Strength of Materials
Hard Level MCQs (SSC JE)
MCQs 101–200
🔹 Topic: Stress–Strain, Elastic Constants
101. A bar is subjected to stress equal to half of its elastic limit. The strain developed will be
A) Half of yield strain
B) Half of elastic strain
C) Half of proportional strain
D) Half of breaking strain
Ans: C
Detail: Hooke’s law valid till proportional limit → strain ∝ stress.
102. If Poisson’s ratio of a material is 0.5, the material is
A) Brittle
B) Perfectly rigid
C) Perfectly plastic
D) Incompressible
Ans: D
Detail: μ = 0.5 → no volume change.
103. Relation between elastic constants is valid only for
A) Plastic materials
B) Anisotropic materials
C) Isotropic materials
D) Brittle materials
Ans: C
Detail: Relations assume isotropy.
104. A cube under pure shear has principal stresses equal to
A) τ and −τ
B) τ and τ
C) 0 and τ
D) 0 and −τ
Ans: A
Detail: In pure shear: σ₁ = +τ, σ₂ = −τ.
105. If E = 200 GPa and μ = 0.25, bulk modulus K is
A) 133 GPa
B) 100 GPa
C) 80 GPa
D) 160 GPa
Ans: A
Detail: K = E / [3(1−2μ)] = 200/[3(0.5)] = 133 GPa.
🔹 Topic: Axial Load & Thermal Stress
106. A bar is fixed between two rigid supports. Temperature rises. The stress developed is independent of
A) E
B) α
C) ΔT
D) Length
Ans: D
Detail: σ = EαΔT → length cancels.
107. Two bars of same length but different areas are in series. Which has higher stress?
A) Larger area
B) Smaller area
C) Same stress
D) Depends on material
Ans: B
Detail: Stress = P/A → smaller A → higher stress.
108. Two bars in parallel carry load P. If areas are equal but moduli differ, stress will be
A) Same
B) Proportional to E
C) Inversely proportional to E
D) Zero in weaker bar
Ans: B
Detail: Equal strain → σ = Eε.
109. A composite bar under temperature rise develops
A) Only tensile stress
B) Only compressive stress
C) Both tensile & compressive
D) No stress
Ans: C
Detail: Depending on restraint & materials.
110. Thermal stress in a bar is maximum when
A) One end fixed
B) Both ends fixed
C) Free expansion
D) Hinged ends
Ans: B
Detail: Fully restrained condition.
🔹 Topic: Torsion of Shafts
111. For same torque and length, angle of twist of hollow shaft compared to solid shaft (same material & weight) is
A) More
B) Less
C) Same
D) Zero
Ans: B
Detail: Hollow shaft has higher J.
112. In a stepped shaft, maximum shear stress occurs at
A) Larger diameter
B) Smaller diameter
C) Mid length
D) Fixed end
Ans: B
Detail: τ = T/J × R → smallest section critical.
113. A shaft transmits same power at double speed. The torque required becomes
A) Double
B) Half
C) Same
D) Four times
Ans: B
Detail: P = 2πNT/60 → T ∝ 1/N.
114. In torsion, plane sections remain
A) Plane
B) Warped
C) Curved
D) Inclined
Ans: A
Detail: Assumption of pure torsion.
115. A circular shaft is subjected to bending and torsion. Maximum stress is governed by
A) Rankine theory
B) Tresca theory
C) Von Mises theory
D) Coulomb theory
Ans: C
Detail: Combined stress in ductile materials.
🔹 Topic: Bending of Beams
116. For a beam of rectangular section, if depth is doubled, bending stress becomes
A) Same
B) Half
C) One-fourth
D) Double
Ans: B
Detail: σ = M/Z, Z ∝ d² → σ ∝ 1/d.
117. A beam is of uniform strength if
A) Stress is constant
B) BM is constant
C) SF is constant
D) Area is constant
Ans: A
Detail: Designed so σ = constant.
118. For a cantilever with point load at free end, slope at free end is
A) WL²/2EI
B) WL²/3EI
C) WL³/3EI
D) WL³/2EI
Ans: A
Detail: Standard deflection formula.
119. A beam has maximum deflection at the point where
A) BM = max
B) SF = 0
C) Load = max
D) Stress = max
Ans: B
Detail: d²y/dx² = M/EI, slope zero at SF = 0.
120. In pure bending, the beam is subjected to
A) Shear force only
B) Bending moment only
C) Axial force only
D) Torsion only
Ans: B
Detail: SF = 0.
🔹 Topic: Shear Stress in Beams
121. Maximum shear stress in rectangular beam is
A) 1.5 × average shear stress
B) 2 × average
C) Same as average
D) 0.75 × average
Ans: A
Detail: τmax = 1.5 V/A.
