An elastic bar of length L, uniform cross sectional area A, coefficient of thermal expansion a, and Young’s modulus E is fixed at the two ends. The temperature of the bar is increased by T, resulting in an axial stress $$\sigma$$. Keeping all other parameters unchanged, if the length of the bar is doubled, the axial stress would be

The value of $$M$$ in the beam $$ABC$$ shown in the figure is such that the joint $$B$$ does not rotate.

The value of support reaction (in $$kN$$) at $$B$$ should be equal to _____________

The figure shows a two $$-$$hinged parabolic arch of span $$L$$ subjected to a uniformly distributed load of intensity $$q$$ per unit length.

The maximum bending moment in the arch is equal to

Consider the beam $$ABCD$$ shown in figure

For a moving concentrated load of $$50$$ $$kN$$ on the beam, the magnitude of the maximum bending moment (in $$kN$$-$$m$$) obtained at the support $$C$$ will be equal to _________