES

JOINT FX FY FZ MX MY MZ

ELE.NO. 16 FOR LOAD CASE 1

12 0.0000E+00 -7.2598E+02 0.0000E+00 2.5934E+03 0.0000E+00 6.3392E+02

2 0.0000E+00 4.2240E+03 0.0000E+00 6.5171E+03 0.0000E+00 9.1771E+03

14 0.0000E+00 -7.3623E+02 0.0000E+00 1.5910E+03 0.0000E+00 1.4592E+03

13 0.0000E+00 -2.7618E+03 0.0000E+00 4.6447E+03 0.0000E+00 2.7218E+03

113

ELE.NO. 16 FOR LOAD CASE 2

12 0.0000E+00 -2.0464E+03 0.0000E+00 7.3102E+03 0.0000E+00 1.7869E+03

2 0.0000E+00 1.1907E+04 0.0000E+00 1.8370E+04 0.0000E+00 2.5869E+04

14 0.0000E+00 -2.0753E+03 0.0000E+00 4.4848E+03 0.0000E+00 4.1133E+03

13 0.0000E+00 -7.7849E+03 0.0000E+00 1.3092E+04 0.0000E+00 7.6721E+03

ELE.NO. 16 FOR LOAD CASE 3

12 0.0000E+00 -9.0748E+02 0.0000E+00 3.2417E+03 0.0000E+00 7.9240E+02

2 0.0000E+00 5.2800E+03 0.0000E+00 8.1464E+03 0.0000E+00 1.1471E+04

14 0.0000E+00 -9.2028E+02 0.0000E+00 1.9888E+03 0.0000E+00 1.8240E+03

13 0.0000E+00 -3.4522E+03 0.0000E+00 5.8058E+03 0.0000E+00 3.4022E+03

ELE.NO. 16 FOR LOAD CASE 4

12 0.0000E+00 -4.5374E+02 0.0000E+00 1.6209E+03 0.0000E+00 3.9620E+02

2 0.0000E+00 2.6400E+03 0.0000E+00 4.0732E+03 0.0000E+00 5.7357E+03

14 0.0000E+00 -4.6014E+02 0.0000E+00 9.9440E+02 0.0000E+00 9.1202E+02

13 0.0000E+00 -1.7261E+03 0.0000E+00 2.9029E+03 0.0000E+00 1.7011E+03

ELE.NO. 16 FOR LOAD CASE 5

12 0.0000E+00 -6.0048E+03 0.0000E+00 2.1451E+04 0.0000E+00 5.2433E+03

2 0.0000E+00 3.4938E+04 0.0000E+00 5.3905E+04 0.0000E+00 7.5907E+04

14 0.0000E+00 -6.0896E+03 0.0000E+00 1.3160E+04 0.0000E+00 1.2070E+04

13 0.0000E+00 -2.2844E+04 0.0000E+00 3.8418E+04 0.0000E+00 2.2513E+04

ELE.NO. 18 FOR LOAD CASE 1

7 0.0000E+00 3.8423E+02 0.0000E+00 -1.1902E+02 0.0000E+00 -1.4592E+03

6 0.0000E+00 2.9364E+02 0.0000E+00 -3.4570E+01 0.0000E+00 -1.0131E+03

15 0.0000E+00 -3.5995E+02 0.0000E+00 -7.0292E+02 0.0000E+00 2.6913E+03

16 0.0000E+00 -3.1792E+02 0.0000E+00 5.6475E+02 0.0000E+00 2.4925E+03

ELE.NO. 18 FOR LOAD CASE 2

7 0.0000E+00 1.0831E+03 0.0000E+00 -3.3548E+02 0.0000E+00 -4.1133E+03

6 0.0000E+00 8.2771E+02 0.0000E+00 -9.7446E+01 0.0000E+00 -2.8558E+03

15 0.0000E+00 -1.0146E+03 0.0000E+00 -1.9814E+03 0.0000E+00 7.5863E+03

114

16 0.0000E+00 -8.9615E+02 0.0000E+00 1.5919E+03 0.0000E+00 7.0258E+03

ELE.NO. 18 FOR LOAD CASE 3

7 0.0000E+00 4.8028E+02 0.0000E+00 -1.4877E+02 0.0000E+00 -1.8240E+03

6 0.0000E+00 3.6705E+02 0.0000E+00 -4.3213E+01 0.0000E+00 -1.2664E+03

15 0.0000E+00 -4.4994E+02 0.0000E+00 -8.7865E+02 0.0000E+00 3.3642E+03

16 0.0000E+00 -3.9740E+02 0.0000E+00 7.0594E+02 0.0000E+00 3.1156E+03

ELE.NO. 18 FOR LOAD CASE 4

7 0.0000E+00 2.4014E+02 0.0000E+00 -7.4385E+01 0.0000E+00 -9.1202E+02

6 0.0000E+00 1.8352E+02 0.0000E+00 -2.1606E+01 0.0000E+00 -6.3320E+02

15 0.0000E+00 -2.2497E+02 0.0000E+00 -4.3933E+02 0.0000E+00 1.6821E+03

16 0.0000E+00 -1.9870E+02 0.0000E+00 3.5297E+02 0.0000E+00 1.5578E+03

ELE.NO. 18 FOR LOAD CASE 5

7 0.0000E+00 3.1781E+03 0.0000E+00 -9.8443E+02 0.0000E+00 -1.2070E+04

6 0.0000E+00 2.4288E+03 0.0000E+00 -2.8595E+02 0.0000E+00 -8.3798E+03

15 0.0000E+00 -2.9773E+03 0.0000E+00 -5.8141E+03 0.0000E+00 2.2261E+04

16 0.0000E+00 -2.6296E+03 0.0000E+00 4.6712E+03 0.0000E+00 2.0616E+04

51. PRINT ELEMENT STRESSES LIST ALL

ELEMENT STRESSES ALL

STAAD PLANE -- PAGE NO. 20

ELEMENT STRESSES FORCE,LENGTH UNITS= POUN FEET

----------------

STRESS = FORCE/UNIT WIDTH/THICK, MOMENT = FORCE-LENGTH/UNIT WIDTH

ELEMENT LOAD SQX SQY MX MY MXY

VONT VONB SX SY SXY

TRESCAT TRESCA

8 1 -1162.59 -1060.00 108.76 639.78 252.83

7862.52 7862.52 0.00 0.00 0.00

7902.95 7902.95

115

TOP : SMAX= 7902.95 SMIN= 81.50 TMAX= 3910.72 ANGLE= 68.2

BOTT: SMAX= -81.50 SMIN= -7902.95 TMAX= 3910.72 ANGLE=-21.8

2 -3277.11 -2987.94 306.58 1803.41 712.68

22162.87 22162.87 0.00 0.00 0.00

22276.84 22276.84

TOP : SMAX= 22276.84 SMIN= 229.74 TMAX= 11023.55 ANGLE= 68.2

BOTT: SMAX= -229.74 SMIN= -22276.84 TMAX= 11023.55 ANGLE=-21.8

3 -1453.24 -1325.01 135.95 799.73 316.04

9828.15 9828.15 0.00 0.00 0.00

9878.69 9878.69

TOP : SMAX= 9878.69 SMIN= 101.88 TMAX= 4888.41 ANGLE= 68.2

BOTT: SMAX= -101.88 SMIN= -9878.69 TMAX= 4888.41 ANGLE=-21.8

4 -726.62 -662.50 67.98 399.86 158.02

4914.07 4914.07 0.00 0.00 0.00

4939.35 4939.35

TOP : SMAX= 4939.35 SMIN= 50.94 TMAX= 2444.20 ANGLE= 68.2

BOTT: SMAX= -50.94 SMIN= -4939.35 TMAX= 2444.20 ANGLE=-21.8

5 -9616.16 -8767.64 899.61 5291.83 2091.24

65033.39 65033.39 0.00 0.00 0.00

65367.85 65367.85

TOP : SMAX= 65367.85 SMIN= 674.14 TMAX= 32346.85 ANGLE= 68.2

BOTT: SMAX= -674.14 SMIN= -65367.85 TMAX= 32346.85 ANGLE=-21.8

10 1 -462.42 124.57 -24.42 -143.62 -92.10

2216.02 2216.02 0.00 0.00 0.00

2340.27 2340.27

TOP : SMAX= 273.96 SMIN= -2066.31 TMAX= 1170.13 ANGLE=-28.5

BOTT: SMAX= 2066.31 SMIN= -273.96 TMAX= 1170.13 ANGLE= 61.5

116

2 -1303.46 351.13 -68.82 -404.83 -259.60

6246.53 6246.53 0.00 0.00 0.00

6596.74 6596.74

TOP : SMAX= 772.23 SMIN= -5824.51 TMAX= 3298.37 ANGLE=-28.5

BOTT: SMAX= 5824.51 SMIN= -772.23 TMAX= 3298.37 ANGLE= 61.5

