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RC-SLAB1 Software

SUMMARY

This program performs analysis and design of RC one way slabs according to Saudi SBC andAmerican ACI codes. Both one-way solid slabs and joist slabs are considered. The slab or the

joist as well as the supporting beams can be analyzed and designed with automatic load transfer

from the slab to beams.

Developed by Professor Abdelhamid Charif

King Saud University, Civil Engineering Department.

Last edited in November 2009.

Both ACI / SBC coefficient method and elastic finite element method can be used for the

analysis. The code method can only be used if all its conditions are satisfied. But even if these

conditions are satisfied, the user can still choose either method for comparison purposes.The user must first choose the type of slab and then enter all the data relevant to the slab and

beam. When entering many values in a single cell, spaces or commas should be left betweenthem. Material data (concrete and steel) can be entered any time. Concrete coefficient beta1 and

steel yield strain are updated and shown automatically. Ultimate steel strain is assumed unlimited

by default (ACI/SBC) but the user can change this and enter any positive value greater than or

equal to 0.010. Concrete displaced by bars in compression zone is considered.The code condition imposing a lower limit (0.005 for SBC or 0.004 for ACI) on steel tensile

strain may be considered with either of ACI and SBC limits.

Load transfer from the solid slab or joist slab to the beams is performed by the software,according to the beam tributary width. Beam loading may include wall line load. In a joist slab,

the inter-rib spaces may be void or contain hourdis blocks.The beams may be designed with the original rectangular section or with the effective T-section

or L-section. The T-section (for internal beams) and L-section (for edge beams) results from theinteraction between the slab and the beam. The T-section or L-section flange width is

automatically determined by the software, according to SBC / ACI provisions.

Checking, analysis and design steps can be performed separately or in one single operation. Theoutput includes results of the various checks (minimum thickness, shear, flange, ...). Values of

the clear lengths, shear and moment coefficients as well as the minimum thickness are displayed

for each span. Shear force and bending moment diagrams are also displayed. When using the

code coefficient method, envelope curves of the diagrams are generated.Design results include required steel areas as well as the number of bars and bar spacing. Code

values for minimum steel and maximum spacing are enforced. The software delivers an optimumreinforcement pattern along the model by performing appropriate bar cutoff. Both demand andcapacity moment diagrams are produced.

Shear design is performed for beams or ribs requiring it. Single stirrup spacing is produced for

the critical section. For span design, variation of stirrup spacing is delivered.

In case of a solid one-way slab, the slab results are sent to the file "Slab-Strip.out", whereas thebeam results are in "Slab-Beam.out". For a joist slab, the rib and beam results are in files "Joist-

Rib.out" and "Joist-Beam.out".'

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Theoretical background

Steps for the analysis and design of one-way solid slab (1-m slab strip):

(1) Thickness: Determine minimum thickness and:

If the thickness is unknown choose a value greater or equal to the minimum value

If the thickness is given, check that it is greater or equal to the minimum value(2) Loading: Determine the dead and live uniform loading on the slab-strip (kN/m) using the

given area loads (kN/m2) for live load (LL) and super imposed dead load (SDL) as well as the

slab self weight: mxhSDLw scD 1)( mxLLwL 1

The ultimate factored load on the slab strip is:LDu www 7.14.1

(3) Flexural analysis: Determine the values of ultimate moments at major locations (exterior

negative moment, interior negative moment and positive span moment) using the appropriate

clear lengths and moment coefficients or elastic analysis.

(4) Flexural RC design: Perform RC design using standard methods starting with the maximum

moment value. Determine the required steel area and compare with code minimum steel area.

Determine the bar spacing and compare with code maximum spacing

(5) Shrinkage reinforcement:Determine shrinkage (temperature) reinforcement and the corresponding spacing

(6) Shear check: Perform shear check that is, check that:uc VV

If it is not checked, the thickness must be increased and repeat steps from (2)

(7) Detailing: Draw execution plans

ACI / SBC coefficient method of analysisThe ACI / SBC method (also called coefficient method) allows for various load patterns where

live load is applied on selected spans and maximum shear force and bending moment values are

obtained by the envelope curves. This simplified and approximate method allows also for the

real rotation restraint at external supports, where the real moment is not equal to zero. Elasticanalysis gives systematic zero moment values at all external pin supports. The coefficient

method is thus more realistic but is only valid for standard cases. It is advised to use this method

whenever its conditions of application are satisfied. Elastic analysis should be used only if theconditions of the code method are not satisfied.

