Chapter-9
Torsion
S K Mondal’s
IES-23.
A shaft is subjected to simultaneous action of a torque T, bending moment M and an axial thrust F. Which one of the following statements is correct for this situation? [IES-2004] (a) One extreme end of the vertical diametral fibre is subjected to maximum compressive stress only (b) The opposite extreme end of the vertical diametral fibre is subjected to tensile/compressive stress only (c) Every point on the surface of the shaft is subjected to maximum shear stress only (d) Axial longitudinal fibre of the shaft is subjected to compressive stress only IES-23. Ans. (a) IES-24. For obtaining the maximum shear stress induced in the shaft shown in the given figure, the torque should be equal to
(b) Wl + T
(a) T
1
2 2 ⎡ 2 ⎛ wL ⎞ ⎤ (c) ⎢(Wl ) + ⎜ ⎟ ⎥ ⎝ 2 ⎠ ⎦⎥ ⎣⎢ 1
2 ⎡⎧ ⎤2 wL2 ⎫ 2 ⎥ + (d) ⎢ ⎨Wl + T ⎬ 2 ⎭ ⎢⎣ ⎩ ⎥⎦
[IES-1999]
IES-24. Ans. (d) Bending Moment, M = Wl + IES-25.
wL 2
Bending moment M and torque is applied on a solid circular shaft. If the maximum bending stress equals to maximum shear stress developed, them M is equal to: [IES-1992]
(a)
T 2
IES-25. Ans. (a) σ = IES-26.
2
(b) T
(c) 2T
(d) 4T
32 × M 16T and τ = π d3 π d3
A circular shaft is subjected to the combined action of bending, twisting and direct axial loading. The maximum bending stress σ, maximum shearing force
3σ and a uniform axial stress σ(compressive) are produced. The maximum compressive normal stress produced in the shaft will be: (a) 3 σ (b) 2 σ (c) σ IES-26. Ans. (a) Maximum normal stress = bending stress σ + axial stress (σ) = 2 σ We have to take maximum bending stress σ is (compressive)
σb
[IES-1998] (d) Zero
2
⎛σ ⎞ The maximum compressive normal stress = − ⎜ b ⎟ + τ xy2 2 ⎝ 2 ⎠ 2
−2σ ⎛ −2σ ⎞ = − ⎜ ⎟ + 2 ⎝ 2 ⎠ IES-27.
( 3σ ) = −3σ 2
Which one of the following statements is correct? Shafts used in heavy duty speed reducers are generally subjected [IES-2004] Page 289 ofto: 429 (a) Bending stress only