3 -578.02 155.71 -30.52 -179.52 -115.12

2770.03 2770.03 0.00 0.00 0.00

2925.33 2925.33

TOP : SMAX= 342.45 SMIN= -2582.89 TMAX= 1462.67 ANGLE=-28.5

BOTT: SMAX= 2582.89 SMIN= -342.45 TMAX= 1462.67 ANGLE= 61.5

4 -289.01 77.85 -15.26 -89.76 -57.56

1385.02 1385.02 0.00 0.00 0.00

1462.67 1462.67

TOP : SMAX= 171.22 SMIN= -1291.44 TMAX= 731.33 ANGLE=-28.5

BOTT: SMAX= 1291.44 SMIN= -171.22 TMAX= 731.33 ANGLE= 61.5

STAAD PLANE -- PAGE NO. 21

ELEMENT STRESSES FORCE,LENGTH UNITS= POUN FEET

----------------

STRESS = FORCE/UNIT WIDTH/THICK, MOMENT = FORCE-LENGTH/UNIT WIDTH

ELEMENT LOAD SQX SQY MX MY MXY

VONT VONB SX SY SXY

TRESCAT TRESCAB

5 -3824.79 1030.33 -201.94 -1187.91 -761.76

18329.45 18329.45 0.00 0.00 0.00

19357.09 19357.09

TOP : SMAX= 2265.98 SMIN= -17091.10 TMAX= 9678.54 ANGLE=-28.5

BOTT: SMAX= 17091.10 SMIN= -2265.98 TMAX= 9678.54 ANGLE= 61.5

117

12 1 0.00 -262.46 -3.55 -20.89 0.00

206.55 206.55 0.00 0.00 0.00

222.87 222.87

TOP : SMAX= -37.89 SMIN= -222.87 TMAX= 92.49 ANGLE= 0.0

BOTT: SMAX= 222.87 SMIN= 37.89 TMAX= 92.49 ANGLE=-90.0

2 0.00 -739.81 -10.01 -58.90 0.00

582.23 582.23 0.00 0.00 0.00

628.24 628.24

TOP : SMAX= -106.80 SMIN= -628.24 TMAX= 260.72 ANGLE= 0.0

BOTT: SMAX= 628.24 SMIN= 106.80 TMAX= 260.72 ANGLE=-90.0

3 0.00 -328.07 -4.44 -26.12 0.00

258.19 258.19 0.00 0.00 0.00

278.59 278.59

TOP : SMAX= -47.36 SMIN= -278.59 TMAX= 115.62 ANGLE= 0.0

BOTT: SMAX= 278.59 SMIN= 47.36 TMAX= 115.62 ANGLE=-90.0

4 0.00 -164.04 -2.22 -13.06 0.00

129.10 129.10 0.00 0.00 0.00

139.30 139.30

TOP : SMAX= -23.68 SMIN= -139.30 TMAX= 57.81 ANGLE= 0.0

BOTT: SMAX= 139.30 SMIN= 23.68 TMAX= 57.81 ANGLE=-90.0

5 0.00 -2170.87 -29.38 -172.82 0.00

1708.46 1708.46 0.00 0.00 0.00

1843.46 1843.46

TOP : SMAX= -313.39 SMIN= -1843.46 TMAX= 765.04 ANGLE= 0.0

BOTT: SMAX= 1843.46 SMIN= 313.39 TMAX= 765.04 ANGLE=-90.0

14 1 462.42 124.57 -24.42 -143.62 92.10

2216.02 2216.02 0.00 0.00 0.00

2340.27 2340.27

118

TOP : SMAX= 273.96 SMIN= -2066.31 TMAX= 1170.13 ANGLE= 28.5

BOTT: SMAX= 2066.31 SMIN= -273.96 TMAX= 1170.13 ANGLE=-61.5

2 1303.46 351.13 -68.82 -404.83 259.60

6246.53 6246.53 0.00 0.00 0.00

6596.74 6596.74

TOP : SMAX= 772.23 SMIN= -5824.51 TMAX= 3298.37 ANGLE= 28.5

BOTT: SMAX= 5824.51 SMIN= -772.23 TMAX= 3298.37 ANGLE=-61.5

3 578.02 155.71 -30.52 -179.52 115.12

2770.03 2770.03 0.00 0.00 0.00

2925.33 2925.33

TOP : SMAX= 342.45 SMIN= -2582.89 TMAX= 1462.67 ANGLE= 28.5

BOTT: SMAX= 2582.89 SMIN= -342.45 TMAX= 1462.67 ANGLE=-61.5

STAAD PLANE -- PAGE NO. 22

ELEMENT STRESSES FORCE,LENGTH UNITS= POUN FEET

STRESS = FORCE/UNIT WIDTH/THICK, MOMENT = FORCE-LENGTH/UNIT WIDTH

ELEMENT LOAD SQX SQY MX MY MXY

VONT VONB SX SY SXY

TRESCAT TRESCAB

4 289.01 77.85 -15.26 -89.76 57.56

1385.02 1385.02 0.00 0.00 0.00

1462.67 1462.67

TOP : SMAX= 171.22 SMIN= -1291.44 TMAX= 731.33 ANGLE= 28.5

BOTT: SMAX= 1291.44 SMIN= -171.22 TMAX= 731.33 ANGLE=-61.5

5 3824.79 1030.33 -201.94 -1187.91 761.76

18329.45 18329.45 0.00 0.00 0.00

19357.09 19357.09

TOP : SMAX= 2265.98 SMIN= -17091.10 TMAX= 9678.54 ANGLE= 28.5

BOTT: SMAX= 17091.10 SMIN= -2265.98 TMAX= 9678.54 ANGLE=-61.5

119

16 1 1162.59 -1060.00 108.76 639.78 -252.83

7862.52 7862.52 0.00 0.00 0.00

7902.95 7902.95

TOP : SMAX= 7902.95 SMIN= 81.50 TMAX= 3910.72 ANGLE=-68.2

BOTT: SMAX= -81.50 SMIN= -7902.95 TMAX= 3910.72 ANGLE= 21.8

2 3277.11 -2987.94 306.58 1803.41 -712.68

22162.87 22162.87 0.00 0.00 0.00

22276.84 22276.84

TOP : SMAX= 22276.84 SMIN= 229.74 TMAX= 11023.55 ANGLE=-68.2

BOTT: SMAX= -229.74 SMIN= -22276.84 TMAX= 11023.55 ANGLE= 21.8

3 1453.24 -1325.01 135.95 799.73 -316.04

9828.15 9828.15 0.00 0.00 0.00

9878.69 9878.69

TOP : SMAX= 9878.69 SMIN= 101.88 TMAX= 4888.41 ANGLE=-68.2

BOTT: SMAX= -101.88 SMIN= -9878.69 TMAX= 4888.41 ANGLE= 21.8

4 726.62 -662.50 67.98 399.86 -158.02

4914.07 4914.07 0.00 0.00 0.00

4939.35 4939.35

TOP : SMAX= 4939.35 SMIN= 50.94 TMAX= 2444.20 ANGLE=-68.2

BOTT: SMAX= -50.94 SMIN= -4939.35 TMAX= 2444.20 ANGLE= 21.8

5 9616.16 -8767.64 899.61 5291.83 -2091.24

65033.39 65033.39 0.00 0.00 0.00

65367.85 65367.85

TOP : SMAX= 65367.85 SMIN= 674.14 TMAX= 32346.85 ANGLE=-68.2

BOTT: SMAX= -674.14 SMIN= -65367.85 TMAX= 32346.85 ANGLE= 21.8

18 1 -22.10 -205.41 -147.90 -870.02 -45.51

120

8641.60 8641.60 0.00 0.00 0.00

9310.67 9310.67

TOP : SMAX= -1547.17 SMIN= -9310.67 TMAX= 3881.75 ANGLE= -3.6

BOTT: SMAX= 9310.67 SMIN= 1547.17 TMAX= 3881.75 ANGLE= 86.4

2 -62.30 -579.02 -416.91 -2452.41 -128.27

24358.93 24358.93 0.00 0.00 0.00

26244.93 26244.93

TOP : SMAX= -4361.16 SMIN= -26244.93 TMAX= 10941.88 ANGLE= -3.6

BOTT: SMAX= 26244.93 SMIN= 4361.16 TMAX= 10941.88 ANGLE= 86.4

STAAD PLANE -- PAGE NO. 23

ELEMENT STRESSES FORCE,LENGTH UNITS= POUN FEET

---------------

STRESS = FORCE/UNIT WIDTH/THICK, MOMENT = FORCE-LENGTH/UNIT WIDTH

ELEMENT LOAD SQX SQY MX MY MXY

VONT VONB SX SY SXY

TRESCAT TRESCAB

3 -27.63 -256.77 -184.88 -1087.52 -56.88

10802.00 10802.00 0.00 0.00 0.00

