25-10-2023
INDIAN INSTITUTE OF TECHNOLOGY ROORKEE
MODELLING AND ANALYSIS
OF BRIDGES
Yogendra Singh
Professor, Railway Bridge Chair
Department of Earthquake Engineering
Indian Institute of Technology Roorkee
Roorkee, India
SEISMIC BEHAVIOUR OF BRIDGES:
OBSERVATIONS DURING PAST
EARTHQUAKES
1
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Earthquake Damage to Bridges – Bearing Failure
Bhuj Earthquake 2001
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Earthquake Damage to Bridges – Pier Failure
SHEAR FAILURE OF PIER
Kobe Earthquake 1995
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2
25-10-2023
Earthquake Damage to Bridges – Inverted Pendulum
Kobe Earthquake 1995
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Earthquake Damage to Bridges – Pier Failure
FLEXURE-SHEAR FAILURE OF PIERS
– IMPROPER CURTAILMENT
Kobe Earthquake 1995
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3
25-10-2023
Earthquake Damage to Bridges – Pier Failure
FAILURE OF PIER AT CURTAILMENT
Kobe Earthquake 1995
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Earthquake Damage to Bridges – Pier Failure
FAILURE OF PIER AT FLARING (COLUMN HEAD)
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4
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SEISMIC ANALYSIS OF BRIDGES:
TYPES OF MODELS
Modelling of Bridges – Different Components
•
•
•
•
•
•
•
Superstructure  Mainly Bending Action, which can be
modelled using Frame Elements, Shell Elements, Truss Elements,
Cable Elements, Grillages
Bearings  Modelled as Restraints, Constraints, Elastic ‘Link’
elements, Inelastic ‘Link’ elements (Base Isolation Bearings)
Dampers and STUs  Dashpots, Nonlinear Link Elements, Gap
and Hook Elements
Piers  Frame Elements, Shell elements
Foundations  Grillage, Shell elements
Soil  Solid Continuum Elements, 2D Continuum (Plane-strain)
elements, Linear Springs + Dampers, Nonlinear Springs +
Dampers
Abutments  Supports, Grillage or Shell elements with soil
modelled as continuum or springs
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Modelling of Bridges – Single Pier Model
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Modelling of Bridges – Foundation
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Modelling of Bridges – Spine and Grillage Models
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Skew and Curvature  Torsional Response
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Unequal Pier Heights  Torsional Response
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Modelling of A Composite Girder Bridge
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Modelling of A Composite Girder Bridge
17
Modelling of A Truss Bridge
18
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Modelling of A Truss Bridge
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Modelling of An Integral Bridge
Bridge arrangement and modelling:
Fixed support
Integral joint
15.5m
P1
P2
P3
55.78m
55.78m
P4
55.78m
P5
Guided bearing
P6
55.78m
55.78m
Schematic arrangement of the considered integral bridge
22.0m
3.5m
0.71m
0.4m
6.2m
4.5m
Typical PSC segment
Component
Element-type
Deck, pylon and pier
Frame element
2.5m
Bearings
Elastic links
Section of Pier
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Modelling of An Integral Bridge
Bridge arrangement and modelling:
3D model of the considered integral bridge in Midas Civil
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Modelling of Cable-Stayed Bridges
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Modelling of Cables
Cable vs Frame element and Cable vs Bar/Trus Element
Cable can not resist bending moment and axial compression and
it sags due to gravity  results in geometrically nonlinear
load-displacement beahviour
Modelling Approaches:
•
•
•
•
Truss Element  Resists compression as well as tension (May
be required in some cases!)
