1
GATE PI 2017
+1
-0.3
If $$E$$ is the modulus of elasticity in $$GPa$$, $$G$$ is the shear modulus in $$GPa$$ and $$v$$ is the Poisson's ratio of a linear elastic and isotropic material, the three terms are related as
A
$$E=G(1-2v)$$
B
$$R=2G(1-v)$$
C
$$E=G(1+2v)$$
D
$$E=2G(1+v)$$
2
GATE PI 2017
+1
-0.3
For a two dimensional state-of-stress defined as $${\sigma _{xx}} = {\sigma _{yy}} = {\tau _{xy}} = S,$$ the Mohr's circle of stress has
A
center at $$(S, 0)$$ and radius $$S$$
B
center at $$(0, 0)$$ and radius $$S$$
C
center at $$(S, 0)$$ and radius $$0$$
D
center at $$(S/2, 0)$$ and radius $$2S$$
3
GATE PI 2017
Numerical
+2
-0
The simply-supported beam shown in the Figure is loaded symmetrically using two equal point loads $$P.$$ The radius of curvature of the deflection-curve is $$15$$ m for the portion of the beam that is subjected to pure bending. The vertical deflection (in mm) at point $$M,$$ equidistant from both the supports is _______ (up to two decimal places).
4
GATE PI 2017
+1
-0.3
The inside and outside radii of a thick- walled cylindrical pressure vessel are denoted by $$a$$ and $$b,$$ respectively. If the vessel is subjected to an internal pressure $$P,$$ then the magnitude of the radial stress $${\sigma _{rr}}$$ is
A
zero at $$r=a$$ and maximum at $$r=b$$
B
maximum at $$r=a$$ and zero at $$r=b$$
C
constant over the entire thickness
D
zero at both $$r=a$$ and $$r=b$$
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