SSC JE Exam - elasticity constants determinate and indeterminate beams bending moment shear force diagrams Online Test (MCQ Quiz)

1. Which of the following is a measure of a material's resistance to elastic deformation under tensile or compressive stress?

A) Shear Modulus B) Bulk Modulus C) Young's Modulus D) Poisson's Ratio

2. What does the Shear Modulus (G) represent?

A) Resistance to change in volume B) Resistance to elastic deformation under shear stress C) Resistance to elastic deformation under tensile stress D) Ratio of lateral strain to axial strain

3. Poisson's Ratio (ν) is defined as the ratio of:

A) Axial strain to lateral strain B) Lateral strain to axial strain C) Tensile stress to tensile strain D) Shear stress to shear strain

4. For a linearly elastic, isotropic, and homogeneous material, which relationship between elasticity constants is generally true?

A) E = 2G(1 + ν) B) E = G(1 + ν) C) E = 2G(1 - ν) D) E = G / (1 + ν)

5. If a beam is subjected to bending, the stress distribution across its depth is:

A) Uniform B) Linear, varying from zero at the neutral axis to a maximum at the extreme fibers C) Parabolic D) Constant at the neutral axis

6. The point in a beam's cross-section where the bending stress is zero is called the:

A) Centroidal axis B) Neutral axis C) Shear center D) Axis of symmetry

7. In a simply supported beam with a concentrated load at the center, the shear force diagram is:

A) A parabola B) A rectangle C) Triangular, changing linearly from a maximum at the supports to zero at the center D) Constant, equal to half the load

8. For a cantilever beam with a uniformly distributed load (UDL) over its entire length, the bending moment diagram is:

A) A straight line B) A parabola C) A cubic curve D) Zero at the free end and maximum at the fixed end

9. The relationship between the bending moment (M), the Young's Modulus (E), and the moment of inertia (I) of a beam is given by:

A) M = EI / R B) EI = M / R C) EI = M * R D) M = EI * R

10. The bending moment is maximum where the shear force is:

A) Maximum B) Minimum C) Zero or changes sign D) Constant

11. A beam that cannot be analyzed by static equilibrium equations alone is termed:

A) Statically determinate B) Statically indeterminate C) Structurally stable D) Load-bearing

12. For a statically indeterminate beam, additional equations are required, which are derived from:

A) Shear force relationships B) Bending moment relationships C) Deformation compatibility or equilibrium D) Material properties alone

13. The degree of indeterminacy of a propped cantilever beam (fixed at one end, simply supported at the other) is:

A) Zero B) One C) Two D) Three

14. In a propped cantilever beam with a UDL, the bending moment at the fixed support is:

A) Zero B) Equal to the bending moment at the prop C) Greater than the bending moment at the prop D) Less than the bending moment at the prop

15. The shear force diagram for a beam under pure bending (no shear) would be:

A) A parabola B) A straight line C) Zero throughout D) A rectangle

16. The deflection of a beam is directly proportional to the cube of its length when subjected to a uniformly distributed load. This statement is:

A) Always true B) True for cantilever beams but not simply supported C) True for simply supported beams but not cantilever D) Generally false, as it depends on the load and support conditions

17. Which of the following elasticity constants is most relevant for analyzing the behavior of a structure under torsion?

A) Young's Modulus B) Bulk Modulus C) Shear Modulus D) Poisson's Ratio

18. The Bulk Modulus (K) is a measure of a material's resistance to:

A) Shear deformation B) Tensile deformation C) Compressive deformation D) Volumetric deformation under hydrostatic pressure

19. For a beam with a rectangular cross-section of width 'b' and depth 'd', the moment of inertia (I) about the neutral axis is:

A) bd³/12 B) b³d/12 C) bd³/3 D) b³d/3

20. In a bending moment diagram, a point of contraflexure occurs where:

A) The bending moment is maximum B) The shear force is zero C) The bending moment changes sign (from positive to negative or vice versa) D) The beam deflects significantly

21. A beam is considered statically indeterminate if the number of unknown reaction components exceeds the number of available equilibrium equations.

A) True B) False C) Depends on the loading D) Only if it's a continuous beam

22. The moment of inertia (I) of a beam's cross-section is a measure of its:

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

23. For a continuous beam, the analysis typically requires:

A) Only static equilibrium equations B) Only deformation compatibility equations C) Both static equilibrium and deformation compatibility equations D) Shear force and bending moment diagrams only

24. The maximum shear stress in a circular cross-section beam subjected to shear occurs at:

A) The extreme fibers B) The neutral axis C) The centroid D) The circumference

25. Which theorem is often used to analyze indeterminate structures by considering the potential energy stored in the structure?