122. In I-section, maximum shear stress occurs at
A) Flange
B) Web at NA
C) Bottom fibre
D) Top fibre
Ans: B
Detail: Shear concentrated in web.
123. Shear stress distribution in triangular section is
A) Uniform
B) Linear
C) Parabolic
D) Cubic
Ans: C
Detail: Similar to rectangular.
124. For circular section, τmax =
A) 1.33 × τavg
B) 1.5 × τavg
C) 2 × τavg
D) τavg
Ans: A
Detail: τmax = 4V/3A.
125. Shear stress is zero at
A) Neutral axis
B) Outer fibre
C) Support
D) Centre
Ans: B
Detail: In bending theory.
🔹 Topic: Columns & Buckling
126. A column fails by crushing when
A) Slenderness ratio is high
B) Slenderness ratio is low
C) Length is large
D) Load is eccentric
Ans: B
Detail: Short columns → crushing.
127. Euler’s formula assumes
A) Plastic behavior
B) Perfect straightness
C) Large deflection
D) Inelastic buckling
Ans: B
Detail: Ideal conditions.
128. A column with both ends fixed is
A) 2 times stronger than hinged
B) 4 times stronger
C) Same strength
D) Half strength
Ans: B
Detail: Pcr ∝ 1/L², Leff = L/2.
129. Rankine’s formula is a combination of
A) Crushing + bending
B) Crushing + buckling
C) Buckling + torsion
D) Bending + torsion
Ans: B
Detail: Empirical approach.
130. A column with eccentric loading fails mainly due to
A) Crushing
B) Buckling
C) Combined stress
D) Shear
Ans: C
Detail: Stress = direct + bending.
🔹 Topic: Strain Energy & Impact
131. Strain energy stored in a bar of length L under axial load P is
A) PL/AE
B) P²L/2AE
C) P²L/AE
D) PL/2AE
Ans: B
Detail: U = Pδ/2.
132. A load W falls from height h on a bar. Maximum stress depends on
A) W only
B) h only
C) W and h
D) L only
Ans: C
Detail: Impact energy W(h+δ).
133. Impact factor for suddenly applied load is
A) 1
B) 2
C) 3
D) 4
Ans: B
Detail: Stress doubles.
134. For same static load, which gives higher stress?
A) Gradually applied load
B) Suddenly applied load
C) Impact load
D) All same
Ans: C
Detail: Highest dynamic effect.
135. Proof resilience is maximum when
A) E is high
B) Yield stress is high
C) Area is high
D) Length is high
Ans: B
Detail: Ur = σ²/2E.
🔹 Topic: Fatigue & Stress Concentration
136. Fatigue failure occurs at stress
A) Greater than ultimate
B) Equal to yield
C) Much lower than yield
D) Zero
Ans: C
Detail: Repeated loading effect.
137. Endurance limit of steel is approximately
A) 0.3 σu
B) 0.5 σu
C) 0.7 σu
D) σu
Ans: B
Detail: Approximate value.
138. Stress concentration is most severe in
A) Gradual change in section
B) Fillet
C) Sharp notch
D) Tapered section
Ans: C
Detail: Sudden geometry change.
139. Which reduces fatigue strength most?
A) Polishing
B) Shot peening
C) Corrosion
D) Fillet
Ans: C
Detail: Corrosion pits → crack initiation.
140. Notch sensitivity is higher in
A) Ductile materials
B) Brittle materials
C) Rubber
D) Plastics
Ans: B
Detail: Brittle materials fail suddenly.
🔹 Topic: Combined Stress & Failure Theories
141. In biaxial stress state, maximum shear stress is
A) (σ₁ + σ₂)/2
B) (σ₁ − σ₂)/2
C) σ₁
D) σ₂
Ans: B
Detail: From Mohr’s circle.
142. Tresca theory is conservative because it
A) Overestimates strength
B) Underestimates strength
C) Ignores shear
D) Ignores normal stress
Ans: B
Detail: Gives lower safe stress.
143. Von Mises theory is based on
A) Max shear stress
B) Max principal stress
C) Distortion energy
D) Total strain energy
Ans: C
Detail: Best for ductile metals.
144. For brittle materials, failure is governed by
A) Tresca
B) Von Mises
C) Rankine
D) Coulomb
Ans: C
Detail: Based on max normal stress.
145. In pure shear, max principal stress equals
A) τ
B) 2τ
C) τ/2
D) Zero
Ans: A
Detail: σ₁ = τ.
🔹 Topic: Deflection of Beams
146. Deflection of a beam varies with
A) L²
B) L³
C) L⁴
D) L⁵
Ans: C
Detail: δ ∝ L⁴.
