Consider two linearly elastic rods HI and IJ. Each of length b, as shown in the figure. The rods are co-linear, and confined between two fixed supports at if and J. Both the rods are initially stress free. The coefficient of linear thermal expansion is a for both the rods. The temperature of the rod IJ is raised by $$\Delta$$T whereas the temperature of rod HI remains unchanged. An external horizontal force P is now applied at node I. It is given that a = 10^$$-$$6 $$^\circ$$C^$$-$$1, $$\Delta$$T = 50$$^\circ$$C, b = 2m, AE = 10⁶N. The axial rigidities of the rods HI and U are 2 AE and AE, respectively.

To make the axial force in rod HI equal to zero, the value of the external force P (in N) is _________. (rounded off to the nearest integer).

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?

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 ($$\theta$$) of the force (F) with respect to x-axis should be

A metal bar of length 100mm is inserted between two rigid supports and its temperature is increased by $$10^o$$C. If the coefficient of thermal expansion is 12 x$$10^{-6}$$ per $$^o$$C and the Young’s modulus is 2 x $$10^{5}$$ MPa, the stress in the bar is