A) Castigliano's Theorem B) Maxwell's Reciprocal Theorem C) Clapeyron's Theorem of Three Moments D) Betti's Law

26. A beam with Young's Modulus E = 200 GPa and Moment of Inertia I = 10⁻⁵ m⁴ has a bending moment of 50 kNm. What is the radius of curvature?

A) 100 m B) 200 m C) 400 m D) 500 m

27. The shear force at a section of a beam is equal to the rate of change of bending moment with respect to distance along the beam. This statement is:

A) True B) False C) True only for UDL D) True only for point loads

28. The bending moment diagram for a simply supported beam with a uniformly distributed load is a:

A) Straight line B) Parabola with maximum at the center C) Parabola with zero at the center D) Cubic curve

29. For a fixed-fixed beam with a central point load, the maximum bending moment occurs:

A) At the center only B) At the supports only C) At the center and at the supports D) Somewhere between the center and the supports

30. The area under the shear force diagram between two sections of a beam represents the:

A) Shear force at the sections B) Bending moment at the second section minus the bending moment at the first section C) Deflection between the sections D) Slope of the elastic curve

31. Which of the following is NOT an elasticity constant?

A) Young's Modulus B) Shear Modulus C) Poisson's Ratio D) Modulus of Rupture

32. The relationship E = 3K(1 - 2ν) connects:

A) Young's Modulus, Shear Modulus, and Poisson's Ratio B) Young's Modulus, Bulk Modulus, and Poisson's Ratio C) Shear Modulus, Bulk Modulus, and Poisson's Ratio D) Young's Modulus, Shear Modulus, and Bulk Modulus

33. In the context of bending of beams, the term 'elastic curve' refers to:

A) The stress distribution across the cross-section B) The deformed shape of the beam under load C) The neutral axis of the beam D) The shear force diagram

34. A beam is considered statically determinate if its reactions and internal forces can be determined solely from the equations of static equilibrium.

A) True B) False C) Only for symmetrical loads D) Only for simple beams

35. For a beam with a triangular cross-section loaded such that the neutral axis passes through the centroid, the maximum shear stress occurs at:

A) The top vertex B) The base C) The centroid D) The extreme fibers

36. The superposition principle can be applied to analyze the deflection of beams when:

A) The material is non-linear B) The loads are applied sequentially and the structure returns to its original position C) The beam is statically indeterminate D) The deflections are very large

37. In a bending moment diagram, a constant value over a section indicates:

A) Zero shear force B) Uniformly distributed load C) Pure bending D) A point of contraflexure

38. The degree of indeterminacy of a continuous beam with 'n' supports is typically:

A) n B) n-1 C) n-2 D) n+1

39. Which of the following statements about shear force and bending moment is correct?

A) Shear force is always maximum where bending moment is maximum B) Bending moment is always maximum where shear force is zero C) Shear force is the derivative of bending moment with respect to length D) Bending moment is the derivative of shear force with respect to length

40. The moment of inertia of a circular cross-section of radius 'r' about its diameter is:

A) πr⁴/4 B) πr⁴/2 C) πd⁴/64 D) πd³/12

41. For a material where E = 200 GPa and G = 80 GPa, what is the approximate value of Poisson's Ratio?

A) 0.20 B) 0.25 C) 0.30 D) 0.35

42. The bending stress (σ) in a beam is given by the formula:

A) σ = M / (EI) B) σ = My / I C) σ = VQ / It D) σ = P / A

43. A beam fixed at both ends with a central point load is an example of a:

A) Statically determinate beam B) Statically indeterminate beam C) Simply supported beam D) Overhanging beam

44. The maximum deflection of a simply supported beam of length L with a central point load P is given by:

A) PL³ / (48EI) B) PL³ / (3EI) C) PL³ / (384EI) D) 5wL⁴ / (384EI)

45. The shear stress (τ) in a beam is generally calculated using the formula:

A) τ = M / (EI) B) τ = My / I C) τ = VQ / It D) τ = P / A

46. For a beam made of a material with a high Young's Modulus, for the same load and geometry, the deflection will be:

A) Higher B) Lower C) The same D) Unpredictable

47. The moment of inertia of a cross-section is crucial in bending calculations because it relates the applied moment to the resulting curvature and stress.

A) True B) False C) Only for indeterminate beams D) Only for determinate beams

48. In drawing shear force and bending moment diagrams, the convention for positive shear force is typically:

A) Clockwise rotation of the right segment B) Counter-clockwise rotation of the right segment C) Upward force on the left face of a segment D) Downward force on the left face of a segment

elasticity constants determinate and indeterminate beams bending moment shear force diagrams - Online Test

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