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Structural Mechanics and Strength of Materials

Covers fundamental concepts in structural analysis including shear forces, bending moments, stress and strain, column buckling, truss analysis, influence lines, and material properties. Essential topics for civil and mechanical engineering students.

21 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

Consider a simply supported beam with a uniformly distributed load having a neutral axis (NA) as shown. For points P (on the neutral axis) and Q (at the bottom of the beam) the state of stress is best represented by which of the following pairs?

  4. Data insufficient or All of the above
Question 2 Multiple Choice (Single Answer)

The value of W that results in the collapse of the beam shown in the adjoining figure and having a plastic moment capacity of Mp is

  1. (4/21) Mp
  2. (3/10) Mp
  3. (7/21) Mp
  4. (13/21) Mp
Question 3 Multiple Choice (Single Answer)

For the cantilever bracket PQRS, loaded as shown in the adjoining figure (PQ = RS = L, and, QR = 2L), which of the following statements is FALSE?

  1. The portion RS has a constant twisting moment with a value of 2WL.
  2. The portion QR has a varying twisting moment with a maximum value of WL.
  3. The portion PQ has a varying bending moment with a maximum value of WL.
  4. The portion PQ has no twisting moment.
Question 4 Multiple Choice (Single Answer)

The major and minor principal stresses at a point are 3 MPa and -3 MPa respectively. The maximum shear stress at the point is

  1. zero
  2. 3 MPa
  3. 6 MPa
  4. 9 MPa
Question 5 Multiple Choice (Single Answer)

For the truss shown in the figure, the force in the member QR is

  1. zero
  2. $\frac{P}{\sqrt{2}}$
  3. P
  4. $\sqrt{2}P$
Question 6 Multiple Choice (Single Answer)

The number of independent elastic constants for a linear elastic isotropic and homogeneous material is

  1. 4
  2. 3
  3. 2
  4. 1
Question 7 Multiple Choice (Single Answer)

The effective length of a column of length L fixed against rotation and translation at one end and free at the other end is

  1. 0.5 L
  2. 0.7 L
  3. 1.414 L
  4. 2 L
Question 8 Multiple Choice (Single Answer)

Two people weighing W each are sitting on a plank of length L floating on water at $\frac{L}{4}$ from either end. Neglecting the weight of the plank, the bending moment at the centre of the plank is

  1. $\frac{WL}{8}$
  2. $\frac{WL}{16}$
  3. $\frac{WL}{32}$
  4. zero
Question 9 Multiple Choice (Single Answer)

An axially loaded bar is subjected to a normal stress of 173 MPa. The shear stress in the bar is

  1. 75 MPa
  2. 86.5 MPa
  3. 100 MPa
  4. 122.3 MPa
Question 10 Multiple Choice (Single Answer)

A steel column, pinned at both ends, has a buckling load of 200 kN. If the column is restrained against lateral movement at its mid-height, its buckling load will be

  1. 200 kN
  2. 283 kN
  3. 400 kN
  4. 800 kN
Question 11 Multiple Choice (Single Answer)

For an isotropic material, the relationship between the Young’s modulus (E), shear modulus (G) and Poisson’s ratio ($\mu$) is given by

  1. $G = \frac{E}{2(1 + \mu)}$
  2. $E = \frac{G}{2(1 + \mu)}$
  3. $G = \frac{E}{(1 +2 \mu)}$
  4. $G = \frac{E}{2(1 - \mu)}$
Question 12 Multiple Choice (Single Answer)

The stiffness coefficient kij indicates

  1. force at i due to a unit deformation at j
  2. deformation at j due to a unit force at i
  3. deformation at i due to a unit force at j
  4. force at j due to a unit deformation at i
Question 13 Multiple Choice (Single Answer)

The Young's modulus of a wire of of length L and radius r is Y Nm2. If the length is reduced to L/2, and radius r/2, its Young's modulus will be

  1. Y/2
  2. Y
  3. 2Y
  4. 4Y
Question 14 Multiple Choice (Single Answer)

A thin-walled cylindrical pressure vessel having a radius of 0.5 m and wall thickness of 25 mm is subjected to an internal pressure of 700 kPa. The hoop stress developed is

  1. 14 MPa
  2. 1.4 MPa
  3. 0.14 MPa
  4. 0.014 Mpa
Question 15 Multiple Choice (Single Answer)

The point within the cross-sectional plane of a beam through which the resultant of the external loading on the beam has to pass through to ensure pure bending without twisting of the cross-section of the beam is called

  1. moment centre
  2. centroid
  3. shear centre
  4. elastic centre
Question 16 Multiple Choice (Single Answer)

T-section of a beam is formed by gluing wooden planks as shown in the figure below. If this beam transmits a constant vertical shear force of 3000 K, the glue at any of the four joints will be subjected to a shear force (in kN per meter length) of

  1. 3.0
  2. 4.0
  3. 8.0
  4. 10.7
Question 17 Multiple Choice (Single Answer)

For the section shown below, second moment of the area about an axis d/4 distance above the bottom of the area is

  1. $\frac{bd^2}{48}$
  2. $\frac{bd^3}{12}$
  3. $\frac{7bd^3}{48}$
  4. $\frac{bd^3}{3}$
Question 18 Multiple Choice (Single Answer)

If a beam of rectangular cross-section is subjected to a vertical shear force V, the shear force carried by the upper one-third of the cross-section is

  1. zero
  2. $\frac{7V}{27}$
  3. $\frac{8V}{27}$
  4. $\frac{V}{3}$
Question 19 Multiple Choice (Single Answer)

Vertical reaction developed at B in the frame be-low due to the applied load of 100 kN (with 150, 000mm2 crosssectional area and 3.125 x 109 mm4 moment of inertia for both members) is

  1. 5.9 kN
  2. 302 kN
  3. 66.3 kN
  4. 94.1 kN
Question 20 Multiple Choice (Single Answer)

Carry-over factor CAB for the beam shown in the figure below is

  1. $\frac{1}{4}$
  2. $\frac{1}{2}$
  3. $\frac{3}{4}$
  4. 1
Question 21 Multiple Choice (Single Answer)

Consider the beam ABCD and the influence line as shown below. The inflience the pertains to

  1. reaction at A, RA
  2. shear force at B, VB
  3. shear force on the left of C, $V_c^-$
  4. shear force on the right of C, $V_c^+$
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