A homogeneous, simply supported prismatic beam of width $$B,$$ depth $$D$$ and span $$L$$ is subjected to a concentrated load of magnitude $$P.$$ The load can be placed anywhere along the span of the beams. The maximum flexural stress developed in beam is

A circular solid shaft of span $$L=5m$$ is fixed at one end and free at the other end. A twisting moment $$T=100$$ $$kN$$-$$m$$ is applied at the free end. The torsional rigidity $$GJ$$ per unit angular twist is $$50000$$ $$kN$$-$${m^2}/rad.$$ Following statements are made for this shaft:

$$1.$$ The maximum rotation is $$0.01$$ radius
$$2.$$ The torsional strain energy is $$1$$ $$kN$$-$$m.$$

With reference to the above statements, which of the following applies?

For the plane truss shown in the figure, the number of zero force members for the given loading is

A three hinged parabolic arch $$ABC$$ has a span of $$20$$ $$m$$ and a central rise of $$4$$ $$m.$$ The arch has hinges at the ends and at the center. A train of two point loads of $$20$$ $$kN$$ and $$10$$ $$kN$$, $$5$$ $$m$$ apart, crosses this arch from left to right, with $$20$$ $$kN$$ load leading. The maximum thrust induced at the supports is