This set of Structural Analysis Multiple Choice Questions & Answers focuses on “Method of Virtual Work: Beams and Frames and Castigliano’s Theorem for Trusses”.
1. What will be the displacement Δ in case of straight members using the energy theorem, where N is the internal force in the member and P is the external force applied?
a) 1⁄4 ΣN(dN/dP)L/AE
b) 1⁄3 ΣN(dN/dP)L/AE
c) 1⁄2 ΣN(dN/dP)L/AE
d) ΣN(dN/dP)L/AE
View Answer
Explanation: The displacement is derived by applying the energy theorem, resulting in the formula ΣN(dN/dP)L/AE.
2. How is the external force P treated in this analysis?
a) constant
b) variable
c) it doesn’t matter
d) depends upon load
View Answer
Explanation: In this analysis, P is treated as a variable, and internal force N is expressed as a function of P.
3. The external force P is applied in the direction of the displacement Δ. Is this statement true or false?
a) true
b) false
View Answer
Explanation: P is applied in above said direction. That is how we have been calculating the work done till now.
4. What causes the internal force N?
a) constant forces
b) variable forces
c) both
d) neither
View Answer
Explanation: The internal force N is caused by both constant and variable external forces applied to the structure.
5. If a beam is subjected to gradually applied loads P1 and P2, causing deflections Δ1 and Δ2, what will be the external work performed during the application of these loads?
a) 1⁄2 (p1 Δ1 + p2 Δ2)
b) 1⁄2 (p2 Δ1 + p1 Δ2)
c) p1 Δ1 + p2 Δ2
d) p2 Δ1 + p1 Δ2
View Answer
Explanation: Since the loads are gradually applied, the external work is the average load times deflection, represented as 1⁄2 (p1 Δ1 + p2 Δ2)
6. What will be the work done during the additional application of dp1?
a) p1 dΔ1 + p2 dΔ2 + dp1d Δ1
b) p1 dΔ1 + p2 dΔ2 + 1⁄2 dp1d Δ1
c) p1 dΔ1 + 1⁄2 p2 dΔ2 + dp1d Δ1
d) 1⁄2 p1 dΔ1 + p2 dΔ2 + dp1d Δ1
View Answer
Explanation: The work done when applying an incremental force dp1 is calculated by adding 1⁄2dp1d Δ1 along with other terms.
7. Additional work done due to application of dp1 is p1 dΔ1 + p2 dΔ2.
Sate whether the above statement is true or false.
a) true
b) false
View Answer
Explanation: It is true as the third term can be ignored as it is very small.
8. What will be the work done if all forces P1, dp1, and p2 are applied simultaneously to the beam?
a) (p1 + dp1)(Δ1 + dΔ1) + (p2)( Δ2 + dΔ2)
b) (p1 + dp1)(Δ1 + dΔ1) + 1⁄2 (p2)( Δ2 + dΔ2)
c) 1⁄2 (p1 + dp1)(Δ1 + dΔ1) + (p2)( Δ2 + dΔ2)
d) 1⁄2 (p1 + dp1)(Δ1 + dΔ1) + 1⁄2 (p2)( Δ2 + dΔ2)
View Answer
Explanation: Now, since all the loads are gradually applied, all will have a factor of half.
9. What will be the change in work done during the initial application of load?
a) p1dΔ1 + dp1 Δ1 + p2dΔ2
b) 1⁄2 p1dΔ1 + dp1 Δ1 + p2dΔ2
c) 1⁄2 p1dΔ1 + 1⁄2 dp1 Δ1 + p2dΔ2
d) 1⁄2 p1dΔ1 + 1⁄2 dp1 Δ1 + 1⁄2 p2dΔ2
View Answer
Explanation: We will get this by just subtracting two works done. This will be termed as dw.
10. Which of the following is equal to Δ1?
a) dw/dp2
b) dw/p1
c) dw/p2
d) dw/dp1
View Answer
Explanation: Just substitute value of p2d Δ2 in dw using one of the earlier equation.
11. Which of the following terms is integrated to calculate the displacement Δ? (Where, Δ = external displacement of the point caused by the real loads)
a) mM/EI
b) M/mEI
c) E/mMI
d) I/EMm
View Answer
Explanation: To calculate Δ we equate work done on both side which will mean m multiplied by angular displacement which is M/EI.
12. If L is the length of beam, then what are the upper and lower limits of the above integration?
a) –L, L
b) –L, 0
c) 0, L
d) ½ L, L
View Answer
Explanation: Integration is done all over the beam, as it will give the work done.
13. Generally, in doing such integrations in which of the following’s term is m expressed?
a) M
b) E
c) I
d) x
View Answer
Explanation: Since we have to integrate wrt x, we express m in terms of x.
14. Which of the following term does 1.Δ represents?
a) work done by actual forces
b) virtual strain energy stored in beam
c) real strain energy stored in beam
d) total work done by actual and virtual forces
View Answer
Explanation: Term shown above basically reprents virual load multiplied by displacement.
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