Tension Only Truss Element  Nonlinear analysis required
(truss element along with a Hook elemnt
Nonlinear cable/catenary element  Takes into accont the
geometric nonlinear behaviour of a cable
Linear truss elemnt with equaivalent stiffness  Equivalent
modulus of elasticity taking into account catenary action
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Modelling of Cable-Stayed Bridges
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12
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SEISMIC ANALYSIS OF BRIDGES:
TYPES OF ANALYSIS
Modes of Vibration
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13
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Equivalent Static Analysis
Single mode method – assumes
whole response is contributed by
single mode
0.8
Sa [g]
0.6
0.4
0.2
0
0
1
2
3
4
5
6
Period [s]
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Response History Analysis
Time History Analysis Using
Multiple Modes
Response in different
modes can be added
directly
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14
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Response Spectrum Analysis
Mode Superposition using
Response Spectrum
Peak response can not be
added directly  SRSS
and CQC Methods
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Time History Analysis
Direct Time History
Analysis of MultiDegrees of Freedom
Model
All the modes are
inherently considered
No approximation
Most rigorous but
sophisticated method
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Sources of Ground Motion Records
•
Time histories for dynamic analysis can be:
Ground accelerations or related quantities, i.e., velocities and
displacements
•
Recorded, artificial or simulated time histories can be used:
Recorded accelerograms at different sites, but that are
representative of site and hazard
 Simulated accelerograms i.e. generated through physical
simulation of source and path mechanisms
 Artificial accelerograms, spectrum-compatible accelerograms

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Sources of Ground Motion Records
Real recorded accelerograms:
 advantages
 Realistic ground-motion characteristics (amplitude and frequency content,
duration and strong-motion duration, shaking cycles, phase characteristics)
 Characteristics of the source, path and site included
 disadvantages
 Generally lack of ground motion records
 Not all combinations (M, distance, soil conditions) are available
Spectrum-compatible/synthesized accelerograms:
Widely regarded as inappropriate since the resulting signals are so unlike
earthquake ground motions
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Method of Analysis (IRC SP 114:2018)
Type Of Bridge
Right Bridge or Simply Supported
Skew Up to
spans
300 or curved
span having
Simply Supported
radius more
spans
than 100 m
Individual
Span
Length/
Condition
of analysis
Pier Height Method
inSeismic Zone
II & III
IV & V
0 to 60m
Up to 30m
ESAM(1)
ESAM
Above 30 m
ERSM(1)
ERSM
ERSM
ERSM
All heights ERSM(2)/
LTHA(2)
ERSM(2)
60 and
above
Continuous/ Integral
Bridges/ Extradosed
Bridges/Balanced
Cantilever
/
LTHA(2)
Remarks
Site Specific spectrum to
be used as applicable as
per clause 2.6.1& Table 2.1
Site Specific spectrum to be
used as applicable as per
clause 2.6.1 & Table 2.1
Spatial Variation of
ground motion to be
considered if required
according to Section
5.3.4.
Site Specific spectrum to
be used as applicable as
per clause 2.6.1 & Table
2.
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Method of Analysis (IRC SP 114:2018)
Type Of Bridge
Right Bridge or
Skew Up to
Major bridges in
300 or curved near-field locations;
span having
bridges located on
radius more
geological
than 100 m
discontinuity(3)
Method of analysis
Pier Height inSeismic Zone
II & III
IV & V
ERSM(2)
All Spans
All heights
ERSM(2)
Filled up
Arch
Bridges
-
ESAM
ESAM
All other
type of
Arches
-
ERSM
ERSM
Difference in Pier
Heights/ Stiffness(4) All Spans
All heights
ERSM
ERSM
Curved in Plan
< 100 m
radius
All heights
ERSM
ERSM
Skew Angle
> 30
All heights
ERSM
ERSM
Arch Bridges
Bridge With
Individual
Span
Length/
Condition
Remarks
Site Specific
Spectrum to be used
Dynamic analysis of
complete bridge shall be
carried out. Modelling
shall include all the spans
and piers to be analyzed
together.
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Method of Analysis (IRC SP 114:2018)
Type Of Bridge
Individual
Span
Length/
Condition
Pier Height
Method of analysis
inSeismic Zone
II & III
Remarks
IV & V
Site specific Spectrum to
be used.
Cable-Stayed and Suspension
Bridges
Bridges on sites susceptible to
liquefaction(5) in all seismic zones
Main Span
< 600m
All Spans
ERSM(2)
Spatial variation of
ground motion to be
considered if required as
per Section 5.3.4
All heights
ERSM(2)
All heights
Site Specific spectrum to
be used as applicable as
EgLTHA(6) per clause 2.6.1 & Table
EgLTHA(6)
/
2.1.
