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Steel I-Girder Designwith special attention to Eurocode provisions
Vidish A. Iyer
Structural Engineer and CAE consultant at Midas IT
Bridging Your Innovat ions to Real i t ies
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midas Civil
About Midas IT
About Midas Civil
Modeling Philosophy
Design Philosophy and Eurocode specifications
BS vs EC design for Composite structures.
CONTENTS
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Bridging Your Innovations to Realitiesmidas Civil
CONTENTS
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MIDAS Programs were being developed since 1989 and have been usedcommercially since 1996.
With our headquarters in South Korea , we currently have corporate offices in
Beijing, Shanghai, Detroit, Dallas, Europe, India and Japan and are ever
expanding .
One of the Largest civil analysis software developers
Proven Reliability with over 5,000 project applications
Intensive quality control system
Analyses verified by various institutions
CONTENTS
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Bridging Your Innovations to Realitiesmidas Civil
ABOUT MIDAS IT
We shal l soon be opening a new branch in Singapore
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Integrated Solution System for Bridge and Civil Engineeringmidas Civil
What is midas Civil?
General Purpose
Special Purpose
FEM FBM BEM
Structural Engineer
Geotechnical Engineer
Bridge Underground Structure BuildingPlant Tunnel Dam
Why midas Civil
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WHAT IS MIDAS CIVIL ?
2-D 3-D
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Integrated Solution System for Bridge and Civil Engineeringmidas Civil
What kind of bridge type can midas Civil handle?
Conventional Bridge
Staged Segmental Bridge
Cable-stayed Bridge & Suspension Bridge
Why midas Civil
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WHAT TYPES OF BRIDGES CAN IT HANDLE ?
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Integrated Solution System for Bridge and Civil Engineeringmidas Civil
CONTENTS
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Bridging Your Innovations to Realitiesmidas Civil
MODELING PHILOSOPHY
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Three main modeling methods
2D Grillage models
3D Grillage models
Meshed Finite Element model
MODELING
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Most common modeling method
Modeled as orthogonal or skewed grillage depending on site
requirements
2D MODELING
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Usual grillage modeling principles apply
For multi-girder bridges , shear lag is unlikely to reduce the effective slabwidth below the slab actual width . Usually models for bare steel condition ,short term composite condition and long term composite condition are
required.
Section properties for the composite main beams should use the fullcomposite second moment of inertia. Intermediate longitudinal elementsshould be given properties of slab only.
Torsional stiffness of the slab should be divided equally between transverseand longitudinal beams. ( bt3/6 in each direction )
Intermediate bracings should be modeled
2D MODELING
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3D Grillages are quite useful when dealing with ladder deck
bridges
3D GRILLAGE MODELING
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Vertical Bending is assigned wholly to the upper members while bottom flange
elements represent only the plan bending of these flanges.
Although this model captures the local effects in a better fashion , it is still not
possible to separate the global and local effects .
3D GRILLAGE MODELING
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More realistic structural response. Accurate representation of local and
global responses.
Models can be built using combination of plate and beam elements .
FINITE ELEMENT MODELING
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There are several actions on any structure that are not normally accountedfor without construction stage analysis . These include :
Creep , Shrinkage and Time dependent strength variation effects
Locked in stresses arising from staged construction , material defects etc.
Prestress Losses
Accounting for the pouring sequence of the deck slab.
Accurate deflectionsthese directly affect the erection process andcamber
For composite structures in particular the pouring sequence, creep ,shrinkage , strength variation and locked in stresses are of great import sincethese factors can significantly affect the overall design.
Construction Stage Analysis
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DESIGN PHILOSOPHY
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Required Codes :
1) EN 1990Load combinations
2) EN 1991-2Moving loads
3) EN 1991-1-1Densities of materials
4) EN 1991-1-4Wind Actions5) EN 1991-1-5Temperature actions
6) EN 1993-1-1Design of steel structures
7) EN 1993-1-5Plated Structural Elements ( for LTB )
8) EN 1993-1-9 - Fatigue
9) EN 1994-2Design of composite structures ( bridges )
10) EN 1997Geotechnical Design
11) EN 1998Seismic Design
12) National Annexes to above codes
DESIGN CODES
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Ultimate Limit State :
Bending Resistance
Shear Resistance
Lateral Torsional Buckling
Fatigue Resistance
Serviceability Limit State :
Deformation
Crack Control
Stress Checks
DESIGN REQUIREMENTS
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Classification of Sections4 classes as per EC3 -1-1
1) Class 1- can form plastic hinge with rotation capacity
2) Class 2can form plastic hinge but limited rotation capacity
3) Class 3can fully develop elastic resistance across section
4) Class 4- buckles before elastic limit is reached
DESIGN PROCEDURE OVERVIEW
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Plastic bending resistance for Classes 1&2
Resistance is for Effective Cross Section ( allowances for Shear
lag & local buckling for class 4)
BENDING RESISTANCE
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The elastic resistance for classes 3&4 can be calculated from the equation :
Where Ma,Edis design moment in steel section alone (during constn. Stage)
Mc,Edis design moment in composite section (after construction)
k is an amplifying factor that causes the stress limit to be reached in
steel or reinforcement (whichever is first )
ELASTIC MOMENT OF RESISTANCE
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In composite beam sections, shear resistance is simply takenas that of the steel section.