11638.34 11638.34

TOP : SMAX= -1933.96 SMIN= -11638.34 TMAX= 4852.19 ANGLE= -3.6

BOTT: SMAX= 11638.34 SMIN= 1933.96 TMAX= 4852.19 ANGLE= 86.4

4 -13.81 -128.38 -92.44 -543.76 -28.44

5401.00 5401.00 0.00 0.00 0.00

5819.17 5819.17

TOP : SMAX= -966.98 SMIN= -5819.17 TMAX= 2426.10 ANGLE= -3.6

BOTT: SMAX= 5819.17 SMIN= 966.98 TMAX= 2426.10 ANGLE= 86.4

5 -182.82 -1699.05 -1223.36 -7196.21 -376.39

71477.41 71477.41 0.00 0.00 0.00

121

77011.55 77011.55

TOP : SMAX= -12797.12 SMIN= -77011.55 TMAX= 32107.21 ANGLE= -3.6

BOTT: SMAX= 77011.55 SMIN= 12797.12 TMAX= 32107.21 ANGLE= 86.4

19 1 -152.22 -242.25 -120.84 -710.80 -29.25

7047.37 7047.37 0.00 0.00 0.00

7597.28 7597.28

TOP : SMAX= -1273.49 SMIN= -7597.28 TMAX= 3161.90 ANGLE= -2.8

BOTT: SMAX= 7597.28 SMIN= 1273.49 TMAX= 3161.90 ANGLE= 87.2

2 -429.08 -682.85 -340.61 -2003.60 -82.44

19865.13 19865.13 0.00 0.00 0.00

21415.22 21415.22

TOP : SMAX= -3589.71 SMIN= -21415.22 TMAX= 8912.76 ANGLE= -2.8

BOTT: SMAX= 21415.22 SMIN= 3589.71 TMAX= 8912.76 ANGLE= 87.2

3 -190.27 -302.81 -151.04 -888.50 -36.56

8809.21 8809.21 0.00 0.00 0.00

9496.60 9496.60

TOP : SMAX= -1591.86 SMIN= -9496.60 TMAX= 3952.37 ANGLE= -2.8

BOTT: SMAX= 9496.60 SMIN= 1591.86 TMAX= 3952.37 ANGLE= 87.2

4 -95.14 -151.41 -75.52 -444.25 -18.28

4404.61 4404.61 0.00 0.00 0.00

4748.30 4748.30

TOP : SMAX= -795.93 SMIN= -4748.30 TMAX= 1976.19 ANGLE= -2.8

BOTT: SMAX= 4748.30 SMIN= 795.93 TMAX= 1976.19 ANGLE= 87.2

5 -1259.06 -2003.73 -999.47 -5879.25 -241.91

58291.07 58291.07 0.00 0.00 0.00

62839.57 62839.57

TOP : SMAX= -10533.43 SMIN= -62839.57 TMAX= 26153.07 ANGLE= -2.8

BOTT: SMAX= 62839.57 SMIN= 10533.43 TMAX= 26153.07 ANGLE= 87.2

122

20 1 0.00 -171.34 -113.38 -666.93 0.00

6592.99 6592.99 0.00 0.00 0.00

7113.95 7113.95

TOP : SMAX= -1209.37 SMIN= -7113.95 TMAX= 2952.29 ANGLE= 0.0

BOTT: SMAX= 7113.95 SMIN= 1209.37 TMAX= 2952.29 ANGLE= 90.0

STAAD PLANE -- PAGE NO. 24

ELEMENT STRESSES FORCE,LENGTH UNITS= POUN FEET

----------------

STRESS = FORCE/UNIT WIDTH/THICK, MOMENT = FORCE-LENGTH/UNIT WIDTH

ELEMENT LOAD SQX SQY MX MY MXY

VONT VONB SX SY SXY

TRESCAT TRESCAB

2 0.00 -482.97 -319.59 -1879.95 0.00

18584.30 18584.30 0.00 0.00 0.00

20052.80 20052.80

TOP : SMAX= -3408.98 SMIN= -20052.80 TMAX= 8321.91 ANGLE= 0.0

BOTT: SMAX= 20052.80 SMIN= 3408.98 TMAX= 8321.91 ANGLE= 90.0

3 0.00 -214.17 -141.72 -833.67 0.00

8241.23 8241.23 0.00 0.00 0.00

8892.44 8892.44

TOP : SMAX= -1511.71 SMIN= -8892.44 TMAX= 3690.36 ANGLE= 0.0

BOTT: SMAX= 8892.44 SMIN= 1511.71 TMAX= 3690.36 ANGLE= 90.0

4 0.00 -107.09 -70.86 -416.83 0.00

4120.62 4120.62 0.00 0.00 0.00

4446.22 4446.22

TOP : SMAX= -755.86 SMIN= -4446.22 TMAX= 1845.18 ANGLE= 0.0

123

BOTT: SMAX= 4446.22 SMIN= 755.86 TMAX= 1845.18 ANGLE= 90.0

5 0.00 -1417.19 -937.79 -5516.41 0.00

54532.68 54532.68 0.00 0.00 0.00

58841.75 58841.75

TOP : SMAX= -10003.10 SMIN= -58841.75 TMAX= 24419.33 ANGLE= 0.0

BOTT: SMAX= 58841.75 SMIN= 10003.10 TMAX= 24419.33 ANGLE= 90.0

21 1 152.22 -242.25 -120.84 -710.80 29.25

7047.37 7047.37 0.00 0.00 0.00

7597.28 7597.28

TOP : SMAX= -1273.49 SMIN= -7597.28 TMAX= 3161.90 ANGLE= 2.8

BOTT: SMAX= 7597.28 SMIN= 1273.49 TMAX= 3161.90 ANGLE=-87.2

2 429.08 -682.85 -340.61 -2003.60 82.44

19865.13 19865.13 0.00 0.00 0.00

21415.22 21415.22

TOP : SMAX= -3589.71 SMIN= -21415.22 TMAX= 8912.76 ANGLE= 2.8

BOTT: SMAX= 21415.22 SMIN= 3589.71 TMAX= 8912.76 ANGLE=-87.2

3 190.27 -302.81 -151.04 -888.50 36.56

8809.21 8809.21 0.00 0.00 0.00

9496.60 9496.60

TOP : SMAX= -1591.86 SMIN= -9496.60 TMAX= 3952.37 ANGLE= 2.8

BOTT: SMAX= 9496.60 SMIN= 1591.86 TMAX= 3952.37 ANGLE=-87.2

4 95.14 -151.41 -75.52 -444.25 18.28

4404.61 4404.61 0.00 0.00 0.00

4748.30 4748.30

TOP : SMAX= -795.93 SMIN= -4748.30 TMAX= 1976.19 ANGLE= 2.8

BOTT: SMAX= 4748.30 SMIN= 795.93 TMAX= 1976.19 ANGLE=-87.2

5 1259.06 -2003.73 -999.47 -5879.25 241.91

124

58291.07 58291.07 0.00 0.00 0.00

62839.57 62839.57

TOP : SMAX= -10533.43 SMIN= -62839.57 TMAX= 26153.07 ANGLE= 2.8

BOTT: SMAX= 62839.57 SMIN= 10533.43 TMAX= 26153.07 ANGLE=-87.2

BOTT: SMAX= -674.14 SMIN= -65367.85 TMAX= 32346.85 ANGLE=-21.8

STAAD PLANE -- PAGE NO. 34

**** MAXIMUM STRESSES AMONG SELECTED PLATES AND CASES ****

MAXIMUM MINIMUM MAXIMUM MAXIMUM MAXIMUM

PRINCIPAL PRINCIPAL SHEAR VONMISES TRESCA

STRESS STRESS STRESS STRESS STRESS

9.844372E+04 -9.844372E+04 4.085414E+04 9.123455E+04 9.844372E+04

PLATE NO. 25 25 25 25 25

CASE NO. 5 5 5 5 5

********************END OF ELEMENT FORCES*******************

STAAD PLANE -- PAGE NO. 35

*********** END OF THE STAAD.Pro RUN ***********

**** DATE= FEB 1,2016 TIME= 22:28:33 ****

************************************************************

* For questions on STAAD.Pro, please contact *

* Bentley Systems or Partner offices *

* *

125

* Telephone Web / Email *

* USA +1 (714) 974-2500 *

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* JAPAN +81 (03)5952-6500 http://www.ctc-g.co.jp *

