Theory Of Structures MCQ

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• The strain energy due to volumetric strain
  ক

  Is directly proportional to the volume

  খ

  Is directly proportional to the square of exerted pressure

  গ

  Is inversely proportional to Bulk modulus

  ঘ

  All the above
• A shaft subjected to a bending moment M and a torque T, experiences
  ক

  Maximum bending stress $$ = \frac{{32{\text{M}}}}{{\pi {{\text{d}}^3}}}$$

  খ

  Maximum shear stress $$ = \frac{{16{\text{T}}}}{{\pi {{\text{d}}^3}}}$$

  গ

  Both A and B

  ঘ

  Neither A nor B
• A shaft rotating N.R.M. under a torque T, transmits a power
  ক

  $$\frac{{{\text{T}}\pi {\text{N}}}}{{30}}$$  Newton metres/sec

  খ

  $$\frac{{{\text{T}}\pi {\text{N}}}}{{30}}$$  Newton metres/min

  গ

  $$\frac{{{\text{T}}\pi {\text{N}}}}{{60}}$$  Newton metres/min

  ঘ

  $$\frac{{{\text{T}}\pi {\text{N}}}}{{60}}$$  Newton metres/sec
• The greatest load which a spring can carry without getting permanently distorted, is called
  ক

  Stiffness

  খ

  Proof resilience

  গ

  Proof stress

  ঘ

  Proof load
• The strain energy stored in a spring when subjected to greatest load without being permanently distorted, is called
  ক

  Stiffness

  খ

  Proof resilience

  গ

  Proof stress

  ঘ

  Proof load
• The area of the core of a column of cross sectional area A, is
  ক

  $$\frac{1}{3}{\text{A}}$$

  খ

  $$\frac{1}{6}{\text{A}}$$

  গ

  $$\frac{1}{{12}}{\text{A}}$$

  ঘ

  $$\frac{1}{{18}}{\text{A}}$$
• The equivalent length of a column of length L having one end fixed and the other end free, is
  ক

  2L

  খ

  L

  গ

  $$\frac{{\text{L}}}{2}$$

  ঘ

  $$\frac{{\text{L}}}{{\sqrt 2 }}$$
• A bar L metre long and having its area of cross-section A, is subjected to a gradually applied tensile load W. The strain energy stored in the bar is
  ক

  $$\frac{{{\text{WL}}}}{{2{\text{AE}}}}$$

  খ

  $$\frac{{{\text{WL}}}}{{{\text{AE}}}}$$

  গ

  $$\frac{{{{\text{W}}^2}{\text{L}}}}{{{\text{AE}}}}$$

  ঘ

  $$\frac{{{{\text{W}}^2}{\text{L}}}}{{2{\text{AE}}}}$$
• In case of a simply supported I-section beam of span L and loaded with a central load W, the length of elasto-plastic zone of the plastic hinge, is
  ক

  $$\frac{{\text{L}}}{2}$$

  খ

  $$\frac{{\text{L}}}{3}$$

  গ

  $$\frac{{\text{L}}}{4}$$

  ঘ

  $$\frac{{\text{L}}}{5}$$
• In case of a simply supported rectangular beam of span L and loaded with a central load W, the length of elasto-plastic zone of the plastic hinge, is
  ক

  $$\frac{{\text{L}}}{2}$$

  খ

  $$\frac{{\text{L}}}{3}$$

  গ

  $$\frac{{\text{L}}}{4}$$

  ঘ

  $$\frac{{\text{L}}}{5}$$
• At any point of a beam, the section modulus may be obtained by dividing the moment of inertia of the section by
  ক

  Depth of the section

  খ

  Depth of the neutral axis

  গ

  Maximum tensile stress at the section

  ঘ

  Maximum compressive stress at the section
• A square column carries a load P at the centroid of one of the quarters of the square. If a is the side of the main square, the combined bending stress will be
  ক

  $$\frac{{\text{P}}}{{{{\text{a}}^2}}}$$

  খ

  $$\frac{{2{\text{P}}}}{{{{\text{a}}^2}}}$$

  গ

  $$\frac{{3{\text{P}}}}{{{{\text{a}}^2}}}$$

  ঘ

  $$\frac{{4{\text{P}}}}{{{{\text{a}}^2}}}$$
• A simply supported beam carries varying load from zero at one end and w at the other end. If the length of the beam is a, the maximum bending moment will be
  ক

  $$\frac{{{\text{wa}}}}{{27}}$$

  খ

  $$\frac{{{\text{w}}{{\text{a}}^2}}}{{27}}$$

  গ

  $$\frac{{{{\text{w}}^2}{\text{a}}}}{{\sqrt {27} }}$$

  ঘ

  $$\frac{{{\text{w}}{{\text{a}}^2}}}{{9\sqrt 3 }}$$
• The locus of the end point of the resultant of the normal and tangential components of the stress on an inclined plane, is
  ক

  Circle

  খ

  Parabola

  গ

  Ellipse

  ঘ

  Straight line
• If Q is load factor, S is shape factor and F is factor of safety in elastic design, the following:
  ক

