Category: Structural Analysis Objective Questions

250+ TOP MCQs on Influence Lines for Floor Girders and Maximum Influence at a Point due to a Series of Concentrated Loads and Answers

Structural Analysis test on “Influence Lines for Floor Girders and Maximum Influence at a Point due to a Series of Concentrated Loads”.

1. Floor loads are transmitted from slabs to which part in a floor girder system?
a) Floor beams
b) Side girders
c) Supporting columns
d) Nowhere
Answer: a
Clarification: Loads get transmitted to floor beams after slabs.

2. Which part transmits floor loads to side girders in a floor girder system?
a) Floor beams
b) Slabs
c) Supporting columns
d) Nowhere
Answer: a
Clarification: Floor beams transmit loads to side girder.

3. Supporting columns are last element of load transfer in a floor girder system.
State whether the above system is true or false.
a) True
b) False
Answer: a
Clarification: Support columns receives floor load at last of the transfer chain.

4. What is the main load carrying member in this system?
a) Floor beams
b) Side girders
c) Supporting columns
d) Nowhere
Answer: b
Clarification: Girders are the main load carrying member and its study is important for the analysis of floor load transmission.

5. Load transfer to girders happen at only some points. What are they called?
a) Girder points
b) Panel points
c) Column points
d) Side points
Answer: b
Clarification: They are called panel points and members between these points are called panels.

6. Generally, which parts’ ILD is given the most preference?
a) Floor beams
b) Side girders
c) Supporting columns
d) Nowhere
Answer: b
Clarification: Side girders are the main load carrying member of the system, so their ILD is given the most preference.

7. Assuming that we need to determine maximum shear at a point C of a beam, which of the following sentences will always be true for that condition?
a) At least one load at end point
b) At least two load at both the end points
c) One of the loads should be at a point in proximity to point C
d) None of the loads should be at a point in proximity to point C
Answer: c
Clarification: For maximum shear at point C one of the loads should be at a point in proximity (just left or just right) to point C.

8. For a cantilevered beam, where would absolute maximum shear occur?
a) At midpoint
b) Depends upon position of load applied
c) Just next to free end
d) Just next to fixed support
Answer: d
Clarification: We can use method of section to prove the above result while applying load at any arbitrary point.

9. For a simply supported beam, where would absolute maximum shear occur?
a) At midpoint
b) Depends upon position of load applied
c) Just next to one of ends
d) At both of the ends
Answer: c
Clarification: Maximum shear would occur depending upon position load, but it will occur at one of the ends.

10. For a cantilevered beam, where would absolute maximum moment occur?
a) At midpoint
b) Depends upon position of load applied
c) Just next to free end
d) Just next to fixed support
Answer: d
Clarification: It would occur at same point as max. Shear, but loads should be applied at far other end of beam so as to maximize it.

11. For a simply supported beam, where would absolute maximum moment occur?
a) At midpoint
b) Depends upon position of load applied
c) Just next to one of ends
d) At both of the ends
Answer: b
Clarification: One will have to analyze properly to find that point in this case.

12. If there are three point loads acting simultaneously on a simply supported beam, where would absolute max. Moment occur?
a) Beneath smallest force
b) Beneath med. force
c) Beneath largest force
d) Can‘t say
Answer: d
Clarification: One can’t say as it would require analysis, although generally it comes under the greatest force.

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250+ TOP MCQs on Method of Virtual Work: Beams and Frames and Castigliano’s Theorem for Trusses and Answers

Structural Analysis Multiple Choice Questions & Answers on “Method of Virtual Work: Beams and Frames and Castigliano’s Theorem for Trusses”.

Δ = displacement caused when force is increased by a small amount
P = external force applied
N = internal force in the member force applied
L = length of member
A = cross-sectional area of member
E = Modulus of elasticity
Same symbol is used for partial and total differentiation and they are pretty obvious.

1. What will be Δ in case of straight members using theorem?
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
Answer: d
Clarification: On substituting value of internal energy in earlier theorem, we can get this.

2. P is treated here as:-
a) constant
b) variable
c) it doesn’t matter
d) depends upon load
Answer: b
Clarification: P is treated as variable and N is expressed in its term for partial differentiation.

3. Force P is applied in the direction of Δ
State whether the above statement is true or false.
a) true
b) false
Answer: a
Clarification: P is applied in above said direction. That is how we have been calculating the work done till now.

4. N is caused by:-
a) constant forces
b) variable forces
c) both
d) neither
Answer: c
Clarification: It is caused by both the constant external force and variable P.
A beam has been subjected to gradually applied load P1 and P2 causing deflection Δ1 and Δ2.
Gradual increase of dp1 causes subsequent deflection of dΔ1 and dΔ2.

5. What will be the external work performed during application of load?
a) 1⁄2 (p1 Δ1 + p2 Δ2)
b) 1⁄2 (p2 Δ1 + p1 Δ2)
c) p1 Δ1 + p2 Δ2
d) p2 Δ1 + p1 Δ2
Answer: a
Clarification: Since loads are gradually applied, work done will be average load times deflection. We can also find by integration.

6. What will be the work done during 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
Answer: b
Clarification: At this time p1 and p2 are already applied, only dp1 is gradually applied.

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
Answer: a
Clarification: It is true as the third term can be ignored as it is very small.

8. What will be the work done if all three forces are place at once on 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)
Answer: d
Clarification: Now, since all the loads are gradually applied, all will have a factor of half.

9. What will be change in work done in both case on 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
Answer: d
Clarification: 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
Answer: d
Clarification: Just substitute value of p2d Δ2 in dw using one of the earlier equation.

X is taken along the axis of beam
1 = external virtual unit load acting on the beam with direction same as that of Δ.
m = internal virtual moment in beam.
Δ = external displacement of the point caused by the real loads.
M = internal moment caused by the real loads.
E = modulus of elasticity .
I = moment of inertia of cross-sectional area.

11. Which of the following term is integrated to calculate Δ.
a) mM/EI
b) M/mEI
c) E/mMI
d) I/EMm
Answer: a
Clarification: 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
Answer: c
Clarification: 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
Answer: d
Clarification: 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
Answer: b
Clarification: Term shown above basically reprents virual load multiplied by displacement.

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