* CHINA +86 21 6288 4040 *

* THAILAND +66 (0)2645-1018/19 partha.p@reisoftwareth.com*

* *

* Worldwide http://selectservices.bentley.com/en-US/ *

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************************************************************

126

Appendix B

Output File For Beam Supported Slab

=====================================================================

BEAM NO. 1 DESIGN RESULTS - FLEXURE PER CODE ACI 318-08

LEN - 2.00FT. FY - 60000. FC - 4000. SIZE - 15.00 X 12.00 INCHES

LEVEL HEIGHT BAR INFO FROM TO ANCHOR

FT. IN. FT. IN. FT. IN. STA END

_____________________________________________________________________

1 0 + 2-3/8 3-NUM.6 0 + 0-0/0 2 + 0-0/0 YES YES

2 0 + 9-1/2 7-NUM.4 0 + 0-0/0 2 + 0-0/0 YES YES

B E A M N O. 1 D E S I G N R E S U L T S - SHEAR

127

AT START SUPPORT - Vu= 2.10 KIPS Tu= 16.65 KIP-FT

Vc= 18.17 KIPS, ACI 318:CLAUSE 11.6.3.1

LOAD 4 TORSION VALUE TOO HIGH, INCREASE MEMBER SIZE.

AT END SUPPORT - Vu= 2.10 KIPS Tu= 16.65 KIP-FT

Vc= 18.17 KIPS, ACI 318:CLAUSE 11.6.3.1

LOAD 4 TORSION VALUE TOO HIGH, INCREASE MEMBER SIZE.

___ 5J____________________ 24.X 15.X 12_____________________ 35J____

| |

||=========================================================================||

| 7#4 H 9. 0.TO 24. |

| |

| 3#6 H 2. 0.TO 24. |

| |

|___________________________________________________________________________|

___________________ ___________________ ___________________

| | | | | |

| ooooooo | | ooooooo | | ooooooo |

| 7#4 | | 7#4 | | 7#4 |

| | | | | |

| 3#6 | | 3#6 | | 3#6 |

| ooo | | ooo | | ooo |

| | | | | |

|___________________| |___________________| |___________________|

128

STAAD SPACE

=====================================================================

BEAM NO. 2 DESIGN RESULTS - FLEXURE PER CODE ACI 318-08

LEN - 2.00FT. FY - 60000. FC - 4000. SIZE - 15.00 X 12.00 INCHES

LEVEL HEIGHT BAR INFO FROM TO ANCHOR

FT. IN. FT. IN. FT. IN. STA END

_____________________________________________________________________

1 0 + 2-3/8 5-NUM.5 0 + 0-0/0 2 + 0-0/0 YES YES

2 0 + 9-1/2 5-NUM.5 0 + 0-0/0 2 + 0-0/0 YES YES

B E A M N O. 2 D E S I G N R E S U L T S - SHEAR

AT START SUPPORT - Vu= 7.98 KIPS Tu= 19.76 KIP-FT

Vc= 18.23 KIPS, ACI 318:CLAUSE 11.6.3.1

LOAD 13 TORSION VALUE TOO HIGH, INCREASE MEMBER SIZE.

129

AT END SUPPORT - Vu= 7.76 KIPS Tu= 19.76 KIP-FT

Vc= 18.23 KIPS, ACI 318:CLAUSE 11.6.3.1

LOAD 13 TORSION VALUE TOO HIGH, INCREASE MEMBER SIZE.

___ 6J____________________ 24.X 15.X 12_____________________ 270J____

||=========================================================================||

| 5#5 H 9. 0.TO 24. |

| |

| 5#5 H 2. 0.TO 24. |

||=========================================================================||

| |

|___________________________________________________________________________|

___________________ ___________________ ___________________

| | | | | |

| ooooo | | ooooo | | ooooo |

| 5#5 | | 5#5 | | 5#5 |

| | | | | |

| 5#5 | | 5#5 | | 5#5 |

| ooooo | | ooooo | | ooooo |

| | | | | |

|___________________| |___________________| |___________________|

=====================================================================

BEAM NO. 3 DESIGN RESULTS - FLEXURE PER CODE ACI 318-08

LEN - 2.00FT. FY - 60000. FC - 4000. SIZE - 15.00 X 12.00 INCHES

130

LEVEL HEIGHT BAR INFO FROM TO ANCHOR

FT. IN. FT. IN. FT. IN. STA END

_____________________________________________________________________

1 0 + 2-3/8 3-NUM.6 0 + 0-0/0 2 + 0-0/0 YES YES

2 0 + 9-1/2 7-NUM.4 0 + 0-0/0 2 + 0-0/0 YES YES

B E A M N O. 3 D E S I G N R E S U L T S - SHEAR

AT START SUPPORT - Vu= 13.82 KIPS Tu= 20.11 KIP-FT

Vc= 17.92 KIPS, ACI 318:CLAUSE 11.6.3.1

LOAD 13 TORSION VALUE TOO HIGH, INCREASE MEMBER SIZE.

AT END SUPPORT - Vu= 13.61 KIPS Tu= 20.11 KIP-FT

Vc= 17.92 KIPS, ACI 318:CLAUSE 11.6.3.1

LOAD 13 TORSION VALUE TOO HIGH, INCREASE MEMBER SIZE.

___ 7J____________________ 24.X 15.X 12_____________________ 443J____

| |

||=========================================================================||

| 7#4 H 9. 0.TO 24. |

| |

| 3#6 H 2. 0.TO 24. |

131

||=========================================================================||

| |

|___________________________________________________________________________|

___________________ ___________________ ___________________

| | | | | |

| ooooooo | | ooooooo | | ooooooo |

| 7#4 | | 7#4 | | 7#4 |

| | | | | |

| 3#6 | | 3#6 | | 3#6 |

| ooo | | ooo | | ooo |

| | | | | |

|___________________| |___________________| |___________________|

=====================================================================

BEAM NO. 8 DESIGN RESULTS - FLEXURE PER CODE ACI 318-08

LEN - 2.00FT. FY - 60000. FC - 4000. SIZE - 15.00 X 12.00 INCHES

LEVEL HEIGHT BAR INFO FROM TO ANCHOR

FT. IN. FT. IN. FT. IN. STA END

_____________________________________________________________________

1 0 + 2-1/4 7-NUM.4 0 + 0-0/0 2 + 0-0/0 YES YES

2 0 + 9-1/8 2-NUM.10 0 + 0-0/0 2 + 0-0/0 YES YES

132

B E A M N O. 8 D E S I G N R E S U L T S - SHEAR

AT START SUPPORT - Vu= 0.05 KIPS Tu= 21.22 KIP-FT

Vc= 19.31 KIPS, ACI 318:CLAUSE 11.6.3.1

LOAD 3 TORSION VALUE TOO HIGH, INCREASE MEMBER SIZE.

AT END SUPPORT - Vu= 0.05 KIPS Tu= 21.22 KIP-FT

Vc= 19.91 KIPS, ACI 318:CLAUSE 11.6.3.1

LOAD 3 TORSION VALUE TOO HIGH, INCREASE MEMBER SIZE.

