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 simply supported beam is subjected to a uniformly distributed load of intensity w per unit length, on half of the span from one end. The length of the spam and the flexural stiffness are denoted as l and El, respectively. The deflection at mid span of the beam is

  1. $\frac{5}{6144} \frac{WI^4}{EI}$
  2. $\frac{5}{768} \frac{WI^4}{EI}$
  3. $\frac{5}{384} \frac{WI^4}{EI}$
  4. $\frac{5}{192} \frac{WI^4}{EI}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For a simply supported beam with UDL on half the span, the deflection at mid-span is calculated using standard beam deflection formulas or superposition.

Multiple choice

Two plates are connected by fillet welds of size 10 mm and subjected o tension, as shown in the sketch. The thickness of each plate is 12 mm. The yield stress and ultimate tensile stress of steel are 250 MPa and 410 MPa, respectively. The welding is done in the workshop ($y_{mw}$= 1.25). As per the Limit State Method of IS 800 : 2007, the minimum length (rounded off to the nearest higher multiple of 5 mm) of each weld to transmit a force P equal to 270 kN is

  1. 100 mm

  2. 105 mm

  3. 110 mm

  4. 115 mm
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

The cross section at mid span of a beam at the edge of a slab is shown in the sketch. A portion of the slab is considered as the effective flange width for the beam. The grades of concrete and reinforcing steel are M25 and Fe 415, respectively. the total area of reinforcing bars (As) is 4000 mm2. At the ultimate limit state, xu denotes the depth of the neutral axis from the top fibre. Treat the section as under reinforced and flanged (xu > 100 mm) The value of xu (in mm) computed as per the Limit State Method of IS 456.2000 is

  1. 200.0

  2. 223.3

  3. 236.3

  4. 273.6
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a flanged beam, the depth of the neutral axis xu is found by equating the compressive force in the flange to the tensile force in the steel. C = 0.36 * fck * bf * xu (assuming xu <= Df). Given As = 4000, fy = 415, fck = 25, T = 0.87 * fy * As = 1442.1 kN. Equating T = C and solving for xu yields 236.3 mm.

Multiple choice

The cross section at mid span of a beam at the edge of a slab is shown in the sketch. A portion of the slab is considered as the effective flange width for the beam. The grades of concrete and reinforcing steel are M25 and Fe 415, respectively. the total area of reinforcing bars (As) is 4000 mm2. At the ultimate limit state, xu denotes the depth of the neutral axis from the top fibre. Treat the section as under reinforced and flanged (xu > 100 mm)

The ultimate moment capacity (in kNm) of the section, as per the Limit State Method of IS 456 : 2000 is:

  1. 475.2

  2. 717.0

  3. 756.4

  4. 762.5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The ultimate moment capacity Mu = 0.87 * fy * As * (d - 0.42 * xu). Using xu = 236.3 mm and effective depth d, calculate the moment. The result matches 717.0 kNm.

Multiple choice

Poisson’s ratio is defined as

  1. $\Big|\frac{\text{axial stress}}{\text{lateral stress}}\Big|$
  2. $\Big|\frac{\text{lateral strain}}{\text{axial strain}}\Big|$
  3. $\Big|\frac{\text{lateral stress}}{\text{axial stress}}\Big|$
  4. $\Big|\frac{\text{axial strain}}{\text{lateral strain}}\Big|$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Poisson's ratio is defined as the negative ratio of lateral strain to axial strain. Since the ratio is typically expressed as a positive value, the absolute value is used.

Multiple choice

Which of the following is categorised as a long-term loss of prestress in a prestressed concrete member?

  1. Loss due to elastic shortening

  2. Loss due to friction

  3. Loss due to relaxation of strands

  4. Loss due to anchorage slip
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Long-term losses in prestressed concrete occur over time due to creep, shrinkage, and steel relaxation. Elastic shortening, friction, and anchorage slip are classified as short-term or immediate losses.

Multiple choice

The cross-section of a thermo-mechanically treated (TMT) reinforcing bar has

  1. soft ferrite-pearlite throughout

  2. hard martensite throughout

  3. a soft ferrite-pearlite core with a hard martensitic rim

  4. a hard martensitic core with a soft pearlite-bainitic rim
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

TMT bars are manufactured through a quenching and tempering process that creates a hard, wear-resistant martensitic outer layer (rim) and a ductile, tough ferrite-pearlite core.

Multiple choice

A 16 mm thick plate measuring 650 mm x 420 mm is used as a base plate for an ISHB 300 column subjected to a factored axial compressive load of 2000 kN. As per IS 456-2000, the minimum grade of concrete that should be used below the base plate for safely carrying the load is

  1. M 15

  2. M 20

  3. M 30

  4. M 40
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

 Plate size and column dimension has nothing to do with minimum grade of concrete, As per IS : 456 - 2000 $$f_{ck} = 20MPa$$

or grade of concrete M-20

Multiple choice

Consider a reinforcing bar embedded in concrete. In a marine environment, this bar undergoes uniform corrosion, which leads to the deposition of corrosion products on its surface and an increase in the apparent volume of the bar. This subjects the surrounding concrete to expansive pressure. As a result, corrosion induced cracks appear at the surface of concrete. Which of the following statements is TRUE?

  1. Corrosion causes circumferential tensile stresses in concrete and the cracks will be parallel to the corroded reinforcing bar.

  2. Corrosion causes radial tensile stresses in concrete and the cracks will be parallel to the corroded reinforcing bar.

  3. Corrosion causes circumferential tensile stresses in concrete and the cracks will be perpendicular to the direction of the corroded reinforcing bar.

  4. Corrosion causes radial tensile stresses in concrete and the cracks will be perpendicular to the direction of the corroded reinforcing bar.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation