The maximum bending moment for the beam shown in the below figure, lies at a distance of ________ from the end B.<br> <img src="/images/question-image/mechanical-engineering/strength-of-materials/1528353950-25.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.)
Strength of Materials in ME mcq question image

Strength of Materials in ME mcq question image

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

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

The maximum bending moment for the beam shown in the below figure, is
Strength of Materials mcq question image

A

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

B

$$\frac{{{\text{w}}{l^2}}}{{6\sqrt 3 }}$$

C

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

D

$$\frac{{{\text{w}}{l^2}}}{{12\sqrt 3 }}$$

For a beam, as shown in the below figure, the maximum deflection lies at
Strength of Materials mcq question image

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 of length 'l' carries a point load 'W' at a point C as shown in the below figure. The maximum deflection lies at
Strength of Materials mcq question image

A

Point A

B

Point B

C

Point C

D

Between points B and C

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
Strength of Materials mcq question image

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

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

In which of the following cases, there exists the situation of Pure Bending in some part of the beam or along the entire beam? i) A simply supported beam subjected to two equally spaced downward concentrated loads ii) A simply supported beam subjected to two equally spaced opposite moments iii) A cantilever beam subjected to clockwise moment at free end iv) An overhanging beam with both side overhangs subjected to different concentrated loads at both the free ends

A

(i) and (iv)

B

(i), (ii) and (iv)

C

(i), (ii) and (iii)

D

(i) and (iii)

Consider the following statements regarding types of supports and beams: 1. When both supports of beams are roller supports, the beam is known as simply supported beam. 2. A beam with one end fixed and the other end free is known as fixed beam. 3. A beam with both ends fixed is known as cantilever beam. 4. A beam with one end fixed and the other simply supported is known as propped cantilever. Which of the above statements is/are correct ?

A

1 only

B

1 and 4 only

C

1, 3 and 4 only

D

2, 3 and 4 only

Consider the following statements with regards to the shear force diagram for the beam ABCD: 1. The beam ABCD is an overhanging beam having supports at A and D only. 2. The beam carries a point load of 20 kN at C. 3. The beam carries a concentrated load of 10 kN at the end B. 4. The beam is an overhanging beam having supports at C and D only. 5. The beam carries a uniformly distributed load of 70 kN over the left hand portion AC only. Which of the above statements are correct?

A

1, 2 and 3 only

B

1, 3 and 5 only

C

2, 3 and 4 only

D

2, 4 and 5 only

The moment of inertia of a uniform sphere of radius, r about an axis passing through its centre is given by $$\frac{2}{5}\left( {\frac{{4\pi }}{3}{r^5}\rho } \right).$$ A rigid sphere of uniform mass density $$\rho $$ and radius R has two smaller spheres of radii $$\frac{R}{2}$$ hollowed out of it as shown in the figure given below.
Classical Mechanics mcq question image

The moment of inertia of the resulting body about Y-axis is

A

$$\frac{{\pi \rho {R^5}}}{4}$$

B

$$\frac{{5\pi \rho {R^5}}}{{12}}$$

C

$$\frac{{7\pi \rho {R^5}}}{{12}}$$

D

$$\frac{{3\pi \rho {R^5}}}{4}$$

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
Strength of Materials mcq question image

A

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

B

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

C

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

D

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

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

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