🔥 Strength of Materials –
Hard Level MCQs
(As per SSC JE & RRB JE pattern)
1.
A bar of uniform cross-section is subjected to axial tensile
load. The strain energy stored in the bar is proportional to:
A) Load
B) Square of load
C) Cube of load
D) Independent of load
Answer: B
Explanation:
2.
A stepped bar with two segments in series is subjected to
axial load. The total elongation is equal to:
A) Average elongation
B) Maximum elongation
C) Sum of elongations of each segment
D) Product of elongations
Answer: C
Explanation:
3.
For a body subjected to pure shear, the maximum normal
stress is equal to:
A) τ
B) 2τ
C) τ/2
D) Zero
Answer: A
Explanation:
In pure shear,
4.
Poisson’s ratio for a perfectly incompressible material is:
A) 0
B) 0.25
C) 0.33
D) 0.5
Answer: D
Explanation:
For incompressible materials, volumetric strain = 0 → μ = 0.5
5.
If bulk modulus 
and shear modulus 
are known, Young’s modulus 
is:
A) 
B) 
C) 
D) 
Answer: C
Explanation:
6.
A bar fixed at both ends is subjected to temperature rise.
Thermal stress developed is:
A) Zero
B) 
C) 
D) 
Answer: B
Explanation:
Free expansion prevented → full thermal stress
7.
Strain energy stored per unit volume is called:
A) Resilience
B) Proof resilience
C) Modulus of resilience
D) Toughness
Answer: C
Explanation:
8.
A bar of length L is subjected to impact load W falling from
height h. The maximum stress induced is proportional to:
A) h
B) √h
C) h²
D) Independent of h
Answer: B
Explanation:
9.
The ratio of lateral strain to longitudinal strain is:
A) Young’s modulus
B) Bulk modulus
C) Poisson’s ratio
D) Modulus of rigidity
Answer: C
10.
A bar is subjected to gradually applied load P and suddenly
applied load P. Ratio of stresses developed is:
A) 1:1
B) 2:1
C) 1:2
D) 4:1
Answer: B
Explanation:
Suddenly applied load produces double the stress of gradual load.
11.
The shear stress distribution in a circular shaft under
torsion is:
A) Uniform
B) Parabolic
C) Linear
D) Exponential
Answer: C
Explanation:
12.
For a hollow shaft, torsional strength increases if:
A) Inner diameter increases
B) Outer diameter decreases
C) Difference between diameters increases
D) Both diameters decrease
Answer: C
13.
Maximum bending stress in a beam occurs at:
A) Neutral axis
B) Top fiber
C) Bottom fiber
D) Farthest fiber from neutral axis
Answer: D
14.
The moment of resistance of a beam section depends upon:
A) Length
B) Elastic modulus
C) Section modulus
D) Load intensity
Answer: C
Explanation:
15.
A simply supported beam of length L carries UDL w. Maximum
deflection is:
A) At midspan
B) At supports
C) At quarter span
D) At any point
Answer: A
16.
The unit of shear modulus is:
A) N
B) N/m
C) N/m²
D) N/m³
Answer: C
17.
In a compound bar subjected to axial load, stress in each
material is:
A) Same
B) Proportional to area
C) Proportional to modulus of elasticity
D) Inversely proportional to length
Answer: C
18.
In torsion equation 
, J represents:
A) Polar moment of area
B) Moment of inertia
C) Section modulus
D) Modulus of rigidity
Answer: A
19.
A beam is said to be in pure bending when:
A) Shear force = 0
B) Bending moment = 0
C) Load = 0
D) Deflection = 0
Answer: A
20.
The neutral axis passes through:
A) Geometric centroid
B) Elastic centroid
C) Center of gravity of area
D) Any point
Answer: C
21.
For a rectangular beam, section modulus is:
A) 
B) 
C) 
D) 
Answer: A
22.
The strain energy stored in a beam due to bending is
proportional to:
A) M
B) M²
C) 1/M
D) √M
Answer: B
23.
