Case Studies Plastic Design
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Transcript of Case Studies Plastic Design
8/3/2019 Case Studies Plastic Design
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29/04/2012 Case Studies of Plastic Analysis 1
Case Studies of Plastic Analysis
Elastic and Plastic Analysis
Using Dr. Frame
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Basic Concept
Elastic Analysis
Element is assumed to obey
Hooke’s law and recover to
original state on removal of load.
Elastic Analysis: determining the
maximum load that cause one
point in any member section to
reach the yield stress or elastic
critical buckling stress.
Plastic Analysis
Stress remains constant while
the strain increases.
The plastic hinge forms.
Collapse occurs when sufficientplastic hinges have formed to
convert the structure to a
mechanism.
Plastic analysis: determining the
minimum load that causes thestructure to collapse.
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Basic Concept
Plastic Moment
Simple plastic moment formula:
Mp = ZFy
Effect of the shear force:
1. Tresca and Von-Mises yieldcriteria
2. In I-beams, the reduction in the
plastic moment is negligible until
the shear force is over 50%
shear capacity of the web
Effect of the axial force:
1. Both tensile and compressive
force reduce the plastic moment
2. Reduced plastic moment formula:
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About Dr. Frame
Plastic Hinge Objects
Installation and removal of plastic
hinges
Before yielding: blue rectangles
After yielding: solid red circlesduring loading, open red circles
during unloading
Simple linear interaction relation
to account for axial force effect
Second-Order Analysis
Load-Dependent EI
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Case Model
Beam: W 310 x 60 Column: W 250 x 67
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Analysis Result: Case 1
Combined mechanism λe = 5.35 λc = 7.70
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Analysis Result: Case 2
Combined mechanism λe = 3.11 λc = 4.73
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Analysis Result: Case 3
Sway mechanism λe = 1.43 λc = 1.95
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Analysis Result: Case 4
Sway mechanism λe = 2.07 λc = 2.96
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Analysis Result: Case 5
Sway mechanism λe = 2.12 λc = 3.06
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Discussion
The bigger axial force, the bigger
reduction in plastic moment
capacity.
Case No. 1 2 3 4 5
N (kN) 309.7 493.7 549.5 631.4 374.9
M (kNm) 298.5 288.8 286.1 279.5 295
N/Np 0.103 0.165 0.184 0.211 0.125
M/Mp 0.947 0.916 0.907 0.886 0.935
Reduction in plastic moment capacity
due to axial force
“Column 1” in all cases are investigated.
W250x67: Np = 2992.5 kN
Mp = 315.35 kNm
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Discussion
Comparison of linear analysis and second-order analysis in Case 1, Case 3
The collapse load factor reduces.
The P- Δ effect is more significant in multistory frame.
Case No. λ c1 λ c2 λ c2/λ c1
1 7.7 7.45 0.97
3 1.95 1.82 0.93
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Discussion
A handy plastic analysis tool --
Dr. Frame
Model and observe plastic
behavior in structure
interactively
Get the order of plastic hinges
formation and the final collapse
mechanism easily and visually
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Plastic Hinge Formation
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Plastic Hinge Formation
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Conclusion
The plastic moment reduction
due to axial force must be
considered in the plastic analysis,
especially when the axial force N
exceeds 15% Np.For more accurate result, one
needs to do the second-order
analysis accounting for the P- Δ
effects and load-dependent EI.
The location of plastic hinges in
frames to form a mechanism
varies with the type of loading,
shape and other physical
properties of the frame.Dr. Frame is a very handy
program to perform plastic
analysis for framed structures of
complicated shape and with a
high degree of redundancy.