Dissertation2008 Pavan[1]

8/12/2019 Dissertation2008 Pavan[1]

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BLIND PREDICTION OF A FULL-SCALE

3D STEEL FRAME TESTED UNDERDYNAMIC CONDITIONS

A Dissertation Submitted in Partial Fulfilment of the Requirements

for the Master Degree in

Earthquake Engineering

By

ANNA PAVAN

Supervisor: Dr RUI PINHO

May, 2008

Istituto Universitario di Studi Superiori di Pavia

Universit degli Studi di Pavia


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The dissertation entitled Blind prediction of a full-scale 3D steel frame tested under dynamic

conditions, by Anna Pavan, has been approved in partial fulfilment of the requirements for

the Master Degree in Earthquake Engineering.

Rui Pinho -------

Stelios Antoniou


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Abstract

i

ABSTRACT

A blind analysis contest for a full-scale four-story building was announced in 2007 by the

executive committee of the E-Defense steel building project, sponsored by the National

Research Institute for Earth Science and Disaster Prevention in Japan.

In this contest, each participant should predict the structural response before and after the test

was performed using the three-dimensions shaking table located in Miki City, Hyogo

Prefecture, Japan.

This work presents the results obtained from dynamic analyses performed on the building

using SeismoStruct, a fibre element-based program. Through comparing the results given by

the program with experimental ones, the aim of the work was to demonstrate that nonlineardynamic response of steel buildings is possible.

The influence that some modelling choices (hysteretic rules, mass discretization, damping

parameter) have on the prediction of the global structural response were investigated in order

to obtain the best representation of the real building.

The final model and analysis have a negligible difference from experimental results validating

computer capabilities in predicting nonlinear dynamic response also of steel buildings.

Keywords: steel structure; blind prediction; fibre element; dynamic non-linear analysis.


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Acknowledgements

ii

ACKNOWLEDGEMENTS

I would like to express my gratitude to Dr. Rui Pinho for everything he taught me, for his patience, his

dedication towards the competition of this work. Many thanks also to all the people that work in

ROSE School for all the enthusiasm they offer to the realization of this important and unique project.

Special thanks to all my friends in ROSE School for the intensity of each moment spent together.


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Index

iii

TABLE OF CONTENTS

ABSTRACT........................................................................................................................................... i

ACKNOWLEDGEMENTS.................................................................................................................. ii

1 INTRODUCTION ........................................................................................................................ 1

1.1 Outline of the Contest ........................................................................................................... 1

1.2 Objectives ............................................................................................................................. 1

1.3 Organization of the work ...................................................................................................... 2

2 OUTILINE OF THE SPECIMEN ................................................................................................ 3

2.1 Geometry............................................................................................................................... 3

2.2 Slabs...................................................................................................................................... 5

2.3 Connections........................................................................................................................... 6

2.4 Non structural Elements........................................................................................................ 7

2.4.1 External Walls................................................................................................................... 7

2.4.2 Internal Partitions, openings and ceiling.......................................................................... 7

2.4.3 Exterior Stairs ................................................................................................................... 7

2.4.4 Safety System.................................................................................................................... 7

2.5 Weights ................................................................................................................................. 8

3 STRUCTURAL MODELLING.................................................................................................. 10


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Index

iv

3.1 Gravity load on beams ........................................................................................................ 10

3.2 Materials ............................................................................................................................. 13

3.2.1 Concrete .......................................................................................................................... 13

3.2.2 Steel................................................................................................................................. 14

3.3 Sections ............................................................................................................................... 23

3.4 Connections......................................................................................................................... 27

3.4.1 Cycling loading test of composite beam......................................................................... 27

3.4.2 Cycling loading test of column....................................................................................... 29

3.4.3 Modelling attempt........................................................................................................... 31

3.5 Element Classes .................................................................................................................. 33

3.6 Damping.............................................................................................................................. 33

3.7 Constraints .......................................................................................................................... 34

3.8 Integration Scheme ............................................................................................................. 34

4 THE LABORATORY TEST...................................................................................................... 35

4.1 Ground Motion.................................................................................................................... 35

4.2 Measurement during the experiment .................................................................................. 38

4.3 Concrete Characteristics Measured during the test............................................................. 39

5 BLIND PREDICTION AND EXPERIMENTAL RESULTS.................................................... 41

5.1 General remarks .................................................................................................................. 41

5.2 Comparison of the results ................................................................................................... 45

5.2.1 Maximum value of relative displacement from the base at each floor ........................... 46

5.2.2 Maximum value of drift angle and residual drift in each story....................................... 48

5.2.3 Maximum value of absolute acceleration at each floor .................................................. 49

5.2.4 Maximum value of story shear ay each story ................................................................. 50

5.2.5 Maximum value of overturning moment at each floor ................................................... 505.2.6 Maximum strain at a specified point in elastic range ..................................................... 51

5.2.7 Time of building collapse ............................................................................................... 52

6 MODEL CALIBRATION .......................................................................................................... 53

7 CONCLUSIONS......................................................................................................................... 61

REFERENCES ................................................................................................................................... 62

APPENDIX A: Structural Drawings ..................................................................................................A1

APPENDIX B: Material Test Results.................................................................................................B1


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Index

v

LIST OF FIGURES

Figure 1_Organization of the work. .................................................................................................... 2

Figure 2_Steel building specimen. Main structure framing elevations. (unit:m) ............................... 3

Figure 3_Steel building specimen. Main structure framing plan. (unit m)......................................... 4

Figure 4_Structure building specimen. Secondary beams plans. (unit:m) ......................................... 4

Figure 5_Overall view of the specimen.............................................................................................. 5

Figure 6_2FL, 3FL, 4FL Floor section detail. (unit: mm).................................................................. 5

Figure 7_RFL Floor section detail. (unit: mm)................................................................................... 6

Figure 8_Beam to Column connection (right) and Base column connection (left). (unit: mm)......... 6

Figure 9_Column trees factory inspection (right). Beam-to-column connection detail (left). ........... 6

