Practice Set For Strength of Materials

 

📘 PRACTICE SET–1

Stress, Strain & Elastic Constants (10 MCQs with detailed answers)

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1. A bar of length 2 m elongates by 1 mm under load. Find the strain.

A) 0.002
B) 0.0005
C) 0.001
D) 0.005

Ans: B

Explanation:

$$\varepsilon = \frac{\Delta L}{L}=\frac{1\text{ mm}}{2000\text{ mm}}=0.0005$$

Strain is dimensionless.

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2. A rod of area 400 mm² carries a load of 80 kN. Stress is

A) 100 MPa
B) 150 MPa
C) 200 MPa
D) 250 MPa

Ans: C

Explanation:

$$\sigma=\frac{P}{A}=\frac{80\times10^3}{400}=200\text{ N/mm}^2=200\text{ MPa}$$

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3. Young’s modulus represents

A) Strength
B) Stiffness
C) Toughness
D) Ductility

Ans: B

Explanation:
Young’s modulus $E=\frac{\text{stress}}{\text{strain}}$.
Higher E → less deformation → stiffer material.

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4. If Poisson’s ratio μ = 0.5, the material is

A) Brittle
B) Plastic
C) Incompressible
D) Perfectly elastic

Ans: C

Explanation:

$$\text{Volumetric strain}=(1-2\mu)\varepsilon$$

If μ = 0.5 → volumetric strain = 0 → no volume change → incompressible.

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5. Hooke’s law is valid up to

A) Elastic limit
B) Yield point
C) Proportional limit
D) Ultimate stress

Ans: C

Explanation:
Hooke’s law: $\sigma \propto \varepsilon$
This linear relation holds only till the proportional limit.

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6. Bulk modulus relates to

A) Linear strain
B) Volumetric strain
C) Shear strain
D) Thermal strain

Ans: B

Explanation:

$$K=\frac{\text{Volumetric stress}}{\text{Volumetric strain}}$$

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7. Working stress is

A) Ultimate stress × FOS
B) Ultimate stress / FOS
C) Yield stress
D) Proof stress

Ans: B

Explanation:
Design is done on safe stress:

$$\sigma_{working}=\frac{\sigma_{ultimate}}{\text{FOS}}$$

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8. Ductile materials fail mainly by

A) Compression
B) Shear
C) Tension
D) Torsion

Ans: C

Explanation:
Ductile materials (steel, aluminium) show large elongation in tension before failure.

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9. Resilience is

A) Total energy till fracture
B) Energy stored in elastic range
C) Plastic energy
D) Impact energy

Ans: B

Explanation:
Resilience = elastic strain energy stored and released on unloading.

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10. Toughness equals area under

A) Elastic part of curve
B) Plastic part
C) Entire stress–strain curve
D) Yield region

Ans: C

Explanation:
Toughness = total energy absorbed before fracture → whole curve.

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📘 PRACTICE SET–2

Axial Load & Thermal Stress (10 MCQs with detailed answers)

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11. Elongation of a bar depends on

A) Load only
B) Length only
C) Area only
D) Load, length, area & E

Ans: D

Explanation:

$$\delta=\frac{PL}{AE}$$

All four parameters affect elongation.

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12. A bar 2 m long, area 400 mm², E = 200 GPa carries 80 kN load. Elongation is

A) 0.5 mm
B) 1 mm
C) 2 mm
D) 4 mm

Ans: B

Explanation:

$$\delta=\frac{80\times10^3\times2000}{400\times200\times10^3}=1\text{ mm}$$

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13. Thermal strain in a bar is

A) αΔT
B) ΔT/α
C) α/ΔT
D) α²ΔT

Ans: A

Explanation:
Basic thermal expansion law:

$$\varepsilon_{th}=\alpha \Delta T$$

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14. Thermal stress develops when

A) Bar is free to expand
B) Expansion is restrained
C) Temperature falls
D) Bar is long

Ans: B

Explanation:
If expansion is free → no stress.
If restrained → stress develops.

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15. A bar fixed at both ends is heated. Stress developed is

A) Tensile
B) Compressive
C) Shear
D) Zero

Ans: B

Explanation:
Heating → tendency to expand → restraint causes compressive stress.

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16. In bars connected in series, which quantity is same?

A) Stress
B) Strain
C) Force
D) Area

Ans: C

Explanation:
Same axial force passes through each bar in series.

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17. In bars connected in parallel, which quantity is same?

A) Stress
B) Strain
C) Force
D) Area

Ans: B

Explanation:
Ends move together → equal elongation → same strain.

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18. Thermal stress in a fully restrained bar is

A) EαΔT
B) αΔT/E
C) ΔT/Eα
D) E/αΔT

Ans: A

Explanation:

$$\sigma=E\alpha\Delta T$$

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19. Thermal stress does NOT depend on

A) E
B) α
C) ΔT
D) Length

Ans: D

Explanation:
From σ = EαΔT → length does not appear.

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20. Strain energy in axially loaded bar is

A) PL/AE
B) P²L/2AE
C) P²L/AE
D) PL/2AE

Ans: B

Explanation:

$$U=\frac{P\delta}{2}=\frac{P}{2}\cdot\frac{PL}{AE}=\frac{P^2L}{2AE}$$

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📘 PRACTICE SET–3

Torsion of Shafts (10 MCQs with detailed answers)

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21. Torsion equation is

A) M/I = σ/y
B) T/J = τ/R = Gθ/L
C) P/A
D) σ = Eε

Ans: B

Explanation:
This is the fundamental torsion relation for circular shafts.

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22. Shear stress in a solid shaft varies

A) Uniformly
B) Linearly with radius
C) Parabolically
D) Randomly

Ans: B

Explanation:

$$\tau=\frac{Tr}{J}\Rightarrow \tau \propto r$$

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23. Maximum shear stress in a solid shaft occurs at

A) Centre
B) Outer surface
C) Mid-radius
D) Neutral axis

Ans: B

Explanation:
Maximum radius → maximum shear stress.

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24. Polar moment of inertia is denoted by

A) I
B) Z
C) J
D) A

Ans: C

Explanation:
$J$ is used in torsion equations.

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25. Torsional rigidity of a shaft is

A) EI
B) EA
C) GJ
D) EJ

Ans: C

Explanation:
Resistance to twisting = GJ.

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26. Power transmitted by a shaft is

A) NT
B) 2πNT/60
C) T/N
D) N/T

Ans: B

Explanation:

$$P=\frac{2\pi NT}{60}$$

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27. A shaft transmits same power at double speed. New torque is

A) Same
B) Double
C) Half
D) Four times

Ans: C

Explanation:

$$P\propto NT \Rightarrow T\propto \frac{1}{N}$$

If N doubles → T halves.

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28. A shaft under pure torsion experiences

A) Normal stress only
B) Shear stress only
C) Both stresses
D) No stress

Ans: B

Explanation:
Torsion produces only shear stress.

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29. Hollow shaft is preferred over solid because

A) Cheaper
B) Less length
C) Higher strength-to-weight ratio
D) Less stress

Ans: C

Explanation:
Material is away from centre → higher polar moment → more torque capacity for same weight.

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30. Failure theory used for ductile shafts is

A) Rankine
B) Tresca
C) Coulomb
D) Mohr

Ans: B

Explanation:
Ductile materials fail by shear → Maximum shear stress theory (Tresca) is used.