Theory of Structures

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

1. ½
2. 1
3. 1½
4. 2

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22. If ∑H and ∑V are the algebraic sums of the forces resolved horizontally and vertically respectively, and ∑M is the algebraic sum of the moments of forces about any point, for the equilibrium of the body acted upon

1. ∑H = 0
2. ∑V = 0
3. ∑M = 0
4. All the above

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23. 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

1. π
2. π/2
3. π/3
4. π/4

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24. If 'D' and 'd' are external and internal diameters of a circular shaft respectively, its polar moment of inertia, is

1. π/2 (D⁴ - d⁴)
2. π/4 (D⁴ - d⁴)
3. π/64 (D⁴ - d⁴)
4. π/32 (D⁴ - d⁴)

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25. The moment of inertia of a circular section about any diameter D, is

1. πD²/64
2. πD⁴/32
3. πD³/64
4. πD⁴/64

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26. A steel plate d × b is sandwiched rigidly between two timber joists each D × B/2 in section. The moment os resistence of the beam for the same maximum permissible stress 'σ' in timber and steel will be (where Young's modulus of steel is m times that of the timber).

1. σ [(BD² + mbd²)/6D]
2. σ [(BD³ + mbd³)/6D]
3. σ [(BD² + mbd³)/4D]
4. σ [(BD² + mbd²)/4D]

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27. If normal stresses due to longitudinal and transverse loads on a bar σ₁ and σ₂respectively, the normal component of the stress on an inclined planeσ° to the

1. σ₁ sin θ x σ₂ θ
2. σ₁ sin θ² + σ₂ θ cos² θ
3. (σ₁ - σ₂) sin2θ/2
4. (σ₁ + σ₂) sin2θ/2

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28. If the normal stress due to longitudinal and transverse loads on a bar are σ₁ and σ₂ respectively, the tangential component of the stress on an inclinced plane through θ°, the longitudinal load is

1. σ₁ sinθ + σ₂ cosθ
2. σ₁ sin²θ + σ₂ cos²θ
3. (σ₁ - σ₂) sin 2θ/2
4. (σ₁ + σ₂) sin 2θ/2

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29. A_b and A_c are the cross sections of bronze and copper bars of equal lengt σ_b, σ_c are their respective stresses due to load P. If P_b and P^c are the loads shared by them, (where E_b and E_c are their modulii).

1. σ_b//σ_c = E_b /E_c
2. P = P_b + P_c
3. P = A_b σ_b + A_c σ_b
4. All the above

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30. 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 E_b = 0.2 MN/mm² and E_b = 0.1 MN/mm², the stresses developed are:

1. σ_b = 10 N/mm² σ_s = 20 N/mm²
2. σ_b = 8 N/mm² σ_s = 16 N/mm²
3. σ_b = 6 N/mm² σ_s = 12 N/mm²
4. σ_b = 5 N/mm² σ_s = 10 N/mm²

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