Strength of Materials
Topic-wise MCQs with Short Answers
#SSC JE #RRB JE
TOPIC 1 – Stress, Strain & Elastic Constants
1. Stress is defined as
A) Load/Area
B) Area/Load
C) Load×Area
D) Load/Volume
Ans: A
Detail: Stress = internal resisting force per unit area.
2. Unit of stress in SI system is
A) N
B) N/mm²
C) N/m²
D) kg/m²
Ans: C
Detail: SI unit is Pascal (N/m²).
3. Strain is
A) Load/Area
B) Change in length / Original length
C) Stress × Strain
D) Length/Area
Ans: B
Detail: Strain is deformation per unit original dimension.
4. Strain has
A) Unit
B) Dimension
C) No unit
D) Only mass unit
Ans: C
Detail: Strain is dimensionless.
5. Hooke’s law states
A) Stress ∝ Load
B) Stress ∝ Strain
C) Load ∝ Area
D) Stress ∝ Area
Ans: B
Detail: Valid up to proportional limit.
6. Young’s modulus is ratio of
A) Stress/Strain
B) Strain/Stress
C) Load/Area
D) Area/Load
Ans: A
Detail: Indicates stiffness of material.
7. Higher Young’s modulus means material is
A) Stronger
B) Harder
C) Stiffer
D) Tougher
Ans: C
Detail: Stiffness = resistance to deformation.
8. Bulk modulus relates to
A) Linear strain
B) Volumetric strain
C) Shear strain
D) Thermal strain
Ans: B
Detail: K = volumetric stress / volumetric strain.
9. Modulus of rigidity relates to
A) Normal stress
B) Bending stress
C) Shear stress
D) Thermal stress
Ans: C
Detail: G = shear stress / shear strain.
10. Poisson’s ratio is
A) Longitudinal strain / lateral strain
B) Lateral strain / longitudinal strain
C) Stress / strain
D) Load / area
Ans: B
Detail: Shows lateral contraction effect.
11. Range of Poisson’s ratio is
A) −1 to 1
B) 0 to 1
C) 0 to 0.5
D) 0.5 to 1
Ans: C
Detail: For stable isotropic materials.
12. Elastic limit is
A) Point of fracture
B) Maximum elastic stress
C) Yield stress
D) Ultimate stress
Ans: B
Detail: Beyond this, permanent deformation begins.
13. Plastic deformation starts after
A) Proportional limit
B) Elastic limit
C) Yield point
D) Breaking point
Ans: C
Detail: Yield point marks plastic flow.
14. Ultimate stress is
A) First stress
B) Maximum stress material can carry
C) Breaking stress
D) Working stress
Ans: B
Detail: Highest point on stress-strain curve.
15. Working stress =
A) Ultimate stress × FOS
B) Ultimate stress / FOS
C) Yield stress × FOS
D) Proof stress × FOS
Ans: B
Detail: Safe design stress.
16. Factor of safety =
A) Working stress / Ultimate stress
B) Ultimate stress / Working stress
C) Yield / Ultimate
D) Proof / Yield
Ans: B
Detail: Indicates margin of safety.
17. Ductile materials fail mainly by
A) Compression
B) Shear
C) Tension
D) Bending
Ans: C
Detail: Large plastic deformation before fracture.
18. Brittle materials fail mainly by
A) Shear
B) Compression
C) Tension
D) Torsion
Ans: C
Detail: Sudden fracture without warning.
19. Resilience is
A) Energy absorbed till fracture
B) Energy absorbed in elastic range
C) Energy absorbed in plastic range
D) Total strain energy
Ans: B
Detail: Ability to store elastic energy.
20. Proof resilience is
A) Max elastic strain energy
B) Total strain energy
C) Plastic energy
D) Impact energy
Ans: A
Detail: Energy at elastic limit.
TOPIC 2 – Axial Load, Thermal Stress
21. Stress in a bar under axial load =
A) P×A
B) P/A
C) A/P
D) P²/A
Ans: B
Detail: Direct stress formula.
22. Elongation of bar depends on
A) P, L, A, E
B) Only P
C) Only L
D) Only A
Ans: A
Detail: δ = PL/AE.