Figure 10_Internal LGS partition panels (right), steel angles reinforcement for aluminium sashes

installation (centre) and lightgauge steel for hanging ceiling............................................................. 7

Figure 11_Safeguard system scheme and specimen almost completed for the test. .......................... 8

Figure 12_Typical floor beams tributary area. (unit: m) ................................................................. 11

Figure 13_Procedure scheme to determine beams additional distributed mass. ............................. 11

Figure 14_Typical stress-block for the two kind of steel used for structural elements. ................... 15

Figure 15_3D model used for eigenvalue analysis ........................................................................... 18


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Index

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Figure 16_North-South component acceleration spectrum. ............................................................. 18

Figure 17_Bi-linear constitutive model for column steel. ................................................................ 21

Figure 18_Bi-linear constitutive model for different steel used for beams. ..................................... 23

Figure 19_Deck slab thickness geometry. ........................................................................................ 24

Figure 20_Applied displacement time history.................................................................................. 25

Figure 21_Model of the beam with the applied displacement. The same analysis was performed for

both slab width.................................................................................................................................. 26

Figure 22_Hysteretic curves for the two beams with different slab effective width........................ 26

Figure 23_Composite beam cycling loading testing set-up.............................................................. 27

Figure 24_Drawings of the specimen. .............................................................................................. 28

Figure 25_Testing results scheme..................................................................................................... 28

Figure 26_Rotation angle bimposed on the beam.......................................................................... 28

Figure 27_Testing results.................................................................................................................. 29

Figure 28_ Column cycling loading testing set-up. .......................................................................... 29

Figure 29_Explanatory scheme spread by the committee. ............................................................... 30

Figure 30_Hypothesis of new testing set-up..................................................................................... 30

Figure 31_Springs calibration results. .............................................................................................. 32

Figure 32_60% scaled NS ground acceleration time history........................................................... 36

Figure 33_60% scaled EW ground acceleration time history........................................................... 36

Figure 34_60% scaled vertical ground acceleration time history..................................................... 36

Figure 35_3D model with dynamic loads applied. ........................................................................... 37

Figure 36_Three consecutive NS components. ................................................................................ 37

Figure 37_Three consecutive EW components. ............................................................................... 37

Figure 38_Three consecutive vertical components........................................................................... 38

Figure 39_Transducers position at 1-st floor(right), 2-nd and 3-rd floor (left). Plan. (unit: mm).... 39Figure 40_4-th floor and roof transducers position. Plan. (unit: mm).............................................. 39

Figure 41_Transducers position. Sections. (unit: mm)..................................................................... 39

Figure 42_Concrete stress-block for different floor slab.................................................................. 40

Figure 43_Definition of floor and story (unit:mm)........................................................................... 41

Figure 44_Gloobal coordinates. ........................................................................................................ 42

Figure 45_Definition of residual drift. .............................................................................................. 43

Figure 46_Position of the strain gage of column 1A. ....................................................................... 44

Figure 47_Strain gage position Figure 48_Strain gauges on the specimen. .................... 45


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Index

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Figure 49_Maximum relative displacements at every level in two directions. ................................ 46

Figure 50_Deformed shape of the pre-test analysis model (out of scale). From left hand, in North-

South direction, East-West, perspective view and detail of the first floor beam-to-column

connection. ........................................................................................................................................ 46

Figure 51_Specimen collapse obtained in the laboratory with a table motion equal to 100% level of

Takatory motion................................................................................................................................ 46

Figure 52_Plastic hinges formation. From left, in y=0m frame, y=6m, x=0m, x=5m and x=10m. . 47

Figure 53_Maximum drift angle at every floor in two directions. ................................................... 48

Figure 54_Maximum residual drift at every floor in two directions. ............................................... 48

Figure 55_Maxima absolute acceleration at every level in two directions....................................... 49

Figure 56_Maximum story shear at very floor in two directions. .................................................... 50

Figure 57_Maximum overturning moment at every floor in two directions. ................................... 50

Figure 58_Maximum strain at column face...................................................................................... 51

Figure 59_Column 1A axial force time-history from pre-test analysis. ........................................... 52

Figure 60_Column 1A stress-block. ................................................................................................. 52

Figure 61_Stress-strain curve for column steel. Detail..................................................................... 54

Figure 62_Maximum floor relative displacement after model calibration. ...................................... 55

Figure 63_Maximum story drift angle after model calibration. ....................................................... 56

Figure 64_Maximum story residual drift angle after model calibration........................................... 56

Figure 65_Maximum floor absolute acceleration after model calibration........................................ 57

Figure 66_Maximum story shear after model calibration................................................................. 57

Figure 67_Maximum story overturning moment after model calibration. ....................................... 58

Figure 68_Column maximum axial strain after model calibration. .................................................. 59

Figure 69_Acceleration and Displacement spectra. Highlighted the two building periods. ............ 59


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Index

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LIST OF TABLES

Table 1_Members schedule (mm) ...................................................................................................... 4

Table 2_Secondary beams schedule (mm) ......................................................................................... 5

Table 3_Table of calculated weights (kN).......................................................................................... 8

Table 4_Floor weights and storey height............................................................................................ 9

Table 5_ Primary Steel elements self weight.................................................................................... 11

Table 6_ Secondary beams and Slab self weight. ............................................................................. 12

Table 7_Weight of slab portion that collaborates in the composite beam........................................ 12

Table 8_Floor net self weight. .......................................................................................................... 13

Table 9_Additional mass distributed on girders. .............................................................................. 13

Table 10_Concrete parameters used in the pre-test model ............................................................... 14

Table 11_Steel parameters derived from experimental data............................................................. 15

Table 12_ Moment of inertia of structural elements......................................................................... 16

Table 13_Elastic frame elements properties. .................................................................................... 17

Table 14_Columns yielding rotation. ............................................................................................... 20

Table 15_Column plastic strain. ....................................................................................................... 20

Table 16_Linear distribution of displacement. ................................................................................. 21


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Index

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Table 17_Plastic strain requested by different girders...................................................................... 22

Table 18_Steel bi-linear constitutive model characteristic parameters. ........................................... 23

Table 19_Effective slab width and thickness for different beams.................................................... 27

Table 20_Input parameters used in the hysteretic model.................................................................. 32

Table 21_Peak ground acceleration for 60% scaled ground motion. ............................................... 36

Table 22_PGA for different ground motion intensities. ................................................................... 38

Table 23_Characteristic parameters for concrete. ............................................................................ 40

Table 24_Error evaluation in predicting relative displacements in different analyses. .................... 47

Table 25_Error evaluation in predicting interstory drift. Residual drift values for different analyses.

........................................................................................................................................................... 48

Table 26_ Error evaluation in predicting absolute acceleration in different analyses...................... 49

Table 27_ Error evaluation in predicting shear forces in different analyses. ................................... 50

Table 28_ Error evaluation in predicting overturning moment in different analyses....................... 51

Table 29_Axial Strain at column face values. .................................................................................. 51

Table 30_Column maximum axial strain comparison...................................................................... 54

Table 31_Error evaluation for floor relative displacement after model calibration. ........................ 55

Table 32_ Error evaluation for floor story drift and residual drift after model calibration. ............. 56

Table 33_Error evaluation for floor absolute acceleration after model calibration. ......................... 57

Table 34_Error evaluation for story shear after model calibration................................................... 58

Table 35_Error evaluation for overturning moment after model calibration. .................................. 58


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Charter 1 . Introduction

1

1 INTRODUCTION1.1 Outline of the ContestIn May 2007 the executive committee of the E-Defense steel building project, sponsored by

the National Research Institute for earth Science and Disaster Prevention in Japan, announced

the 2007 Blind Analysis Contest for a full-scale four-story steel building, which was tested to

collapse in September 2007 on the world's largest three-dimensional shaking table located at

Miki City, Hyogo Prefecture, Japan. The test was conducted by applying a scaled version of

near-fault motion recorded during the 1995 Kobe earthquake.

Two analysis method were categorized as 2D and 3D and, inside these two, participants weredivided between researchers and practicing engineers. Each participant had to predict the

response before and after the test. Because the actual loadings were determined during the

course of the testing based on observed response, the contest was organized in two parts: pre-

test analysis based on anticipated earthquake loadings, and post-test analysis using the actual

loadings. The requirement was that analytical model for the post-test analysis had to be

identical to that for pre-test analysis.

Under executive committee, two working groups were organized: the Analysis Method and

Verification WG was responsible for the announcement, distribution of data, answering

questions, and determination of contest winners and the "Building Collapse Simulation WGthat produced the experimental data for the collapse of the building.

The work presented in following pages analyzed a 3D model of the building and was part of

the researcher category.

1.2 ObjectivesThe aim of this work was to demonstrate the that a good prediction of nonlinear dynamic

response of a steel structure is possible through appropriate modelling choices.


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Charter 1 . Introduction

2

In the past, the precision in foreboding the response of reinforce concrete buildings was

largely verified; the same started to occur for steel frames more recently and with a smaller

amount of example.

The contest at E-Defense represented an opportunity to compare computer analysis resultswith experimental ones, adding one more prove to their validation in predicting also steel

frames behaviour.

1.3 Organization of the workThe first part of the work was focused in collecting all the information from the Analysis

Method and Verification Working Group. Structural geometry was provided, together with

details of loading conditions, material test results on steel, ideal acceleration time-history and

response spectrum of seismic motion.

On the base of collected data, a 3D model was constructed to be analyzed in SeismoStruct.

Different modelling choices (mass discretization, hysteretic rules, damping) were studied in

order to obtain the best representation of the real building. A pre-test nonlinear dynamic

analysis was performed for and incipient collapse level.

After the test was carried out, some supplemental data were provided (material test results on

concrete and measured acceleration). Analytical model was updated with the new data and

analyzed once more for three consecutive seismic levels: elastic, incipient collapse and

collapse level.This stage of the process was called post-test analysis and it was still a blind

prediction.

Results obtained through the blind prediction were compared to experimental ones and

several other investigations regarding modelling choices were made to improve the response

prediction validity.

Figure 1_Organization of the work.


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Charter 2 . Outline of the Specimen

3

2 OUTILINE OF THE SPECIMEN2.1 GeometryThe building is made by four-storey steel moment resisting frames. Along x-direction there

are two frames composed by two bays 5m long, while in y-direction the frames are three, with

one bay 6m long. Interstorey height is 3.5m and at the top of the building there is a parapet

0.9m height from the net height of the roof slab, for a total height of the building equal to

15.275m.

Figure 2_Steel building specimen. Main structure framing elevations. (unit:m)


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4

Figure 3_Steel building specimen. Main structure framing plan. (unit m)

The frames consist in square tube columns and composite beams with wide flanges girders.

The geometry of steel elements is presented in the following table.

Table 1_Members schedule (mm)

Beam Column

Floor G1 G11 G12 Story

R H- 346x174x6x9 H- 346x174x6x9 H- 346x174x6x9 4 RHS- 300x300x9

4 H- 350x175x7x11 H- 350x175x7x11 H- 340x175x9x14 3 RHS- 300x300x9



H- height x width x web thickness x flange thickness, RHS- height x width x thickness

At each floor there are also secondary beams,the geometry of which depends from the level.

1_GF+800 Level 2_ 2FL, 3FL

3_ 4FL 4_RFL

Figure 4_Structure building specimen. Secondary beams plans. (unit:m)


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Table 2_Secondary beams schedule (mm)

B20 H- 200x100x5.5x8

B29 H- 294x200x8x12

B34 H- 346x174xx9

B35 H- 350x175x7x11

Figure 5_Overall view of the specimen.

2.2

Slabs

Slabs at second, third and forth level consist in composite deck floor, 175mm height. Instead,

roof floor is a reinforced concrete slab, with a flat steel deck at its bottom, for an overall

thickness of 150mm.

Figure 6_2FL, 3FL, 4FL Floor section detail. (unit: mm)


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6

Figure 7_RFL Floor section detail. (unit: mm)

2.3 ConnectionsAll connections are made using details and fabrication practice developed following the 1995Hyogoken-Nanbu earthquake. The figure below shows a typical beam-to-column connection.

First a column tree is built by welding together the column and the starting part of the

beam. After, the rest of the beam is connected to the tree using a bolted connection. This type

of connection forces the eventual formation of the plastic hinge away from the weaker joint

between the column and the beam.

Figure 8_Beam to Column connection (right) and Base column connection (left). (unit: mm)

Column bases are connected to concrete blocks (1.5m height) with steel plates, anchored to

them through steel bolts; these concrete blocks create the connection with the shaking table.

Figure 9_Column trees factory inspection (right). Beam-to-column connection detail (left).


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7

2.4 Non structural Elements2.4.1 External WallsExternal walls consist in ALC (autoclaved, aerated concrete) panels, 0.125m thick, fixed on to

the support beams at the top and the bottom of their edges. These panels are connected

between them using the HDR (Hebel Dry Rocking) method, which does not use mortar but

rabbet type panel that are allowed to rock in case of earthquake.

Panels are fixed to the girder at every level through ruler angles and plates to maintain

equilibrium against overturning but are effectively supported by wide flanges beams H-

300x150x6.5x9 (see drawing S03.1 in Appendix A), positioned at 500mm (axis position)

from the bottom end of the building. In this way, all the weight coming from the weight of the

ALC panel is unloaded directly at the foundations, without affecting any other structural

element above.

2.4.2 Internal Partitions, openings and ceilingInternal partitions are made using LGS (light gauge steel) backing board installed on

aluminium frames. Glass windows with aluminium sash were installed within external ALC

panels openings and reinforced by steel angles. A lightgauge steel was used to hanging ceiling

at each floor.

Figure 10_Internal LGS partition panels (right), steel angles reinforcement for aluminium sashes

installation (centre) and lightgauge steel for hanging ceiling.

2.4.3 Exterior StairsDuring construction phases, steel stairs were put up to facilitate the building process. After the

specimen was completed, they were removed. This specification was made because all

elevation drawings in Appendix A show the presence of these stairs but effectively their

presence did not need to be taken in consideration for modelling.

2.4.4 Safety SystemAn anti-collapse safeguard system was built to protect shaking table from collapse of the

structure. The system has four components: steel blocks inside the building at each floor (see

drawing S07.1 in Appendix A), outside fence at first story, diagonal cables at first two stories

(see drawing S17.1 in Appendix A) and jumbo tray lay directly of the shaking table. The

system prevent interstory drift beyond 1/3.5 rad (equal to 0.29 rad circa).


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8

Figure 11_Safeguard system scheme and specimen almost completed for the test.

2.5 WeightsThe following table presents the weights of each part spreadby the committee.

Table 3_Table of calculated weights (kN)

Floor

Steel

Frame

Exterior

Wall

Interior

Wall Ceiling Parapet

Safeguard

System

Cantilevel

Floor Total

Roof Floor 459 20 12 71 2 565

4-th Story 19 79 35 133

4-th Floor 270 24 3 47 4 349

3-rd Story 18 73 30 122

3-rd Floor 260 32 3 47 4 347

2-nd Story 18 73 30 8 130

2-nd Floor 260 41 47 4 352

1-st story 27 76 12 115

Total 1248 200 302 95 19 71 162 15 2113


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9

Each part includes:

Floor: slab, steel beams, deck plates, handrails

Steel Frame (Story): columns, diaphragms, connection panels

Steel Frame (Floor): girders, stud bolts, high tension bolts, slice plates, fire resistive covering

materials

Exterior Wall: ALC panels, reinforcement material for openings, ALC support beam on 1-st

floor, glass, sash

Interior Wall: plaster boards, light-gauge steel backing, doors

Ceiling: plaster boards, rock wool sound absorbing boards, light-gauge steel backing

Parapet: RC parapet on roof floor

Safeguard System: steel tables on floor slab, diagonal wires

Cantilever floor: cantilever floor for temporary stairs, handrails

The following table is a summarizes which is the load applied at every floor. It has to be

reminded that the weight of external ALC panels was not considered to affect any structural

element a part from the beams at 1-st floor. For this reason it was not taken in consideration in

the calculation of the floor weight.

Table 4_Floor weights and storey height

Floor number

j

Floor weight

Wj(kN)

Story number

i

Story height

hi(m)

5 631.5 4 3.5

4 476.5 3 3.5

3 473.0 2 3.5

2 474.5 1 3.875

total 2055.5


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Charter 3 . Structural Modelling

10

3 STRUCTURAL MODELLINGAll analysis have been carried out using SeismoStruct, a finite element analysis program, used

for seismic analysis of framed building. The software is fibre element-based, able to predict

accurately the distribution of damage because it spreads material inelasticity both along the

element length and across its section depth.

In what follows, both eingenvalue and dynamic time-history analysis performed are

presented. The first was used to evaluate the natural period of vibration of the building while

the second one was use to predict the nonlinear inelastic response of the structure whensubjected to earthquake loading.

In this chapter, all the choices made to model the real building in the most accurate way are

explained. Some of them were made on the base of data spread by the committee; other ones

needed to derive from self-made assumption, based on engineering judgement and software

capabilities.

3.1 Gravity load on beamsTo determine the amount of mass to apply on each beam, its tributary area was defined on thegeometry of the problem, assuming a distributed mass over the diaphragm. Mass was

internally converted in vertical load by the software. As a consequence, the vertical load on

the beam was independent of the span direction of the slab. This had a little consequence on

the results since building global response (i.e. floor shear, floor acceleration, etc.) depends on

the mass per floor and not really from how the weight is transferred to the beams.


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11

Figure 12_Typical floor beams tributary area. (unit: m)

Starting from the given data, the additional distributed mass to apply on each beam wascalculated, subtracting the self weight of the structure (composite beams and columns). The

following scheme explains the process followed to arrive to the additional mass value.

Figure 13_Procedure scheme to determine beams additional distributed mass.

Table 5_ Primary Steel elements self weight.

