# Questions & Answers of Simple stress and strain relationship, Stress and strain in two dimensions

An elastic bar of lenght L, uniform cross sectional area A, coefficient of thermal expansion $\style{font-family:'Times New Roman'}\alpha$, and Yong's moduls E is fixed at the two ends. The temperature of the bar is increased by T, resulting in an axial strees $\style{font-family:'Times New Roman'}\sigma$. Keeping all other parameter unchanged if the length of the bar is doubled, the axial stress would be

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 mm2 and 60 mm2, Young's moduls of $\style{font-family:'Times New Roman'}{2\times10^5\mathrm{MPa}\;\mathrm{and}\;3\times10^{5\;}\mathrm{MPa}}$, 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 ___________

In a material under a state of plane strain, a 10 × 10 mm square centered at a point gets deformed as shown in the figure.

If the shear strain $\style{font-family:'Times New Roman'}{\gamma_{xy}}$ at this point is expressed as 0.001k (in rad), the value of k is

A 2 m long, axially loaded mild steel rod of 8 mm diameter exhibits the load-displacement $\style{font-family:'Times New Roman'}{(P-\delta)}$  behavior as shown in the figure.

Assume the yield stress of steel as 250 MPa. The complementary strain energy (in N-mm) stored in the bar up to its linear elastic behavior will be ___________