Category: Structural Analysis Objective Questions

250+ TOP MCQs on Shear and Moment Diagrams for a Beam and Answers

Structural Analysis Multiple Choice Questions on “Shear and Moment Diagrams for a Beam”.

Following sign convention for force direction is followed:-

For moments, clockwise is considered –ve.

1. In case of a beam, resistance to normal force is considered to be more important than resistance to bending and shear force.
State whether the above statement is true or false.
a) True
b) False
Answer: b
Clarification: Resistance to bending and shear force is given more importance than resistance to normal force in most cases involving beams.

2. What is the exceptional case when resistance to normal force is considered to be more important than resistance to bending and shear force in beams?
a) Expansive axial force
b) Compressive axial force
c) Bending moment at both ends
d) Bending moment at one end
Answer: b
Clarification: In these cases, buckling effects have to be nullified.

Following figure is used in Q3-Q8.
In the following figure, all supports are roller type and B and D are hinges. All the options are given in KN and KN/M wherever applicable.
BMD and SFD starts from point A.
AB = BC = CD = DE = EF = FG = 2m

3. What will be the starting value of SFD?
a) 10
b) -10
c) 5
d) -5
Answer: b
Clarification: Support reaction at point A is 10KN in downward direction.

4. What will be the shape of SFD in the entire beam?
a) Straight line
b) Straight line with point of discontinuities
c) Curve
d) Curve with point of discontinuities
Answer: b
Clarification: Since load is not a function of x, so SFD will always be straight line. But, since load varies suddenly at some points, SFD will have discontinuities.

5. How many points of discontinuities will be there in the SFD?
a) 1
b) 2
c) 3
d) 4
Answer: c
Clarification: 3 discreet loads are applied in between the beam (excluding starting and end points). So, 3 discontinuities will be there.

6. What will be the starting value of BMD?
a) 20
b) -20
c) 5
d) -5
Answer: a
Clarification: Bending moment at point A is +20KN/M. So, curve will start with +20.

7. What will be the shape of BMD in the entire beam?
a) Straight line
b) Straight line with point of discontinuities
c) Curve
d) Straight line with varying slope
Answer: d
Clarification: Since, SFD is always parallel to the x axis (as load is always discreet) BMD will always be a straight line. Since, there is an absence of discreet external moment in between the beam, there won’t be any discontinuities in the graph. But, slopes will vary as SFD has discontinuities.

8. How many times would slope of BMD change?
a) 1
b) 2
c) 3
d) 4
Answer: c
Clarification: There are 3 points of discontinuities in SFD. So, slope will also change at those three points.

Following figure is used in Q9-Q14
In the following figure AB=BC=CD=2m, and DE=EF=1m.
A is a fixed support while C and F are of roller type. B and D are hinges.
All the options are given in KN and KN/M wherever applicable.
BMD and SFD starts from point A.

9. What will be the starting value of SFD?
a) 25
b) -25
c) 15
d) -15
Answer: a
Clarification: Support reaction at point A comes out to be 25KN in upward direction upon solving as shown in earlier questions.

10. What will be the shape of SFD in the entire beam?
a) Straight line
b) Straight line with points of discontinuities
c) Curve
d) Straight line with points of discontinuities parallel to x axis
Answer: b
Clarification: On integrating load SFD comes out to be straight line. It will have points of discontinuities too as discreet loads are there in between. But, SFD won’t be always be parallel to x axis as continuous load is applied.

11. How many points of discontinuities will be there in the SFD?
a) 1
b) 2
c) 3
d) 4
Answer: b
Clarification: 2 discreet loads are applied in between the beam (excluding starting and end points). So, 3 discontinuities will be there.

12. What will be the starting value of BMD?
a) 20
b) -20
c) 10
d) -10
Answer: d
Clarification: Bending moment at point A is -10KN/M. So, curve will start with -10.

13. What will be the shape of BMD in the entire beam?
a) Straight line
b) Straight line with point of discontinuities
c) Curve
d) Combination of curve and straight line
Answer: d
Clarification: A combination of discreet and continuous load will lead to such BMD.

14. How many times would slope of BMD change?
a) 1
b) 2
c) 3
d) infinite
Answer: d
Clarification: Since a part of BMD is curve, it will change its slope continuously.

250+ TOP MCQs on Deflection Diagrams and the Elastic Curve and Answers

Structural Analysis Multiple Choice Questions on “Deflection Diagrams and the Elastic Curve”.

