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 ___________

A box of weight 100 kN shown in the figure is to be lifted without swinging. If all forces are coplanar, the magnitude and direction (θ) of the force (F) with respect to x-axis should be

Mathematical idealization of a crane has three bars with their vertices arranged as shown in the figure with a load of 80 kN hanging vertically. The coordinates of the vertices are given in parentheses. The force in the member QR, FQR will be