Deflection of Beams · Strength of Materials · GATE ME

The effective stiffness of a cantilever beam of length L and flexural rigidity EI subjected to a transverse tip load W is

A cantilever beam having square cross-section of side $$a$$ is subjected to an end load. If a is increases by $$19$$%, the tip deflection decreases approximately by

A cantilever beam of length $$L$$ is subjected to a moment $$M$$ at the free end. The moment of inertia of the beam cross section about the neutral axis is $$I$$ and the Young’s modulus is $$E$$. The magnitude of the maximum deflection is

A cantilever type gate hinged at $$Q$$ is shown in the figure. $$P$$ and $$R$$ are the centers of gravity of the cantilever part and the counterweight respectively. The mass of the cantilever part is $$75$$ kg. The mass of the counterweight, for static balance, is

Two identical cantilever beams are supported as shown, with their free ends in contact through a rigid roller. After the load P is applied, the free ends will have

An L-shaped elastic member ABC with slender arms AB and BC of uniform crosssection is clamped at end A and connected to a pin at end C. The pin remains in continuous contact with and is constrained to move in a smooth horizontal slot. The section modulus of the member is same in both the arms. The end C is subjected to a horizontal force P and all the deflections are in the plane of the figure. Given the length AB is 4a and length BC is 𝑎, the magnitude and direction of the normal force on the pin from the slot, respectively, are

A simply supported beam of length $$2L$$ is subjected to a moment $$M$$ at the mid-point $$x = 0$$ as shown in the figure. The deflection in the domain $$0 \le x \le L$$ is given by $$$W = {{ - Mx} \over {12EIL}}\left( {L - x} \right)\left( {x + c} \right)$$$

Where $$E$$ is the Young’s modulus, $$I$$ is the area moment of inertia and $$c$$ is a constant (to be determined).

The slope at the center $$X=0$$ is

A beam of length $$L$$ is carrying a uniformly distributed load $$w$$ per unit length. The flexural rigidity of the beam is $$EI$$. The reaction at the simple support at the right end is

A cantilever beam with square cross-section of 6 mm side is subjected to a load of 2kN normal to the top surface as shown in 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 ________

A cantilever beam with flexural rigidity of 200 N.m² is loaded as shown in the figure. The deflection (in mm) at the tip of the beam is _______ .

A frame is subjected to a load $$P$$ as shown in the figure. The frame has a constant flexural rigidity $$EI$$. The effect of axial load is neglected. The deflection at point $$A$$ due to the applied load $$P$$ is

A cantilever beam of length, $$L,$$ with uniform cross-section and flexural rigidity $$ EI,$$ is loaded uniformly by a vertical load, $$w$$ per unit length. The maximum vertical deflection of the beam is given by

The flexural rigidity $$(EI)$$ of a cantilever beam is assumed to be constant over the length of the beam as shown in figure. If a load $$P$$ and bending moment $$PL/2$$ are applied at the free end of the beam then the value of the slope at the free end is

A force $$P$$ is applied at a distance $$x$$ from the end of the beam as shown in the figure. What would be the value of $$x$$ so that the displacement at $$'A'$$ is equal to zero?

A triangular-shaped cantilever beam of uniform- thickness is shown in the figure. The young's modulus of the material of the beam is $$E$$. $$A$$ concentrated load $$P$$ is applied at the free end of the beam.

The area moment of inertia of inertia about the neutral axis of a cross-section at a distance $$x$$ measured from the free end is

A frame of two arms of equal length $$L$$ is shown in the adjacent figure. The flexural rigidity of each arm of the frame is $$EI$$. The vertical deflection at the point of application of load $$P$$ is

A triangular-shaped cantilever beam of uniform- thickness is shown in the figure. The young's modulus of the material of the beam is $$E$$. $$A$$ concentrated load $$P$$ is applied at the free end of the beam.

The maximum deflection of the beam is

A uniformly loaded propped cantilever beam and its free body diagram are shown below. The reactions are

A steel beam of breadth 120 mm and height 750 mm is loaded as shown in the figure. Assume modulus of elasticity as 200 GPa.

The beam is subjected to a maximum bending moment of

A steel beam of breadth 120 mm and height 750 mm is loaded as shown in the figure. Assume modulus of elasticity as 200 GPa.

The value of maximum deflection of the beam is

A simply supported laterally loaded beam was found to deflect more than a specified value. Which of the following measures will reduce the deflection?