A plate in equilibrium is subjected to uniform stresses along its edges with magnitude $ \sigma_{xx}=30 $ MPa and $ \sigma_{xx}=50 $ MPa as shown in the figure.
The Young’s modulus of the material is 2×10^{11} N/m^{2} and the Poisson’s ratio is 0.3. If $\style{font-family:'Times New Roman'}{\sigma_{zz}}$ is negligibly small and assumed to be zero, then the strain $\style{font-family:'Times New Roman'}{\varepsilon_{zz}}$ is
An elastic bar of lenght L, uniform cross sectional area A, coefficient of thermal expansion $\style{font-family:'Times New Roman'}\alpha$, and Young's modulus 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 mm^{2} and 60 mm^{2}, Young's modulus 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 ___________
An elastic isotropic body is in a hydrostatic state of stress as shown in the figure. For no change in the volume to occur, what should be its Poisson's ratio?
Consider the structural system shown in the figure under the action of weight W. All the joints are hinged. The properties of the members in terms of length (L), area (A) and the modulus of elasticity (E) are also given in the figure. Let L, A and E be 1 m, 0.05 m^{2} and 30 × 106 N/m^{2}, respectively, and W be 100 kN.
Which one of the following sets gives the correct values of the force, stress and change in length of the horizontal member QR?
A tapered circular rod of diameter varying from 20 mm to 10 mm is connected to another uniform circular rod of diameter 10 mm as shown in the following figure. Both bars are made of same material with the modulus of elasticity, E = 2 × 10^{5} MPa. When subjected to a load P = 30$\mathrm{\pi}$ kN, the deflection at point A is ________ mm.
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, F_{QR} will be