Test: Slope & Deflection Level - 2 | 15 Questions MCQ Test Engineering Mechanics Mechanical Engineering

QUESTION: 1

For the beam shown in the figure, the elastic curve between the supports B and C will be

A. Circular
B. Parabolic
C. Elliptic
D. A straight line

Solution: BMD for the loading will be

Between B and C, BMD is a straight line BM = Constant

Now,

⇒ R = Constant Means curve of constant radius.

Hence, circular.

QUESTION: 2

The maximum deflection of a cantilever of 10.0 m span, an EI = 200.0MN/m² subjected to a distributed load of 8.0 kN/m is

A. 20 mm
B. 50 mm
C. 225 mm
D. 500 mm

Solution:

= 0.05m = 50mm

QUESTION: 3

A cantilever of length (L) carries a distributed load whose intensity varies uniformly from zero at the fixed end to ‘w’ per unit length at the free end. The deflection at the free end will be

A.
B.
C.
D.

Solution:

δ₁ =

δ₂ =

δ₃ = δ₁ − δ₂ =

=

QUESTION: 4

If the deflection at the free end of a uniformly loaded cantilever beam is 15 mm and the slope of the deflection curve at the free end is 0.02 radian. then the length of the beam is

A. 0.8 m
B. 1 m
C. 1.2 m
D. 1.5 m

Solution:

Deflection at free end, δ = = 15 mm

Slope at free end, θ = = 0.02

∴ From the two

L = 1 m

QUESTION: 5

A cantilever beam of uniform cross-section and length L is subjected to upward force W at mid-span and downward force P at the free end. For the deflection to be zero at the free end. W and P are related by

A. W = 2P
B. W = 16P/5
C. W = 3P
D. W = 5P

Solution:

Deflection at free end due to load, p =

Deflection at free end due to support load W

∴ The deflection at free end is zero

W = 16/5P

QUESTION: 6

The slope at the free end of a cantilever of length 1 m is 1°. If the cantilever carries uniformly distributed load over the whole length then the deflection at the free end will be

A. 1 cm
B. 1.309 cm
C. 2.618 cm
D. 3.927 cm

Solution: δ =

= = 1.309cm

QUESTION: 7

A simply supported beam 'A' of length L carries a central point load W. Another beam 'B' is loaded with a uniformly distributed load such that the total load on the beam is W. The ratio of maximum deflections between the beams A and B is

A. 5/8
B. 8/5
C. 5/4
D. 4/5

Solution:

Maximum deflection of beam A,

Maximum deflection of beam B,

y_B =

=

QUESTION: 8

A simply supported beam of span 4m subjected to a point load of 4 kN at a distance of 3m from the left support. The maximum slope occurs

A. At the left support
B. At right support
C. At mid-span
D. Under the point load

Solution: The load is closer to right support; the slope is max at right.

QUESTION: 9

If the depth of a simply supported rectangular beam subjected to concentric load at the Centre is doubled, the deflection at the Centre will be reduced to

A. 25%
B. 12.5%
C. 37.5%
D. 40%

Solution: y₁ =

= 12.5%

QUESTION: 10

A simply supported rectangular beam of span L and depth d carries a central load W, modulus of elasticity is E, the ratio of maximum deflection to maximum bending stress is

A.
B.
C.
D.

Solution:

QUESTION: 11

A cantilever of span L subjected to uniformly distributed gravity loading w/m is subjected to an upward force P at a distance L/2 from the free end. If the deflection at the free end of the beam is zero, (wL/P) is

A. 1.50
B. 2.00
C. 0.67
D. 0.83

Solution:

Deflection at free end due to vertical load

δ₁ =

Deflection at free end due to support P

δ₂ =

=

∴ Deflection at free end is zero

= 0.83

QUESTION: 12

A simply supported beam of 10m span is carrying a load of 4.8kN at mid-span. If Young's modulus of elasticity (E) is 2 x 108 kN/m² and moment of inertia (I) is 20 cm⁴ , then the maximum deflection will be