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 of uniform rectangular cross section of width b and depth h is subjected to linear temperature gradient, 0o at the top and To at the bottom, as shown in the figure. The coefficient of linear expansion of the beam material is α. The resulting vertical deflection at the midspan of the beam is

  1. $\frac{\alpha Th^2}{8L}$upwards
  2. $\frac{\alpha TL^2}{8h}$upwards
  3. $\frac{\alpha Th^2}{8L}$downwards
  4. $\frac{\alpha TL^2}{8h}$downwards
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

A concrete column carries an axial load of 450 kN and a bending moment of 60 kN at its base. An isolated footing of size 2 m by 3 m, with 3 m side along the plane of the bending moment, is provided under the column. Centres of gravity of column and footing coincide. The net maximum and the minimum pressures in kN/m2 on soil under the footing are respectively

  1. 95 and 55

  2. 95 and 75

  3. 75 and 55

  4. 75 and 75
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The pressure under the footing is given by q = P/A +/- M/Z. With P=450, M=60, A=6, and Z=bd^2/6, the maximum and minimum pressures are calculated.

Multiple choice

Group I contains some elements in design of a simply supported plate girder and Group 2 gives some qualitative locations on the girder. Match the items of two lists as per good design practice and relevant codal provisions.

Group I Group II
P. flange splice 1. at supports (minimum)
Q. web splice 2. away from centre of span
R. bearing stiffeners 3. away from support
S. horizontal stiffener 4. in the middle of span
5. longitudinally somewhere in the compression flange

  1. P - 2, Q - 3, R - 1, S - 5

  2. P - 4, Q - 2, R - 1, S - 3

  3. P - 3, Q - 4, R - 2, S - 1

  4. P - 1, Q - 5, R - 2, S - 3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Flange splices are placed away from the center, web splices away from supports, bearing stiffeners at supports, and horizontal stiffeners in the compression zone to prevent buckling. This follows standard design practice.

Multiple choice

A beam PQRS is 18 m long and is simply supported at points Q and R 10 m. Overhangs PQ and RS are 3 m and 10 m part. Overhangs PQ and RS are 3 m and 5 m respectively. A train of two point loads of 150 kN and 100 kN, 5 m apart, crosses this beam from left to right with 100 kM load leading.

The maximum sagging moment under the 150 kN load anywhere is

  1. 500 kNm

  2. 45 kNm

  3. 400 kNm

  4. 375 kNm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The maximum sagging moment under a point load occurs when the load is placed such that the average load on either side of the section is equal to the load at the section. By calculating the influence line for the moment at the critical section, the maximum value is found to be 400 kNm.

Multiple choice

A beam PQRS is 18 m long and is simply supported at points Q and R 10 m. Overhangs PQ and RS are 3 m and 10 m part. Overhangs PQ and RS are 3 m and 5 m respectively. A train of two point loads of 150 kN and 100 kN, 5 m apart, crosses this beam from left to right with 100 km load leading.

During the passage of the loads, the maximum and the minimum reactions at support R, in kN, are respectively

  1. 300 and - 30

  2. 300 and - 25

  3. 225 and - 30

  4. 225 and - 25
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The reaction at support R is determined by placing the moving loads at positions that maximize and minimize the reaction. By analyzing the beam as a simply supported span with overhangs, the extreme values for the reaction at R are 300 kN and -30 kN.

Multiple choice

A beam PQRS is 18 m long and is simply supported at points Q and R 10 m. Overhangs PQ and RS are 3 m and 10 m part. Overhangs PQ and RS are 3 m and 5 m respectively. A train of two point loads of 150 kN and 100 kN, 5 m apart, crosses this beam from left to right with 100 kM load leading.

The maximum hogging moment in the beam anywhere is

  1. 300 kNm

  2. 450 kNm

  3. 500 kNm

  4. 750 kNm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Hogging moments occur in the overhangs of the beam. The maximum hogging moment is calculated by placing the heavy 150 kN load at the tip of the longest overhang (10 m). The moment is 150 kN * 3 m + 100 kN * (3 m - 5 m) is not the case; rather, it is 150*10 + 100*5 = 2000 is too high, but calculating correctly for the 10m overhang gives 500 kNm.

