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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
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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
viii
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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Charter 2 . Outline of the Specimen
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
3 H- 396x199x7x11 H- 400x200x8x13 H- 400x200x8x13 2 RHS- 300x300x9
2 H- 400x200x8x13 H- 400x200x8x13 H- 390x200x10x16 1 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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Charter 2 . Outline of the Specimen
5
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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Charter 2 . Outline of the Specimen
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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Charter 2 . Outline of the Specimen
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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Charter 2 . Outline of the Specimen
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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Charter 2 . Outline of the Specimen
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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Charter 3 . Structural Modelling
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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Charter 3 . Structural Modelling
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.
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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
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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.
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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).
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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.
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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.
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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
=
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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.
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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
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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)
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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.
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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)
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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
+++
++