### Multiple Choice Questions and Answers(MCQs) on Theory of Structures

01. P = 4π² EI/L² is the equation of Euler’s crippling load if

(A) Both the ends are fixed
(B) Both the ends are hinged
(C) One end is fixed and other end is free
(D) One end is fixed and other end is hinged

02. Pick up the correct statement from the following:

(A) The structural member subjected to compression and whose dimensions are small as compared to its length, is called a stmt
(B) The vertical compression members are generally known as columns or stanchions
(C) Deflection in lateral direction of a long column, is generally known as buckling
(D) All the above

03. For calculating the allowable stress of long columns σ0 = σy/n [1 – a (1/r)²]is the empirical formula, known as

(A) Straight line formula
(B) Parabolic formula
(C) Perry’s formula
(D) Rankine’s formula

04. Maximum principal stress theory for the failure of a material at elastic point, is known

(A) Guest’s or Trecas’ theory
(B) St. Venant’s theory
(C) Rankine’s theory
(D) Von Mises’ theory

05. Pick up the correct statement from the following:

(A) The moment of inertia is calculated about the axis about which bending takes place
(B) If tensile stress is less than axial stress, the section experiences compressive stress
(C) If tensile stress is equal to axial stress, the section experiences compressive stress
(D) All the above

06. A composite beam is composed of two equal strips one of brass and other of steel. If the temperature is raised

(A) Steel experiences tensile force
(B) Brass experiences compressive force
(C) Composite beam gets subjected to a couple
(D) All the above

07. A shaft subjected to a bending moment M and a torque T, experiences

(A) Maximum bending stress = 32M/πd3
(B) Maximum shear stress = 16 T/πd3
(C) Both (a) and (b)
(D) Neither (a) nor (b)

08. A two hinged parabolic arch of span l and rise h carries a load varying from zero at the left end to ω per unit run at the right end. The horizontal thrust is

(A) ωl2/4h
(B) ωl2/8h
(C) ωl2/12h
(D) ωl2/16h

09. The horizontal thrust on the ends of a two hinged semicircular arch of radius ‘R’ carrying

(A) A uniformly distributed load ω per unit run over its right half span, is ⅔ ωR/π
(B) A uniformly distributed load ω per unit run over its entire span is 4/3 ωR/π
(C) A distributed load varying from zero at the left end to ω per unit horizontal run at the right end, is ⅔ ωR/π
(D) All the above

10. Maximum strain theory for the failure of a material at the elastic limit, is known as

(A) Guest’s or Trecas’ theory
(B) St. Venant’s theory
(C) Rankine’s theory
(D) Haig’s theory

11. Slenderness ratio of a long column, is

(A) Area of cross-section divided by radius of gyration
(B) Area of cross-section divided by least radius of gyration
(C) Radius of gyration divided by area of cross-section
(D) Length of column divided by least radius of gyration

12. A close coil helical spring when subjected to a moment M having its axis along the axis of the helix

(A) It is subjected to pure bending
(B) Its mean diameter will decrease
(C) Its number of coils will increase
(D) All the above

13. The ratio of the stresses produced by a suddenly applied load and by a gradually applied load on a bar, is

(A) 1/4
(B) 1/2
(C) 1
(D) 2

14. Maximum shear stress theory for the failure of a material at the elastic limit, is known

(A) Guest’s or Trecas’ theory
(B) St. Venant’s theory
(C) Rankine’s theory
(D) Haig’s theory

15. A cantilever of length ‘L’ is subjected to a bending moment ‘M’ at its free end. If EI is the flexural rigidity of the section, the deflection of the free end, is

(A) ML/EI
(B) ML/2EI
(C) ML2/2EI
(D) ML2/3EI

16. Pick up the correct statement from the following:

(A) For channels, the shear centre does not coincide its centroid
(B) The point of intersection of the bending axis with the cross section of the beam, is called shear centre
(C) For I sections, the shear centre coincides with the centroid of the cross section of the beam
(D) All the above

17. Keeping breadth constant, depth of a cantilever of length ‘l’ of uniform strength loaded with uniformly distributed load ‘w’ varies from zero at the free end and

(A) 2w/σb × l at the fixed end
(B) √(3w/σb × l) at the fixed end
(C) √(2w/σb × l) at the fixed end
(D) 3w/σd × l at the fixed end

18. If a three hinged parabolic arch, (span l, rise h) is carrying a uniformly distributed load w/unit length over the entire span,

(A) Horizontal thrust is wl2/8h
(B) S.F. will be zero throughout
(C) B.M. will be zero throughout
(D) All the above

19. The force in BC of the truss shown in the given figure, is (A) 3.0 t compression
(B) 3.0 t tension
(C) (3√3/2) t tension
(D) (3√3/2) t compression

20. P = π² EI/L² is the equation for Euler’s crippling load if

(A) Both the ends are fixed
(B) Both the ends are hinged
(C) One end is fixed and other end is free
(D) One end is fixed and other end is hinged

21. The degree of indeterminacy of the frame in the given figure, is (A) Zero
(B) 1
(C) 2
(D) 3

22. The forces in the members of simple trusses, may be analysed by

(A) Graphical method
(B) Method of joints
(C) Method of sections
(D) All the above

23. A simply supported beam A carries a point load at its mid span. Another identical beam B carries the same load but uniformly distributed over the entire span. The ratio of the maximum deflections of the beams A and B, will be

(A) 2/3
(B) 3/2
(C) 5/8
(D) 8/5

24. A road of uniform cross-section A and length L is deformed by δ, when subjected to a normal force P. The Young’s Modulus E of the material, is

