1
GATE CE 2017 Set 1
Numerical
+2
-0
Consider the stepped bar made with a linear elastic material and subjected to an axial load of $$1$$ $$kN$$, as shown in the figure

Segment $$1$$ and $$2$$ have cross-sectional area of $$100\,\,m{m^2}$$ and $$60\,\,m{m^2}$$, Young's modulus of $$2 \times {10^5}\,\,MPa$$ and $$3 \times {10^5}\,\,MPa,$$ and length of $$400$$ $$mm$$ and $$900$$ $$mm,$$ respectively. The strain energy (in $$N$$-$$mm,$$ up to one decimal place) in the bar due to the axial load is _________

2
GATE CE 2009
+2
-0.6
A vertical rod $$PQ$$ of length $$L$$ is fixed at its top end $$P$$ and has a flange fixed to the bottom end $$Q.A$$ weight $$W$$ is dropped vertically from a height $$h\left( { < L} \right)$$ on to the flange. The axial stress in the rod can be reduced by
A
increasing the length of the rod
B
Decreasing the length of the rod
C
Decreasing the area of cross-section of the rod
D
Increasing the modulus of elasticity of the material
3
GATE CE 2008
+2
-0.6
A mild steel specimen is under uniaxial tensile stress. Young's modulus and yield stress for mild steel are $$2 \times {10^5}\,\,MPa$$ and $$250$$ $$MPa$$ respectively. The maximum amount of strain energy per unit volume that can be stored in this specimen without permanent set is
A
$$156\,\,N$$-$$mm/m{m^3}$$
B
$$15.6\,\,N$$-$$mm/m{m^3}$$
C
$$1.56\,\,N$$-$$mm/m{m^3}$$
D
$$0.156\,\,N$$-$$mm/m{m^3}$$
4
GATE CE 2004
+2
-0.6
$${U_1}$$ and $${U_2}$$ are the strain energies stored in a prismatic bar due to axial tensile forces $${P_1}$$ and $${P_2},$$ respectively. The strain energy $$U$$ stored in the same bar due to combined action of $${P_1}$$ and $${P_2}$$ will be
A
$$U = {U_1} + {U_2}$$
B
$$U = {U_1}{U_2}$$
C
$$U < {U_1} + {U_2}$$
D
$$U > {U_1} + {U_2}$$
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