Element QuantityCross Section

Area(m2)Length (m) Self Weight (kN)

2G1 4 0.0083 5 13.006

3G1 4 0.0071 5 11.140

4G1 4 0.0063 5 9.814

RG1 4 0.0052 5 8.182

2G11 2 0.0083 6 7.803

3G11 2 0.0083 6 7.803

4G11 2 0.0063 6 5.888

RG11 2 0.0052 6 4.909

2G12 1 0.0101 6 4.736

3G12 1 0.0083 6 3.902

4G12 1 0.0079 6 3.675

RG12 1 0.0052 6 2.455

Column 6 0.0102 14.052 67.079

Total 150.393


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12

The following table presents secondary beams self weight that, together with primary steel

elements self weight, was subtracted to find slab self weight.

Table 6_ Secondary beams and Slab self weight.

Floor Element QuantityLength

(m)

Cross section

area (m2)

Beams Self

Weight

(kN)

Slab Self

Weight

(kN)

Slab Self

Weight

(kN/m2)

B35 2 6 0.006 5.753

B29 8 2.5 0.007 10.858

B20 4 2 0.003 1.6302-3

CB20 4 1.25 0.003 1.019

240.741 4.012

B35 2 6 0.006 5.753

B29 16 2.5 0.007 21.715

B20 4 0.75 0.003 0.611

4

CB20 4 1.25 0.003 1.019

240.902 4.015

B34 2 6 0.0051 4.774

B20 2 1.5 0.003 0.611

CB20 2 1.25 0.003 0.509RF

B25 2 2.5 0.004 1.420

343.685 5.728

In SeismoStruct, beams were defined as Composite I sections. In this way the program

considers also the weight of the strip of slab that collaborates with the girder in the composite

action as self weight. For this reason, this portion of load does have to be considered in the

definition of additional mass. In paragraph 3.2.2the procedure followed to determine beams

effective width is presented. Here, just the final results is used to calculate beams effective

self weight.

Table 7_Weight of slab portion that collaborates in the composite beam.

Girder beff(m)

Length

(m) Aeff(m2)

Slab Self

Weight (kN)

2G1 0.575 5 2.875 11.536

2G11 0.575 4.85 2.78875 11.189

2G12 1.15 4.85 5.5775 22.379

3G1 0.571 5 2.855 11.455

3G11 0.575 4.858 2.79335 11.208

3G12 1.15 4.858 5.5867 22.416

4G1 0.525 5 2.625 10.539

4G11 0.525 4.95 2.59875 10.434

4G12 1.05 4.95 5.1975 20.868

RG1 0.496 5 2.48 14.206

RG11 0.496 5.008 2.483968 14.228

RG12 0.496 5.008 2.483968 14.228

Hence, subtracting from initial data the weights of steel elements and collaborating slab, it

was possible to determine the net weight of the slab.


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Table 8_Floor net self weight.

Floor number

j

Floor weight

Wj(kN)

Net Floor weight

Wj net (kN)

5 631.5 508.0284 476.5 356.401

3 473 342.675

2 474.5 340.870

tot. 2055.5 1547.97

Finally, the following table presents values of additional mass per unit length applied to the

beams in the model.

Table 9_Additional mass distributed on girders.

Floor number

j

Net Floor

weightWj net (kN)

Element

Tributary

Area(m2)

Load on the

element(kN)

Length(m)

Load

(kN/m)

Additional

Mass(ton/m)

RG1 6.2511 45.532 5 11.326 1.155

RG11 8.7489 63.725 6 12.841 1.3095 437.0281

RG12 17.4978 127.450 6 21.242 2.165

4G1 6.2511 37.132 5 7.426 0.757

4G11 8.7489 51.969 6 8.661 0.8834 356.401

4G12 17.4978 103.937 6 17.323 1.766

3G1 6.2511 35.702 5 7.140 0.728

3G11 8.7489 49.967 6 8.328 0.8493 342.675

3G12 17.4978 99.934 6 16.656 1.698

2G1 6.2511 35.514 5 7.103 0.724

2G11 8.7489 49.704 6 8.284 0.8442 340.870

2G12 17.4978 99.408 6 16.568 1.689

3.2 Materials3.2.1 ConcreteFor pre-test analysis, precise data regarding properties of concrete were not distributed by the

organizing committee. Actually, they had the intent to determine the effective stress-strain

relation during the shacking table test (experimental results regarding concrete constitutive

model can be consulted in paragraph 4.3).

The only specification made from them during pre test preparation says that (see drawing

S04.1 in Appendix A):

the concrete shall be as follow

Position Concretetype

Design Strength(N/mm2)

Quality Strength(n/mm2)

Slump (cm) Max.size of coarseaggregate (mm)

Floor Slab Plain 21 24 15

20(Crushed stone)20 (Ballast)

1

The value presented here is the results of the net weight of 5-th floor minus parapet self weight: 508.028-71=437.028 kN. Actually, the weight of the parapet was then added as additional distributed mass only on RG1and RG11 beams because the central beam RG12 is not affected by it.


25/95


14

The strength of structural concrete can be the compression strength of the specimen

sampled at the factory. The difference between the strength of structural concrete and

the specimen can be considered to be F(=3N/mm2). The curing method of specimen is

as shown below and shall refer to the administrated age.1) 28 days: standard water curing or site water curing

2) Over 28 days and less that 91 days: site can sealed curing

In the computer model, a nonlinear constant confinement concrete model was adopted for the

concrete of slabs. It is a uniaxial model in which a constant confining pressure is assumed

through the entire stress-strain range.

Five parameters that characterized the model were calibrated using values able to generalize

as much as possible the properties of any type of concrete, to overcome the lack of

information.For the compressive strength, the suggested value of 24MPa was assumed. The

tensile strength was considered to be equal to 1/10 of the compressive one. The strain at peak

stress, for normal strength plain concrete, usually varies between 0.002 and 0.0022mm/mm. A

default value equal to 0.002 was assumed. The constant confinement factor kcis used to scale

up the stress-strain relationship throughout all the strain range and is defined as the ratio

between the confined and the unconfined compressive stress of the concrete. Also in his case,

the default value of 1. was assumed. Finally, the concrete specific weight was specified.

