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

A reinforced concrete beam of rectangular cross section of breadth 230 mm and effective depth 400 mm is subjected to maximum factored shear force of 120kN. The grades of concrete, main steel and stirrup steel are M20, Fe415 and Feb250 respectively. For the area of main steel provided, the design shear strength $ \tau_c $ is per IS: 456-2000 is 0.48 N/mm2. The beam is designed for collapse limit state.

The spacing (mm) of 2-legged 8mm stirrups to be provided is

  1. 40

  2. 115.323

  3. 250

  4. 400
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

 

Multiple choice

A reinforced concrete beam of rectangular cross section of breadth 230 mm and effective depth 400 mm is subjected to maximum factored shear force of 120 kN. The grades of concrete, main steel and stirrup steel are M20, Fe415 and Feb250 respectively. For the area of main steel provided, the design shear strength $ \tau_c $ is per IS: 456-2000 is 0.48 N/mm2. The beam is designed for collapse limit state.

In addition, the beam is subjected to a torque whose factored value is 10.90 kNm. the stirrups have to be provided to carry a shear (kN) equal to

  1. 50.42

  2. 130.56

  3. 151.67

  4. 200.23
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

 

Multiple choice

Rivet value is defined as

  1. lesser of the bearing strength of rivet and the shearing strength of the rivet

  2. lesser of the bearing strength of rivet and the tearing strength of thinner plate

  3. greater of the bearing strength of rivet and the shearing strength of the rivet

  4. lesser of the shearing strength of the rivet and the tearing strength of thinner plate
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

 Rivet value should confine to rivet only and should be lesser of bearing strength of rivet and shearing strength of the rivet.

Multiple choice

In a plate girder, the web plate is connected to the flange plates by fillet welding. The size of the fillet welds, is designed to safety resist

  1. the bending stresses in the flanges

  2. the vertical shear force at the section

  3. the horizontal shear force between the flanges and the web plate

  4. the forces causing buckling in the web
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

 When there is change in the width of section, shear stress increases abruptly and shear strength is less for fillet. Hence, size of fillet weld should be designed to resist horizontal shear force between the flanges and the web plate.

Multiple choice

In the context of flexible pavement design, the ratio of contact pressure to tyre pressure is called the Rigidity Factor. This factor is less than unity when the tyre pressure is

  1. less than 0.56 N/mm2

  2. equal to 0.56 N/mm2

  3. equal to 0.7 N/mm2

  4. more than 0.7 M/mm2
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The rigidity factor is the ratio of contact pressure to tyre pressure. It is less than unity when the tyre pressure is high (typically > 0.7 N/mm^2) because the contact area is smaller than the theoretical area.

Multiple choice

A homogeneous simply supported prismatic beam of width B, depth D and span L is subjected to a concentrated load of magnitude P. The load can be placed anywhere along the span of the beam. The maximum flexural stress developed in beam is

  1. $\frac{2}{3} \frac{PL}{BD^2}$
  2. $\frac{3}{4} \frac{PL}{BD^2}$
  3. $\frac{4}{3} \frac{PL}{BD^2}$
  4. $\frac{3}{2} \frac{PL}{BD^2}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For a simply supported beam with a central point load P, the maximum bending moment is M = PL/4. The maximum flexural stress is sigma = M*y/I = (PL/4) * (D/2) / (B*D^3/12) = (PL*D/8) * (12/B*D^3) = 1.5 * PL / (B*D^2).

Multiple choice

A three-hinged parabolic arch ABC has a span of 20 m and a central rise of 4 m. The arch has hinges at the ends at the centre. A train of two point loads of 20 kN and 10 kN, 5 m apart, crosses this arch from left to right, with 20 kN load leading. The maximum thrust induced at the supports is

  1. 25.00 kN

  2. 28.13 kN

  3. 31.25 kN

  4. 32.81 kN
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a three-hinged arch, the horizontal thrust H = sum(P*x*(L-x)) / (L*h). With loads 20 kN and 10 kN at specific positions, the maximum thrust is calculated by placing the loads to maximize the influence line for H. The calculated value is 31.25 kN.

Multiple choice

In a two dimensional stress analysis, the state of stress at a point is shown below. If s = 120 MPa and t = 70 MPa, then sx and sy are respectively

  1. 26.7 MPa and 172.5 MPa

  2. 54 MPa and 128 MPa

  3. 67.5 MPa and 213.3 MPa

  4. 16 MPa and 138 MPa
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using Mohr's circle, the center is at (sx + sy)/2 and the radius is sqrt(((sx - sy)/2)^2 + t^2). Given the state of stress and the provided values, the principal stresses can be calculated, or the equations for stress transformation can be applied to solve for sx and sy.