Physics

Solid Mechanics

537 Questions

Solid mechanics questions evaluate the understanding of stress, strain, and material deformation under various loads. Topics include analyzing beams, cantilevers, and structural steel designs using specific industrial standards. These principles are strictly examined in engineering and civil services preliminary tests.

Stress and strainBeam analysisPrestressed concreteMaterial strengthStructural design

Solid Mechanics Questions

Multiple choice

A solid circular shaft of diameter d and length L is fixed at one end and free at the other end. A torque T is applied at the free end. The shear modulus of the material is G. The angle of twist at three free ends is
  1. $\frac{16TL}{\pi d^4 G}$
  2. $\frac{32TL}{\pi d^4 G}$
  3. $\frac{64TL}{\pi d^4 G}$
  4. $\frac{128TL}{\pi d^4 G}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The angle of twist for a circular shaft is given by the formula theta = TL / (GJ), where J is the polar moment of inertia. For a solid circular shaft, J = (pi * d^4) / 32. Substituting J gives theta = TL / (G * pi * d^4 / 32) = 32TL / (pi * d^4 * G).

Multiple choice

A double cover butt riveted joint is used to connect two flat plates of 200 mm width and 14 mm thickness as shown in the figure. There are twelve power driven rivets of 20 mm diameter at a pitch of 50 mm in both directions on either side of the plate. Two cover plates of 10 mm thickness are used. The capacity of the joint in tension considering bearing and shear ONLY, with permissible bearing and shear stresses as 300 MPa respectively is

  1. 1083.6 kN

  2. 871.32 kN

  3. 541.18 kN

  4. 433.7 kN
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

 

Multiple choice

Consider the following statements in the context of cement concrete pavements. I. Warping stresses in cement concrete pavements are caused by the seasonal variation in temperature. II. Tie bars are generally provided across transverse joints of cement concrete pavements. The correct option evaluating the above statements is

  1. I: True II: False

  2. I: False II: True

  3. I: True II: True

  4. I: False II: False
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Warping stresses are caused by temperature gradients between the top and bottom of the slab, not seasonal variation. Tie bars are used in longitudinal joints to prevent lateral spreading, while dowel bars are used in transverse joints to transfer load.

Multiple choice

Direction: A doubly reinforced rectangular concrete beam has a width of 300 mm and an effective depth of 500 mm. The beam is reinforced with 2200 mm2 of steel in tension and 628 mm2 of steel in compression. The effective cover for compression steel is 50 mm. Assume that both tension and compression steel yield. The grades of concrete and steel used are M20 and Fe250 respectively. The stress lock parameters (rounded off to first two decimal places) for concrete shall be as per IS 456:200.

The moment of resistance of the section is

  1. 206.00 kN-m

  2. 209.20 kN-m

  3. 236.80 kN-m

  4. 251.90 kN-m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

 

Multiple choice

Direction: A doubly reinforced rectangular concrete beam has a width of 300 mm and an effective depth of 500 mm. The beam is reinforced with 2200 mm2 of steel in tension and 628 mm2 of steel in compression. The effective cover for compression steel is 50 mm. Assume that both tension and compression steel yield. The grades of concrete and steel used are M20 and Fe250 respectively. The stress lock parameters (rounded off to first two decimal places) for concrete shall be as per IS 456:200.

The depth of neutral axis is

  1. 205.30 mm

  2. 184.56 mm

  3. 160.91 mm

  4. 145.30 mm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

 

Multiple choice

Directions: Carry One Mark Each.

For the given fluctuating fatigue load, the values of stress amplitude and stress ratio respectively are

  1. 100 MPa and 5

  2. 250 MPa and 5

  3. 100 MPa and 0.20

  4. 250 MPa and 0.20
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\text{For given fluctuating load, stress amplitude is}\\ =\frac{\sigma_{max}-\sigma_{man}}{2}=\frac{250-50}{2}=\frac{200}{2}=100MPa\\ \text {and stress ratio is}\\ =\frac{\sigma_{max}}{\sigma_{min}}=\frac{250}{50}=5$