1. When a material returns to its undeformed original position after removal of load, then this behavior is called linear elastic material response.
State whether the above statement is true or false.
a) True
b) False
Answer: a
Clarification: We have considered structures which show linear elastic material response.

2. Which of the following causes greatest deflection for beams?
a) Internal axial force
b) Internal bending
c) Both causes equal deflections
d) External loads
Answer: b
Clarification: Internal bending causes greatest deflection for beam and frames.

3. In a truss, maximum deflection is caused by internal bending.
State whether the above statement is true or false
a) True
b) False
Answer: b
Clarification: Internal axial force causes most deflections in trusses.

4. In deflection diagrams, which of the following can’t have zero deflection in vertical direction?
a) Pin support
b) Roller support
c) Fixed support
d) Hinge
Answer: d
Clarification: Rest all can’t move from their initial positions as they all exert vertical force.

5. In deflection diagrams, which of the following can have zero angular deflection?
a) Pin support
b) Roller support
c) Fixed support
d) Hinge
Answer: c
Clarification: Only fixed support exerts moment at its point of contact.

6. What is the relation between angular deflections between two legs connected by a fixed-connected joint?
a) They are unequal
b) They are equal
c) Can’t say
d) They don’t show angular deflection
Answer: b
Clarification: Since it is a fixed joint, they can’t have a relative angular deflection in between them.

7. What is the relation between angular deflections between two legs connected by a pin-connected joint?
a) They are unequal
b) They are equal
c) Can’t say
d) They don’t show angular deflection
Answer: a
Clarification: Since it is a pin joint, they can have a relative angular deflection in between them.

8. A positive moment by standard sign convention would bend a horizontal beam:-
a) Concave upward
b) Concave downward
c) Convex upward
d) Can’t say
Answer: a
Clarification: It is the same as used earlier. We can take reference from the earlier diagram also.

250+ TOP MCQs on Determinacy and Stability and Answers

Structural Analysis Multiple Choice Questions on “Determinacy and Stability”.

1. For the validity of principle of superposition, materials should behave in which manner?
a) linear-elastic
b) non-linear-elastic
c) Non-linear- inelastic
d) Linear- inelastic
Answer: d
Clarification: They should behave in a linear elastic manner so that, Hooke’s law is valid.

2. If in planar system, X parts/members are there with Y no. of forces, then condition for statically determinacy is:-
a) Y < 3X
b) Y > 3X
c) Y = 3X
d) None of the mentioned
Answer: c
Clarification: There can be at max. 3 equilibrium equations for each part.

3. If Y > 3X (X and Y are from the above question) then, the system is:-
a) Statically indeterminate
b) Statically determinate
c) Can’t say
d) Depends on other conditions
Answer: a
Clarification: As there can be at max. 3X equations, at least one of the forces will be unsolvbale.

4. If in a planar system, only 2 reaction forces are acting, then the system is:-
a) Essentially unstable
b) Essentially stable
c) Can’t say
d) None of the mentioned
Answer: a
Clarification: If no. of reactions is less than 3 in any planar system, then the system is essentially unstable.

5. If all the reactions acting on a planar system are concurrent in nature, then the system is:-
a) Can’t say
b) Essentially stable
c) Essentially unstable
d) None of the mentioned
Answer: c
Clarification: The system can rotate about the point of concurrency. So, it is essentially unstable.

6. If 4 reactions are acting on a beam, then the system is:-
a) Unstable & indeterminate
b) Stable & indeterminate
c) Stable & determinate
d) Can’t say
Answer: d
Clarification: 4 reactions mean that the system is definitely indeterminate. But stability would depend upon the nature of forces acting on the planar structure.

7. If a system has more equations of equilibrium than no. of forces, then the system is:-
a) Improperly constrained
b) Partially constrained
c) Stable
d) Solvable
Answer: b
Clarification: In these cases, system is unstable and unsolvable and is termed as partially constrained.

8. How many cases out of the following are improperly constrained?
Parallel forces, concurrent forces, perpendicular forces, only moment
a) 1
b) 2
c) 3
d) 4
Answer: b
Clarification: parallel and concurrent are improperly constrained.

9. If a structure has total 10 joints, then what should be the minimum no. of joints in which equilibrium equations should be concurrently satisfied for stability?
a) 7
b) 8
c) 9
d) 10
Answer: d
Clarification: For stability, equilibrium equations should be satisfied concurrently at each and every joint of the structure.

