Identify, from the following, the correct value of the bending moment $${M_A}\,\,$$ (in $$kNm$$ units) at the fixed end $$A$$ in the statically determinate beam shown below (with internal hinges at $$B$$ and $$D),$$ when a uniformly distributed load of $$10$$ $$kN/m$$ is placed on the spans. (Hint: Sketching the influence line for $${M_A}\,\,$$ or applying the Principle of Virtual Displacements makes the solution easy).

Identify the FALSE statement from the following, pertaining to the effects due to a temperature rise $$\Delta T$$ of the bar $$BD$$ alone in the plane truss shown below :

The frame below shows three beam elements $$OA, OB$$ and $$OC$$, with identical length $$L$$ and flexural rigidity $$EI$$, subject to an external moment $$M$$ applied at the rigid joint $$O.$$ The correct set of bending moments $$\left\{ {{M_{OA}},\,{M_{O{\bf{B}}}},{M_{OC}}} \right\}$$

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.