EqLRSM(6)
/
Soil-foundation system
EqLRSM(6)
to be adequately
modelled as per clause
8.4
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Method of Analysis (IRC SP 114:2018)
Type Of Bridge
Individual
Span
Length/
Condition
Pier Height
Method of analysis
inSeismic Zone
II & III
Bridges with seismic devices
(Shock Transmission Units (STU),
Seismic isolation or Seismic dampers
etc.) which can be represented by
the equivalent linear loaddeformation relationship
Bridges with seismic devices
(Shock Transmission Units (STU),
Seismic isolation or Seismic dampers
etc.) which cannot be represented by
equivalent linear load-deformation
relationship
All Spans
Remarks
IV & V
Site Specific spectrum to
be used as applicable as
EgLTHA(6) per clause 2.6.1 & Table
EgLTHA(6)
/
2.1.
All heights
EqLRSM(6)
/
Site period(7) to be
EqLRSM(6)
considered in case of
bridges with seismic
isolation.
Site specific
spectrum to be used as
applicable as per clause
2.6.1 & Table 2.1
All Spans
All heights
NLTHA
NLTHA
Site period(7) to be
considered in case of
bridges with seismic
isolation.
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CAPACITY DESIGN:
HOW TO AVOID BRITTLE MODES
OF FAILURE ?
Capacity Design Philosophy
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Building vs. Bridge Structure
Plastic Hinge formation in beams
Plastic Hinge formation in column
Framed Building
Framed Pier
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Capacity Design of Bridges
H
H
Mo
h
Mo
h
 Pi  H
H 2
H
Mo
H P
i
Mo
h2
P  H
i
Mo
H
Pi
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Capacity Design of Bridges
• The capacity to resist and dissipate energy are related to the
exploitation of the non-linear response.
• The structure is designed to ensure ductile behavior, the locations
of plastic hinges are pre-selected to develop plastic mechanism.
• Adequate ductility is ensured by proper detailing of these plastic
hinge regions.
• All other regions are provided with additional strength called
capacity design effects so that they remain elastic when the
selected plastic hinges develop their over strength.
• The shear resistance of plastic hinges as well as shear and flexural
resistance of other regions shall thus be designed to resist
capacity design effects in order to avoid brittle failure and localize
the damage.
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Capacity Design of Bridges
• The superstructure should remain elastic even when the plastic
hinge location in columns/piers reach their plastic moment
capacity. Capacity design principle shall be adopted to ensure this
elastic behavior.
• The fixed bearings, connections and foundations would be
designed to remain elastic under seismic conditions. These
components should thus be designed for the forces determined
from the capacity design effect.
• Force demands on the foundations and bearings should be based
on the plastic capacity of columns/piers multiplied by overstrength factor.
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21
25-10-2023
Earthquake Damage to Bridges – Bearing Failure
Bhuj Earthquake 2001
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Earthquake Damage to Bridges – Pier Failure
SHEAR FAILURE OF PIER
Kobe Earthquake 1995
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22
25-10-2023
Earthquake Damage to Bridges – Inverted Pendulum
Kobe Earthquake 1995
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Earthquake Damage to Bridges – Pier Failure
FLEXURE-SHEAR FAILURE OF PIERS
– IMPROPER CURTAILMENT
Kobe Earthquake 1995
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23
25-10-2023
Earthquake Damage to Bridges – Pier Failure
FAILURE OF PIER AT CURTAILMENT
Kobe Earthquake 1995
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What Went Wrong in Curtailment ?
Provided
Moment
Capacity
Point of
Curtailment
Actual Moment
During Earthquake
Design Moment
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Earthquake Damage to Bridges – Pier Failure
FAILURE OF PIER AT FLARING (COLUMN HEAD)
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What Went Wrong in Flaring ?
Mo
h
Mo
H
h2
Mo
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What Went Wrong in Flaring ?