There are two basic components : Vertical shear resistance
and buckling shear resistance ( Both taken from EC3)
For shear buckling , contributions from web and flange are
dealt separately ( refer EC 3-1-1 , cl. 5.1,2,3,8)
For contribution from the flange , in case of composite beams
the bottom flange should be used for shear resistance
calculationeven if it is larger .
SHEAR RESISTANCE IN BEAM WEBS
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BENDING AND SHEAR INTERACTION
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For composite beams , buckling usually happens in the bottom flanges
when they are in compression .
Here buckling is not true lateral torsional buckling but rather a distortional
buckling
Nevertheless , EC 3 & 4 prescribe rules for LTB based on non dimensionalslenderness
BUCKLING RESISTANCE
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The following sets of equations are used :
The relationship between LT and LTcan be seen from EC3-1-1
BUCKLING RESISTANCE
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A simplified method , as outlined in EN 1993-1-1 is often used for
calculating the buckling resistance .
BUCKLING RESISTANCE
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Restraint effect in Integral Bridges
Beams curved in planpresence of radial force necessitates provision oflateral restraints at intervals
Flange curved in elevationpresence of vertical radial force which results
in transverse plan bending of flange and vertical stresses in web.
Plan bending from interaction with cross girdersof special concern in
ladder decks where vehicle loading may induce lateral actions.
OTHER EFFECTS IN MAIN GIRDERS
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Fatigue is the progressive and localized structural damage that occurs when a material is
subjected to cyclic loading
For road bridges , the Eurocode advises the use of EN 1992-2 and EN 1992-3 by using fatigue
load model LM 3 (basically its a moving load analysis)
EN 1993-2 and EN 1993-1-9 should be referred to for detailed provisions regarding fatigue
Per these codes :
a) Determine the stress range pdue to the passage of the fatigue load model 3 vehicle
b) Determine damage equivalence factor .
c) Determine the design value of the stress range
Fatigue Analysis
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Basic Check for fatigue :
cis the reference value of fatigue strength at 2 x 106cycles, which is
numerically the same as the relevant detail category according to BS EN 1993-
1-9 Tables 8.1 to 8.10.
Fatigue Analysis
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Three categories of combinations of actions are
proposed in EN:
characteristic(normally used for irreversible limit states,e.g. for exceeding of some cracking limits in concrete)
frequent(is normally used for reversible limit states) and
quasi-permanent(is normally used for assessment of long-term effects)
Serviceability Limit StateLoad Combinations
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Stress checks are done as per SLS
combinations for unfactored values of
characteristic actions.
Basically there should be no inelastic behavior.
Stress limits in Concrete , steel , reinforcement
and studs are reduced by certain values ( k
factors )
Serviceability Limit State - Stress
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EC 4 refers us to EC 3-2 for deflection limits.
Basically deformations are calculated from the
Frequent load combinations
EC 3 is silent on any actual limits for deformation .Normal practices for deflection limits can apply .
National annexes should also be referred to .
Serviceability Limit State - Deflection
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The Eurocode advises section 7.4.2 of EC4-2 which prescribes
minimum reinforcement in lieu of more accurate method and
describes this as a conservative approach.
Serviceability Limit StateCrack Control
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For direct loading, limitation of crack widths can be achieved by limiting bar
spacing /bar diameter as per the following tables
Serviceability Limit StateCrack Control
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Although it would seem that the Eurocodes represent asignificant departure from the earlier BS code practices, the two are closer than they appear .
The differences are not that numerous and most of thedesign practices and methods are quite similar in bothcodes.
The next few slides highlight some major points ofdifference between EC4 and BS-5950-3 provisions forcomposite design.
DESIGN PROCEDUREBS VS EC
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EC 4concrete strength is taken from cylinder
BSconcrete strength is taken from Cube
Sample : C20/25 ( cube str = 25 , cyl str =20 )
CONCRETE STRENGTH
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BS 5950-3: characteristic resistance of studs in solid slabs is given for
various combinations of height, diameter and concrete strength.
EC4 calculates the resistance as the minimum of two equationsone for
failure of concrete by crushing and one for shearing of the stud
SHEAR CONNECTION
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The graph below shows a comparison for stud
resistance between EC4 and BS 5950-3.
SHEAR CONNECTION
li k di i l l
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Minimum Shear Connection RequirementsBS code simply states these as afunction of span length but Eurocodes consider asymmetry of the section as
well.
SHEAR CONNECTION
id i Y I i li iCli k di M i l l
id i Y I i li iid Ci il
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As per British code , Eff. Width = Span/8 subject to conditions
For Eurocodes it varies along the length of the beam
EFFECTIVE WIDTH
B id i Y I ti t R litiCli k t dit M t titl t l
B id i Y I ti t R litiid Ci il
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Different Shear Areas for BS and EC ( slightly larger
for EC than for BS )
VERTICAL SHEAR
B id i Y I ti t R litiCli k t dit M t titl t l
B id i Y I ti t R litiid Ci il
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THANK YOU
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