Identify the most efficient butt joint (with double cover plates) for a plate in tension from the patterns (plan views) shown below, each comprising $$6$$ identical bolts with the same pitch and gauge.

The bending moment (in $$kN$$-$$m$$ units) at the mid-span location $$X$$ in the beam with overhangs shown below is equal

The degree of static indeterminacy, $${N_s}$$ and the degree of kinematic indeterminacy, $${N_k}$$ for the plane frame shown below, assuming axial deformations to be negligible, are given by:

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.