Physics

Solid Mechanics

510 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

Consider two RCC beams P and Q, each having the section 400 mm x 750 mm (effective depth, d = 750 mm) made with concrete having a $\tau_{c max}$= 2.1 N/mm2. For the reinforcement provided and the grade of concrete used, it may be assumed that the $\tau_c$= 0.75 N/mm2. The design shear in beam P is 400 kN and in beam Q is 750 kN. Considering the provisions of IS 456 — 2000, which of the following statements is TRUE?

  1. Shear reinforcement should be designed for 175 kN for beam P and the section for beam Q should be revised.

  2. Nominal shear reinforcement is required for beam P and the shear reinforcement should be designed for 120 kN for beam Q.

  3. Shear reinforcement should be designed for 175 kN for beam P and the shear reinforcement should be designed for 525 kN for beam Q.

  4. The sections for both beams P and Q need to be revised.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

 

Multiple choice

The adjoining figure shows a schematic representation of a steel plate girder to be used as a simply supported beam with a concentrated load. For stiffeners PQ (running along the beam axis) and RS (running between the top and bottom flanges), which of the following pairs of statements will be TRUE?

  1. (i) RS should be provided under the concentrated load only. (ii) PQ should be placed in the tension side of the flange.

  2. (i) RS helps to prevent local buckling of the web. (ii) PQ should be placed in the compression side of the flange.

  3. (i) RS should be provided at supports. (ii) PQ should be placed along the neutral axis.

  4. (i) RS should be provided away from points of action of concentrated loads. (ii) PQ should be provided on the compression side of the flange.

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

 

Multiple choice

Consider a bar of diameter ‘D’ embedded in a large concrete block as shown in the adjoining figure, with a pull out force P being applied. Let $\sigma_b$ and $\sigma_{st}$ be the bond strength (between the bar and concrete) and the tensile strength of the bar respectively. If the block is held in position and it is assumed that the material of the block does not fail, which of the following options represents the maximum value of P?
  1. Maximum of $\Big(\frac{\pi}{4}D^2\sigma_b\Big) and (\pi DL \sigma_{st})$
  2. Maximum of $\Big(\frac{\pi}{4}D^2\sigma_{st}\Big) and (\pi DL \sigma_b)$
  3. Minimum of $\Big(\frac{\pi}{4}D^2\sigma_{st}\Big) and (\pi DL \sigma_b)$
  4. Minimum of $\Big(\frac{\pi}{4}D^2\sigma_b\Big) and (\pi DL \sigma_{st})$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

 

Multiple choice

Directions: A rigid beam is hinged at one end and supported on linear elastic springs (both having a stiffness of ‘k’) at points ‘1’ and ‘2’, and an inclined load acts at ‘2’, as shown.

Which of the following options represents the deflections $\delta_1$ and $\delta_2$ at points ‘1’ and ‘2’?
  1. $\delta_1 = \frac{2}{5} \Big(\frac{2P}{k}\Big) and \delta_2 \frac{4}{5}\Big(\frac{2P}{k}\Big)$
  2. $\delta_1 = \frac{2}{5} \Big(\frac{P}{k}\Big) and \delta_2 \frac{4}{5}\Big(\frac{P}{k}\Big)$
  3. $\delta_1 = \frac{2}{5} \Big(\frac{P}{\sqrt{2}k}\Big) and \delta_2 \frac{4}{5}\Big(\frac{P}{\sqrt{2}k}\Big)$
  4. $\delta_1 = \frac{2}{5} \Big(\frac{\sqrt{2}P}{k}\Big) and \delta_2 \frac{4}{5}\Big(\frac{\sqrt{2}P}{k}\Big)$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

 

Multiple choice

Which of the following types of stress-strain relationships best describes the behaviour of brittle materials, such as ceramics and thermosetting plastics? ($\sigma$ = stress and $\epsilon$ = strain)

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

We know that brittle materials do not show elongation when external load is applied on them and they get altered by certain amount of load and thus, get cracked from unexpected points. The amount of ultimate load and point of fracture cannot be predetermined and elongation is also very, very less. These properties are best described by option (4).

Multiple choice

As per India standard code of practice for pre stressed concrete (IS:1343 –1980) the minimum grades of concrete to be used for post-tensioned and pre-tensioned structural elements are respectively

  1. M20 for both

  2. M40 and M30

  3. M15 and M20

  4. M30 and M40
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

 As per code minimum grade concrete used for post-tension is M-30 and pre-tension is M-40. Reason for this is that in pre-tension losses are more than post-tension and a high strength concrete required for pre-stress so that it can safely bear the high local stress.

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).