lecture - plastic hinging and moment redistribution

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


Consider the following two-span beam with a concentrated

load at each mid-span:


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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)


If sufficientlyductile sections toallowredistribution


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If sufficientlyductile sections toallowredistribution


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 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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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

lecture - plastic hinging and moment redistribution

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