Mo
Mo
H 
h 2
h  h
h
H  H
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Effect of P-M Interaction on Capacity Shear
P
M u  M ur
Mc  Mb
M 0  1.35M c
Pe
Pu
Mu
Mc
Mur
M
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Capacity Shear in Multi-Column Piers
AASHTO LRFD 2017
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Capacity Shear Estimation in Multi-Column Piers
AASHTO LRFD 2017
•
Increase in axial force due to
transverse seismic action in case
of multicolumn pier should be
considered as per an iterative
procedure given in Clause
3.10.9.4.3c of AASHTO 2017.
•
Alternatively, the maximum
moment capacity (corresponding
to balance failure) should be
considered. However, it may be
quite conservative.
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MISCELLANEOUS ISSUES:
STABILITY OF SUPERSTRSUCTURE
DURING EARTHQUAKE
Overturning and Holding Down Devices
S
Superstructure
Pier Cap
• U is the effect of
EL(H) and EL(V)
(Elastic, i.e. R=1)
• Combined as per
Cl. 7, i.e.
1.5 EL(H) + 0.45 EL(V)
And
0.45 EL(H) + 1.5 EL(V)
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Overturning and Holding Down Devices – IRS SDC
• If U > 0.5 D  Vertical hold down devices are to be
provided
• If 0.5 D < U < D, the hold down device will be
designed for minimum 10% of D
• If U > DL, the hold down device will be designed for
1.2 (U-D) and minimum 10% of D
 It is desirable to also check for the case
0.9 D + 0.5L +/- 1.5 EL(H) - 0.45 EL(V)
and
0.9 D + 0.5L +/- 0.45 EL(H) - 1.5 EL(V)
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Overturning and Holding Down Devices
•
Holding–down devices are necessary when the reaction due to ELy ±
0.3ELz and 0.3ELy ± ELz (elastic, i.e. R=1) is greater than 50 % of the
reaction under 0.9DL.
•
The design of holding down devices will be performed according to IRS
Seismic Code (Clause 13) same as in IRC SP 114 (Clause 8.5.3.3).
IRC SP 114:2018
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Unseating of Bridge Superstructure
The Showa Bridge after the 1964 Niigata, Japan earthquake.
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Seat Width for Unseating Prevention
N= Seating Width
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Seat Width for Unseating Prevention
•
As per IRS Seismic Code 2020-
•
As per IRS Bridge Rules-
•
As per AASHTO LRFD-
L-Minimum support span from bearing
H-Height of support (0 for single span Bridges)
S-Skew of support
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Seat Width for Unseating Prevention
Support requirement as per IRC SP 114:2018
Lov=lm+deg+des
Lm- minimum support length (40cm)
deg- displacement of the two supports due to different ground displacement (shall
be doubled if bridge is close to an active fault)
Where deg=sLeff<2deg
Leff- effective length of deck
s=2dg /Lg
dg- design values of PGD=0.025gSTCTD
g=ground acceleration S-soil factor
Tc- upper period limit of acceleration control range
TD- lower period limit of displacement control range
Lg- distance beyond which ground motion is uncorrelated=500m
des- displacement of support due to deformation of structure
which include seismic movement, long term displacement due
to creep shrinkage and temperature movement
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Stoppers/Restrainers for Unseating Prevention
• Stoppers are
superstructure
directions.
used to prevent unseating of
in longitudinal and transverse
• Stoppers are to be subjected to impact loading in
addition to earthquake forces. These should be
provided in all bridges as second line of defence (after
failure of bearings) against dislodgement and should
be designed for forces 2 times of those used to design
the bearings.
• Designed as corbel as per the requirement of Clause
17.2.3 of IRS CBC.
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Stoppers/Restrainers of RC
Avf- Shear Friction reinforcement
At- Direct tension reinforcement
Af- Flexural tension reinforcement
As- total tensile reinforcement
Ah-Horizontal stirrups
Source: Handbook by V.K. Raina
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Stoppers/Restrainers – Different Arrangements
IRC SP 114:2018
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Stoppers/Restrainers – Different Arrangements
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Stoppers/Restrainers – Different Arrangements
Section A-A
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Stoppers/Restrainers – Different Arrangements
Section A-A
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MISCELLANEOUS ISSUES:
DESIGN OF RETAINING WALLS
AND ABUTMENTS
Forces Acting on Retaining Walls
KhxWsurcharge
Psurcharge
+Dynamic Increment
KhxWs
Ws
KhxWw
PAE
+Dynamic Increment
Ww
Passive
- Dynamic Decrement
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Forces Acting on An Abutment
KhxWsuper
KhxWsurcharge
WSuper
Psurcharge
+Dynamic Increment
KhxWs
KhxWw
Ws
PAE
+Dynamic Increment
Ww
Passive
- Dynamic Decrement
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Design of Abutments and Retaining Walls
•
Backfill inertia and self-inertia of the abutment and foundation shall be
considered for stability checks including sliding, overturning and base pressure
check.
