# Design of Steel Structures Questions and Answers – Conditions of Plastic Analysis

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This set of Design of Steel Structures Multiple Choice Questions & Answers (MCQs) focuses on “Conditions of Plastic Analysis”.

1. What is the condition for equilibrium in plastic analysis?
a) bending moment distribution defined by assumed plastic hinges must not be in static equilibrium with applied loads and reactions
b) shear force distribution defined by assumed plastic hinges must be in static equilibrium with applied loads and reactions
c) bending moment distribution defined by assumed plastic hinges must be in static equilibrium with applied loads and reactions
d) shear force distribution defined by assumed plastic hinges must not be in static equilibrium with applied loads and reactions

Explanation: The bending moment distribution defined by assumed plastic hinges must not be in static equilibrium with applied loads and reactions.

2. Which of the following is true?
a) ultimate load is reached when a mechanism is formed
b) ultimate load is not reached when a mechanism is formed
c) plastic hinges are not required for beam to form a mechanism
d) frictionless hinges are not required for beam to form a mechanism

Explanation: There must be sufficient number of plastic and frictionless hinges for the beam/structure to form a mechanism. The ultimate load is reached when a mechanism is formed.

3. Which of the following relation is correct?
a) -Mp ≥ M
b) M > Mp
c) M ≥ Mp
d) M ≤ Mp

Explanation: The bending moment in any section of a structure must be less than the plastic moment of the section -Mp ≤ M ≤ Mp.
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4. Lowest plastic limit load is obtained when _____
a) only equilibrium condition of plastic analysis is satisfied
b) only equilibrium and mechanism condition of plastic analysis are satisfied
c) only mechanism condition of plastic analysis is satisfied
d) equilibrium, mechanism and plasticity condition of plastic analysis are satisfied

Explanation: The lowest plastic limit load is obtained when all the conditions of equilibrium, mechanism and plasticity of plastic analysis are satisfied.

5. Which load is obtained when equilibrium and mechanism conditions of plastic analysis are satisfied?
b) upper bound solution of true ultimate load
c) lower bound solution of true ultimate load
d) no solution

Explanation: When equilibrium and mechanism conditions of plastic analysis are satisfied, an upper bound solution of true ultimate load is obtained.

6. Which load is obtained when equilibrium and plasticity conditions of plastic analysis are satisfied?
b) upper bound solution of true ultimate load
c) lower bound solution of true ultimate load
d) no solution

Explanation: When equilibrium and plasticity conditions of plastic analysis are satisfied, an lower bound solution of true ultimate load is obtained.

7. What is principle of virtual work?
a) work done by external forces is greater than work done by internal forces
b) work done by external forces is less than work done by internal forces
c) work done by external forces is equal to work done by internal forces
d) work done by internal forces is greater than work done by external forces

Explanation: The principle of virtual work may be stated as if a system of forces in equilibrium is subjected to virtual displacement, the work done by external forces is equal to work done by internal forces.

8. Principle of virtual work is used to satisfy _____
a) mechanism condition
b) equilibrium condition
c) plasticity condition
d) no condition is satisfied

Explanation: The principle of virtual work is used to satisfy equilibrium condition of plastic analysis. If the work condition is formulated correctly the equilibrium condition is automatically satisfied.

9. Virtual work is used to determine _____

Explanation: Virtual work principle is used to determine collapse load. It is the application of principle of least action to study forces and movement of a system.