1
GATE ME 2014 Set 2
+2
-0.6
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
$${1 \over 2}$$ $${{P{L^2}} \over {EI}}$$
B
$${{P{L^2}} \over {EI}}$$
C
$${3 \over 2}$$ $${{P{L^2}} \over {EI}}$$
D
$${5 \over 2}$$ $${{P{L^2}} \over {EI}}$$
2
GATE ME 2014 Set 4
+2
-0.6
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
$${1 \over 3}\,{{P{L^3}} \over {EI}}$$
B
$${2 \over 3}\,{{P{L^3}} \over {EI}}$$
C
$${{P{L^3}} \over {EI}}$$
D
$${4 \over 3}\,{{P{L^3}} \over {EI}}$$
3
GATE ME 2014 Set 3
+2
-0.6
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
$$0.5L$$
B
$$0.25L$$
C
$$0.33L$$
D
$$0.66L$$
4
GATE ME 2009
+2
-0.6
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
$${{bx{t^3}} \over {6L}}$$
B
$${{bx{t^3}} \over {12L}}$$
C
$${{bx{t^3}} \over {24L}}$$
D
$${{x{t^3}} \over {12}}$$
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