A beam of triangular section is placed with its base horizontal. The maximum shear stress occurs at

A semicircular disc rests on a horizontal surface with its top flat surface horizontal and circular portion touching down. The coefficient of friction between semi circular disc and horizontal surface is µ. This disc is to be pulled by a horizontal force applied at one edge and it always remains horizontal. When the disc is about to start moving, its top horizontal force will

A

Remain horizontal

B

Slant up towards direction of pull

C

Slant down towards direction of pull

D

None of the above

According to maximum shear stress failure criterion, yielding in material occurs, when the maximum shear stress is equal to __________ times the yield stress.

A

0.5

B

2

C

$$\sqrt 2 $$

D

$$\sqrt {\frac{3}{2}} $$

The maximum shear stress developed in a beam of circular section is __________ the average shear stress.

A

Equal to

B

$$\frac{4}{3}$$ times

C

1.5 times

D

Twice

The maximum shear stress developed in a beam of rectangular section is __________ the average shear stress.

A

Equal to

B

$$\frac{4}{3}$$ times

C

1.5 times

D

Twice

For a given stress, the ratio of moment of resistance of a beam of square cross-section when placed with its two sides horizontal to the moment of resistance with its diagonal horizontal, is

A

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

B

1

C

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

D

$$\sqrt 2 $$

The ratio of maximum shear stress to average shear stress of a circular beam, is

A

$$\frac{2}{3}$$

B

$$\frac{3}{2}$$

C

$$\frac{3}{4}$$

D

$$\frac{4}{3}$$

When a body is subjected to biaxial stress i.e. direct stresses ($${\sigma _{\text{x}}}$$) and ($${\sigma _{\text{y}}}$$) in two mutually perpendicular planes accompanied by a simple shear stress ($${\tau _{{\text{xy}}}}$$ ), then maximum shear stress is

A

$$\frac{1}{2}\sqrt {{{\left( {{\sigma _{\text{x}}} - {\sigma _{\text{y}}}} \right)}^2} + 4\tau _{{\text{xy}}}^2} $$

B

$$\frac{1}{2}\sqrt {{{\left( {{\sigma _{\text{x}}} + {\sigma _{\text{y}}}} \right)}^2} + 4\tau _{{\text{xy}}}^2} $$

C

$$\sqrt {{{\left( {{\sigma _{\text{x}}} - {\sigma _{\text{y}}}} \right)}^2} + \tau _{{\text{xy}}}^2} $$

D

$$\sqrt {{{\left( {{\sigma _{\text{x}}} + {\sigma _{\text{y}}}} \right)}^2} + \tau _{{\text{xy}}}^2} $$

When a body is subjected to a direct tensile stress ($${\sigma _{\text{x}}}$$) in one plane accompanied by a simple shear stress ($${\tau _{{\text{xy}}}}$$ ), the maximum shear stress is

A

$$\frac{{{\sigma _{\text{x}}}}}{2} + \frac{1}{2}\sqrt {\sigma _{\text{x}}^2 + 4\tau _{{\text{xy}}}^2} $$

B

$$\frac{{{\sigma _{\text{x}}}}}{2} - \frac{1}{2}\sqrt {\sigma _{\text{x}}^2 + 4\tau _{{\text{xy}}}^2} $$

C

$$\frac{{{\sigma _{\text{x}}}}}{2} + \frac{1}{2}\sqrt {\sigma _{\text{x}}^2 - 4\tau _{{\text{xy}}}^2} $$

D

$$\frac{1}{2}\sqrt {\sigma _{\text{x}}^2 + 4\tau _{{\text{xy}}}^2} $$

The design stress, which is more than the damaging stress, is the least unit stress that will render a member unfit for service before the end of its normal life. The design stress factor or factor of safety indicates the margin between design stress and the __________ stress.

A

Working

B

Damaging

C

Allowable

D

None of these

Moment of inertia of a triangular section of base (b) and height (h) about an axis passing through its vertex and parallel to the base, is __________ than that passing through its C.G. and parallel to the base.

A

Nine times

B

Six times

C

Four times

D

Two times

A beam of triangular section is placed with its base horizontal. The maximum shear stress occurs at

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