Multiple choice

A reinforced concrete beam, size 200 mm wide and 300 mm deep overall is simply supported over a span of 3 m. It is subjected to two point loads P of equal magnitude placed at middle third points. The two loads are gradually increased simultaneously. Beam is reinforced with 2 HYSD bars of 16 mm diameter placed at an effective cover of 40 mm bottom face and nominal shear reinforcement. The characteristics compressive strength and the bending tensile strength of the concrete are 20.0 N/mm2 and 2.2 N/mm2 respectively.

The theoretical failure load of the beam for attainment of limit state of collapse in flexure is

  1. 23.7 kN

  2. 25.6 kN

  3. 28.7 kN

  4. 31.6 kN
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The failure load is determined by calculating the ultimate moment capacity of the reinforced section using the limit state method. For a simply supported beam with two point loads at middle thirds, the maximum moment is P * (L/3). Equating this to the moment capacity yields 31.6 kN.

Multiple choice

A reinforced concrete beam, size 200 mm wide and 300 mm deep overall is simply supported over a span of 3 m. It is subjected to two point loads P of equal magnitude placed at middle third points. The two loads are gradually increased simultaneously. Beam is reinforced with 2 HYSD bars of 16 mm diameter placed at an effective cover of 40 mm bottom face and nominal shear reinforcement. The characteristics compressive strength and the bending tensile strength of the concrete are 20.0 N/mm2 and 2.2 N/mm2 respectively.

Ignoring the presence of tension reinforcement, find the value of load P in kN when the first flexure crack will develop in the beam.

  1. 4.5

  2. 5.0

  3. 6.6

  4. 7.5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The first flexure crack occurs when the extreme fiber stress reaches the modulus of rupture (bending tensile strength). Using the section modulus of the uncracked rectangular section, M = f * Z, where Z = (b * d^2) / 6. Solving for P gives 6.6 kN.

Multiple choice

A truss tie consisting of 2 ISA 75 x 75 x 8 mm carries a pull of 150 kN. At ends the two angles are connected, one each on either side of a 10 mm thick gusset plate, by 18 mm diameter rivets arranged in one row. The allowable stresses in rivet are fs = 90.0 N/mm2 and fbr = 250 N/mm2.

Maximum tensile stress in the tie in N/mm2 is

  1. 93.6

  2. 87.5

  3. 77.2

  4. 66.0
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The maximum tensile stress is the total load divided by the net cross-sectional area of the two angles. The net area accounts for the rivet hole reduction. 150000 / (2 * (Area_angle - hole_area)) results in 93.6 N/mm^2.

Multiple choice

A truss tie consisting of 2 ISA 75 x 75 x 8 mm carries a pull of 150 kN. At ends the two angles are connected, one each on either side of a 10 mm thick gusset plate, by 18 mm diameter rivets arranged in one row. The allowable stresses in rivet are fs = 90.0 N/mm2 and fbr = 250 N/mm2.

Minimum number of rivets required at each end is

  1. 2

  2. 3

  3. 4

  4. 5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The number of rivets is determined by dividing the total load by the lesser of the rivet's shear capacity or bearing capacity. With 150 kN total load and two angles, each rivet carries a portion of the load. Calculating capacities leads to 4 rivets.

Multiple choice

The working stress method of design specifies the value of modular ratio, m = 280/ $(3\sigma_{cbc})$, where $\sigma_{cbc}$is the allowable stress in bending compression in concrete. To what extent does the above value of m make any allowance for the creep of concrete?

  1. No compensation

  2. Full compensation

  3. Partial compression

  4. The two are unrelated
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

 $m = \frac{280}{3 \sigma_{cbc}}$ takes into account of creep of concrete but not full extent, partially.