When a series of wheel loads crosses a simply supported girder, the maximum bending moment under any given wheel load occurs when

The maximum bending moment due to a train of wheel loads on a simply supported girder

A

Always occurs at centre of span

B

Always occurs under a wheel load

C

Never occurs under a wheel load

D

None of the above

When a uniformly distributed load, longer than the span of the girder, moves from left to right, then the maximum bending moment at mid section of span occurs when the uniformly distributed load occupies

A

Less than the left half span

B

Whole of left half span

C

More than the left half span

D

Whole span

The natural frequency of free transverse vibrations due to uniformly distributed load acting over a simply supported shaft is (where $$\delta {\text{S}}$$ = Static deflection of simply supported shaft due to uniformly distributed load)

A

$$\frac{{0.4985}}{{\sqrt {\delta {\text{S}}} }}$$

B

$$\frac{{0.5615}}{{\sqrt {\delta {\text{S}}} }}$$

C

$$\frac{{0.571}}{{\sqrt {\delta {\text{S}}} }}$$

D

$$\frac{{0.6253}}{{\sqrt {\delta {\text{S}}} }}$$

The natural frequency of free transverse vibrations due to a point load acting over a simply supported shaft is equal to (where $$\delta $$ = Static deflection of a simply supported shaft due to the point load)

A

$$\frac{{0.4985}}{{\sqrt \delta }}$$

B

$$\frac{{0.5615}}{{\sqrt \delta }}$$

C

$$\frac{{0.571}}{{\sqrt \delta }}$$

D

$$\frac{{0.6253}}{{\sqrt \delta }}$$

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

A

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

B

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

C

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

D

$$\frac{{{\text{w}}{{\text{a}}^2}}}{{9\sqrt 3 }}$$

The maximum bending moment of a simply supported beam of span $$l$$ and carrying a point load W at the center of beam, is

A

$$\frac{{{\text{W}}l}}{4}$$

B

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

C

$${\text{W}}l$$

D

$$\frac{{{\text{W}}{l^2}}}{4}$$

When a uniformly distributed load, shorter than the span of the girder, moves from left to right, then the conditions for maximum bending moment at a section is that

A

The head of the load reaches the section

B

The tail of the load reaches the section

C

The load position should be such that the section divides it equally on both sides

D

The load position should be such that the section divides the load in the same ratio as it divides the span

If W is total load per unit area on a panel, D is the diameter of the column head, L is the span in two directions, then the sum of the maximum positive bending moment and average of the negative bending moment for the design of the span of a square flat slab, should not be less than

A

$$\frac{{{\text{WL}}}}{{12}}{\left( {{\text{L}} - \frac{{2{\text{D}}}}{3}} \right)^2}$$

B

$$\frac{{{\text{WL}}}}{{10}}{\left( {{\text{L}} + \frac{{2{\text{D}}}}{3}} \right)^2}$$

C

$$\frac{{{\text{WL}}}}{{10}}{\left( {{\text{L}} - \frac{{2{\text{D}}}}{3}} \right)^2}$$

D

$$\frac{{{\text{WL}}}}{{12}}{\left( {{\text{L}} - \frac{{\text{D}}}{3}} \right)^2}$$

The bending moment in the center of a simply supported beam carrying a uniformly distributed load of w per unit length is

A

Zero

B

$$\frac{{{\text{w}}{l^2}}}{2}$$

C

$$\frac{{{\text{w}}{l^2}}}{4}$$

D

$$\frac{{{\text{w}}{l^2}}}{8}$$

The bending moment diagram for a simply supported beam carrying a uniformly distributed load of ‘w’ per unit length, will be

A

A horizontal line

B

A vertical line

C

An inclined line

D

A parabolic curve

When a series of wheel loads crosses a simply supported girder, the maximum bending moment under any given wheel load occurs when

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