A continuous beam is loaded as shown in the figure below. Assuming a plastic moment capacity equal to $${{M_P}}$$, the minimum load at which the beam would collapse is

The shape of the cross-section, which has the largest shape factor, is

The members $$EJ$$ and $$IJ$$ of a steel truss shown in the figure below are subjected to a temperature rise of $${30^ \circ }C.$$ The coefficient of thermal expansion of steel is $$0.000012$$ per $${^ \circ }C.$$ per unit length. The displacement ($$mm$$) of joint $$E$$ relative to joint $$H$$ along the direction $$HE$$ of truss, is

The span$$(s)$$ to be loaded uniformly for maximum positive (upward) reaction at support $$P,$$ as shown in the figure below, is $$(are)$$