A material is said to be ductile if it has:
A) High ultimate stress
B) Large plastic deformation
C) High stiffness
D) High hardness
Answer: B
24.
In Mohr’s circle, the diameter represents:
A) Principal stress
B) Shear stress
C) Difference of principal stresses
D) Average normal stress
Answer: C
25.
The maximum shear stress in a material under uniaxial
tension is:
A) σ
B) σ/2
C) 2σ
D) σ/3
Answer: B
26.
For a beam of uniform strength, the cross-section varies
such that:
A) Stress is constant
B) Bending moment is constant
C) Shear force is constant
D) Deflection is constant
Answer: A
27.
The critical load for a column varies inversely with:
A) Length
B) Area
C) Square of length
D) Modulus
Answer: C
Explanation:
28.
Slenderness ratio is defined as:
A) 
B) 
C) 
D) 
Answer: B
29.
A column will buckle in the plane of:
A) Maximum moment of inertia
B) Minimum moment of inertia
C) Equal inertia
D) Any plane
Answer: B
30.
The ratio of maximum deflection of cantilever beam to simply
supported beam (same span, same load at free end) is:
A) 1
B) 2
C) 4
D) 8
Answer: C
31.
In a circular shaft under torsion, angle of twist is
proportional to:
A) Torque
B) Length
C) Inverse of diameter⁴
D) All of these
Answer: D
32.
A beam is statically indeterminate if:
A) Unknown reactions > equilibrium equations
B) Unknown reactions < equilibrium equations
C) Unknown reactions = equilibrium equations
D) No reactions
Answer: A
33.
Complementary shear stresses are:
A) Equal in magnitude
B) Opposite in direction
C) On perpendicular planes
D) All of these
Answer: D
34.
The maximum principal stress is given by:
A) 
B) 
C) 
D) 
Answer: C
35.
If μ = 0.25 and E = 200 GPa, find G.
A) 40 GPa
B) 60 GPa
C) 80 GPa
D) 100 GPa
Answer: C
Explanation:
36.
A bar is subjected to equal tensile stress in three mutually
perpendicular directions. Volumetric strain is:
A) Zero
B) 
C) 
D) 
Answer: C
37.
In strain rosette, minimum number of gauges required to find
principal strains is:
A) 2
B) 3
C) 4
D) 6
Answer: B
38.
The energy absorbed up to fracture per unit volume is
called:
A) Toughness
B) Resilience
C) Hardness
D) Ductility
Answer: A
39.
A beam with fixed ends has maximum bending moment at:
A) Midspan
B) Supports
C) Quarter span
D) One-third span
Answer: B
40.
The shear stress at neutral axis in a rectangular beam is:
A) Zero
B) Maximum
C) Minimum
D) Equal to average
Answer: B
41.
For a cantilever beam with point load at free end, slope at
free end is:
A) Zero
B) Maximum
C) Minimum
D) Constant
Answer: B
42.
The torsional rigidity of a shaft is given by:
A) GJ
B) EJ
C) EI
D) GA
Answer: A
43.
A beam of uniform strength in bending will have:
A) Constant depth
B) Constant width
C) Variable section modulus
D) Constant moment of inertia
Answer: C
44.
Euler’s formula is applicable for:
A) Short columns
B) Intermediate columns
C) Long columns
D) All columns
Answer: C
45.
If factor of safety is increased, allowable stress will:
A) Increase
B) Decrease
C) Remain same
D) Become zero
Answer: B
46.
The area under stress-strain curve up to elastic limit
represents:
A) Toughness
B) Resilience
C) Hardness
D) Strength
Answer: B
47.
For a fixed beam, maximum deflection compared to simply
supported beam is:
A) Same
B) Less
C) More
D) Infinite
Answer: B
48.
The product EI in beam theory is called:
A) Flexural rigidity
B) Torsional rigidity
C) Axial rigidity
D) Shear rigidity
Answer: A
49.
In thin cylinders, circumferential stress is:
A) Twice the longitudinal stress
B) Half the longitudinal stress
C) Equal to longitudinal stress
D) Zero
Answer: A
50.