___ 13J____________________ 24.X 15.X 12_____________________ 54J____

| |

||=========================================================================||

| 2#10H 9. 0.TO 24. |

| |

| 7#4 H 2. 0.TO 24. |

||=========================================================================||

| |

|___________________________________________________________________________|

___________________ ___________________ ___________________

| | | | | |

| OO | | OO | | OO |

| 2#10 | | 2#10 | | 2#10 |

| | | | | |

| 7#4 | | 7#4 | | 7#4 |

| ooooooo | | ooooooo | | ooooooo |

133

| | | | | |

|___________________| |___________________| |___________________|

=====================================================================

BEAM NO. 9 DESIGN RESULTS - FLEXURE PER CODE ACI 318-08

LEN - 2.00FT. FY - 60000. FC - 4000. SIZE - 15.00 X 12.00 INCHES

LEVEL HEIGHT BAR INFO FROM TO ANCHOR

FT. IN. FT. IN. FT. IN. STA END

_____________________________________________________________________

1 0 + 2-1/4 8-NUM.4 0 + 0-0/0 2 + 0-0/0 YES YES

2 0 + 9-1/2 8-NUM.4 0 + 0-0/0 2 + 0-0/0 YES YES

B E A M N O. 9 D E S I G N R E S U L T S - SHEAR

AT START SUPPORT - Vu= 0.19 KIPS Tu= 18.61 KIP-FT

Vc= 18.50 KIPS, ACI 318:CLAUSE 11.6.3.1

LOAD 3 TORSION VALUE TOO HIGH, INCREASE MEMBER SIZE.

AT END SUPPORT - Vu= 0.19 KIPS Tu= 18.61 KIP-FT

Vc= 18.50 KIPS, ACI 318:CLAUSE 11.6.3.1

LOAD 3 TORSION VALUE TOO HIGH, INCREASE MEMBER SIZE.

134

___ 14J____________________ 24.X 15.X 12_____________________ 280J____

| |

||=========================================================================||

| 8#4 H 9. 0.TO 24. |

| |

| 8#4 H 2. 0.TO 24. |

||=========================================================================||

| |

|___________________________________________________________________________|

___________________ ___________________ ___________________

| | | | | |

| oooooooo | | oooooooo | | oooooooo |

| 8#4 | | 8#4 | | 8#4 |

| | | | | |

| 8#4 | | 8#4 | | 8#4 |

| oooooooo | | oooooooo | | oooooooo |

| | | | | |

|___________________| |___________________| |___________________|

=====================================================================

BEAM NO. 10 DESIGN RESULTS - FLEXURE PER CODE ACI 318-08

LEN - 2.00FT. FY - 60000. FC - 4000. SIZE - 15.00 X 12.00 INCHES

LEVEL HEIGHT BAR INFO FROM TO ANCHOR

FT. IN. FT. IN. FT. IN. STA END

135

_____________________________________________________________________

1 0 + 2-3/8 5-NUM.5 0 + 0-0/0 2 + 0-0/0 YES YES

2 0 + 9-3/8 6-NUM.6 0 + 0-0/0 2 + 0-0/0 YES YES

B E A M N O. 10 D E S I G N R E S U L T S - SHEAR

AT START SUPPORT - Vu= 0.07 KIPS Tu= 19.64 KIP-FT

Vc= 18.37 KIPS, ACI 318:CLAUSE 11.6.3.1

LOAD 3 TORSION VALUE TOO HIGH, INCREASE MEMBER SIZE.

AT END SUPPORT - Vu= 0.07 KIPS Tu= 19.64 KIP-FT

Vc= 18.37 KIPS, ACI 318:CLAUSE 11.6.3.1

LOAD 3 TORSION VALUE TOO HIGH, INCREASE MEMBER SIZE.