147. A beam becomes stiffer if
A) Length increases
B) Depth increases
C) Load increases
D) Area decreases
Ans: B
Detail: I ∝ d³.
148. Conjugate beam method is used to find
A) BM
B) SF
C) Slope & deflection
D) Stress
Ans: C
Detail: Structural analysis tool.
149. Unit load method is based on
A) Virtual work
B) Strain energy
C) Equilibrium
D) Compatibility
Ans: A
Detail: Work-energy principle.
150. For simply supported beam with central load, max deflection occurs at
A) Quarter span
B) Mid span
C) Support
D) One-third span
Ans: B
Detail: Symmetry.
🔹 Topic: Miscellaneous Advanced
151. Shear centre coincides with centroid in
A) Channel section
B) T-section
C) I-section
D) Angle section
Ans: C
Detail: Due to symmetry.
152. A beam with unsymmetrical section bends about
A) Major axis only
B) Minor axis only
C) Principal axes
D) Neutral axis only
Ans: C
Detail: Product of inertia ≠ 0.
153. Neutral axis does not pass through centroid when
A) Material is homogeneous
B) Bending is pure
C) Section is composite
D) Load is vertical
Ans: C
Detail: Different E values.
154. A bar under axial load and bending experiences
A) Uniform stress
B) Only tensile stress
C) Combined stress
D) Only shear stress
Ans: C
Detail: σ = P/A ± My/I.
155. A beam of constant strength has
A) Constant BM
B) Variable section
C) Constant area
D) Constant depth
Ans: B
Detail: Section varies with BM.
🔹 Final Mixed Hard MCQs
156. The most accurate theory for ductile material under combined loading is
A) Rankine
B) Tresca
C) Von Mises
D) Coulomb
Ans: C
Detail: Distortion energy theory.
157. The weakest column end condition is
A) Hinged–hinged
B) Fixed–hinged
C) Fixed–fixed
D) Fixed–free
Ans: D
Detail: Leff = 2L.
158. A bar subjected to pure bending has
A) Uniform stress
B) Linearly varying stress
C) Constant stress
D) Parabolic stress
Ans: B
Detail: σ ∝ y.
159. Which property is area under elastic portion of stress–strain curve?
A) Toughness
B) Resilience
C) Ductility
D) Hardness
Ans: B
Detail: Energy in elastic range.
160. A structure is statically indeterminate if
A) Equilibrium equations < unknowns
B) Unknowns < equations
C) Unknowns = equations
D) No load
Ans: A
Detail: Needs compatibility equations.
161. Stress concentration factor is theoretical because
A) Ignores plasticity
B) Assumes linear elasticity
C) Assumes uniform load
D) Assumes zero shear
Ans: B
Detail: Based on elastic analysis.
162. The safest design for brittle materials uses
A) Yield stress
B) Ultimate stress
C) Proof stress
D) Endurance limit
Ans: B
Detail: Brittle → fracture governs.
163. The ratio of lateral strain to longitudinal strain is negative because
A) Directions are same
B) Directions are opposite
C) Stress is negative
D) Strain is zero
Ans: B
Detail: Contraction vs extension.
164. A member under plane stress has
A) Three principal stresses
B) Two principal stresses
C) One principal stress
D) No stress
Ans: B
Detail: σz ≈ 0.
165. The condition for maximum bending moment is
A) BM = 0
B) SF = 0
C) Load = 0
D) Stress = 0
Ans: B
Detail: dM/dx = V.
166. A beam of uniform cross-section subjected to pure bending has
A) Constant BM
B) Constant SF
C) Zero BM
D) Zero SF
Ans: A
Detail: Pure bending region.
167. Maximum normal stress in a shaft under torsion is
A) Zero
B) τ
C) 2τ
D) τ/2
Ans: A
Detail: Only shear exists.
168. A beam under transverse load develops
A) Direct stress
B) Shear + bending stress
C) Torsional stress
D) Thermal stress
Ans: B
Detail: Main stresses in beams.
169. The stiffness of a spring is defined as
A) Load × deflection
B) Deflection / load
C) Load / deflection
D) Stress / strain
Ans: C
Detail: k = P/δ.
170. A long column made of brittle material should be designed based on
A) Crushing stress
B) Yield stress
C) Ultimate stress
D) Buckling stress
Ans: D
Detail: Stability governs.
171. The safest theory for design of rotating shafts is
A) Rankine
B) Tresca
C) Von Mises
D) Coulomb
Ans: C
Detail: Combined stress state.
172. A beam of constant depth and variable width is called
A) Uniform beam
B) Non-prismatic beam
C) Composite beam
D) Tapered beam
Ans: B
Detail: Cross-section changes.
173. The strain energy method is used to determine
A) Stress only
B) Deflection
C) BM
D) SF
Ans: B
Detail: Castigliano’s theorem.