23. If length doubles, elongation becomes
A) Half
B) Same
C) Double
D) Four times
Ans: C
Detail: δ ∝ L.
24. Thermal strain =
A) αΔT
B) ΔT/α
C) α/ΔT
D) αΔT²
Ans: A
Detail: Expansion per unit length.
25. Thermal stress develops when
A) Bar is free
B) Expansion is restrained
C) Temperature is low
D) Bar is long
Ans: B
Detail: No stress in free expansion.
26. Thermal stress formula is
A) σ = EαΔT
B) σ = αΔT/E
C) σ = E/αΔT
D) σ = α/EΔT
Ans: A
Detail: Fully restrained bar.
27. Composite bar analysis uses
A) Same stress
B) Same strain
C) Same force
D) Same area
Ans: B
Detail: Compatibility condition.
28. If two bars in series are loaded, stress is
A) Same
B) Different
C) Zero
D) Infinite
Ans: B
Detail: Force same, area different.
29. If two bars in parallel are loaded, stress is
A) Same
B) Different
C) Zero
D) Infinite
Ans: A
Detail: Equal strain → equal stress.
30. Temperature rise in restrained bar causes
A) Compression
B) Tension
C) Shear
D) Bending
Ans: A
Detail: Expansion prevented → compressive stress.
TOPIC 3 – Torsion of Shafts
31. Torsion equation is
A) T/J = τ/R = Gθ/L
B) M/I = σ/y
C) P/A
D) E = σ/ε
Ans: A
Detail: Basic torsion relation.
32. Polar moment of inertia is
A) I
B) J
C) Z
D) A
Ans: B
Detail: Used in torsion.
33. Shear stress in solid shaft is max at
A) Centre
B) Outer surface
C) Mid radius
D) Neutral axis
Ans: B
Detail: τ ∝ r.
34. Hollow shaft is stronger than solid shaft of same weight because
A) More mass
B) Less length
C) Material is away from centre
D) More density
Ans: C
Detail: Higher polar moment.
35. Torsional rigidity =
A) GJ
B) EI
C) EA
D) EJ
Ans: A
Detail: Resistance to twisting.
36. Angle of twist is directly proportional to
A) Torque
B) Diameter
C) Rigidity
D) Area
Ans: A
Detail: θ ∝ T.
37. Power transmitted by shaft =
A) 2πNT/60
B) NT
C) T/N
D) N/T
Ans: A
Detail: Standard power equation.
38. Maximum torque for given stress depends on
A) Polar moment
B) Area only
C) Length only
D) Density
Ans: A
Detail: T = τJ/R.
39. Shaft under pure torsion has
A) Normal stress
B) Shear stress only
C) Bending stress
D) Tensile stress
Ans: B
Detail: No normal stress.
40. Failure of ductile shaft in torsion is governed by
A) Max shear stress theory
B) Max principal stress theory
C) Max strain theory
D) Coulomb theory
Ans: A
Detail: Tresca theory used.
TOPIC 4 – Bending of Beams
41. Neutral axis passes through
A) Top fibre
B) Bottom fibre
C) Centroid
D) Shear centre
Ans: C
Detail: For homogeneous sections.
42. Bending stress equation is
A) σ = My/I
B) σ = M/I
C) σ = My
D) σ = I/My
Ans: A
Detail: Flexure formula.
43. Max bending stress occurs at
A) Neutral axis
B) Centroid
C) Farthest fibre
D) Shear centre
Ans: C
Detail: y is maximum there.
44. Section modulus is
A) I/ymax
B) I×ymax
C) y/I
D) A/y
Ans: A
Detail: Measure of bending strength.
45. Stronger beam section has
A) Larger area
B) Larger section modulus
C) Larger weight
D) Larger length
Ans: B
Detail: Design parameter.
46. In cantilever beam, max BM occurs at
A) Free end
B) Fixed end
C) Mid span
D) Quarter span
Ans: B
Detail: Always at fixed support.
47. In simply supported beam with UDL, max BM at
A) Supports
B) Quarter span
C) Mid span
D) One-third span
Ans: C
Detail: At centre.
48. Point of contraflexure is where
A) BM = 0
B) SF = 0
C) Stress = 0
D) Deflection = 0
Ans: A
Detail: Bending changes sign.
