A rectangular region in a solid is in a state of plane strain. The $$(x,y)$$ coordinates of the corners of the undeformed rectangle are given by $$P(0,0), Q(4,0), R(4,3), S(0,3).$$ The rectangle is subjected to uniform strains, $${\varepsilon _{xx}} = 0.001,\,\,{\varepsilon _{yy}} = 0.002,\,\,{\gamma _{xy}} = 0.003.$$ The deformed length of the elongated diagonal, upto three decimal places, is ______________ units.

Consider a beam with circular cross-section of diameter $$d.$$ The ratio of the second moment of area about the neutral axis to the section modulus of the area is

A motor driving a solid circular steel shaft transmits $$40$$ $$kW$$ of power at $$500$$ $$rpm$$. If the diameter of the shaft is $$40$$ $$mm,$$ the maximum shear stress in the shaft is ________ $$MP$$a.

An initially stress-free massless elastic beam of length $$L$$ and circular cross-section with diameter $$d (d < < L)$$ is held fixed between two walls as shown. The beam material has Young's modulus $$E$$ and coefficient of thermal expansion $$\alpha .$$

If the beam is slowly and uniformly heated, the temperature rise required to cause the beam to buckle is proportional to