___ 15J____________________ 24.X 15.X 12_____________________ 453J____

| |

||=========================================================================||

| 6#6 H 9. 0.TO 24. |

| |

| 5#5 H 2. 0.TO 24. |

||=========================================================================||

| |

|___________________________________________________________________________|

136

___________________ ___________________ ___________________

| | | | | |

| oooooo | | oooooo | | oooooo |

| 6#6 | | 6#6 | | 6#6 |

| | | | | |

| 5#5 | | 5#5 | | 5#5 |

| ooooo | | ooooo | | ooooo |

| | | | | |

|___________________| |___________________| |___________________|

6.2 Staad Pro. Output File for Slab

112 BOTT: Longitudinal direction - Only minimum steel required.

112 TOP : Transverse direction - Only minimum steel required.

112 TOP : 0.130 1.95 / 4 0.130 2.15 / 2

BOTT: 0.130 1.95 / 3 0.180 3.54 / 15

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

113 TOP : Longitudinal direction - Only minimum steel required.

113 BOTT: Longitudinal direction - Only minimum steel required.

137

113 TOP : Transverse direction - Only minimum steel required.

113 TOP : 0.130 2.08 / 4 0.130 1.87 / 2

BOTT: 0.130 2.53 / 17 0.167 3.29 / 14

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

114 TOP : Longitudinal direction - Only minimum steel required.

114 TOP : Transverse direction - Only minimum steel required.

114 TOP : 0.130 1.80 / 4 0.130 1.59 / 2

BOTT: 0.143 3.15 / 16 0.148 2.91 / 15

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

115 TOP : Longitudinal direction - Only minimum steel required.

115 TOP : Transverse direction - Only minimum steel required.

115 TOP : 0.130 1.31 / 4 0.130 1.34 / 2

BOTT: 0.152 3.35 / 17 0.131 2.60 / 14

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

116 TOP : Longitudinal direction - Only minimum steel required.

116 TOP : Transverse direction - Only minimum steel required.

116 BOTT: Transverse direction - Only minimum steel required.

116 TOP : 0.130 0.73 / 4 0.130 1.19 / 2

BOTT: 0.141 3.11 / 17 0.130 2.40 / 14

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

138

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

117 TOP : Longitudinal direction - Only minimum steel required.

117 TOP : Transverse direction - Only minimum steel required.

117 BOTT: Transverse direction - Only minimum steel required.

117 TOP : 0.130 0.12 / 4 0.130 1.14 / 2

BOTT: 0.137 3.02 / 13 0.130 2.34 / 15

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

118 TOP : Longitudinal direction - Only minimum steel required.

118 BOTT: Longitudinal direction - Only minimum steel required.

118 TOP : Transverse direction - Only minimum steel required.

118 BOTT: Transverse direction - Only minimum steel required.

118 TOP : 0.130 0.49 / 3 0.130 1.18 / 2

BOTT: 0.130 2.65 / 13 0.130 2.40 / 14

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

119 TOP : Longitudinal direction - Only minimum steel required.

119 BOTT: Longitudinal direction - Only minimum steel required.

119 TOP : Transverse direction - Only minimum steel required.

119 TOP : 0.130 1.06 / 3 0.130 1.33 / 2

BOTT: 0.130 1.73 / 13 0.131 2.60 / 14

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

139

120 TOP : Longitudinal direction - Only minimum steel required.

120 BOTT: Longitudinal direction - Only minimum steel required.

120 TOP : Transverse direction - Only minimum steel required.

120 TOP : 0.130 1.87 / 17 0.130 1.56 / 2

BOTT: 0.130 1.53 / 4 0.147 2.90 / 15

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

121 BOTT: Longitudinal direction - Only minimum steel required.

121 TOP : Transverse direction - Only minimum steel required.

121 TOP : 0.152 3.35 / 17 0.130 1.80 / 2

BOTT: 0.130 1.72 / 4 0.166 3.27 / 15

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

123 BOTT: Longitudinal direction - Only minimum steel required.

123 TOP : Transverse direction - Only minimum steel required.

123 TOP : 0.180 3.93 / 17 0.130 1.99 / 2

BOTT: 0.130 1.39 / 4 0.180 3.54 / 14

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

124 TOP : Longitudinal direction - Only minimum steel required.

124 BOTT: Longitudinal direction - Only minimum steel required.

124 TOP : Transverse direction - Only minimum steel required.

124 TOP : 0.130 2.38 / 13 0.130 1.99 / 2

BOTT: 0.130 1.42 / 3 0.181 3.55 / 14

140

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

125 TOP : Longitudinal direction - Only minimum steel required.

125 BOTT: Longitudinal direction - Only minimum steel required.

125 TOP : Transverse direction - Only minimum steel required.

125 TOP : 0.130 1.71 / 4 0.130 1.83 / 2

BOTT: 0.130 1.71 / 3 0.167 3.29 / 15

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

126 TOP : Longitudinal direction - Only minimum steel required.

126 BOTT: Longitudinal direction - Only minimum steel required.

126 TOP : Transverse direction - Only minimum steel required.

126 TOP : 0.130 1.47 / 4 0.130 1.61 / 2

BOTT: 0.130 2.26 / 17 0.150 2.96 / 15

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

127 TOP : Longitudinal direction - Only minimum steel required.

127 BOTT: Longitudinal direction - Only minimum steel required.

127 TOP : Transverse direction - Only minimum steel required.

127 TOP : 0.130 0.94 / 4 0.130 1.40 / 2

BOTT: 0.130 2.28 / 16 0.137 2.72 / 14

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

141

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

128 TOP : Longitudinal direction - Only minimum steel required.

128 BOTT: Longitudinal direction - Only minimum steel required.

128 TOP : Transverse direction - Only minimum steel required.

128 TOP : 0.130 0.32 / 4 0.130 1.30 / 2

BOTT: 0.130 1.81 / 13 0.130 2.58 / 15

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

129 TOP : Longitudinal direction - Only minimum steel required.

129 BOTT: Longitudinal direction - Only minimum steel required.

129 TOP : Transverse direction - Only minimum steel required.

129 TOP : 0.130 0.33 / 3 0.130 1.30 / 2

BOTT: 0.130 1.81 / 13 0.130 2.58 / 15

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

130 TOP : Longitudinal direction - Only minimum steel required.

130 BOTT: Longitudinal direction - Only minimum steel required.

130 TOP : Transverse direction - Only minimum steel required.

130 TOP : 0.130 0.95 / 3 0.130 1.40 / 2

BOTT: 0.130 1.27 / 13 0.137 2.72 / 15

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

131 TOP : Longitudinal direction - Only minimum steel required.

131 BOTT: Longitudinal direction - Only minimum steel required.

142

131 TOP : Transverse direction - Only minimum steel required.

131 TOP : 0.130 1.87 / 17 0.130 1.60 / 2

BOTT: 0.130 1.47 / 4 0.150 2.96 / 15

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

132 BOTT: Longitudinal direction - Only minimum steel required.

132 TOP : Transverse direction - Only minimum steel required.

132 TOP : 0.146 3.21 / 16 0.130 1.82 / 2

BOTT: 0.130 1.71 / 4 0.167 3.29 / 15

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

134 BOTT: Longitudinal direction - Only minimum steel required.

134 TOP : Transverse direction - Only minimum steel required.

134 TOP : 0.173 3.79 / 16 0.130 1.99 / 2

BOTT: 0.130 1.41 / 4 0.180 3.55 / 14

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

136 TOP : Longitudinal direction - Only minimum steel required.

136 BOTT: Longitudinal direction - Only minimum steel required.

136 TOP : Transverse direction - Only minimum steel required.

136 TOP : 0.130 1.61 / 4 0.130 1.31 / 2

BOTT: 0.130 1.79 / 16 0.176 3.45 / 15

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

143

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

137 TOP : Longitudinal direction - Only minimum steel required.

137 BOTT: Longitudinal direction - Only minimum steel required.

137 TOP : Transverse direction - Only minimum steel required.

137 TOP : 0.130 1.76 / 4 0.130 1.19 / 2

BOTT: 0.130 2.43 / 17 0.163 3.21 / 15

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

138 TOP : Longitudinal direction - Only minimum steel required.

138 TOP : Transverse direction - Only minimum steel required.

138 TOP : 0.130 1.59 / 4 0.130 1.06 / 2

BOTT: 0.133 2.94 / 16 0.145 2.87 / 15

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

139 TOP : Longitudinal direction - Only minimum steel required.

139 TOP : Transverse direction - Only minimum steel required.

139 BOTT: Transverse direction - Only minimum steel required.

139 TOP : 0.130 1.20 / 4 0.130 0.93 / 2

BOTT: 0.142 3.12 / 16 0.130 2.55 / 15

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

140 TOP : Longitudinal direction - Only minimum steel required.

140 TOP : Transverse direction - Only minimum steel required.

140 BOTT: Transverse direction - Only minimum steel required.

144

140 TOP : 0.130 0.69 / 4 0.130 0.85 / 2

BOTT: 0.131 2.90 / 17 0.130 2.35 / 15

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

141 TOP : Longitudinal direction - Only minimum steel required.

141 BOTT: Longitudinal direction - Only minimum steel required.

141 TOP : Transverse direction - Only minimum steel required.

141 BOTT: Transverse direction - Only minimum steel required.

141 TOP : 0.130 0.12 / 4 0.130 0.82 / 2

BOTT: 0.130 2.76 / 13 0.130 2.30 / 15

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

142 TOP : Longitudinal direction - Only minimum steel required.

142 BOTT: Longitudinal direction - Only minimum steel required.

142 TOP : Transverse direction - Only minimum steel required.

142 BOTT: Transverse direction - Only minimum steel required.

142 TOP : 0.130 0.44 / 3 0.130 0.85 / 2

BOTT: 0.130 2.39 / 13 0.130 2.41 / 15

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

143 TOP : Longitudinal direction - Only minimum steel required.

143 BOTT: Longitudinal direction - Only minimum steel required

=====================================================================

145

BEAM NO. 1 DESIGN RESULTS - FLEXURE PER CODE ACI 318-08

LEN - 2.00FT. FY - 60000. FC - 4000. SIZE - 15.00 X 12.00 INCHES

LEVEL HEIGHT BAR INFO FROM TO ANCHOR

FT. IN. FT. IN. FT. IN. STA END

_____________________________________________________________________

1 0 + 2-3/8 3-NUM.6 0 + 0-0/0 2 + 0-0/0 YES YES

2 0 + 9-1/2 7-NUM.4 0 + 0-0/0 2 + 0-0/0 YES YES

B E A M N O. 1 D E S I G N R E S U L T S - SHEAR

AT START SUPPORT - Vu= 2.10 KIPS Tu= 16.65 KIP-FT

Vc= 18.17 KIPS, ACI 318:CLAUSE 11.6.3.1

LOAD 4 TORSION VALUE TOO HIGH, INCREASE MEMBER SIZE.

AT END SUPPORT - Vu= 2.10 KIPS Tu= 16.65 KIP-FT

Vc= 18.17 KIPS, ACI 318:CLAUSE 11.6.3.1

LOAD 4 TORSION VALUE TOO HIGH, INCREASE MEMBER SIZE.

___ 5J____________________ 24.X 15.X 12_____________________ 35J____

| |

||=========================================================================||

146

| 7#4 H 9. 0.TO 24. |

| |

| 3#6 H 2. 0.TO 24. |

| |

|___________________________________________________________________________|

___________________ ___________________ ___________________

| | | | | |

| ooooooo | | ooooooo | | ooooooo |

| 7#4 | | 7#4 | | 7#4 |

| | | | | |

| 3#6 | | 3#6 | | 3#6 |

| ooo | | ooo | | ooo |

| | | | | |

|___________________| |___________________| |___________________|

STAAD SPACE

=====================================================================

BEAM NO. 2 DESIGN RESULTS - FLEXURE PER CODE ACI 318-08

LEN - 2.00FT. FY - 60000. FC - 4000. SIZE - 15.00 X 12.00 INCHES

147

LEVEL HEIGHT BAR INFO FROM TO ANCHOR

FT. IN. FT. IN. FT. IN. STA END

_____________________________________________________________________

1 0 + 2-3/8 5-NUM.5 0 + 0-0/0 2 + 0-0/0 YES YES

2 0 + 9-1/2 5-NUM.5 0 + 0-0/0 2 + 0-0/0 YES YES

B E A M N O. 2 D E S I G N R E S U L T S - SHEAR

AT START SUPPORT - Vu= 7.98 KIPS Tu= 19.76 KIP-FT

Vc= 18.23 KIPS, ACI 318:CLAUSE 11.6.3.1

LOAD 13 TORSION VALUE TOO HIGH, INCREASE MEMBER SIZE.

AT END SUPPORT - Vu= 7.76 KIPS Tu= 19.76 KIP-FT

Vc= 18.23 KIPS, ACI 318:CLAUSE 11.6.3.1

LOAD 13 TORSION VALUE TOO HIGH, INCREASE MEMBER SIZE.