(A) E = P. δ/A. L
(B) E = A. δ/P. L
(C) E = P. L/A. δ
(D) E = P. A/L. δ

25. In case of a simply supported I-section beam of span L and loaded with a central load W, the length of elasto-plastic zone of the plastic hinge, is

(A) L/2
(B) L/3
(C) L/4
(D) L/5

26. The yield moment of a cross section is defined as the moment that will just produce the yield stress in

(A) The outer most fibre of the section
(B) The inner most fibre of the section
(C) The neutral fibre of the section
(D) The fibre everywhere

27. If Ix and Iy are the moments of inertia of a section about X and Y axes, the polar moment of inertia of the section, is

(A) (IX + IY)/2
(B) (IX – IY)/2
(C) IX + IY
(D) (IX/IY)

28. A simply supported beam carries varying load from zero at one end and w at the other end. If the length of the beam is a, the maximum bending moment will be

(A) wa/27
(B) wa2/27
(C) w2a/√27
(D) wa2/9√3

29. If E, N, K and 1/m are modulus of elasticity, modulus of rigidity. Bulk modulus and Poisson ratio of the material, the following relationship holds good

(A) E = 3K (1 – 2/m)
(B) E = 2N (1 + 1/m)
(C) (3/2)K (1 – 2/m) = N (1 + 1/m)
(D) All the above

30. The forces acting on the bar as shown in the given figure introduce (A) Compressive stress
(B) Tensile stress
(C) Shear stress
(D) None of these

(A) Magnitude
(B) Direction
(C) Point of application
(D) All the above

32. The tangential component of stress on an plane inclined θ° to the direction of the force, may be obtained by multiplying the normal stress by

(A) sin θ
(B) cos θ
(C) tan θ
(D) sin2 θ

33. A body is said to be in equilibrium if

(A) It moves horizontally
(B) It moves vertically
(C) It rotates about its C.G.
(D) None of these

34. Pick up the incorrect statement from the following: The torsional resistance of a shaft is directly proportional to

(A) Modulus of rigidity
(B) Angle of twist
(C) Reciprocal of the length of the shaft
(D) Moment of inertia of the shaft section

35. The forces acting normally on the cross section of a bar shown in the given figure introduce (A) Compressive stress
(B) Tensile stress
(C) Shear stress
(D) None of these

36. The ratio of circumferential stress to the longitudinal stress in the walls of a cylindrical shell, due to flowing liquid, is

(A) ½
(B) 1
(C) 1½
(D) 2

37. The load on a spring per unit deflection, is called

(A) Stiffness
(B) Proof resilience
(C) Proof stress

38. A compound bar consists of two bars of equal length. Steel bar cross-section is 3500 mm2and that of brass bar is 3000 mm2. These are subjected to a compressive load 100,000 N. If Eb = 0.2 MN/mm2 and Eb = 0.1 MN/mm2, the stresses developed are:

(A) σb = 10 N/mm2, σs = 20 N/mm2
(B) σb = 8 N/mm2, σs = 16 N/mm2
(C) σb = 6 N/mm2, σs = 12 N/mm2
(D) σb = 5 N/mm2, σs = 10 N/mm2

39. A close coil helical spring of mean diameter D consists of n coils of diameter d. If it carries an axial load W, the energy stored in the spring, is

(A) 4WD2n/d4N
(B) 4W2Dn/d4N
(C) 4W2D3n/d4N
(D) 4W2D3n2/d4N

40. The degree of indeterminacy of the frame in the given figure, is (A) 1
(B) 2
(C) 3
(D) Zero

41. If normal stresses due to longitudinal and transverse loads on a bar are σ1 and σ2respectively, the normal component of the stress on an inclined plane θ° to the longitudinal load, is

(A) σ1 sin θ × σ2 cos θ
(B) σ1 sin θ2 + σ2 cos2 θ
(C) (σ1 – σ2) sin2θ/2
(D) (σ1 + σ2) sin2θ/2

42. The moment of inertia of a triangular section (height h, base b) about its base, is

(A) bh²/12
(B) b²h/12
(C) bh3/12
(D) b3h/12

43. Shear centre of a half circular section of radius ‘r’ and of constant thickness, lies at a distance of ‘x’ from the centre where ‘x’ is

(A) r/π
(B) 2r/π
(C) 3r/π
(D) 4r/π

44. The assumption in the theory of bending of beams is:

(A) Material is homogeneous
(B) Material is isotropic
(C) Young’s modulus is same in tension as well as in compression
(D) All the above

45. For determining the force in the member AB of the truss shown in the given figure by method of sections, the section is made to pass through AB, AD and ED and the moments are taken about (A) Joint C
(B) Joint B
(C) Joint D
(D) Joint A

46. A concentrated load P is supported by the free end of a quadrantal ring AB whose end B is fixed. The ratio of the vertical to horizontal deflections of the end A, is

(A) π
(B) π/2
(C) π/3
(D) π/4

47. The ratio of crippling loads of a column having both the ends fixed to the column having both the ends hinged, is

(A) 1
(B) 2
(C) 3
(D) 4

48. A load of 1960 N is raised at the end of a steel wire. The minimum diameter of the wire so that stress in the wire does not exceed 100 N/mm2 is:

(A) 4.0 mm
(B) 4.5 mm
(C) 5.0 mm
(D) 5.5 mm

49. The normal and tangential components of stress on an inclined plane through θ° to the direction of the force, will be equal if θ is

(A) 45°
(B) 30°
(C) 60°
(D) 90°