Conditions of application of ACI / SBC coefficient method:

1. Two spans or more2. Spans not too different. Ratio of any two adjacent spans less or equal to 1.2. For two

successive spans (i) and (i+1), we must have : 2.1),(

),(

1

1

ii

ii

LLMin

LLMax

3. Uniform loading4. Unfactored live load less or equal to three times unfactored dead load: DLLL 3 5. Beams with prismatic sectionsUltimate moment and shear force are given by: 2)( numu lWCM

2

n

uvu

lWCV

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For shear force, span positive moment and external negative moment, lnis the clear length of the

span. For internal negative moment, lnis the average of clear lengths of the adjacent spans.

Cm and Cv are the moment and shear coefficients given by SBC / ACI Tables

End

span

Interior

span

End (exterior)

support

Interior

support

Interior face

of end supportExterior face of first

interior support

Other faces of

Interior supports

Cm

0

Cv

-1/10 -1/11 -1/11 -1/11 -1/11 -1/11

+1/11 +1/16 +1/16

1.0 1.0 1.0 1.0 1.0 1.01.15

a/ ACI terminology

b/ Unrestrained endMore than 2 spans

Cm-1/24(-1/16)*

Cv

-1/10 -1/11 -1/11 -1/11 -1/11 -1/11

+1/14 +1/16 +1/16

1.0 1.0 1.0 1.0 1.0 1.01.15

c/ Integral endMore than 2 spans

Cm-1/24 (-1/16)*

Cv

-1/9 -1/9 -1/24 (1/16)

+1/14 +1/14

1.0 1.15 1.01.15

d / Integral end with 2 spans

)( 1nLM

)(2

121 nn LLM

)( 1nLM )( 2nLM

)(2

121 nn LLM

)( 1nLV )( 2nLV )( 1nLV

* : The exterior negative moment depends on the type of support

If the support is a beam or a girder, the coefficient is: -1/24

If the support is a column, the coefficient is: -1/16

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Minimum thickness for beams and one way slabsMinimum thickness is given by SBC / ACI codes as shown in this Table.

Minimum thickness for beams (ribs) and one-way slabs

unless deflections are computed and checked

Simply

supported

One end

continuous

Both ends

continuous Cantilever

Solid one-

way slabL / 20 L / 24 L / 28 L / 10

Beams

or ribsL / 16 L / 18.5 L / 21 L / 8

In a continuous beam or slab strip, the minimum thickness must be determined for each span and

the final value is the greatest of them: ),...,,,( min,3min2min1minmin nhhhhMaxh

A thickness less than the minimum value may be used but the deflections must then be computed

and checked.

Load transfer from one way solid slab to beams

Load is transferred to the beam according to its tributary width lt. The tributary width is

computed using mid-lines between beams, except for edge beams where it must include all thebeam width (to account for all area) and any slab offset.

The beam dead load must include the beam web weight and any possible wall load.

Dead wallbwbwctscbD whblxhSDLw )( Live tbL lxLLw

Effective beam section

Because of the interaction between the slab and beam, the effective beam section is:

T-section for internal beamsL-section for edge beams

The flange width is determined according to SBC /ACI provisions.

Beam analysis and design is performed following similar steps except that shear step is a design

step where stirrups are designed.

Bar spacing and bar layer number, are updated and many re-design cycles are performed as

required.

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Steps for the analysis and design of one-way joist slab

(1) Thickness: Determine minimum thickness and:

If the thickness is unknown choose a value greater or equal to the minimum valueIf the thickness is given, check that it is greater or equal to the minimum value

(2) Geometry and loading: Check the joist dimension conditions and determine the dead and

live uniform loading on the joist (kN/m) using the given area loads (kN/m

2

) for live load (LL)and super imposed dead load (SDL) as well as the joist self weight.The joist tributary width is the flange width. The dead load must include the possible hourdis

block weight.

Dead jwbjwjwcjfjfcjD ShhbbxhSDLw )( Live jfsL bxLLw

The ultimate factored load on the joist is:LDu www 7.14.1

(3) Flexural analysis: Determine the values of ultimate moments at major locations (exterior

negative moment, interior negative moment and positive span moment) using the appropriate

clear lengths and moment coefficients or elastic analysis.

