A truss tie consisting of $$2$$ $$ISA$$ $$75 \times 75 \times 8\,\,mm$$ carries a pull of $$150$$ $$kN.$$ At ends the two angles are connected, one each on either side of a $$10$$ $$mm$$ thick gusset plate, by $$18$$ $$mm$$ diameter rivets arranged in one row. The allowable stresses in rivet are $${f_s} = 90.0\,\,N/m{m^2}$$ and $${f_{br}} = 250\,\,N/m{m^2}$$.

Maximum tensile stress in the tie in $$N/m{m^2}$$ is

A stepped steel shaft shown below is subjected to $$10$$ $$N$$-$$m$$ torque. If the modulus of rigidity is $$80$$ $$GPa,$$ the strain energy in the shaft in $$N$$-$$mm$$ is

A long structural column (length $$-L$$) with both ends hinged is acted upon by an axial compressive load $$P.$$ The differential equation governing the bending of column is given by: $$$EI{{{d^2}y} \over {d{x^2}}} = - Py$$$

Where $$y$$ is the structural lateral deflection and $$EI$$ is the flexural rigidity. The first critical load on column responsible for its buckling is given by

For linear elastic systems, the type of displacement function for the strain energy is