If a beam is loaded within elastic limit, then:
A) Permanent deformation occurs
B) Hooke’s law is valid
C) Yield point is reached
D) Fracture occurs
Answer: B
🔥 SoM Hard MCQs (51–100)
with Explanations
51.
A bar of length L is fixed at one end and free at other. If
temperature rises by ΔT, free end elongation is:
A) 0
B) 
C) 
D) 
Answer: B
Explanation:
Free expansion → no stress, only strain
52.
If a body is subjected to equal tensile stress in x, y and z
directions, shape of Mohr’s circle will be:
A) Circle
B) Ellipse
C) Point
D) Straight line
Answer: C
Explanation:
All principal stresses equal → no shear → Mohr’s circle reduces to a point.
53.
A bar of varying cross-section under axial load P will have maximum
stress at:
A) Largest area
B) Smallest area
C) Mid-length
D) Free end
Answer: B
54.
For a rectangular beam, the ratio of max shear stress to
average shear stress is:
A) 1
B) 1.25
C) 1.5
D) 2
Answer: C
Explanation:
55.
If the diameter of a solid shaft is doubled, its torsional
strength becomes:
A) 2 times
B) 4 times
C) 8 times
D) 16 times
Answer: D
Explanation:
(For stress capacity → ∝ d³; for rigidity
→ ∝
d⁴)
56.
In thin cylindrical shells, longitudinal stress is:
A) Twice hoop stress
B) Half hoop stress
C) Equal to hoop stress
D) Zero
Answer: B
57.
If Poisson’s ratio μ = 0.5, then the material is:
A) Perfectly elastic
B) Perfectly plastic
C) Incompressible
D) Brittle
Answer: C
58.
A column with one end fixed and other end free has effective
length:
A) L
B) 2L
C) L/2
D) L/√2
Answer: B
59.
The unit of strain energy is:
A) N
B) Nm
C) N/m²
D) Dimensionless
Answer: B
Explanation:
Strain energy is work → Joule (Nm)
60.
In a beam subjected to pure bending, the bending moment is:
A) Zero
B) Constant
C) Maximum
D) Varying linearly
Answer: B
61.
The relation between bulk modulus K and Young’s modulus E
is:
A) 
B)
C) 
D) 
Answer: B
62.
For a beam, the point where bending moment changes sign is
called:
A) Neutral axis
B) Point of contraflexure
C) Inflection point
D) Both B and C
Answer: D
63.
A beam of length L is fixed at both ends. Compared to simply
supported beam, maximum deflection is:
A) Same
B) Double
C) Half
D) One-fourth
Answer: D
64.
The maximum principal strain is given by:
A) 
B) 
C) 
D) 
Answer: C
65.
If length of a column is doubled, its critical load becomes:
A) Double
B) Half
C) One-fourth
D) Four times
Answer: C
66.
The ratio of longitudinal stress to circumferential stress
in thin cylinder is:
A) 1:1
B) 1:2
C) 2:1
D) 3:1
Answer: B
67.
A beam is said to have uniform strength when:
A) Depth is constant
B) Stress is constant
C) Load is uniform
D) Shear force is constant
Answer: B
68.
The shear stress distribution in a rectangular beam is:
A) Uniform
B) Triangular
C) Parabolic
D) Hyperbolic
Answer: C
69.
The strain energy in a bar due to gradually applied load is:
A) 
B) 
C) 
D) 
Answer: C
70.
A suddenly applied load causes stress equal to:
A) Same as gradual load
B) Half of gradual load
C) Double of gradual load
D) Four times gradual load
Answer: C
71.
For a solid shaft, polar moment of inertia is:
A) 
B) 
C) 
D) 
Answer: B
72.
The stress at neutral axis in bending is:
A) Maximum
B) Minimum
C) Zero
D) Average
Answer: C
73.
If a beam is over-reinforced, it will fail by:
A) Steel yielding
B) Concrete crushing
C) Shear failure
D) Buckling
Answer: B
74.