  Q = S + F

  খ

  Q = S - F

  গ

  Q = F - S

  ঘ

  Q = S × F
• The vertical reaction for the arch is
  ক

  $$\frac{{{\text{Wa}}}}{{2l}}$$

  খ

  $$\frac{{{\text{W}}l}}{{\text{a}}}$$

  গ

  $$\frac{{{\text{Wa}}}}{l}$$

  ঘ

  $$\frac{{{\text{W}}{{\text{a}}^2}}}{{2l}}$$
• For the close coil helical spring of the maximum deflection is
  ক

  $$\frac{{{\text{W}}{{\text{D}}^3}{\text{n}}}}{{{{\text{d}}^4}{\text{N}}}}$$

  খ

  $$\frac{{2{\text{W}}{{\text{D}}^3}{\text{n}}}}{{{{\text{d}}^4}{\text{N}}}}$$

  গ

  $$\frac{{4{{\text{W}}^2}{{\text{D}}^3}{\text{n}}}}{{{{\text{d}}^4}{\text{n}}}}$$

  ঘ

  $$\frac{{8{\text{W}}{{\text{D}}^3}{\text{n}}}}{{{{\text{d}}^4}{\text{n}}}}$$
• Stress may be defined as
  ক

  Force per unit length

  খ

  Force per unit volume

  গ

  Force per unit area

  ঘ

  None of these
• The ratio of circumferential stress to the longitudinal stress in the walls of a cylindrical shell, due to flowing liquid, is
  ক

  $$\frac{1}{2}$$

  খ

  1

  গ

  $$1\frac{1}{2}$$

  ঘ

  2
• The ratio of the stresses produced by a suddenly applied load and by a gradually applied load on a bar, is
  ক

  $$\frac{1}{4}$$

  খ

  $$\frac{1}{2}$$

  গ

  1

  ঘ

  2
• Inertia of a rectangular section of width and depth about an axis passing the moment of through C.G. and parallel to its width is
  ক

  $$\frac{{{\text{B}}{{\text{D}}^2}}}{6}$$

  খ

  $$\frac{{{\text{B}}{{\text{D}}^3}}}{6}$$

  গ

  $$\frac{{{\text{B}}{{\text{D}}^3}}}{{12}}$$

  ঘ

  $$\frac{{{{\text{B}}^2}{\text{D}}}}{6}$$
• The ratio of moments of inertia of a triangular section about its base and about a centroidal axis parallel to its base, is
  ক

  1.0

  খ

  1.5

  গ

  2.0

  ঘ

  3.0
• A close coil helical spring of mean diameter D consists of n coils of diameter d. If it carries an axial load W, the energy stored in the spring, is
  ক

  $$\frac{{4{\text{W}}{{\text{D}}^2}{\text{n}}}}{{{{\text{d}}^4}{\text{N}}}}$$

  খ

  $$\frac{{4{{\text{W}}^2}{\text{Dn}}}}{{{{\text{d}}^4}{\text{N}}}}$$

  গ

  $$\frac{{4{{\text{W}}^2}{{\text{D}}^3}{\text{n}}}}{{{{\text{d}}^4}{\text{N}}}}$$

  ঘ

  $$\frac{{4{{\text{W}}^2}{{\text{D}}^3}{{\text{n}}^2}}}{{{{\text{d}}^4}{\text{N}}}}$$
• A body is said to be in equilibrium if
  ক

  It moves horizontally

  খ

  It moves vertically

  গ

  It rotates about its C.G.

  ঘ

  None of these
• Maximum strain theory for the failure of a material at the elastic limit, is known as
  ক

  Guest's or Trecas' theory

  খ

  St. Venant's theory

  গ

  Rankine's theory

  ঘ

  Haig's theory
• The stiffness of the close coil helical spring is
  ক

  $$\frac{{{{\text{d}}^4}{\text{N}}}}{{8{{\text{D}}^3}{\text{n}}}}$$

  খ

  $$\frac{{{{\text{d}}^4}{\text{N}}}}{{4{{\text{D}}^3}{\text{n}}}}$$

  গ

  $$\frac{{4{{\text{D}}^3}{\text{N}}}}{{{{\text{d}}^4}{\text{n}}}}$$

  ঘ

  $$\frac{{8{{\text{D}}^3}{\text{N}}}}{{{{\text{d}}^4}{\text{n}}}}$$
• A simply supported uniform rectangular bar breadth b, depth d and length L carries an isolated load W at its mid-span. The same bar experiences an extension e under same tensile load. The ratio of the maximum deflection to the elongation, is
  ক

  $$\frac{{\text{L}}}{{\text{d}}}$$

  খ

  $$\frac{{\text{L}}}{{2{\text{d}}}}$$

  গ

  $${\left( {\frac{{\text{L}}}{{2{\text{d}}}}} \right)^2}$$

  ঘ

  $${\left( {\frac{{\text{L}}}{{3{\text{d}}}}} \right)^2}$$
• A simply supported beam which carries a uniformly distributed load has two equal overhangs. To have maximum B.M. produced in the beam least possible, the ratio of the length of the overhang to the total length of the beam, is
  ক

  0.207

  খ

  0.307

  গ

  0.407

  ঘ

  0.508
• In plastic analysis, the shape factor for a triangular section, is
  ক

  1.5

  খ

  1.34

  গ

  2.34

  ঘ

  2.5
• In plastic analysis, the shape factor for rectangular section, is
  ক

  1.4

  খ

  1.5

  গ

  1.6

  ঘ

  1.7