Table 10_Concrete parameters used in the pre-test model

fcu cylinder compressive strength 24 MPa

ft tensile strength 2.4 MPa

c strain at peak stress 0.002 mm/mm

1.0 if unconfinedkc confinement factor

1.2 if confined

specific weight 24 kN/m3

3.2.2 SteelFor steel elements all experimental data regarding constitutive law were released by the

committee. For beam elements, both data about flanges and web were given. Moreover, data

regarding base plates, diaphragms and anchor bolts were given. This last set of data, regarding

detailing specifications and not really primary structural elements, was not utilized in the

computer model. The choice was to consider column bases as fully fixed to the ground,

without modelling base-plates and anchor bolts. Furthermore, the panel zone was not treated

in any detailed way: beams were connected directly to columns edge points. This choice was

taken considering that the lack of contribution to global deformation coming from panel zone

yielding could be compensated by the absence in the model of non structural elements (as for

example internal partitions) that add stiffness and reduce structural deflection

Two different kinds of steel were utilized in the specimen: SN400B for beams and BCR295

for column. The probable yield stress for SN400B is 300 MPa while for BCR295 is 380


26/95


15

MPa. Following two graphs present and example of the stress strain curve for the two kind of

steel. On the left hand side, it is possible to see the BCR295 relation, which seems to have a

more constant post-yielding behaviour, compared to the SN400B, in which hardening begins

suddenly, after an accumulation of strain at a more or less constant level of stress.

Column

0

100

200

300

400

500

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Strain (mm/mm)

Stress(MPa)

Beam

0

100

200

300

400

500

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Strain (mm/mm)

Stress(MPa)

Figure 14_Typical stress-block for the two kind of steel used for structural elements.

More precisely, the committee specified that for first floor columns a different kind of steel

was utilized with respect to the steel used for columns at all the other levels.

The committee specified the yielding stress y of for every element; the relative value of

yielding strain was red from the graph and the Elastic Modulus was calculated as

y

yE

=

The following table is a summary of the yielding stress and strain values experimentally

determined for different type of steel and the calculated Elastic Modulus..2

Table 11_Steel parameters derived from experimental data.

Element E (MPa) y(MPa)

Column 1 89351 330 0.0037

Column 2 92222 332 0.0036

Flanges 203750 326 0.00162G1-2G11-3G11-3G12

Web 181951 373 0.0021

Flanges 212827 308.6 0.00164G12

Web 221562 354.5 0.0016

Flanges 201818 333 0.0017RG1-RG11-RG12Web 206703 382.4 0.0019

Flanges 223482 301.7 0.00144G1-4G11

Web 216364 349.9 0.0017

Flanges 174765 297.1 0.00172G12

Web 204258 316.6 0.0016

Flanges 199551 311.3 0.00163G1

Web 194211 369 0.0019

From the table, it can be noticed is that yielding stress for columns is quite smaller than the

expected value, while beam flanges3 follow more often the expected behaviour (around

2All data regarding experimental results about material properties can be consulted in Appenix B.


27/95


16

300MPa). Furthermore, columns yielding strain is significantly bigger than beams one

(sometimes even the double). As a consequence, also columns Young ModulusEresults to be

considerably far from the usual value that is 200000MPa, assuming an unexpected value

around 90000MPa.

As a conclusion, steel used in columns resulted to be softer than the one used for beams.

Another argument needs to be underline at this point. As known, the geometry of a structural

element determines its moments of inertiaIiaround the i-axis, and its stiffness is a function of

the productEIi.

In the following table it is possible to read the second moment of inertia of the several

elements used in the structure.

Table 12_ Moment of inertia of structural elements.

Element Ix(mm4) Iy(mm4)

COL 142,000,000 142,000,000

2G1-2G11-3G11-3G12 235,000,000 17,400,000

4G12 156,000,000 12,500,000

RG1-RG11-RG12 110,000,000 7,910,000

4G1-4G11 135,000,000 9,840,000

2G12 267,000,000 21,300,000

3G1 198,000,000 14,500,000

As can be noticed, Ix value for columns is generally smaller than the one for beams. This

point, together with the one above regarding elements Young Modulus, started to give some

suggestions about building expected response, in particular its deformation. Beams resulted to

be stiffer than columns, letting to think that probably the majority of the deformation will

occur in the columns.

These considerations could be confirmed or denied only by the performed analysis and by the

experimental test. However, at this point, they needed to be noticed to have an idea about

what the model should be able and was expected to reproduce.

In the model, a bi-linear curve was adopted to represent the constitutive law for the steel, on

the base of the experimental data given by the committee. The aim of the bi-linearization wasto offer the best linear regression of the experimental data.

Every element, columns and girders, was characterized using its specific stress-strain curve.

Steel models used for girders were calibrated using flanges constitutive law. In fact, flanges

were considered to better represent the post-yielding behaviour, being the first part that

plasticizes in the section.

The procedure followed to obtain the bi-linear model was quite simple and based on equal

energy dissipation principle. Since the yielding point was determined by experimental results

worked on specimens, the main issue was to determine the hardening parameter, defined as3Flanges constitutive rule is of particular interest for the modelling (see what follows).


28/95


17

the ratio between the initial elastic modulus and the post-yielding modulus. The starting point

was to determine for which amount of strain the parameter needed to be defined because this

could generate different values of post yielding modulus. The assumption was to determined

the plastic strain required by girders when the building equivalent single-degree of freedom is

subjected to spectral acceleration.

An Eingenvalue Analysis was performed to determine the building elastic natural period of

frequency. For this type of analysis, the program considers that the elastic properties of

elements remain constant during all the procedure and hence it requires just the specification

of sectional mechanical properties, not of material and section type.

The following table presents the data utilized to characterize the elastic frame elements of the

model.

Table 13_Elastic frame elements properties.

