🧠 SSC JE – Strength of Materials

Exam-Level Practice (50 MCQs with Detailed Answers)

1) Stress–Strain & Elastic Constants

1. A steel rod of area 400 mm² carries 80 kN. Stress is
A) 100 MPa B) 150 MPa C) 200 MPa D) 250 MPa
Ans: C
Why: $\sigma=P/A=80{,}000/400=200$ N/mm² = 200 MPa.

2. A bar elongates 1 mm over 2 m. Strain is
A) 0.002 B) 0.001 C) 0.0005 D) 0.005
Ans: C
Why: $\varepsilon=\Delta L/L=1/2000=0.0005$ .

3. If μ = 0.5, material is
A) Brittle B) Plastic C) Incompressible D) Rigid
Ans: C
Why: Volumetric strain $(1-2\mu)\varepsilon=0$ .

4. Hooke’s law is valid up to
A) Elastic limit B) Yield point C) Proportional limit D) Ultimate stress
Ans: C
Why: Linear stress–strain relation holds till proportional limit.

5. Working stress equals
A) $\sigma_u\times$ FOS B) $\sigma_u/$ FOS C) $\sigma_y$ D) Proof stress
Ans: B
Why: Design on safe stress.

2) Axial Load & Thermal Stress

6. Elongation of a bar depends on
A) P only B) L only C) A only D) P, L, A, E
Ans: D
Why: $\delta=PL/AE$ .

7. A bar fixed at both ends is heated. Stress developed is
A) Tensile B) Compressive C) Shear D) Zero
Ans: B
Why: Expansion restrained → compressive stress.

8. Thermal stress does not depend on
A) E B) α C) ΔT D) Length
Ans: D
Why: $\sigma=E\alpha\Delta T$ .

9. Bars in series have same
A) Stress B) Strain C) Force D) Area
Ans: C
Why: Same axial force passes.

10. Bars in parallel have same
A) Stress B) Strain C) Force D) Area
Ans: B
Why: Equal elongation → equal strain.

3) Torsion of Shafts

11. Torsion equation is
A) $M/I=\sigma/y$
B) $T/J=\tau/R=G\theta/L$
C) $P/A$
D) $\sigma=E\varepsilon$
Ans: B

12. Max shear stress in solid shaft occurs at
A) Centre B) Outer surface C) Mid-radius D) NA
Ans: B
Why: $\tau\propto r$ .

13. Hollow shaft is preferred because
A) Cheaper B) Less weight
C) Higher strength/weight D) Less stress
Ans: C
Why: Higher polar moment for same weight.