•
The inertial force corresponding to backfill and abutment can be combined with
the total (including dynamic) earth pressure, as per 100:50 rule. In no case the
50% of total dynamic earth pressure will be less than the static active earth
pressure.
•
Backfill inertia shall also be considered while computing forces for design of
abutment foundation along with vertical seismic coefficient in both upward and
downward direction.
•
The backfill inertia need not be considered for structural design of abutment
wall (stem), but self-inertia of the structural component in consideration, and all
the components supported on it and transferring the horizontal load to it, shall
be taken in design calculations.
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Transverse Stability of Abutment in Hilly Regions
Difference in
height
between left
and
right
ground
fill
across
abutment.
Earthfill
Return Wall
Return Wall
PAE
Passive E.P.
Active E.P.
+ Dynamic Increment
PPE
- Dynamic Decrement
Foundation
Transverse Section of Abutment
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MISCELLANEOUS ISSUES:
DESIGN OF RC PLATE AND SHELL
STRUCTURES ANALYSED USING
FINITE ELEMENT MODELS
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Stress Resultants in Plate Element
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Design of Slabs and Walls (Wood-Armer Method)
•
In slabs reinforced by an orthogonal system of bars in x and y directions, the
problem is to determine the design moments for which the reinforcement
should be designed for to get adequate strength in all directions.
•
These moments, Mx* and My*, are known as Wood-Armer moments.
Bottom Reinforcement
Top Reinforcement
If either of Mx* and My* are negative or zero, then
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MISCELLANEOUS ISSUES:
DESIGN SLABS AND
FOUNDATIONS FOR TWO-WAY
(PUNCHING) SHEAR
Punching Shear (IRC:112, EUROCODE)
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Punching Shear (IRC:112, EUROCODE)
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Punching Shear (IRC:112, EUROCODE)
Punching Shear resistance without reinforcement
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Punching Shear (IRC:112, EUROCODE)
Punching Shear reinforcement
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Punching Shear (IRC:112, EUROCODE)
Punching Shear reinforcement
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Punching Shear (IRC:112, EUROCODE)
Punching Shear reinforcement
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MISCELLANEOUS ISSUES:
DESIGN HOLLOW CIRCULAR RC
PIERS
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Design of Hollow Circular RC Sections
• The models for computation of shear capacity of hollow piers is
not provided in IRS and IRC codes.
• Giulio Ranzo and M J N Priestley “Seismic Performance of Large
RC Circular Hollow Columns” published in 12WCEE, 2000.
• Use of equivalent solid square/circular section is not valid for
this purpose.
• For confinement of concrete in hollow piers, circular hoops are
to be provided on both inner and outer faces and adequate
stirrups/ties between the two hoops are to be provided.
• The area of the confining stirrups and ties should be calculated
to provide same volumetric ratio as in case of a solid pier.
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Shear Capacity of Hollow Circular RC Sections
•
The nominal shear capacity is expressed as-
Asn- section shear area
- aspect ratio
- longitudinal reinforcement
- ductility
c-depth of compression zone at flexural capacity
Co- cover concrete
Fyh- yield stress of transverse steel
- 35, inclination of diagonal cracks
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Shear Capacity of Hollow Circular RC Sections
P- axial load
L- length of inflection
Ast- area of longitudinal steel
= Di/D, Di- inside diameter of section
An- net area
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Future Trend – Pushover Analysis
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Future Trend – Pushover Analysis
Demand Reduced
Based on Inelastic
Capacityof building
Sa
Performance Point
des
Sd
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THANK YOU !
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