Element

Cross

Section area

(m2)

E

(kN/m2)Ix (m4) Iy (m4)

G

(kN/m2)J (m4)

Own

mass

(tonnes)

EA (kN)

EIx

(kNm2)

EIy

(kNm2)

GJ

(kNm2)

Applied

Mass4

(tonnes/m)

COL 0.01020 8.94E+07 0.00014 0.00014 3.44E+07 2.83E-07 0.7956 911380 12688 12688 9.7204 0.7956

2G1 0.00834 2.04E+08 0.00024 0.00002 7.84E+07 3.57E-07 0.6503 1698664 47881 3545 27.9578 1.3743

3G1 0.00714 2.00E+08 0.00020 0.00001 7.68E+07 2.19E-07 0.5570 1424994 39511 2893 16.8344 1.2850

4G1 0.00629 2.23E+08 0.00014 0.00001 8.60E+07 1.93E-07 0.4907 1405919 30170 2199 16.5707 1.2477

RG1 0.00525 2.02E+08 0.00011 0.00001 7.76E+07 1.08E-07 0.4091 1058535 22200 1596 8.3972 1.5641

2G11 0.00834 2.04E+08 0.00024 0.00002 7.84E+07 3.57E-07 0.6503 1698664 47881 3545 27.9578 1.4943

3G11 0.00834 2.04E+08 0.00024 0.00002 7.84E+07 3.57E-07 0.6503 1698664 47881 3545 27.9578 1.4993

4G11 0.00629 2.23E+08 0.00014 0.00001 8.60E+07 1.93E-07 0.4907 1405919 30170 2199 16.5707 1.3737

RG11 0.00525 2.02E+08 0.00011 0.00001 7.76E+07 1.08E-07 0.4091 1058535 22200 1596 8.3972 1.7181

2G12 0.01012 1.75E+08 0.00027 0.00002 6.72E+07 6.65E-07 0.7894 1768622 46662 3722 44.7309 2.4784

3G12 0.00834 2.04E+08 0.00024 0.00002 7.84E+07 3.57E-07 0.6503 1698664 47881 3545 27.9578 2.3483

4G12 0.00785 2.13E+08 0.00016 0.00001 8.19E+07 4.42E-07 0.6125 1671338 33201 2660 36.1548 2.3785

RG12 0.00525 2.02E+08 0.00011 0.00001 7.76E+07 1.08E-07 0.4091 1058535 22200 1596 8.3972 2.5741

Where:

E = elastic modulus

Ix= moment of inertia around the major axis

Iy= moment of inertia around the minor axis

G = shear modulusJ = modulus of rigidity

4It was obtained as the sum of the own mass and the applied one.


29/95


18

Figure 15_3D model used for eigenvalue analysis

Form the analysis, the first mode period of vibration is equal to sec30.1=T .

The spectral acceleration of the equivalent single degree of freedom was then found from the

North-South (x-direction in the model) response spectrum5spread by the committee.

NS Component Acceleration Spectrum

0

5

10

15

20

25

30

35

0.1 1 10

T sec

Sam/s2

Figure 16_North-South component acceleration spectrum.

From the spectrum, 2/06.25 smSa = .

Since the pre-test analysis is conducted using a load whose intensity is scaled at 60% of its

original intensity, the scaled spectral acceleration was determined.

2

60 /034.15 smSa =

The equivalent SDOF own circular frequency of vibration was defined as

5Only the North-South spectrum was considered for simplicity of the procedure.


30/95


19

sec8489.4

2 rad

T==

and its height was assumed to be

mHH topeff 13.10475.147.07.0 === .

At this point, spectral displacement could be find: mSS ad 639.0260

60 ==

.

From the displacement, it was possible to determine the SDOF-base rotation, defined as

radH

S

eff

dTOT 06312.0

13.10

639.060 ===

At this point, it was possible to determine the plastic deformation required to the several

structural elements by the applied acceleration.

TOT is the column rotation, and it is given by the sum of an elastic (y) and a plastic (p)

component:

pyTOT +=

As known, yis the column rotation at yielding point. Before it was underlined as beams are

quite stiffer than columns. This allows (for the purpose of this calculation) to consider

columns as fully fixed at both edges, and hence their deformed shaped under lateral loads

could look like in the figure below.

From elasticity relations, it was possible to know

- the displacement at column mid-height123

2

2

2/ 2HH

H yy =

=

- the yielding curvature in the column section2/c

y

y h

=

- the yielding rotation in the column

62/

H

H

y

y

==

Hence, yielding rotation in the column resulted to be:

62/

H

hc

y

y

=


31/95


20

Where

= displacement at column mid-height

H = column height

y = yielding curvature of column section

y= yielding strain of column steel

hc= column cross section width

y= column yielding rotation

Hand hcwere already determined by the geometry of the problem and ywas known from

column stress-block. Columns yielding rotation was then calculated.

Table 14_Columns yielding rotation.

H(m) hc (m) y y(rad)

col 1 3.875 0.30 0.0037 0.01593

col 2 3.5 0.30 00036 0.014

Colum plastic strain could be calculated from its plastic rotation.

yTOTp = and ppp L=

2/c

p

ph

=

2

c

p

yTOT

p

h

L

=

Where

p= column plastic rotation

p = plastic curvature of column section

Lp= plastic hinge length (an average value of 0.5 x column width was assumed)

p= column max plastic strain

Table 15_Column plastic strain.

p (rad) Lp(m) p

col 1 0.04719 0.15 0.04719

col 2 0.04912 0.15 0.04912

Once the level of strain was known, the second branch of the bi-linear curve could be

determined. The slope was determined such that there was equal area under both theexperimental and bi-linear relations between the yield point and the strain request.


32/95


21

Column

0

100

200

300

400

500

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Strain (mm/mm)

Stress

(MPa)

Figure 17_Bi-linear constitutive model for column steel.

Considering that the height of the building is quite small, a linear distribution of the

displacements with height was adopted. The table below presents displacements calculated in

North-South direction for every level, starting from the equivalent SDOF system

displacement 60dS , through the relation:

eff

diH

hiSu 60=

Where

ui= lateral displacement at i-th level

hi= i-th level height

Heff

= equivalent SDOF system height

Sd60= equivalent SDOF lateral displacement

Table 16_Linear distribution of displacement.

