Strain Energy Method · Strength of Materials Or Solid Mechanics · GATE CE

For linear elastic systems, the type of displacement function for the strain energy is

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 _________

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 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

$${U_1}$$ 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 stepped steel shaft shown below is subjected to $$10$$ $$N$$-$$m$$ torque. If the modulus of rigidity is $$80$$ $$GPa,$$ the strain energy in the shaft in $$N$$-$$mm$$ is