49. Shear force is maximum at
A) Mid span
B) Supports
C) Neutral axis
D) Free end
Ans: B
Detail: Reaction points.
50. Deflection of beam is proportional to
A) 1/EI
B) EI
C) Area
D) Stress
Ans: A
Detail: Higher stiffness → less deflection.
TOPIC 5 – Columns & Buckling
51. Column fails mainly due to
A) Bending
B) Shear
C) Buckling
D) Torsion
Ans: C
Detail: Stability failure.
52. Slenderness ratio =
A) L/A
B) L/k
C) A/k
D) I/L
Ans: B
Detail: k = radius of gyration.
53. Euler’s formula applies to
A) Short columns
B) Long columns
C) Intermediate columns
D) All columns
Ans: B
Detail: Elastic buckling only.
54. Critical load is
A) Yield load
B) Buckling load
C) Breaking load
D) Impact load
Ans: B
Detail: Load at instability.
55. Effective length depends on
A) Material
B) Area
C) End conditions
D) Load
Ans: C
Detail: Fixity changes buckling length.
56. Column with both ends fixed has effective length
A) L
B) L/2
C) 2L
D) L/√2
Ans: B
Detail: Strongest end condition.
57. Column with one end fixed and other free has effective length
A) L
B) 2L
C) L/2
D) √2L
Ans: B
Detail: Weakest condition.
58. Rankine formula is applicable for
A) Short columns
B) Long columns
C) Intermediate columns
D) All columns
Ans: D
Detail: Combines crushing + buckling.
59. Buckling load is proportional to
A) L
B) L²
C) 1/L
D) 1/L²
Ans: D
Detail: Euler: Pcr ∝ 1/L².
60. Radius of gyration k =
A) √(I/A)
B) I/A
C) A/I
D) √(A/I)
Ans: A
Detail: Indicates section efficiency.
TOPIC 6 – Strain Energy, Impact & Fatigue
61. Strain energy is stored due to
A) Load
B) Deformation
C) Weight
D) Temperature
Ans: B
Detail: Energy of distortion.
62. Strain energy per unit volume is
A) Toughness
B) Proof resilience
C) Hardness
D) Ductility
Ans: B
Detail: Elastic energy density.
63. Impact loading increases
A) Stress
B) Strain
C) Deflection
D) All
Ans: D
Detail: Dynamic effect.
64. Impact factor increases when
A) Height increases
B) Area increases
C) Length decreases
D) Modulus increases
Ans: A
Detail: Higher velocity → higher stress.
65. Fatigue failure occurs due to
A) Static load
B) Repeated load
C) Impact load
D) Thermal load
Ans: B
Detail: Cyclic stress.
66. Endurance limit is
A) Max stress
B) Min stress
C) Safe cyclic stress
D) Breaking stress
Ans: C
Detail: Below this, infinite life.
67. Fatigue failure is dangerous because
A) No warning
B) Large deformation
C) Loud noise
D) Slow process
Ans: A
Detail: Sudden fracture.
68. Stress concentration causes
A) Local high stress
B) Uniform stress
C) Low stress
D) Zero stress
Ans: A
Detail: At notches, holes.
69. Stress concentration factor =
A) Max stress / Nominal stress
B) Nominal / Max
C) Stress / strain
D) Load / area
Ans: A
Detail: Measures severity.
70. Fillets reduce
A) Weight
B) Stress concentration
C) Cost
D) Length
Ans: B
Detail: Smoothens geometry.
TOPIC 7 – Combined Stress & Failure Theories
71. Maximum principal stress theory is
A) Rankine theory
B) Tresca theory
C) Von Mises theory
D) Coulomb theory
Ans: A
Detail: Used for brittle materials.
72. Maximum shear stress theory is
A) Rankine
B) Tresca
C) Von Mises
D) Guest
Ans: B
Detail: For ductile materials.
73. Maximum distortion energy theory is
A) Rankine
B) Tresca
C) Von Mises
D) Coulomb
Ans: C
Detail: Most accurate for ductile metals.
