This set of Design of Steel Structures Multiple Choice Questions & Answers focuses on “Theorem of Plastic Collapse & Methods of Plastic Analysis”.

1. What is static theorem ?

a) load must be greater than collapse load

b) load must be less than collapse load

c) load must be not equal to collapse load

d) load cannot be related to collapse load

View Answer

Explanation: For a given frame and loading if there exists any distribution of bending moments throughout the frame which is both safe and statically admissible with set of load P, then value of load P must be less than or equal to collapse load.

2. Which of the following is true about static theorem?

a) it represents upper limit to true ultimate load

b) it represents plastic load

c) it has minimum factor of safety

d) it satisfies equilibrium and yield conditions

View Answer

Explanation: The static method represents the lower limit to the true ultimate load and has maximum factor of safety. The theorem satisfies equilibrium and yield conditions.

3. Which of the following condition is true for kinematic theorem?

a) load must be greater than collapse load

b) load must be less than collapse load

c) load must be not equal to collapse load

d) load cannot be related to collapse load

View Answer

Explanation: For a given frame subjected to a set of loads P, the value of P which is found to correspond to any assumed mechanism, must be greater than or equal to the collapse load Pu.

4. Which of the following is true about kinematic theorem?

a) it represents lower limit to true ultimate load

b) it represents plastic load

c) it has small factor of safety

d) it satisfies equilibrium and yield conditions

View Answer

Explanation: Load computed on basis of this mechanism will always be greater than or at least equal to true ultimate load. Hence, kinematic method represents an upper limit to the true ultimate load and has a smaller factor of safety. This theorem satisfies equilibrium and continuity conditions.

5. Which of the following condition is true for uniqueness theorem?

a) load must be greater than collapse load

b) load must be less than collapse load

c) load must be equal to collapse load

d) load cannot be related to collapse load

View Answer

Explanation: For given frame and loading, if at least one safe and statically admissible bending moment distribution can be found, and if in this distribution bending moment is equal to fully plastic moment at sufficient cross sections to cause failure of frame as a mechanism due to rotation of plastic hinges, then corresponding load will be equal to collapse load.

6. Load is called as correct collapse load when

a) static theorem is not satisfied

b) kinematic theorem is not satisfied

c) only static theorem is satisfied

d) both static and kinematic theorem are satisfied

View Answer

Explanation: Load that satisfies both static and kinematic theorem at the same time is called correct collapse load.

7. Which of the following is true about kinematic analysis?

a) virtual work equations are not used to determine collapse load

b) virtual work equations are used to determine collapse load

c) equilibrium condition is assumed

d) plasticity condition is assumed

View Answer

Explanation: In kinematic method, a mechanism is assumed and virtual work equations are used to determine the collapse load.

8. The number of independent mechanism is related to number of possible plastic hinge locations by ________

a) n = h * r

b) n = h / r

c) n = h + r

d) n = h – r

View Answer

Explanation: The number of independent mechanism (n) is related to number of possible plastic hinge locations (h) and number of degree of redundancy (r) of the frame by equation n = h-r.

9. In static method of analysis, moment at any section is _______ plastic moment capacity.

a) greater than

b) two times

c) less than

d) three times

View Answer

Explanation: In static method of analysis, an equilibrium moment diagram is obtained such that the moment at any section is less than or equal to the plastic moment capacity.

10. Which of the following relation between load factor, collapse load(Wc) and working load (W)

a) F = W_{c} / W

b) F = W / W_{c}

c) F = W_{c} W

d) F = W_{c} + W

View Answer

Explanation: Load factor is ratio of collapse load to working load. It is represented by, F = W

_{c}/ W.

11. Which of the following is load factor for simply supported beam with central point load?

a) (f_{y}f_{bc})v

b) (f_{bc}/ f_{y})v

c) (f_{y}/f_{bc})v

d) (f_{y} + f_{bc})v

View Answer

Explanation: For a simply supported beam with central point load,

M = WL/4 = f

_{bc}Z

_{e}, M

_{p}= W

_{c}L/4 = f

_{y}vZ

_{e}, where v is shape factor

F = M

_{p}/M = W

_{c}/W = (f

_{y}/f

_{bc})v.

12. What is the value of load factor for I-section when f_{bc}= 0.66f_{y} and mean value of v is 0.14?

a) 1.727

b) 2.7

c) 1.56

d) 3.98

View Answer

Explanation: Load factor, F = (f

_{y}/f

_{bc})v. F = (1/0.66) x 0.14 = 1.27.

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