___ 6J____________________ 24.X 15.X 12_____________________ 270J____

||=========================================================================||

| 5#5 H 9. 0.TO 24. |

| |

| 5#5 H 2. 0.TO 24. |

148

||=========================================================================||

| |

|___________________________________________________________________________|

___________________ ___________________ ___________________

| | | | | |

| ooooo | | ooooo | | ooooo |

| 5#5 | | 5#5 | | 5#5 |

| | | | | |

| 5#5 | | 5#5 | | 5#5 |

| ooooo | | ooooo | | ooooo |

| | | | | |

|___________________| |___________________| |___________________|

=====================================================================

BEAM NO. 3 DESIGN RESULTS - FLEXURE PER CODE ACI 318-08

LEN - 2.00FT. FY - 60000. FC - 4000. SIZE - 15.00 X 12.00 INCHES

LEVEL HEIGHT BAR INFO FROM TO ANCHOR

FT. IN. FT. IN. FT. IN. STA END

_____________________________________________________________________

1 0 + 2-3/8 3-NUM.6 0 + 0-0/0 2 + 0-0/0 YES YES

2 0 + 9-1/2 7-NUM.4 0 + 0-0/0 2 + 0-0/0 YES YES

149

B E A M N O. 3 D E S I G N R E S U L T S - SHEAR

AT START SUPPORT - Vu= 13.82 KIPS Tu= 20.11 KIP-FT

Vc= 17.92 KIPS, ACI 318:CLAUSE 11.6.3.1

LOAD 13 TORSION VALUE TOO HIGH, INCREASE MEMBER SIZE.

AT END SUPPORT - Vu= 13.61 KIPS Tu= 20.11 KIP-FT

Vc= 17.92 KIPS, ACI 318:CLAUSE 11.6.3.1

LOAD 13 TORSION VALUE TOO HIGH, INCREASE MEMBER SIZE.

___ 7J____________________ 24.X 15.X 12_____________________ 443J____

| |

||=========================================================================||

| 7#4 H 9. 0.TO 24. |

| |

| 3#6 H 2. 0.TO 24. |

||=========================================================================||

| |

|___________________________________________________________________________|

___________________ ___________________ ___________________

| | | | | |

| ooooooo | | ooooooo | | ooooooo |

| 7#4 | | 7#4 | | 7#4 |

| | | | | |

| 3#6 | | 3#6 | | 3#6 |

| ooo | | ooo | | ooo |

150

| | | | | |

|___________________| |___________________| |___________________|

=====================================================================

BEAM NO. 8 DESIGN RESULTS - FLEXURE PER CODE ACI 318-08

LEN - 2.00FT. FY - 60000. FC - 4000. SIZE - 15.00 X 12.00 INCHES

LEVEL HEIGHT BAR INFO FROM TO ANCHOR

FT. IN. FT. IN. FT. IN. STA END

_____________________________________________________________________

1 0 + 2-1/4 7-NUM.4 0 + 0-0/0 2 + 0-0/0 YES YES

2 0 + 9-1/8 2-NUM.10 0 + 0-0/0 2 + 0-0/0 YES YES

B E A M N O. 8 D E S I G N R E S U L T S - SHEAR

AT START SUPPORT - Vu= 0.05 KIPS Tu= 21.22 KIP-FT

Vc= 19.31 KIPS, ACI 318:CLAUSE 11.6.3.1

LOAD 3 TORSION VALUE TOO HIGH, INCREASE MEMBER SIZE.

AT END SUPPORT - Vu= 0.05 KIPS Tu= 21.22 KIP-FT

Vc= 19.91 KIPS, ACI 318:CLAUSE 11.6.3.1

LOAD 3 TORSION VALUE TOO HIGH, INCREASE MEMBER SIZE.

151

___ 13J____________________ 24.X 15.X 12_____________________ 54J____

| |

||=========================================================================||

| 2#10H 9. 0.TO 24. |

| |

| 7#4 H 2. 0.TO 24. |

||=========================================================================||

| |

|___________________________________________________________________________|

___________________ ___________________ ___________________

| | | | | |

| OO | | OO | | OO |

| 2#10 | | 2#10 | | 2#10 |

| | | | | |

| 7#4 | | 7#4 | | 7#4 |

| ooooooo | | ooooooo | | ooooooo |

| | | | | |

|___________________| |___________________| |___________________|

=====================================================================

BEAM NO. 9 DESIGN RESULTS - FLEXURE PER CODE ACI 318-08

LEN - 2.00FT. FY - 60000. FC - 4000. SIZE - 15.00 X 12.00 INCHES

LEVEL HEIGHT BAR INFO FROM TO ANCHOR

FT. IN. FT. IN. FT. IN. STA END

152

_____________________________________________________________________

1 0 + 2-1/4 8-NUM.4 0 + 0-0/0 2 + 0-0/0 YES YES

2 0 + 9-1/2 8-NUM.4 0 + 0-0/0 2 + 0-0/0 YES YES

B E A M N O. 9 D E S I G N R E S U L T S - SHEAR

AT START SUPPORT - Vu= 0.19 KIPS Tu= 18.61 KIP-FT

Vc= 18.50 KIPS, ACI 318:CLAUSE 11.6.3.1

LOAD 3 TORSION VALUE TOO HIGH, INCREASE MEMBER SIZE.

AT END SUPPORT - Vu= 0.19 KIPS Tu= 18.61 KIP-FT

Vc= 18.50 KIPS, ACI 318:CLAUSE 11.6.3.1

LOAD 3 TORSION VALUE TOO HIGH, INCREASE MEMBER SIZE.

___ 14J____________________ 24.X 15.X 12_____________________ 280J____

| |

||=========================================================================||

| 8#4 H 9. 0.TO 24. |

| |

| 8#4 H 2. 0.TO 24. |

||=========================================================================||

| |

|___________________________________________________________________________|

153

___________________ ___________________ ___________________

| | | | | |

| oooooooo | | oooooooo | | oooooooo |

| 8#4 | | 8#4 | | 8#4 |

| | | | | |

| 8#4 | | 8#4 | | 8#4 |

| oooooooo | | oooooooo | | oooooooo |

| | | | | |

|___________________| |___________________| |___________________|

=====================================================================

BEAM NO. 10 DESIGN RESULTS - FLEXURE PER CODE ACI 318-08

LEN - 2.00FT. FY - 60000. FC - 4000. SIZE - 15.00 X 12.00 INCHES

LEVEL HEIGHT BAR INFO FROM TO ANCHOR

FT. IN. FT. IN. FT. IN. STA END

_____________________________________________________________________

1 0 + 2-3/8 5-NUM.5 0 + 0-0/0 2 + 0-0/0 YES YES

2 0 + 9-3/8 6-NUM.6 0 + 0-0/0 2 + 0-0/0 YES YES

B E A M N O. 10 D E S I G N R E S U L T S - SHEAR

154

AT START SUPPORT - Vu= 0.07 KIPS Tu= 19.64 KIP-FT

Vc= 18.37 KIPS, ACI 318:CLAUSE 11.6.3.1

LOAD 3 TORSION VALUE TOO HIGH, INCREASE MEMBER SIZE.

AT END SUPPORT - Vu= 0.07 KIPS Tu= 19.64 KIP-FT

Vc= 18.37 KIPS, ACI 318:CLAUSE 11.6.3.1

LOAD 3 TORSION VALUE TOO HIGH, INCREASE MEMBER SIZE.

