A simply supported beam of length 'l' carries a point load 'W' at a point C as shown in the below figure. The maximum deflection lies at<br> <img src="/images/question-image/mechanical-engineering/strength-of-materials/1528354433-39.JPG" title="Strength of Materials mcq question image" alt="Strength of Materials mcq question image">

For a beam, as shown in the below figure, the deflection at C is (where E = Young's modulus for the beam material and $$I$$ = Moment of inertia of the beam section.)

A

$$\frac{{{\text{W}}{l^3}}}{{48{\text{E}}I}}$$

B

$$\frac{{{\text{W}}{{\text{a}}^2}{{\text{b}}^2}}}{{3{\text{E}}Il}}$$

C

$$\frac{{{\text{Wa}}}}{{{\text{a}}\sqrt 3 {\text{E}}Il}} \times {\left( {{l^2} - {{\text{a}}^2}} \right)^{\frac{3}{2}}}$$

D

$$\frac{{5{\text{W}}{l^3}}}{{384{\text{E}}I}}$$

A simply supported beam with a gradually varying load from zero at ‘B’ and ‘w’ per unit length at ‘A’ is shown in the below figure. The shear force at ‘B’ is equal to

A

$$\frac{{{\text{w}}l}}{6}$$

B

$$\frac{{{\text{w}}l}}{3}$$

C

$${\text{w}}l$$

D

$$\frac{{2{\text{w}}l}}{3}$$

For a beam, as shown in the below figure, when the load W is applied in the center of the beam, the maximum deflection is

A

$$\frac{{{\text{W}}{l^3}}}{{48{\text{E}}I}}$$

B

$$\frac{{5{\text{W}}{l^3}}}{{384{\text{E}}I}}$$

C

$$\frac{{{\text{W}}{l^3}}}{{392{\text{E}}I}}$$

D

$$\frac{{{\text{W}}{l^3}}}{{384{\text{E}}I}}$$

A simply supported beam 'A' of length ‘l’, breadth ‘b’ and depth ‘d’ carries a central load ‘W’. Another beam 'B' of the same dimensions carries a central load equal to 2W. The deflection of beam 'B' will be __________ as that of beam 'A'.

A

One-fourth

B

One-half

C

Double

D

Four times

For a beam, as shown in the below figure, the maximum deflection lies at

A

$$\frac{l}{3}$$ from B

B

$$\frac{l}{3}$$ from A

C

$$\sqrt {\frac{{{l^2} - {{\text{a}}^2}}}{3}} $$ from B

D

$$\sqrt {\frac{{{l^2} - {{\text{b}}^2}}}{3}} $$ from A

A simply supported beam 'A' of length l, breadth b, and depth d carries a central point load W. Another beam 'B' has the same length and depth but its breadth is doubled. The deflection of beam 'B' will be __________ as compared to beam 'A'.

A

One-fourth

B

One-half

C

Double

D

Four times

The maximum bending moment for the beam shown in the below figure, lies at a distance of ________ from the end B.

A

$$\frac{l}{2}$$

B

$$\frac{l}{3}$$

C

$$\frac{l}{{\sqrt 2 }}$$

D

$$\frac{l}{{\sqrt 3 }}$$

The simply supported beam 'A' of length '$$l$$' carries a central point load 'W'. Another beam 'B' is loaded with a uniformly distributed load such that the total load on the beam is 'W'. The ratio of maximum deflections between beams 'A' and 'B' is

A

$$\frac{5}{8}$$

B

$$\frac{8}{5}$$

C

$$\frac{5}{4}$$

D

$$\frac{4}{5}$$

A simply supported beam A carries a point load at its mid span. Another identical beam B carries the same load but uniformly distributed over the entire span. The ratio of the maximum deflections of the beams A and B, will be

A

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

B

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

C

$$\frac{5}{8}$$

D

$$\frac{8}{5}$$

There are two beams of equal length L and a load P is acting on centre of both beams. One of them is simply supported at both ends while the other one is fixed at both ends. Deflection of centre of simply supported beam will be __________ times that of defection of centre of fixed beam.

A

1

B

2

C

3

D

4