In Mohr’s circle, radius represents:
A) Average stress
B) Max shear stress
C) Principal stress
D) Normal stress
Answer: B
75.
The modulus of rigidity is related to Young’s modulus by:
A) 
B) 
C) 
D) 
Answer: B
76.
The point where shear force is zero corresponds to:
A) Maximum deflection
B) Maximum bending moment
C) Minimum bending moment
D) Zero slope
Answer: B
77.
A beam carrying UDL has maximum bending moment at:
A) Supports
B) Midspan
C) Quarter span
D) Anywhere
Answer: B
78.
The ratio of flexural rigidity of two beams depends on:
A) E only
B) I only
C) EI
D) Length
Answer: C
79.
A material with high resilience will have:
A) High yield stress
B) High toughness
C) High ductility
D) High brittleness
Answer: A
80.
In a cantilever beam with UDL, maximum bending moment occurs
at:
A) Free end
B) Midspan
C) Fixed end
D) Quarter span
Answer: C
81.
A beam fixed at one end and simply supported at other is
called:
A) Cantilever
B) Propped cantilever
C) Fixed beam
D) Continuous beam
Answer: B
82.
If the shear modulus of a material is zero, it behaves like:
A) Solid
B) Fluid
C) Gas
D) Plastic
Answer: B
83.
For a beam, the relation between load, shear force and
bending moment is:
A) 
B) 
C) 
D) 
Answer: C
84.
A bar is subjected to tensile stress σ. Maximum shear stress
developed is:
A) σ
B) σ/2
C) σ/3
D) 2σ
Answer: B
85.
The area under stress–strain curve up to fracture gives:
A) Resilience
B) Toughness
C) Hardness
D) Strength
Answer: B
86.
A circular shaft is subjected to bending and torsion
simultaneously. The maximum stress is found using:
A) Euler theory
B) Rankine theory
C) Maximum shear stress theory
D) Combined stress theory
Answer: D
87.
The bending equation is:
A) 
B) 
C) 
D) 
Answer: B
88.
A beam is called statically determinate when:
A) Reactions > equations
B) Reactions = equations
C) Reactions < equations
D) No reactions
Answer: B
89.
If the load on a beam is doubled, bending stress will:
A) Remain same
B) Double
C) Become half
D) Become four times
Answer: B
90.
The strain energy stored in a shaft due to torsion is
proportional to:
A) T
B) T²
C) 1/T
D) √T
Answer: B
91.
For a beam of triangular section, neutral axis passes
through:
A) Base
B) Apex
C) Centroid
D) Mid-height
Answer: C
92.
The allowable stress in design is:
A) Yield stress
B) Ultimate stress
C) Working stress
D) Proof stress
Answer: C
93.
If μ = 0, the material shows:
A) No lateral strain
B) Infinite lateral strain
C) Maximum lateral strain
D) Perfect plasticity
Answer: A
94.
The maximum shear force in a simply supported beam with UDL
occurs at:
A) Midspan
B) Supports
C) Quarter span
D) Anywhere
Answer: B
95.
For a column with both ends hinged, effective length is:
A) L
B) 2L
C) L/2
D) L/√2
Answer: A
96.
A brittle material fails when:
A) Yield stress is reached
B) Ultimate stress is reached
C) Elastic limit is exceeded
D) Plastic deformation occurs
Answer: B
97.
If the diameter of a beam is increased, bending stress will:
A) Increase
B) Decrease
C) Remain same
D) Become zero
Answer: B
98.
The ratio of maximum bending stress in two beams depends on:
A) Loads only
B) Length only
C) Section modulus
D) Modulus of elasticity
Answer: C
99.
A bar of constant cross-section is subjected to varying
axial load. Stress variation will be:
A) Uniform
B) Linear
C) Depends on load variation
D) Parabolic
Answer: C
100.
In elastic range, the slope of stress–strain curve
represents:
A) Resilience
B) Toughness
C) Young’s modulus
D) Proof stress
Answer: C