21. 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 A. $$\frac{{\text{P}}}{{{{\text{a}}^2}}}$$ B. $$\frac{{2{\text{P}}}}{{{{\text{a}}^2}}}$$ C. $$\frac{{3{\text{P}}}}{{{{\text{a}}^2}}}$$ D. $$\frac{{4{\text{P}}}}{{{{\text{a}}^2}}}$$

$$ rac{{ ext{P}}}{{{{ ext{a}}^2}}}$$
$$ rac{{2{ ext{P}}}}{{{{ ext{a}}^2}}}$$
$$ rac{{3{ ext{P}}}}{{{{ ext{a}}^2}}}$$
$$ rac{{4{ ext{P}}}}{{{{ ext{a}}^2}}}$$

Detailed SolutionA 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 A. $$\frac{{\text{P}}}{{{{\text{a}}^2}}}$$ B. $$\frac{{2{\text{P}}}}{{{{\text{a}}^2}}}$$ C. $$\frac{{3{\text{P}}}}{{{{\text{a}}^2}}}$$ D. $$\frac{{4{\text{P}}}}{{{{\text{a}}^2}}}$$

24. Pick up the correct statement from the following: A. For a uniformly distributed load, the shear force varies linearly B. For a uniformly distributed load, B.M. curve is a parabola C. For a load varying linearly, the shear force curve is a parabola D. All the above

For a uniformly distributed load, the shear force varies linearly
For a uniformly distributed load, B.M. curve is a parabola
For a load varying linearly, the shear force curve is a parabola
All the above

Detailed SolutionPick up the correct statement from the following: A. For a uniformly distributed load, the shear force varies linearly B. For a uniformly distributed load, B.M. curve is a parabola C. For a load varying linearly, the shear force curve is a parabola D. All the above

25. The vertical reaction for the arch is A. $$\frac{{{\text{Wa}}}}{{2l}}$$ B. $$\frac{{{\text{W}}l}}{{\text{a}}}$$ C. $$\frac{{{\text{Wa}}}}{l}$$ D. $$\frac{{{\text{W}}{{\text{a}}^2}}}{{2l}}$$

$$ rac{{{ ext{Wa}}}}{{2l}}$$
$$ rac{{{ ext{W}}l}}{{ ext{a}}}$$
$$ rac{{{ ext{Wa}}}}{l}$$
$$ rac{{{ ext{W}}{{ ext{a}}^2}}}{{2l}}$$

Detailed SolutionThe vertical reaction for the arch is A. $$\frac{{{\text{Wa}}}}{{2l}}$$ B. $$\frac{{{\text{W}}l}}{{\text{a}}}$$ C. $$\frac{{{\text{Wa}}}}{l}$$ D. $$\frac{{{\text{W}}{{\text{a}}^2}}}{{2l}}$$

26. For the close coil helical spring of the maximum deflection is A. $$\frac{{{\text{W}}{{\text{D}}^3}{\text{n}}}}{{{{\text{d}}^4}{\text{N}}}}$$ B. $$\frac{{2{\text{W}}{{\text{D}}^3}{\text{n}}}}{{{{\text{d}}^4}{\text{N}}}}$$ C. $$\frac{{4{{\text{W}}^2}{{\text{D}}^3}{\text{n}}}}{{{{\text{d}}^4}{\text{n}}}}$$ D. $$\frac{{8{\text{W}}{{\text{D}}^3}{\text{n}}}}{{{{\text{d}}^4}{\text{n}}}}$$

$$ rac{{{ ext{W}}{{ ext{D}}^3}{ ext{n}}}}{{{{ ext{d}}^4}{ ext{N}}}}$$
$$ rac{{2{ ext{W}}{{ ext{D}}^3}{ ext{n}}}}{{{{ ext{d}}^4}{ ext{N}}}}$$
$$ rac{{4{{ ext{W}}^2}{{ ext{D}}^3}{ ext{n}}}}{{{{ ext{d}}^4}{ ext{n}}}}$$
$$ rac{{8{ ext{W}}{{ ext{D}}^3}{ ext{n}}}}{{{{ ext{d}}^4}{ ext{n}}}}$$

Detailed SolutionFor the close coil helical spring of the maximum deflection is A. $$\frac{{{\text{W}}{{\text{D}}^3}{\text{n}}}}{{{{\text{d}}^4}{\text{N}}}}$$ B. $$\frac{{2{\text{W}}{{\text{D}}^3}{\text{n}}}}{{{{\text{d}}^4}{\text{N}}}}$$ C. $$\frac{{4{{\text{W}}^2}{{\text{D}}^3}{\text{n}}}}{{{{\text{d}}^4}{\text{n}}}}$$ D. $$\frac{{8{\text{W}}{{\text{D}}^3}{\text{n}}}}{{{{\text{d}}^4}{\text{n}}}}$$

30. 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 A. $$\frac{{{\text{B}}{{\text{D}}^2}}}{6}$$ B. $$\frac{{{\text{B}}{{\text{D}}^3}}}{6}$$ C. $$\frac{{{\text{B}}{{\text{D}}^3}}}{{12}}$$ D. $$\frac{{{{\text{B}}^2}{\text{D}}}}{6}$$

$$ rac{{{ ext{B}}{{ ext{D}}^2}}}{6}$$
$$ rac{{{ ext{B}}{{ ext{D}}^3}}}{6}$$
$$ rac{{{ ext{B}}{{ ext{D}}^3}}}{{12}}$$
$$ rac{{{{ ext{B}}^2}{ ext{D}}}}{6}$$

Detailed SolutionInertia of a rectangular section of width and depth about an axis passing the moment of through C.G. and parallel to its width is A. $$\frac{{{\text{B}}{{\text{D}}^2}}}{6}$$ B. $$\frac{{{\text{B}}{{\text{D}}^3}}}{6}$$ C. $$\frac{{{\text{B}}{{\text{D}}^3}}}{{12}}$$ D. $$\frac{{{{\text{B}}^2}{\text{D}}}}{6}$$