74. Principal stresses occur on planes where
A) Normal stress is zero
B) Shear stress is zero
C) Bending stress is zero
D) Load is zero
Ans: B
Detail: Definition.
75. Maximum shear stress occurs at
A) 0°
B) 30°
C) 45°
D) 90°
Ans: C
Detail: From Mohr’s circle.
76. Mohr’s circle is used to find
A) Bending moment
B) Deflection
C) Principal stresses
D) Torque
Ans: C
Detail: Graphical stress transformation.
77. State of pure shear has
A) Only normal stress
B) Only shear stress
C) Both
D) No stress
Ans: B
Detail: τ ≠ 0, σ = 0.
78. In plane stress condition
A) σx, σy, τxy exist
B) σz exists
C) τxz exists
D) τyz exists
Ans: A
Detail: Thin plates.
79. Plane strain occurs in
A) Thin plates
B) Long dams
C) Shafts
D) Beams
Ans: B
Detail: No strain in one direction.
80. Complementary shear stresses act on
A) Parallel planes
B) Same plane
C) Perpendicular planes
D) Inclined planes
Ans: C
Detail: For equilibrium.
TOPIC 8 – Shear Stress in Beams
81. Shear stress distribution in rectangular beam is
A) Linear
B) Parabolic
C) Constant
D) Triangular
Ans: B
Detail: Max at NA.
82. Maximum shear stress in rectangular beam occurs at
A) Top fibre
B) Bottom fibre
C) Neutral axis
D) Corners
Ans: C
Detail: Shear formula.
83. Shear stress in circular beam is
A) Uniform
B) Parabolic
C) Linear
D) Zero
Ans: B
Detail: Similar trend.
84. Average shear stress =
A) V/A
B) VQ/It
C) M/I
D) T/J
Ans: A
Detail: Basic average formula.
85. Shear stress is zero at
A) Neutral axis
B) Outer surface
C) Supports
D) Mid span
Ans: B
Detail: In rectangular section.
TOPIC 9 – Miscellaneous
86. Hardness means resistance to
A) Fatigue
B) Impact
C) Scratching
D) Bending
Ans: C
Detail: Surface property.
87. Toughness is
A) Elastic energy
B) Plastic energy
C) Total energy till fracture
D) Only impact energy
Ans: C
Detail: Area under full curve.
88. Ductility is measured by
A) % elongation
B) % reduction in area
C) Both
D) None
Ans: C
Detail: Tensile test.
89. Cast iron is best in
A) Tension
B) Compression
C) Torsion
D) Bending
Ans: B
Detail: High compressive strength.
90. Steel is generally
A) Brittle
B) Ductile
C) Fragile
D) Soft
Ans: B
Detail: Large plastic range.
91. Proof stress is used for
A) Ductile materials
B) Brittle materials
C) Materials without clear yield point
D) Rubber
Ans: C
Detail: Aluminium, etc.
92. Neutral axis shifts when
A) Section is symmetrical
B) Section is unsymmetrical
C) Load is zero
D) Moment is zero
Ans: B
Detail: Unequal distribution.
93. Shear centre is point where
A) Load causes bending only
B) Load causes no twisting
C) Load causes torsion only
D) Load causes shear only
Ans: B
Detail: Important in thin sections.
94. Deflection increases when
A) Span increases
B) Depth increases
C) EI increases
D) Width increases
Ans: A
Detail: δ ∝ L⁴.
95. Stress concentration can be reduced by
A) Notches
B) Fillets
C) Holes
D) Grooves
Ans: B
Detail: Smooth transition.
96. Column with both ends hinged has effective length
A) L
B) 2L
C) L/2
D) √2L
Ans: A
Detail: Standard case.
97. Euler load is independent of
A) Length
B) Area
C) Modulus
D) End condition
Ans: B
Detail: Depends on I, not A.
98. Bending stress varies linearly with
A) Distance from NA
B) Area
C) Length
D) Load
Ans: A
Detail: σ ∝ y.
99. In pure bending, shear force is
A) Zero
B) Maximum
C) Constant
D) Negative
Ans: A
Detail: Definition.
100. The most suitable theory for ductile materials is
A) Rankine
B) Tresca
C) Von Mises
D) Coulomb
Ans: C
Detail: Distortion energy theory.