Steel Structures - Plastic Theory

1. Pick the wrong statement with regard to plastic analysis of a structure
(a) plastic moment Mp must not be exceeded anywhere in the structure except the point of maximum bending moment
(b) sum of forces and moments acting on structure must be equal to zero
(c) at ultimate collapse load, the number of plastic hinges must be just enough to form a mechanism
(d) both statical and kinematic methods can be used for plastic analysis of a structure

2. Various steps (in random order) involved in plastic analysis of a structure by kinematic method are
1. Select independent and combined mechanisms
2. Select possible locations of plastic hinges
3. Check that bending moment at every point in the structure is less than or equal to plastic moment Mp
4. Form and solve equilibrium equations for virtual work.
The correct sequence of steps is
(a) 1,2,3,4
(b) 2,1,3,4
(c) 3,1,2,4
(d) 2,1,4,3

3. Possible locations of plastic hinges are
(a) load points
(b) frame joints
(c) maximum bending moment points
(d) all the above*

4. At the location of plastic hinge
(a) radius of curvature is infinite
(b) curvature is infinite
(c) moment is infinite
(d) flexural stress is infinite (IES 1995)

5. Which of the following statements is/are true?
1. Plastic hinges are reached first at sections subjected to greatest curvature
2. Formation of plastic hinges allows a subsequent redistribution of moment until fully plastic moments is reached at each critical section.
3. The maximum load is attained when a mechanism forms.
(a) 1, 2, 3
(b) 1, 2
(c) 1, 3
(d) 2, 3 (IES 2001)

6. If H is number of plastic hinges and R is number of redundants then number of independent mechanisms are
(a) H + R
(b) H - R
(c) √(H - R)
(d) H/R

7. In a plastic hinge, the actual distribution of strain across the section will be as in
(a)
(b) 
(c)
(d) 
(IES 1999)

8. Pick the wrong statement
(a) bending moment developed at plastic hinge is termed as partially plastic moment
(b) in the case of distributed loads, the location of plastic hinges is difficult to determine
(c) in general plastic hinges are formed at points of maximum moment
(d) a plastic hinge allows a kinematic freedom of motion

9. The length of the plastic hinge zone for a simple beam with udl is
(a) span/3
(b) span/2
(c) span/√2
(d) span/√3

10. A cantilever beam of length L and a cross section with shape factor f supports a concentrated load P as shown below

The length Lp of the plastic zone, when the maximum bending moment equals the plastic moment Mp, given by
(a) {L_P}/L = 1/f  
(b) {L_P}/L = L(1 - f)  
(c) \frac{{{L_P}}}{L} = 1 - \frac{1}{{\sqrt f }} 
(d) \frac{{{L_P}}}{L} = 1 - \frac{1}{f} (GATE 2000)

Answers

    1. (a)    2. (d)    3. (d)    4. (a)    5. (d)
    6. (b)    7. (a)    8. (a)    9. (d)    10. (d)

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