Past Year Questions: Shear Force and Bending Moment

# Past Year Questions: Shear Force and Bending Moment | Solid Mechanics - Mechanical Engineering PDF Download

Q.1 A simply supported beam is subjected to a uniformly distributed load. Which one of the following statements is true?    [2017 : 1 Mark, Set-I]
(a) Maximum or minimum shear force occurs where the curvature is zero.
(b) Maximum or minimum bending moment occurs where the shear force is zero.
(c) Maximum or minimum bending moment occurs where the curvature is zero.
(d) Maximum bending moment and maximum shear force occur at the same section.
Ans.
(B)

Q.2 Consider the three prismatic beams with the clamped supports P, Q and R as shown in the figures.

Given that the modulus of elasticity, E is 2.5 x 104 MPa; and the moment of inertia, I is 8 x 108 mm4, the correct comparison of the magnitudes of the shear force Sand the bending moment M developed at the supports is    [2017 : 2 Marks, Set-II]
(a) SP < SQ < SR: MP = MQ - MR
(b) SP = SQ < SR: MP = MQ > MR
(c) SP < SQ > SR: MP = MQ = MR
(d)  SP < SQ < SR: MP < MQ < MR
Ans.
(C)
Solution:

Hence correct option is (c).

Q.3 A rigid member ACB is shown in the figure. The member is supported at A and B by pinned and guided roller supports, respectively. A force Pacts at Cas shown. Let RAh and RBh be the horizontal reactions at supports A and B, respectively, and RAv be the vertical reaction at support A. Selfweight of the member may be ignored.

Which one of the following sets gives the correct magnitudes of RAv, RBh and RAv?    [2016 : 2 Marks, Set-I]

Ans.
(D)
Solution:

Q.4 The following statement are related to bending of beams
I. The slope of the bending moment diagram is equal to the shear force.
II. The slope of the shear force diagram is equal to the load intensity.
III. The slope of the curvature is equal to the fiexural rotation.
IV. The second derivative of the deflection is equal to the curvature.
The only FALSE statement is    [2012 : 1 Mark]
(a) I
(b) II
(c) III
(d) IV
Ans.
(C)
Solution:
We know that,

Q.5 For the cantilever bracket, PQRS, loaded as shown in the a djoining figure ( PQ = RS = L, and QR = 2L), which of the following statements is FALSE?    [2011 : 2 Marks]

(a) The portion RS has a constant twisting moment with a value of 2WL.
(b) The portion QR has a varying twisting moment with a maximum value of WL.
(c) The portion PQ has a varying bending moment with a maximum value of WL.
(d) The portion PQ has no twisting moment,
Ans.
(B)
Solution:

Bending moment at a distance x from P, M= Wx Member PQ has varying BM with a maximum value of WL at Q and it has no twisting moment.

Now moment WL will act as a twisting moment for the member QR. Portion QPhas varying BM with a maximum value of 2WL at R.

Now moment 2 Wl will act as a twisting moment for portion RS which is constant in nature.

Q.6 For the simply supported beam of length L, subjected to a uniformly distributed moment M kN-m per unit length as shown in the figure, the bending moment (in kN-m) at the mid-span of the beam is    [2010 : 2 Marks]

(a) Zero
(b) M
(c) ML
(d) M/L
Ans.
(A)
Solution:
Let the reaction at the right hand support be VR upwards. Taking moments about left hand support, we get,
VR x L - ML = 0 ⇒ VR = M
Thus, the reaction at the left hand support VL will be M downwards.
∴ Moment at the mid-span

Infact the bending moment through out the beam is zero.

Q.7 Two people weighing Weach are sitting on a plank of length L floating on water at L/4 from either end. Neglecting the weight of the plank, the bending moment at the centre of the plank is    [2010 : 1 Mark]
(a) WL/8
(b) WL/16
(c) WL/32
(d) zero
Ans.
(D)
Solution:
The plank will be balanced by the buoyant force acting under its bottom. Let the intensity of buoyant force be w.

For equilibrium, w x L = W + W

Thus, the bending moment at the centre of the plank will be,

The document Past Year Questions: Shear Force and Bending Moment | Solid Mechanics - Mechanical Engineering is a part of the Mechanical Engineering Course Solid Mechanics.
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## Solid Mechanics

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## FAQs on Past Year Questions: Shear Force and Bending Moment - Solid Mechanics - Mechanical Engineering

 1. What is shear force and bending moment?
Shear force is the internal force that acts parallel to the cross-section of a structural element, while bending moment is the internal force that causes a structural element to bend or deform.
 2. How do shear force and bending moment affect the design of structures?
Shear force and bending moment are important considerations in structural design as they help engineers determine the required strength and stiffness of materials. These forces help in determining the dimensions and selection of appropriate materials for a structure.
 3. How are shear force and bending moment calculated?
Shear force is calculated by summing up all the external forces acting on a structure in a specific section. Bending moment, on the other hand, is calculated by summing up the moments caused by all the external forces acting on the structure.
 4. What are the signs of shear force and bending moment?
Shear force can have both positive and negative signs, indicating the direction of the force. Positive shear force indicates a force acting in one direction, while negative shear force indicates a force acting in the opposite direction. Bending moment can have positive or negative signs, depending on whether the structure is in compression or tension.
 5. How do shear force and bending moment diagrams help in analyzing structures?
Shear force and bending moment diagrams provide a graphical representation of the internal forces and moments in a structure along its length. These diagrams help engineers identify critical sections, determine the maximum stresses, and design the structure accordingly. They also help in understanding the structural behavior under different loading conditions.

## Solid Mechanics

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