Structural Analysis Multiple Choice Questions on “Moment-Area Theorems”.
1. The change in slope between any two points on the elastic curve equals the area of M/EI diagram between both end points of beam.
State whether the above statement is true or false.
a) True
b) False
Answer: b
Clarification: Change in slope will be equal to area of M/EI diagram between those two points.
2. θB/A refers to:-
a) Angle of tangent at B measured wrt the tangent at A
b) Angle of tangent at A measured wrt the tangent at B
c) Angle of tangent at A measured wrt x axis
d) Angle of tangent at A measured wrt y axis
Answer: a
Clarification: In the above given equation, if A is first point and B is second, then θB/A is the LHS.
3. If area of M/EI diagram between points A and B is –ve, then angle from tangent A to tangent B will be measured :-
a) Counterclockwise
b) Clockwise
c) Can be anything
d) Angle will be 0
Answer: b
Clarification: Standard sign convention is applied everywhere in the proof, so it is quite obvious.
4. What is the dimension of θB/A if area is measured in SI unit:-
a) Degree
b) Radian
c) Dimensionless
d) Can be any of them
Answer: b
Clarification: Since area is measured in SI units, result too will be in Si units.
5. The vertical deviation is measured along (if first point is A and second point is B):-
a) A vertical line passing through centre of A and B
b) A vertical line passing through A
c) A vertical line passing through B
d) A vertical line passing through either of the end points
Answer: b
Clarification: This makes the integration much easier during calculation of deflection.
6. The vertical deviation of tangent at point say A on the elastic curve with respect to the tangent extended from another point say B equals the “moment” of the area under the M/EI diagram between the two points about point :-
a) A
b) B
c) Between A and B
d) One of the end points
Answer: a
Clarification: Since, we are taking A as origin.
7. –ve M/EI area means tangent at A is:-
a) Higher than that extended from B
b) Lower than that extended from B
c) Can’t say
d) Both are equal
Answer: b
Clarification: Since, during derivation we have always assumed upward to be positive.
8. In general tA/B implies:-
a) Vertical deflection of tangent at B wrt that at A
b) Vertical deflection of tangent at A wrt that at B
c) Vertical deflection of extended tangent at B wrt tangent at A
d) Vertical deflection of tangent at A wrt extended tangent at B
Answer: d
Clarification: It is just a standard to differentiate between tA/B and tB/A.
9. TA/B and tB/A are:-
a) Always equal
b) Always unequal
c) Can’t say
d) One of them is zero
Answer: c
Clarification: In one case, we will take moment about point A while in other case moment is taken about point B. So, it can be anything.
10. –ve moment bends the beam convex down.
State whether the above sentence is true or false.
a) True
b) False
Answer: b
Clarification: -ve moment bends a beam concave down.