Solved Questions on Shear Force and Bending Moment
Question 1. The shapes of the bending moment diagram for a uniform cantilever beam carrying a uniformly distributed load over its length is
(A) A straight line
(B) An ellipse
(C) A hyperbola
(D) A parabola
GATE-ME-2001
Hint 1. (Ans D)
is the equation of parabola.
Question 2. A concentrated load P acts on a simply supported beam of span L at a distance L/3 from the left support. The bending moment at the point of application of the load is given by
(A) PL/3
(B) 2PL/3
(C) PL/9
(D) 2PL/9
GATE-ME-2003
Hint 2. (Ans D)
For vertical equilibrium
Taking moment about 
, we have
The bending moment at the point of application of load =Area under OABC
Question 3. A cantilever beam carriers the anti symmetric load as shown, where w is the peak intensity of the distributed load. Qualitatively, the correct bending moment diagram for the beam is
(A) 
(B) 
(C) 
(D) 
GATE-ME-2005
Hint 3. (Ans C)
Here make hit and trial method
Consider first option (A) of moment diagram.
At right end B, slope must be zero as there is no shear force at B so option A is wrong.
Now, consider option (B)
Due to symmetric load intensity at left side too the shear force equal to zero so slope at left side must be zero. So option (B) wrong.
Now consider option (C)
Here at both ends, slope is zero means shear force is zero and also when we move from right to left, the rate of increase of shear force decreases due triangular shape of load intensity and at middle slope should be maximum and there after decreases so in option (C) all these criterion fulfills. Here (C) is the correct option.
As far as (D) option is concerned its middle part slope and right most part slope is strictly not agreeing with the load shown.
Question 4. A beam is made up of two identical bars AB and BC by hinging them together at B. the end A is built in (cantilevered) and the end C is simply supported. With the load P acting as shown, the bending moment at A is
(A) Zero
(B) PL/2
(C) 3PL/2
(D) Indeterminate
GATE-ME-2005
Hint 4. (Ans B)
Question 5. A uniformly loaded propped cantilever beam and its free body diagram are shown below. The reaction are
(A) 
(B) 
(C) 
(D) 
GATE-ME-2007
Hint 5. (Ans A)
Moment about (1),
Moment about (2),
From (i), (ii), (iii), we get 
Question 6. In a simply-supported beam loaded as shown below, the maximum bending moment is Nm is
(A) 25
(B) 30
(C) 35
(D) 60
GATE-ME-2007
Hint 6.(Ans B)
Taking moment about A,
Question 7. A simple supported beam PQ is loaded by a moment of 1 kN-m at the mid span of the beam as shown in the figure. The reaction force RP and RQ at supports P and Q respectively are
(A) 1 KN downward, 1 kN upward
(B) 0.5 kN upward, 0.5 kN downward
(C) 0.5 kN downward, 0.5 kN upward
(D) 1 kN upward , 1 kN downward
GATE-ME-2011
Hint 7. (Ans A)
Question 8. A simply supported beam of length L is subjected to a varying distributed load sin (3
)Nm-1, where the distance x is measured from the left support. The magnitude of the vertical reaction force in N at the left support is
(A) Zero
(B) L/3
(C) L/
(D) 2L/
GATE-ME-2013
Hint 8. (Ans B)
AS loading is symmetric, reaction are going to be same.
Answer keys
1. (D) 2. (D) 3. (C) 4. (B) 5. (A) 6. (B) 7. (A) 8. (B)