Level height (m) displ(m)

1 3.500 0.221

2 7.000 0.441

3 10.525 0.664

4 14.052 0.886

The target rotation at the column base is the one explained before, while the rotation at thebeam ends can be estimated from this through the geometry.

pcb

bcb

lhl

l

=

Where:

b= is the rotation at the beam end

c= is the rotation at the column base

lb= is the length of the beam


33/95


22

hc= is the column width

lp= is the beam plastic hinge length (an average value of 0.5 x the depth of the beam was

assumed).

Hence, through the relations:

p

bp

l

= and

2/b

p

ph

=

Where:

p = is the strain request

p = is the curvature of the beam section

hb= is the width of the beam

it was then possible to estimate the strain request for every girder.

Table 17_Plastic strain requested by different girders.

Girder Span(m) hb(m) lp(m) b(rad) b (m-1)

p

2G1 5 0.4 0.18 0.0698 0.3879 0.078

2G11 6 0.4 0.18 0.0686 0.3812 0.076

2G12 6 0.39 0.1755 0.0686 0.3906 0.076

3G1 5 0.396 0.1782 0.0698 0.3917 0.0783G11 6 0.4 0.18 0.0686 0.3812 0.076

3G12 6 0.4 0.18 0.0686 0.3812 0.076

4G1 5 0.35 0.1575 0.0695 0.4411 0.077

4G11 6 0.35 0.1575 0.0683 0.4338 0.076

4G12 6 0.34 0.153 0.0683 0.4462 0.076

RG1 5 0.346 0.1557 0.0694 0.4460 0.077

RG11 6 0.346 0.1557 0.0683 0.4387 0.076

RG12 6 0.346 0.1557 0.0683 0.4387 0.076

2G1- 2G11 - 3G11 - 3G12 Flanges

0

100

200

300

400

500

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Strain (mm/mm)

Stress(MPa)

4G12 Flanges

0

100

200

300

400

500

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Strain (mm/mm)

Stress(MPa)


34/95


23

RG1 - RG11 - RG12 Flanges

0

100

200

300

400

500

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Strain (mm/mm)

Stress(MPa)

4G1 - 4G11 Flanges

0

100

200

300

400

500

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Strain (mm/mm)

Str

ess(MPa)

2G12 Flanges

0

100

200

300

400

500

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Strain (mm/mm)

Stress(MPa)

3G1 Flanges

0

100

200

300

400

500

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Strain (mm/mm)

Stress(MPa)

Figure 18_Bi-linear constitutive model for different steel used for beams.

The following table presents characteristic parameters (Elastic Modulus, yielding stress and

hardening parameter) obtained after bi-linearization for each set of elements and used to

model different steel types constitutive rule.

Table 18_Steel bi-linear constitutive model characteristic parameters.

Element E (MPa) y (MPa) r

Column 1 89351 330 0.05

Column 2 92222 332 0.05

2G1-2G11-3G11-3G12 203750 326 0.12

4G12 212830 308.6 0.1

RG1-RG11-RG12 201820 333 0.15

4G1-4G11 223480 301.7 0.13

2G12 174770 279.1 0.2

3G1 199550 311.1 0.18

3.3 SectionsColumns were modelled using Rectangular Hollow section, characterized by steel modelled

as explained before. Girders were modelled using Composite I section for which three

materials had to be defined: the steel for the profile, the concrete for the cover and the

confined concrete6. Moreover, to use this type of section some information about slab

thickness and its effective width needed to be input. SeismoStruct does not allow the

modelling of a slab with a shape different from the flat one.For this reason, for girders at

second, third and forth level, it was necessary to define an equivalent slab thickness to model

6Definition of material was explained in paragraph 3.2.


35/95


24

a flat slab able to give the same contribution to the compression strength given by the real

slab.

Taking in consideration that the slab spans in x-direction, girders were characterized with

different values of equivalent slab thickness, depending from their spanning direction.

Figure 19_Deck slab thickness geometry.

For beam spanning parallel to the slab, the contribution to compression strength given fromthis last was considered to derive from and average thickness obtained as:

mh

hHts 1375.02

1 =+=

While, for girders spanning in y-direction, only the thinner part of slab was considered as

effectively able to contribute to beam compression strength.

mhHt 1.02 ==

To use this type of section it was also necessary to define the effective width of slab that

collaborates with the steel girder in steel-concrete composite action.

Different Codes present different formulae to calculate slab width. To decide which one to

follow for the modelling, a comparison between two of them was performed to demonstrate

that results are not really conditioned by this parameter. The internal girder 2G11, which

spans in y-direction for 6 meters, was taken as example. The slab effective width in this case

resulted to be equal to 0.1m.

Two codes were then compared: LRFD (Load and Resistance Factor Design) from AISC

(AmericanInstitute of Steel Construction), Second Edition 1994, and the New Zealand Code

3101.

The LRFD requires that:

+= eieff bbb 0 and2

iei

bb <

Where

b0= distance between the centres of the outstand shear connectors (0 in this case because shear

connectors lie in one line. See figure 6)


36/95


25

bei= value of the effective width of the concrete flange on each side of the web, taken as L e/8

but not greater than the geometric width bi (5m in this case). Le should be taken as the

approximate distance between points of zero bending moment.The code specifies that, for

multi-span beams, Lecan be considered to be equal to 0.7L = 4.2m, where L in the span

length. In this case, the beam is a single-span, so Le has a greater value. However, Le

cannot be considered equal to L because at beam edges there is a moment resistance given

by the connection with the column. To mediate between these two limit conditions Le

was considered to be equal to 5m.

For LRFD provisions, slab effective width results to be equal to mLe 625.0

8

5

8==

New Zealand Code, for fully composite, completely connected beams, provides the effective

width to be:

4

Ltb weff += and

)()(

)('

)(

8

21

1

sbsb

sbeff

sbeff

seff

tdtd

tdLb

tdb

tb

+++

++

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