Moment Area Theorem

Q. If the hinged end of a propped cantilever of span L settles by an amount $\delta ,$ then the rotation of the hinged end will be

1. $\frac{\delta }{L}$
2. $\frac{2\delta }{L}$
3. $\frac{3\delta }{2L}$
4. $\frac{4\delta }{3L}$

Q. A cantilever beam with square cross-section of 6 mm side is subjected to a load of 2 kN normal to the top surface as shown in the figure. The Young's modulus of elasticity of the material of the beam is 210 GPa. The magnitude of slope (in radian) at Q (20 mm from the fixed end) is _________ .

1. 0.1587

Q. If a cantilever beam of span L and flexural rigidity EI carries a moment M at the free end, the deflection at the end is

1. $\frac{ML}{24EI}$
2. $\frac{M{L}^2}{12EI}$
3. $\frac{ML}{6EI}$
4. $\frac{M{L}^2}{2EI}$

Q. A cantilever beam of length, L, and flexural rigidity, EI, is subjected to an end moment , M, as shown in the figure. The deflection of the beam at $x=\frac{L}{2}$ is

1. $\frac{M{L}^2}{16EI}$
2. $\frac{M{L}^2}{4EI}$
3. $\frac{M{L}^2}{2EI}$
4. $\frac{M{L}^2}{8EI}$

Q. A beam (El = constant) of span L is subjected to clockwise moments M at both the ends A and B. The rotation of end A works out to be

1. $\frac{ML}{2EI}$
2. $\frac{ML}{3EI}$
3. $\frac{ML}{4EI}$
4. $\frac{ML}{6EI}$

Q. Consider a propped cantilever beam ABC under two loads of magnitude P each as shown in the figure below. Flexural rigidity of the beam is EI



The rotation at $B$ is

1. $\frac{5PLa}{16EI}$ (clockwise)
2. $\frac{5PLa}{16EI}$ (anticlockwise)
3. $\frac{59PLa}{16EI}$ (clockwise)
4. $\frac{59PLa}{16EI}$ (anticlockwise)

Q. A cantilever beam with a uniform flexural rigidity $(EI=200\times {10}^{6}N{m}^2)$ is loaded with a concentrated force at its free end. The area of the bending moment diagram corresponding to the full length of the beam is 10000 $N{m}^2$. The magnitude of the slope of beam at its free end is ___ micro radian (round off to the nearest integer)

1. 50

Q. Which of the following is/are determined at a point pf a given beam by moment area method ?
1. Shear force
2. Bending moment
3. Slope
4. Deflection

Selection the correct answer using the codes given below :

1. 1 and 2
2. 3 alone
3. 4 alone
4. 3 and 4

Q. What is the moment at A for a frame as shown in figure below ?



Each members indicated in dark lines has very large moment of interia.

1. $\frac{PL}{2}$
2. $\frac{PL}{4}$
3. $\frac{PL}{8}$
4. $\frac{PL}{16}$

Q. A prismatic, straight, elastic, cantilever beam is subjected to a linearly distributed transverse load as shown below. If the beam length is L, Young's modulus E and area moment of inertia I, the magnitude of the maximum deflection is

1. $\frac{q{L}^4}{10EI}$
2. $\frac{q{L}^4}{60EI}$
3. $\frac{q{L}^4}{15EI}$
4. $\frac{q{L}^4}{30EI}$