GATE CE

Strength of Materials Or Solid Mechanics

Deflection of Beams

Previous Years Questions

## Marks 1

In a real beam, at an end, the boundary condition of zero slope and zero vertical displacement exists. In the corresponding conjugate beam, the bounda...

## Marks 2

Two prismatic beams having the same flexural rigidity of $$1000\,kN$$-$${m^2}$$ are shown in the figures.
If the mid-span deflections of these beams...

A $$3$$ $$m$$ long simply supported beam of uniform cross section is subjected to a uniformly distributed load of $$w = 20$$ $$kN/m$$ in the central $...

A simply supported reinforced concrete beam of length $$10$$ $$m$$ sags while undergoing shrinkage. Assuming a uniform curvature of $$0.004\,\,{m^{ - ...

For the cantilever beam of span $$3$$ $$m$$ (shown below), a concentrated load of $$20$$ $$kN$$ applied at the free end causes a vertical displacement...

A simply supported beam is subjected to a uniformly distributed load of intensity $$w$$ per unit length. On half of the span from one end. The length ...

In the cantilever beam $$PQR$$ shown in figure below, the segment $$PQ$$ has flexural $$EI$$ and the segment $$QR$$ has infinite flexural rigidity
T...

In the cantilever beam $$PQR$$ shown in figure below, the segment $$PQ$$ has flexural $$EI$$ and the segment $$QR$$ has infinite flexural rigidity
T...

The stepped cantilever is subjected to moments, $$M$$ as shown in the figure below. The vertical deflection at the free end (neglecting the self weigh...

Beam $$GHI$$ is supported by these pontoons as shown in the figure below. The horizontal cross sectional area of each pontoon is $$8\,\,{m^2},$$ the f...

Beam $$GHI$$ is supported by these pontoons as shown in the figure below. The horizontal cross sectional area of each pontoon is $$8\,\,{m^2},$$ the f...

A two span continuous beam having equal spans each of length $$L$$ is subjected to a uniformly distributed load $$\omega $$ per unit length. The beam ...

A two span continuous beam having equal spans each of length $$L$$ is subjected to a uniformly distributed load $$\omega $$ per unit length. The beam ...

Consider the beam $$AB$$ shown in the figure below. Part $$AC$$ of the beam is rigid while Part $$CB$$ has the flexural rigidity $$EI$$. Identify the ...

A $$''H''$$ Shaped frame of uniform flexural rigidity $$EI$$ is loaded as shown in the figure. The relative outward displacement between points $$K$$ ...

In the propped cantilever beam carrying a uniformly distributed load of $$w$$-$$kN/m,$$ shown in the following figure, the reaction at the support $$'...

The bending moment (in $$kN$$-$$m$$ units) at the mid-span location $$X$$ in the beam with overhangs shown below is equal
...

A two span beam with an internal hinge is shown below.
Conjugate beam corresponding to this beam is...

For the structure shown below, the vertical deflection at point $$A$$ is given by
...

A cantilever beam is shown in the figure. The moment to be applied at free end for zero vertical deflection at the point is
...

A cantilever beam of span $$'L'$$ is loaded with a concentrated load $$'P'$$ at the free end. Deflection of the beam at the free end is

A propped cantilever beam of span $$L,$$ is loaded with uniformly distributed load of intensity $$w/unit$$ length, all through the span. Bending mome...

A cantilever beam of span $$l$$ subjected to a uniformly distributed load $$'w'$$ per unit length resting on a rigid prop at the tip of cantilever. Th...

A simply supported beam of span length $$L$$ and flexural stiffness $$EI$$ has another spring support at the center span of stiffness $$K$$ as shown i...

A cantilever beam of span, $$'L'$$ is subjected to a downward load of $$800$$ $$kN$$ uniformly distributed over its length and a concentrated upward l...

Two elastic rods $$AB$$ and $$BC$$ are hinged at $$B$$. The joint $$A$$ is a hinged one, joint $$C$$ is over a roller and the joint $$B$$ is supporte...