SSC JE – Strength of Materials

Full Mock Test: 100 MCQs with Solutions

🔹 PART–A: Stress, Strain & Elastic Constants

1. A bar of area 500 mm² carries 100 kN. Stress is
A) 100 MPa B) 150 MPa C) 200 MPa D) 250 MPa
Ans: C
Sol: $\sigma=P/A=100000/500=200$ N/mm² = 200 MPa.

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

3. Young’s modulus measures
A) Strength B) Stiffness C) Toughness D) Ductility
Ans: B
Sol: Higher E → less deformation.

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

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

6. Working stress equals
A) $\sigma_u\times$ FOS
B) $\sigma_u/$ FOS
C) $\sigma_y$
D) Proof stress
Ans: B

7. Bulk modulus relates to
A) Linear strain B) Volumetric strain C) Shear strain D) Thermal strain
Ans: B

8. Ductile materials mainly fail by
A) Compression B) Shear C) Tension D) Torsion
Ans: C

9. Resilience is
A) Total energy to fracture
B) Elastic energy stored
C) Plastic energy
D) Impact energy
Ans: B

10. Toughness equals area under
A) Elastic part
B) Plastic part
C) Entire stress–strain curve
D) Yield region
Ans: C

🔹 PART–B: Axial Load & Thermal Stress

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

12. A bar (L=2 m, A=400 mm², E=200 GPa) carries 80 kN. Elongation =
A) 0.5 mm B) 1 mm C) 2 mm D) 4 mm
Ans: B
Sol: $\delta=\frac{80\times10^3\times2000}{400\times200\times10^3}=1$ mm.

13. Thermal strain is
A) αΔT B) ΔT/α C) α/ΔT D) α²ΔT
Ans: A

14. Thermal stress develops when
A) Bar is free
B) Expansion is restrained
C) Temperature falls
D) Bar is long
Ans: B

15. A bar fixed at both ends is heated. Stress is
A) Tensile B) Compressive C) Shear D) Zero
Ans: B

16. In bars in series, same quantity is
A) Stress B) Strain C) Force D) Area
Ans: C

17. In bars in parallel, same quantity is
A) Stress B) Strain C) Force D) Area
Ans: B

18. Thermal stress does NOT depend on
A) E B) α C) ΔT D) Length
Ans: D

19. Composite bars require
A) Equilibrium only
B) Compatibility only
C) Both equilibrium & compatibility
D) Geometry only
Ans: C

20. Strain energy in axially loaded bar is
A) $PL/AE$
B) $P^2L/2AE$
C) $P^2L/AE$
D) $PL/2AE$
Ans: B

🔹 PART–C: Torsion of Shafts

21. 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

22. Max shear stress in solid shaft at
A) Centre B) Outer surface C) Mid-radius D) NA
Ans: B

23. Hollow shaft preferred because
A) Cheaper
B) Less weight
C) Higher strength/weight
D) Less stress
Ans: C

24. Polar moment of inertia is
A) I B) Z C) J D) A
Ans: C

25. Torsional rigidity =
A) EI B) EA C) GJ D) EJ
Ans: C

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

27. Same power at double speed → new torque
A) Same B) Double C) Half D) Four times
Ans: C

28. Shaft under pure torsion has
A) Normal stress only
B) Shear stress only
C) Both
D) No stress
Ans: B

29. Failure theory for ductile shaft
A) Rankine B) Tresca C) Coulomb D) Mohr
Ans: B

30. Shear stress in shaft varies
A) Uniform
B) Linearly with radius
C) Parabolic
D) Random
Ans: B

🔹 PART–D: Bending of Beams

31. Neutral axis passes through
A) Top fibre B) Bottom fibre C) Centroid D) Shear centre
Ans: C

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

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

34. Section modulus
A) $I/y_{max}$ B) $Iy_{max}$ C) $A/y$ D) $y/I$
Ans: A

35. Stronger beam section has
A) Larger area
B) Larger Z
C) Larger length
D) Larger weight
Ans: B

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

37. In SSB with UDL, max BM at
A) Supports B) Mid-span C) Quarter span D) One-third span
Ans: B

38. Point of contraflexure where
A) BM = 0 B) SF = 0 C) Stress = 0 D) Deflection = 0
Ans: A

39. In pure bending, shear force is
A) Zero B) Max C) Constant D) Negative
Ans: A

40. Condition for max BM
A) BM = 0 B) SF = 0 C) Load = 0 D) Stress = 0
Ans: B

🔹 PART–E: Shear Stress in Beams

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

42. 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

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

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

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

🔹 PART–F: Columns & Buckling

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

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

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

49. Effective length of fixed–fixed column
A) $L$ B) $2L$ C) $L/2$ D) $\sqrt2L$
Ans: C

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

🔹 PART–G: Strain Energy & Impact

51. Strain energy in bar
A) $PL/AE$
B) $P^2L/2AE$
C) $P^2L/AE$
D) $PL/2AE$
Ans: B

52. Suddenly applied load → max stress
A) Static B) Half static C) Double static D) Zero
Ans: C

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

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

55. Toughness equals
A) Elastic energy
B) Plastic energy
C) Total energy to fracture
D) Impact energy
Ans: C

🔹 PART–H: Fatigue, Stress Concentration & Theories

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

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

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

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

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

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

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

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

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

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

🔹 PART–I: Deflection & Misc.

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

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

68. Unit load method finds
A) Stress B) BM C) Deflection D) Torque
Ans: C

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

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

🔹 PART–J: Rapid-Fire SSC JE Facts (71–100)

Hardness = resistance to → Scratching
Ductility measured by → % elongation
Cast iron best in → Compression
Steel is → Ductile
Proof stress used when → Yield point not clear
NA shifts when → Section unsymmetrical
Beam under transverse load → Shear + bending stress
Weakest column end condition → Fixed–free
Column buckles in plane of → Minimum I
Radius of gyration → √(I/A)
Euler load ∝ → 1/L²
Rankine formula combines → Crushing + buckling
Strain energy method finds → Deflection
Most dangerous load → Impact load
Fatigue dangerous because → No warning before failure
Stress concentration highest at → Sharp corner
Tresca conservative because → Lower safe stress
Von Mises best for → Ductile materials
Rankine best for → Brittle materials
Shear stress in shaft at centre → Zero
Pure bending → Only BM acts
Condition for max BM → SF = 0
Slenderness ratio → L/k
Spring energy → ½kδ²
Perfectly plastic material → Constant stress after yield
Beam of equal strength → Constant Z
Safest shaft in torsion → Hollow
Deflection reduces when → EI increases
Plane stress occurs in → Thin plates
Plane strain occurs in → Long dams

SSC JE – Strength of Materials Full Mock Test: 100 MCQs with Solutions