14. Power transmitted by shaft is
A) $NT$ B) $2\pi NT/60$ C) $T/N$ D) $N/T$
Ans: B

15. Same power at double speed → new torque
A) Same B) Double C) Half D) Four times
Ans: C
Why: $T\propto1/N$ .

4) Bending of Beams

16. Neutral axis of homogeneous beam passes through
A) Top fibre B) Bottom fibre C) Centroid D) Shear centre
Ans: C

17. Flexure formula is
A) $\sigma=M/I$ B) $\sigma=My/I$ C) $\sigma=Iy/M$ D) $\sigma=M/y$
Ans: B

18. Max bending stress occurs at
A) NA B) Farthest fibre C) Centroid D) Support
Ans: B

19. Section modulus $Z$ equals
A) $I/y_{max}$ B) $I\,y_{max}$ C) $A/y$ D) $y/I$
Ans: A

20. In cantilever beam, max BM occurs at
A) Free end B) Fixed end C) Mid-span D) Quarter span
Ans: B

5) Shear Stress in Beams

21. Average shear stress
A) $V/A$ B) $VQ/It$ C) $M/I$ D) $T/J$
Ans: A

22. Max shear stress in rectangular beam
A) $\tau_{avg}$ B) $1.5\tau_{avg}$ C) $2\tau_{avg}$ D) $0.5\tau_{avg}$
Ans: B

23. Shear stress is zero at
A) NA B) Outer surface C) Centre D) Supports
Ans: B

24. In I-section, max shear stress occurs at
A) Flange B) Web at NA C) Top fibre D) Bottom fibre
Ans: B

25. Shear stress distribution in rectangular beam is
A) Uniform B) Linear C) Parabolic D) Triangular
Ans: C

6) Columns & Buckling

26. Column failure mainly by
A) Crushing B) Buckling C) Shear D) Torsion
Ans: B

27. Slenderness ratio
A) $L/A$ B) $L/k$ C) $A/L$ D) $I/A$
Ans: B

28. Euler formula valid for
A) Short B) Intermediate C) Long D) All
Ans: C

29. Column with both ends fixed → effective length
A) $L$ B) $2L$ C) $L/2$ D) $\sqrt2L$
Ans: C

30. Buckling load varies as
A) $L$ B) $L^2$ C) $1/L$ D) $1/L^2$
Ans: D

7) Strain Energy & Impact

31. Strain energy in bar under axial load
A) $PL/AE$
B) $P^2L/2AE$
C) $P^2L/AE$
D) $PL/2AE$
Ans: B
Why: $U=P\delta/2$ .

32. Suddenly applied load causes max stress equal to
A) Static B) Half static C) Double static D) Zero
Ans: C

33. Impact loading produces
A) Lower stress B) Same stress C) Higher stress D) Zero stress
Ans: C

34. Proof resilience is
A) Total strain energy
B) Elastic strain energy per unit volume
C) Plastic energy
D) Impact energy
Ans: B

35. Toughness equals area under
A) Elastic part B) Plastic part C) Entire curve D) Yield region
Ans: C

8) Fatigue, Stress Concentration & Theories

36. Fatigue failure occurs due to
A) Static load B) Repeated load C) Impact load D) Thermal load
Ans: B

37. Endurance limit means
A) Max stress B) Safe cyclic stress C) Yield stress D) Ultimate stress
Ans: B

38. Stress concentration occurs due to
A) Uniform section B) Sudden change in section
C) Smooth surface D) Long length
Ans: B

39. Stress concentration factor
A) $\sigma_{max}/\sigma_{nom}$
B) $\sigma_{nom}/\sigma_{max}$
C) Stress/strain D) Load/area
Ans: A

40. Fillets are provided to
A) Increase stress B) Reduce stress concentration
C) Reduce weight D) Increase length
Ans: B

41. Tresca theory is based on
A) Max principal stress B) Max shear stress
C) Distortion energy D) Total strain energy
Ans: B

42. Von Mises theory is based on
A) Max shear stress B) Max principal stress
C) Distortion energy D) Total strain energy
Ans: C

43. Rankine theory is best for
A) Ductile materials B) Brittle materials
C) Rubber D) Plastics
Ans: B

44. In biaxial stress, max shear stress is
A) $(\sigma_1+\sigma_2)/2$
B) $(\sigma_1-\sigma_2)/2$
C) $\sigma_1$
D) $\sigma_2$
Ans: B

45. Principal stresses act on planes where
A) Normal stress is zero
B) Shear stress is zero
C) Bending stress is zero
D) Load is zero
Ans: B

9) Deflection & Misc.

46. Beam deflection varies with
A) $L^2$ B) $L^3$ C) $L^4$ D) $L^5$
Ans: C

47. Max deflection in SSB with central load occurs at
A) Quarter span B) Mid span C) Support D) One-third span
Ans: B

48. Unit load method is used to find
A) Stress B) BM C) Deflection D) Torque
Ans: C

49. Shear centre is the point where load causes
A) Bending only
B) No twisting
C) Shear only
D) Torsion only
Ans: B

50. Safest design theory for ductile materials under combined loading is
A) Rankine B) Tresca C) Von Mises D) Coulomb
Ans: C

5. Strength of Materials MCQs With Detailed Answers