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




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.




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:




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




Case Model

Beam: W 310 x 60 Column: W 250 x 67




Analysis Result: Case 1

Combined mechanism λe = 5.35 λc = 7.70





Combined mechanism λe = 3.11 λc = 4.73





Sway mechanism λe = 1.43 λc = 1.95




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




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




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




Plastic Hinge Formation




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.

case studies plastic design

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