174. A shaft is safest in torsion when
A) Solid
B) Hollow
C) Stepped
D) Tapered
Ans: B
Detail: Higher strength-to-weight ratio.
175. A beam with large depth-to-span ratio is likely to fail by
A) Bending
B) Shear
C) Buckling
D) Torsion
Ans: B
Detail: Deep beams → shear failure.
176. The energy stored in a spring of stiffness k and deflection δ is
A) kδ
B) kδ²
C) kδ²/2
D) k/δ
Ans: C
Detail: U = ½kδ².
177. In a composite beam, the neutral axis shifts towards
A) Material with higher E
B) Material with lower E
C) Centroid
D) Shear centre
Ans: A
Detail: Stiffer material attracts more stress.
178. The product of inertia is zero when
A) Section is unsymmetrical
B) One axis is principal
C) Both axes are principal
D) Load is zero
Ans: C
Detail: By definition.
179. The maximum bending stress in a composite beam depends on
A) Area only
B) Modulus ratio
C) Length only
D) Load only
Ans: B
Detail: Transformed section method.
180. A beam of equal strength has
A) Constant I
B) Constant Z
C) Variable Z
D) Constant A
Ans: B
Detail: σ = M/Z = constant.
181. The weakest mode of failure in ductile materials is
A) Tension
B) Shear
C) Compression
D) Bending
Ans: B
Detail: Yield governed by shear.
182. A material having large elongation before fracture is
A) Brittle
B) Ductile
C) Hard
D) Tough
Ans: B
Detail: Ductility measure.
183. The slope of stress–strain curve in elastic range gives
A) Toughness
B) Resilience
C) Modulus of elasticity
D) Hardness
Ans: C
Detail: E = slope.
184. A bar under gradually applied load stores strain energy equal to
A) Pδ
B) Pδ/2
C) 2Pδ
D) δ/P
Ans: B
Detail: Linear loading.
185. A shaft of circular section under pure torsion has
A) Uniform shear stress
B) Linearly varying shear stress
C) Parabolic shear stress
D) Constant shear stress
Ans: B
Detail: τ ∝ r.
186. A long column with pinned ends has effective length
A) L
B) 2L
C) L/2
D) √2L
Ans: A
Detail: Standard Euler case.
187. The maximum shear stress in a beam occurs at
A) Top fibre
B) Bottom fibre
C) Neutral axis
D) Corners
Ans: C
Detail: Rectangular beam.
188. The bending equation is based on
A) Hooke’s law
B) Bernoulli’s theorem
C) Plane sections remain plane
D) All of the above
Ans: D
Detail: Fundamental assumptions.
189. A beam subjected to uniformly varying load has maximum BM at
A) Mid span
B) Where SF = 0
C) Support
D) Quarter span
Ans: B
Detail: General rule.
190. A column will buckle in the plane of
A) Maximum I
B) Minimum I
C) Maximum area
D) Minimum area
Ans: B
Detail: Least radius of gyration.
191. A stress–strain curve with no yield point uses
A) Ultimate stress
B) Proof stress
C) Endurance limit
D) Crushing stress
Ans: B
Detail: Aluminium, brass.
192. A beam with central hinge is called
A) Fixed beam
B) Simply supported beam
C) Continuous beam
D) Overhanging beam
Ans: B
Detail: Hinge = zero BM.
193. The neutral surface in bending is the surface of
A) Zero strain
B) Zero stress
C) Max stress
D) Max strain
Ans: A
Detail: Neutral axis is its line.
194. A shaft designed on strength basis may fail in
A) Rigidity
B) Stability
C) Fatigue
D) All
Ans: C
Detail: Cyclic loading ignored.
195. A beam subjected to torsion only is
A) Shaft
B) Plate
C) Column
D) Slab
Ans: A
Detail: Shafts resist torsion.
196. A cantilever beam has maximum shear force at
A) Free end
B) Fixed end
C) Mid span
D) Quarter span
Ans: B
Detail: Reaction point.
197. A composite bar is analyzed using
A) Equilibrium only
B) Compatibility only
C) Both equilibrium & compatibility
D) Geometry only
Ans: C
Detail: Essential conditions.
198. A beam of rectangular section is replaced by I-section of same area. Strength will
A) Increase
B) Decrease
C) Remain same
D) Become zero
Ans: A
Detail: Higher section modulus.
199. A perfectly plastic material has
A) Infinite E
B) Zero yield stress
C) Constant stress after yield
D) No strain
Ans: C
Detail: Ideal plastic behavior.
200. The most dangerous type of load for a structure is
A) Gradually applied
B) Suddenly applied
C) Impact load
D) Static load
Ans: C
Detail: Causes highest dynamic stress.