In the following questions, j represent no. of joints and r represents no. of external forces.
10. If a structure has 2j – r no. of members, then it will be:-
a) stable
b) unstable
c) depends upon structure
d) depends upon magnitude of load
Answer: c
Clarification: In these cases, structures can be stable as well unstable.

11. If a truss consists of a non-triangular element, then it will essentially be unstable.
State whether the above statement is true or false.
a) true
b) false
Answer: b
Clarification: In these cases, instability is the most probable occurrence, but there are a lot of examples which are unstable.

250+ TOP MCQs on Shear and Moment Diagrams for a Frame-1 and Answers

Structural Analysis Multiple Choice Questions on “Shear and Moment Diagrams for a Frame-1 “.

Following sign convention for force direction is followed:-

For moments, clockwise is considered –ve.

All the options are given in KN and KN/M wherever applicable.
Following figure is used in Q1-Q10.
In the following figure, point A has pin support, while point C has roller type support. Point B is a fixed end.
AB = 4m and BC = 8m.

1. Direction of shear force will always be towards x axis in this frame.
Sate whether the above statement is true or false.
a) True
b) False
Answer: b
Clarification: Direction of shear force is always perpendicular to that of beam. In this frame, orientation of beams is different and so will be that of shear forces.

2. What will be the value of shear force at point A?
a) 100
b) 110
c) 120
d) 130
Answer: c
Clarification: On balancing force in the x direction, we will find that since support C can’t exert any force in x direction, shear force at A will be 120 KN.

3. What will be the shape of SFD of beam AB?
a) Triangular
b) Rectangular
c) Trapezoid
d) Arbitrary curve
Answer: a
Clarification: Since the loading is uniform and parallel to beam AB and point B has no shear, SFD will be of triangular shape.

4. How many points of discontinuities will be there in the SFD of beam BC?
a) 0
b) 1
c) 2
d) 3
Answer: a
Clarification: Since there is no discreet loading on the beam BC so, there won’t be any points of discontinuities in beam BC.

5. What will be the shape of SFD of beam BC?
a) Triangular
b) Rectangular
c) Trapezoid
d) Arbitrary curve
Answer: b
Clarification: There is no point of discontinuity, so the curve will basically two end values. Since both comes out to be same in this case, shape will e rectangular.

6. What will be the shape of BMD of beam AB?
a) Triangular
b) Rectangular
c) Trapezoid
d) Arbitrary curve
Answer: d
Clarification: As the shape of SFD of beam AB is triangular, it will yield on curve on integrating.

7. What will be the slope of BMD of beam AB at point B (options are in degrees)?
a) 0
b) 15
c) 30
d) 45
Answer: a
Clarification: Value of shear at point B is 0 for beam AB. So, slope of BMD will be zero at that point.

8. What will be the shape of BMD of beam BC?
a) Triangular
b) Rectangular
c) Trapezoid
d) Arbitrary curve
Answer: a
Clarification: BMD will be of triangular shape as SFD is of rectangular shape and one end of BMD comes out to be zero.

9. At what point would the slope of BMD of beam AB be 0?
a) A
b) B
c) In between
d) Never
Answer: b
Clarification: Because at point B, shear force comes out to be zero.

10. At what point would the slope of BMD of beam BC be 0?
a) A
b) B
c) In between
d) Never
Answer: d
Clarification: Shear force never becomes zero in the beam BC.

250+ TOP MCQs on Elastic-Beam Theory and Answers

Structural Analysis Multiple Choice Questions on “Elastic-Beam Theory”.

Here, p = the radius of curvature at a specific point on the elastic curve
M = the internal moment in the beam at a point
E = material’s modulus of elasticity
I = the beam’s moment of inertia computed about the neutral axis

1. Which of the following is correct?
a) 1/M = EI/p
b) 1/M = E/pI
c) 1/M = p/EI
d) 1/p = EI/m
Answer: c
Clarification: It can be derived by taking small elements and using Hooke’s law and flexural formula.

2. Elastic-Beam theory can be applied on a non-linear elastic material.[/expand]
State whether the above statement is true or false.
a) True
b) False
Answer: b
Clarification: For elastic-beam theory to be applicable Hooke’s law must be applicable and for that material must behave in a linear-elastic manner.

