Consider the portal frame shown in the figure and assume the modulus of elasticity, $$E = \,2.5 \times {10^4}\,\,MPa$$ and the moment of inertia, $${\rm I} = 8 \times {10^8}\,\,m{m^4}$$ for all the members of the frame.

The rotation (in degrees, up to decimal place) at the rigid joint $$Q$$ would be ____________

Two beams $$PQ$$ (fixed at $$P$$ and with a roller support at $$Q,$$ as shown in Figure $$I,$$ which allows vertical movement) and $$XZ$$ (with a hinge at $$Y$$) are shown in the Figures $$I$$ and $$II$$ respectively. The spans of $$PQ$$ and $$XZ$$ are L and $$2L$$ respectively. Both the beams are under the action of uniformly distributed load $$(W)$$ and have the same flexural stiffness, $$EI$$ (where, $$E$$ and $$I$$ respectively denote modulus of elasticity and moment of inertia about axis of bending). Let the maximum deflection and maximum rotation be $${\delta _{\max 1}}$$ and $${\theta _{\max 1}},$$ respectively, in the case of beam $$PQ$$ and the corresponding quantities for the beam $$XZ$$ be $${\delta _{\max 2}}$$ and $${\theta _{\max 2}},$$ respectively.

Which one of the following relationships is true?

The two-span continuous beam shown below is subject to a clockwise rotational slip $${\theta _A} = 0.004$$ radian at the fixed end $$A.$$ Applying the slope-deflection method of analysis, determine the slope $${\theta _B}$$ at $$B.$$ Given that the flexural rigidity $$EI = 25000\,kN$$ - $${m^2}$$ and span $$L=5$$ $$m,$$ determine the end moments (in $$kN$$-$$m$$ units ) in the two spans, and draw the bending moment diagram.