presentation lecture 1
TRANSCRIPT
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Plastic Design Lecture 1
Associate Professor Bill Wong
Department of Civil Engineering
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Introduction The plastic method usually results in a more
economical design, especially for structures with high
degree of indeterminacy.
The first structure designed plastically in the U.S. wasin 1957.
Examples are .......
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Plastic design example First high-rise building designed by plastic
method:Bladensburg, Maryland, USA
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Introduction Material behaviour for a beam
Maximum moment at mid-span
Stress variation as load increases
Compression
Tension
Plastic
neutral axis
fy
fy
fe fy
fe fy
fy
fy
Elastic Elastic-plastic Plastic
Mp
= Ms
curvature
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Plastic analysis for indeterminate
structures When the bending moment at a section reaches its
plastic moment Mp (=Ms), the section behaves like
a hinge. This section is called a plastic hinge (within avery small length).
As load increases, more plastic hinges occur until the
structure collapses. For design, Design load = Collapse load.
Load
Collapse
load
Cross-section in fully plastic state
Collapse
Deflection
Slope Stiffness of structureElastic
state
Elastic-plastic state
(reserve strength)
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Plastic vs. elastic design
Elastic design: the first plastic hinge should occurat or above the design load level
Plastic design: the last plastic hinge should occurat or above the design load level
Load Design
load
Plastic design
Elastic design
Deflection
Reserve
strength
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Limitations when using plastic method Sections showing no sign of local buckling: use
compact sections - Mp =Ms =Zefyand Ze = lesser
of S and 1.5Z
Ductile enough to undergo plastic rotation
Hot-formed, doubly-symmetric I-sections with fy 450 MPa
No fatigue requirements e
fy
0.15
0.2 fy
y 6e
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Limitations when using plastic method No lateral-torsional buckling:
Ms
=Mb
=s
m
Ms
and s
m
1.0
Provide adequate lateral restraints:
L
r fym
y +( )80 50
250
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Plastic bending:
Local buckling:
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Spreadsheet method for plastic analysis Example
100 kN
6m 6m
AB
C
Mp =
270 kNm
225 kNm 187.5 kNm
AB
Mp =
270 kNm
225 kNm
A B
Cup filling analogy:
Stage 1:
For P = 100 kN,
MA
= 3PL/16 = 225 kNm,
MB = 5PL/32 = 187.5 kNm
For A, A
= 270/225 = 1.2
For B, B
= 270/187.5 = 1.44
load factor1 = 1.2, hinge formed at A.
Total MA
= 1.2x225 = 270 kNm,
Total MB
= 1.2x187.5 = 225 kNm.
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Spreadsheet method for plastic analysis Stage 2:
Total c =1+2 =1.2 + 0.15 = 1.35
Collapse load Pw =cP = 1.35x100 = 135 kN
For P = 100 kN,
MA
= 0, MB
= PL/4 = 300 kNm
For B, remaining plastic moment capacity
= 270-225 = 45kNmload factor
2= 45/300 = 0.15,
Total MA
= 270 kNm,
Total MB = 225 + 0.15x300 = 270 kNm.
Mp =
270 kNm
225 kNm
A B
45 kNm
Fig. 8.8
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Spreadsheet implementation
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Notes to computer analysis1. Perform a linear analysis by computer for the
structure subject to original loading.
2. Scale the loading and calculate the load factor foreach member; the smallest is the critical cr.
3. Calculate the residual plastic moments for all othersections.
4. Insert hinge at the section with cr and repeat theabove (1) to (4) until collapse.
5. Theory: Determinant of [K] = 0. When using
computer: Run time error due to zero determinant,or dramatic increase in displacements.
6. Collapse load = design load X . cr