3. From where is radius of curvature measured?
a) From centre of bar
b) From one of the ends of bar
c) From any internal point
d) From an external point.
Answer: d
Clarification: It is measured from centre of curvature and it lies at an external point.

4. Which of the following can be a possible value of EI?
a) 1
b) -1
c) -2
d) -3
Answer: a
Clarification: It is referred to EI and it is always positive.

5. What is the general form of elastic curve of a beam?
a) Linear first-order differential equation
b) Linear second-order differential equation
c) Non-linear first-order differential equation
d) Non-linear second-order differential equation
Answer: d
Clarification: On expressing 1/p in terms of x and y, we can reach to the curve equation.

6. What is the assumption for deriving above mentioned equation?
a) Deflection is only due to shear force
b) Deflection is only due to bending
c) Deflection is due to both shear and bending
d) Axial forces caused bending
Answer: b
Clarification: While deriving, we have only considered bending forces by assuming that length is much greater than thickness.

7. Slope of a deflected curve is generally:-
a) Very large
b) Very small
c) In between
d) Can’t say
Answer: b
Clarification: Slope is very small and is generally assumed to be zero to predict the curve more properly.

8. On the elastic curve, points will be only displaced vertically not horizontally.
State whether the above statement is true or false.
a) True
b) False
Answer: a
Clarification: Since we have assumed slope to be zero, there won’t be any horizontal displacement.

250+ TOP MCQs on Beams & Frames Static Indeterminacy and Answers

Structural Analysis Multiple Choice Questions on “Beams & Frames Static Indeterminacy”.

1. The number of equilibrium equations for the following space frame is ________

a) 1
b) 3
c) 6
d) 4
Answer: c
Clarification: There are six equilibrium equations available for space frames are as follows ∑Fx=0, ∑Fy=0, ∑Fz=0, ∑Mx=0, ∑My=0, and ∑Mz = 0.

2. Which of the following is statically determinate structure?
a) Fixed beam
b) Continuous beam
c) Two hinged arch
d) Double overhanging
Answer: d
Clarification: Double overhanging can be analysed by available three equilibrium equations i.e. ∑Fx=0, ∑Fy=0, and ∑M = 0.

3. External Static Indeterminacy of the following beam is _______

a) 2
b) 4
c) 3
d) 0
Answer: c
Clarification: This is case of vertical loading only. Static indeterminacy = (2+2+1)–2 = 3.

4. External Static Indeterminacy for the following frame is _____

a) 0
b) 3
c) 4
d) 6
Answer: b
Clarification: Frames are always of General loading case. Static indeterminacy = (3+3)–3=3.

5. External Static Indeterminacy for the following space frame is ________

a) 18
b) 9
c) 6
d) 10
Answer: a
Clarification: This is space frame. Thus, fixed end will have six reactions and available equilibrium equations are also 6. Therefore, External Static Indeterminacy = (6+6+6+6)-6 = 18.

6. Internal Static Indeterminacy for the following space frame is _____

a) 18
b) 9
c) 6
d) 10
Answer: c
Clarification: Internal static indeterminacy of space frame = 6 * no of boxes the structure has. Therefore, Internal static indeterminacy = 6*1 = 6.

7. Force release for the following space frame is _____

a) 3
b) 2
c) 6
d) 0
Answer: c
Clarification: Force release for space frame is given by 3(m-1), where m is the no of member joining at hinged end. Therefore, Force release = 3(3-1) = 3*2 = 6.

8. Static Indterminacy for the following space frame is _____

a) 18
b) 9
c) 6
d) 0
Answer: a
Clarification: Static Equilibrium = External Static Indeterminacy + Internal static indeterminacy – Internal static indeterminacy. Therefore Static Equilibrium = 18 + 6 – 6 = 18.

9. Static Indeterminacy for rigid jointed plane frame is given by __________
a) (m + r) – 2j
b) (m + r) – 3j
c) (3m + r) -3j
d) (6m + r) – 6j
Answer: c
Clarification: Static Indeterminacy for rigid jointed plane frame is given by (3m + r) -3j. Where m, r and j stands for number of members, reactions and number of joints respectively.

10. Stresses will develop due to change in temperature in statically determinate structure.
a) True
b) False
Answer: b
Clarification: Stresses will develop due to change in temperature, sinking of support and lack of fit in statically indeterminate structure only.