(4) Flexural RC design: Perform RC design using standard methods starting with the maximum

moment value. Determine the required steel area and compare with code minimum steel area.

Determine the bar number and check layer number.(5) Shrinkage reinforcement:Determine shrinkage (temperature) reinforcement and the corresponding spacing

(6) Shear check: Perform shear check that is, check that:uc VV

SBC and ACI allow 10 % increase for concrete shear strength in joists.

If it is not checked, stirrups must be provided.

(7) Flange check: The flange with little or no reinforcement must be checked as a plain

concrete member, taking into account concrete tensile strength.

(8) Detailing: Draw execution plans

Load transfer from joist slab to beamsLoad is transferred by joists to the beam according to its tributary width lt. Area load is equal to

the joist load divided by the flange width.

In order to avoid duplication of the joist-beam joint, we must use the clear tributary width ltn. It is

obtained by subtracting the beam width:bttn bll

The dead load includes possible wall loading

Dead wallbbbctnjf

jD

bD wbxSDLhblb

ww Live tbL lxLLw

For a flange thickness less than 100 mm, the software rejects the effective T-section or L-section

for internal or edge beams. The flange must be thick enough to incorporate top steel bars with

appropriate covers. Rectangular section design is then recommended.

All the steps for one way solid slab or joist slab as well as the supporting beams are integrated in

RC-SLAB1 software.

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Users manual

Figure 1 shows RC-SLAB1 main screen. A solid one way slab is analyzed in this case.

Figure 1: Main screen of RC-SLAB1 software

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Figure 2 shows analysis results for the slab-strip.

Figure 2: Analysis results for slab strip using ACI/SBC coefficient method

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Figures 2 and 3 shows the analysis results for the slab strip, using ACI/SBC method and the

elastic method.

Figure 3: Analysis results for slab strip using elastic method

Figure 4 shows RC design results highlighting demand and capacity moment diagrams. Variablebar spacing along the model is shown. Maximum spacing and minimum steel conditions are

enforced.

Figure 4: RC design results for slab strip showing bar spacing

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Figure 5 shows design results for the beam modeled as a T-section. Optimum bar cutoff is

delivered with demand and capacity moment diagrams. It can be noted that design for

maximum\negative moment requires compression steel bars.

Figure 5: Design results for the beam

The output shows stirrup design results as well:

Shear design of the beamShear design using 10-mm stirrups with 3 legs

Maximum shear force at support (kN) = 407.252

Shear force at mid-span from envelope curve (kN) = 53.120

Shear force at a distance d from support (kN) = 357.398

Stirrup spacing (mm) is = 157.28 Max spacing (mm) is = 135.50

Adopted spacing (mm) = 130

Constant spacing along the span

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Figure 6 shows the data dialog box in case of joist slabs.

Figure 6: Data dialog box for joist slabs

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The partial listing below shows checking results and particularly detailed results of flange check

as a plain concrete member.

Analysis and design of a joist (rib) with 4 spans

Performing various checks:

The actual thickness (mm) is: 300.00The code minimum thickness (mm) is: 216.22

The minimum thickness is checked

All conditions on joist dimensions are satisfied

Flange check as plain concrete member doubly fixed

Flange ultimate uniform load on 1-m strip (kN/m): 10.28000

Ultimate moment Mu (kN.m): 0.21417

Concrete tensile strength (MPa) : 3.50000

Nominal moment Mn (kN.m): 1.45833

Phi * Mn (kN.m): 0.94792

Flange check is OK

The unfactored dead load (kN/m) is : 4.514

The unfactored live load (kN/m) is : 1.860

The factored ultimate uniform load (kN/m) is : 9.482All conditions of coefficient method satisfied

Concrete strength f'c (MPa) = 25.00

Nominal concrete shear strength Vc = 1.1 x sqrt(fc') x bw x d/6

Effective steel depth d (mm) = 266.00

Nominal concrete shear strength Vc (kN) = 29.260

Phi x Vc (kN) = 21.945

Maximum ultimate shear force Vu (kN) = 20.172

Shear strength is OK. No stirrups required

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Figure 7 shows RC design results highlighting demand and capacity moment diagrams.

Shrinkage steel spacing is also delivered.

Figure 7: RC design results highlighting demand and capacity moment diagrams for the joist