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7/25/2019 Lecture - Plastic Hinging and Moment Redistribution
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CVG 5144 AdvancedReinforced Concrete
Plastic Hinging, PlasticLoad Capacity and Moment
Redistribution
Plastic Hinging and
Moment Redistribution In continuous members the failure does not occur
immediately after a section reaches its ultimate capacity.
Upon reaching the ultimate moment capacity, the section
develops a plastic hinge. As the hinge rotates under
constant moment (equal to moment capacity), the
member can sustain additional loads.
Redistribution of moments occur under increased loads
until others hinges form at other locations. The redistribution continues until the collapse
mechanism if formed.
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Plastic Hinging andMoment Redistribution
Redistribution occurs only if plastic hinging regions have
sufficient ductility.
M
Ductile Behaviour
Brittle Behaviour
Plastic Hinging andMoment Redistribution
Consider the following two-span beam with a concentrated
load at each mid-span:
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Plastic Hinging andMoment Redistribution
Plastic Hinging andMoment Redistribution
Plastic Capacity
If
If
IfFirst yielding takes place
over supports
First yielding takes place atmid-span
Both supports and mid-
span yield simultaneously
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Plastic Hinging and MomentRedistribution
If the section where the first yield occurs has sufficientductility, then the plastic hinge forms and the hinge start
rotating, as moments and stresses are distributed towards
elastic regions until other sections start yielding.
Collapse occurs when sufficient number of hinges develop
along the length of the member and the member becomes
unstable, resulting in the collapse mechanism.
Plastic hinges must have sufficient ductility to allow
redistribution. Otherwise, the failure of the hinging region
occurs prior to developing other hinges.
Ductility of a Plastic Hinge In the previous example, how much does the negative
moment hinge rotate before yielding takes place in the
positive moment region?
This can be computed. The rotation required to form
moment redistribution is called Rotation Demand.
A convenient way to compute the Rotation Demand is to
use the Moment Area Theorem.
The Moment Area Theorem can be applied by consideringelastic and plastic components separately.
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Ductility of a Plastic Hinge
Just before the collapse mechanism has formed
(all hinges have formed)
If the load was placed on a simplysupported beam:
Rotation = Area under the M/EI
diagram between two tangents
Ductility of a Plastic HingeWhen the negative moment is applied
on a simply supported beam:
Rotation = Deflection between twotangents divided by the distancebetween the tangents.
Deflection= Moment of the area underM/EI diagram between two tangents
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Ductility of a Plastic Hinge
Rotational demand to form thecollapse mechanism
Plastic Rotation Capacity
Plastic rotation
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Available Ductility
Available Rotation =
Ductile MemberIf
Brittle MemberIf
For ductile behaviour
Progressive CollapseA progressive collapse is a chain reaction of failureof building members to an extent disproportionate tothe original localized damage. Such damage mayresult in upper floors of a building collapsing ontolower floors.
DoD 2005
Progressive collapse is a situation where local failure
of a primary structural component leads to thecollapse of adjoining members which, in turn, leads toadditional collapse. Hence the total damage isdisproportionate to the original cause.
GSA 2003
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Progressive Collapse
Progressive collapse is defined as the spread ofan initial local failure from element to element,eventually resulting in the collapse of an entirestructure or disproportionately large part of it
ASCE7-05
Progressive collapse can be triggered by a varietyof events. Bomb blast is a typical overload that
may lead to progressive collapse.
Accidental Explosion
Ronan Point Apartment Building London, England
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Accidental Explosion
Ronan Point Apartment Building London, England
Blast Shock Wave
Murrah Building Oklahoma City
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Blast Shock Wave
Khobar Building - Saudi Arabia
Blast Shock Wave
The building was ableto redistribute itsloads.
No progressivecollapse.
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Blast Pressures
Typical Impulse
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Structural Response to Blast
Seismic versus Blast
Progressive Collapse Analysis andDesign
Alternate Load Path: Arrange structural elements toprovide stability to the entire structural system bytransferring loads from any locally damaged region toadjacent regions.
Provide;
Continuity and ductility
Redundancy in lateral and vertical load paths
Capacity for load reversals
Increase shear capacity for ductility
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Potential
loss of acolumn
Column Removal
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Beam Longitudinal Reinforcement
Earthquake Resistant Design Good for Blast Resistance
Beam Transverse Reinforcement
l
4/ds1
mm300s1
bar.longb1 )d(8s
hoopb1 )d(24s
Hoops shall be provided through entire beam length
Earthquake Resistant Design Good for Blast Resistance
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GSA Progressive
Collapse Analysis
GSA
Progressive
Collapse
Analysis
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GSA Progressive Collapse Analysis
Loading for static analysis:
Load = 2(DL + 0.25LL)
Demand/Capacity Ratio DCR:
DCR = QD/QC
QD = Force demand (moment, axial force, shear)QC = Unfactored capacity (may be increased by
using 1.25 fy)
GSA Progressive Collapse Analysis
If sufficientlyductile sections toallowredistribution
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GSA Progressive Collapse Analysis
If sufficientlyductile sections toallowredistribution
GSA Progressive Collapse Analysis
Acceptance Criteria:
DCR 2.0 for typical structural configurations
DCR 1.5 for atypical structural configurations
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Progressive Collapse Example
Consider the removal
of an interior column
due to blast damage
and assess different
scenarios.
W = 60 kN/m W = 60 kN/m
57.6 kN.m 57.6 kN.m
115 kN.m 115 kN.m
250 kN.m
500 kN.m 500 kN.m
W = 60 kN/m W = 60 kN/m
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W = 60 kN/mW = 60 kN/m
Capacity
Capacity
500
250 kN.m
200
600550
Required (Demand)
Progressive Collapse Example
Progressive Collapse ExampleLoad carried at the formation of hinge at mid-span
(3/8) l
Mc
Load carried after the formation
of the hinge at mid-spanw2
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Progressive Collapse Example
Mc = 19.4 kN.m for EI = 4.3 x 1013 N.mm2
(p)d= 0.00054 radw2
uy
e
Capacity
(p)cap = (u y) lp
= (2 x 10-5 0.5 x 10-5) 500
= 0.0075 rad
Therefore, the beam hassufficient ductility