___ 15J____________________ 24.X 15.X 12_____________________ 453J____

| |

||=========================================================================||

| 6#6 H 9. 0.TO 24. |

| |

| 5#5 H 2. 0.TO 24. |

||=========================================================================||

| |

|___________________________________________________________________________|

___________________ ___________________ ___________________

| | | | | |

| oooooo | | oooooo | | oooooo |

| 6#6 | | 6#6 | | 6#6 |

| | | | | |

| 5#5 | | 5#5 | | 5#5 |

| ooooo | | ooooo | | ooooo |

| | | | | |

|___________________| |___________________| |___________________|

155

6.2 Staad Pro. Output File for Slab

112 BOTT: Longitudinal direction - Only minimum steel required.

112 TOP : Transverse direction - Only minimum steel required.

112 TOP : 0.130 1.95 / 4 0.130 2.15 / 2

BOTT: 0.130 1.95 / 3 0.180 3.54 / 15

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

113 TOP : Longitudinal direction - Only minimum steel required.

113 BOTT: Longitudinal direction - Only minimum steel required.

113 TOP : Transverse direction - Only minimum steel required.

113 TOP : 0.130 2.08 / 4 0.130 1.87 / 2

BOTT: 0.130 2.53 / 17 0.167 3.29 / 14

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

114 TOP : Longitudinal direction - Only minimum steel required.

114 TOP : Transverse direction - Only minimum steel required.

114 TOP : 0.130 1.80 / 4 0.130 1.59 / 2

BOTT: 0.143 3.15 / 16 0.148 2.91 / 15

156

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

115 TOP : Longitudinal direction - Only minimum steel required.

115 TOP : Transverse direction - Only minimum steel required.

115 TOP : 0.130 1.31 / 4 0.130 1.34 / 2

BOTT: 0.152 3.35 / 17 0.131 2.60 / 14

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

116 TOP : Longitudinal direction - Only minimum steel required.

116 TOP : Transverse direction - Only minimum steel required.

116 BOTT: Transverse direction - Only minimum steel required.

116 TOP : 0.130 0.73 / 4 0.130 1.19 / 2

BOTT: 0.141 3.11 / 17 0.130 2.40 / 14

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

117 TOP : Longitudinal direction - Only minimum steel required.

117 TOP : Transverse direction - Only minimum steel required.

117 BOTT: Transverse direction - Only minimum steel required.

117 TOP : 0.130 0.12 / 4 0.130 1.14 / 2

BOTT: 0.137 3.02 / 13 0.130 2.34 / 15

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

118 TOP : Longitudinal direction - Only minimum steel required.

157

118 BOTT: Longitudinal direction - Only minimum steel required.

118 TOP : Transverse direction - Only minimum steel required.

118 BOTT: Transverse direction - Only minimum steel required.

118 TOP : 0.130 0.49 / 3 0.130 1.18 / 2

BOTT: 0.130 2.65 / 13 0.130 2.40 / 14

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

119 TOP : Longitudinal direction - Only minimum steel required.

119 BOTT: Longitudinal direction - Only minimum steel required.

119 TOP : Transverse direction - Only minimum steel required.

119 TOP : 0.130 1.06 / 3 0.130 1.33 / 2

BOTT: 0.130 1.73 / 13 0.131 2.60 / 14

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

120 TOP : Longitudinal direction - Only minimum steel required.

120 BOTT: Longitudinal direction - Only minimum steel required.

120 TOP : Transverse direction - Only minimum steel required.

120 TOP : 0.130 1.87 / 17 0.130 1.56 / 2

BOTT: 0.130 1.53 / 4 0.147 2.90 / 15

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

121 BOTT: Longitudinal direction - Only minimum steel required.

121 TOP : Transverse direction - Only minimum steel required.

158

121 TOP : 0.152 3.35 / 17 0.130 1.80 / 2

BOTT: 0.130 1.72 / 4 0.166 3.27 / 15

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

123 BOTT: Longitudinal direction - Only minimum steel required.

123 TOP : Transverse direction - Only minimum steel required.

123 TOP : 0.180 3.93 / 17 0.130 1.99 / 2

BOTT: 0.130 1.39 / 4 0.180 3.54 / 14

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

124 TOP : Longitudinal direction - Only minimum steel required.

124 BOTT: Longitudinal direction - Only minimum steel required.

124 TOP : Transverse direction - Only minimum steel required.

124 TOP : 0.130 2.38 / 13 0.130 1.99 / 2

BOTT: 0.130 1.42 / 3 0.181 3.55 / 14

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

125 TOP : Longitudinal direction - Only minimum steel required.

125 BOTT: Longitudinal direction - Only minimum steel required.

125 TOP : Transverse direction - Only minimum steel required.

125 TOP : 0.130 1.71 / 4 0.130 1.83 / 2

BOTT: 0.130 1.71 / 3 0.167 3.29 / 15

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

159

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

126 TOP : Longitudinal direction - Only minimum steel required.

126 BOTT: Longitudinal direction - Only minimum steel required.

126 TOP : Transverse direction - Only minimum steel required.

126 TOP : 0.130 1.47 / 4 0.130 1.61 / 2

BOTT: 0.130 2.26 / 17 0.150 2.96 / 15

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

127 TOP : Longitudinal direction - Only minimum steel required.

127 BOTT: Longitudinal direction - Only minimum steel required.

127 TOP : Transverse direction - Only minimum steel required.

127 TOP : 0.130 0.94 / 4 0.130 1.40 / 2

BOTT: 0.130 2.28 / 16 0.137 2.72 / 14

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

128 TOP : Longitudinal direction - Only minimum steel required.

128 BOTT: Longitudinal direction - Only minimum steel required.

128 TOP : Transverse direction - Only minimum steel required.

128 TOP : 0.130 0.32 / 4 0.130 1.30 / 2

BOTT: 0.130 1.81 / 13 0.130 2.58 / 15

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

129 TOP : Longitudinal direction - Only minimum steel required.

160

129 BOTT: Longitudinal direction - Only minimum steel required.

129 TOP : Transverse direction - Only minimum steel required.

129 TOP : 0.130 0.33 / 3 0.130 1.30 / 2

BOTT: 0.130 1.81 / 13 0.130 2.58 / 15

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

130 TOP : Longitudinal direction - Only minimum steel required.

130 BOTT: Longitudinal direction - Only minimum steel required.

130 TOP : Transverse direction - Only minimum steel required.

130 TOP : 0.130 0.95 / 3 0.130 1.40 / 2

BOTT: 0.130 1.27 / 13 0.137 2.72 / 15

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

131 TOP : Longitudinal direction - Only minimum steel required.

131 BOTT: Longitudinal direction - Only minimum steel required.

131 TOP : Transverse direction - Only minimum steel required.

131 TOP : 0.130 1.87 / 17 0.130 1.60 / 2

BOTT: 0.130 1.47 / 4 0.150 2.96 / 15

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

132 BOTT: Longitudinal direction - Only minimum steel required.

132 TOP : Transverse direction - Only minimum steel required.

132 TOP : 0.146 3.21 / 16 0.130 1.82 / 2

BOTT: 0.130 1.71 / 4 0.167 3.29 / 15

161

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

134 BOTT: Longitudinal direction - Only minimum steel required.

134 TOP : Transverse direction - Only minimum steel required.

134 TOP : 0.173 3.79 / 16 0.130 1.99 / 2

BOTT: 0.130 1.41 / 4 0.180 3.55 / 14

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

136 TOP : Longitudinal direction - Only minimum steel required.

136 BOTT: Longitudinal direction - Only minimum steel required.

136 TOP : Transverse direction - Only minimum steel required.

136 TOP : 0.130 1.61 / 4 0.130 1.31 / 2

BOTT: 0.130 1.79 / 16 0.176 3.45 / 15

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

137 TOP : Longitudinal direction - Only minimum steel required.

137 BOTT: Longitudinal direction - Only minimum steel required.

137 TOP : Transverse direction - Only minimum steel required.

137 TOP : 0.130 1.76 / 4 0.130 1.19 / 2

BOTT: 0.130 2.43 / 17 0.163 3.21 / 15

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

138 TOP : Longitudinal direction - Only minimum steel required.

162

138 TOP : Transverse direction - Only minimum steel required.

138 TOP : 0.130 1.59 / 4 0.130 1.06 / 2

BOTT: 0.133 2.94 / 16 0.145 2.87 / 15

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

139 TOP : Longitudinal direction - Only minimum steel required.

139 TOP : Transverse direction - Only minimum steel required.

139 BOTT: Transverse direction - Only minimum steel required.

139 TOP : 0.130 1.20 / 4 0.130 0.93 / 2

BOTT: 0.142 3.12 / 16 0.130 2.55 / 15

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

140 TOP : Longitudinal direction - Only minimum steel required.

140 TOP : Transverse direction - Only minimum steel required.

140 BOTT: Transverse direction - Only minimum steel required.

140 TOP : 0.130 0.69 / 4 0.130 0.85 / 2

BOTT: 0.131 2.90 / 17 0.130 2.35 / 15

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

141 TOP : Longitudinal direction - Only minimum steel required.

141 BOTT: Longitudinal direction - Only minimum steel required.

141 TOP : Transverse direction - Only minimum steel required.

141 BOTT: Transverse direction - Only minimum steel required.

141 TOP : 0.130 0.12 / 4 0.130 0.82 / 2

163

BOTT: 0.130 2.76 / 13 0.130 2.30 / 15

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

142 TOP : Longitudinal direction - Only minimum steel required.

142 BOTT: Longitudinal direction - Only minimum steel required.

142 TOP : Transverse direction - Only minimum steel required.

142 BOTT: Transverse direction - Only minimum steel required.

142 TOP : 0.130 0.44 / 3 0.130 0.85 / 2

BOTT: 0.130 2.39 / 13 0.130 2.41 / 15

FY: 60.000 KSI FC: 4.000 KSI COVER (TOP): 0.750 IN

COVER (BOTTOM): 0.750 IN TH: 6.000 IN

143 TOP : Longitudinal direction - Only minimum steel required.

143 BOTT: Longitudinal direction - Only minimum steel required