A bracket is attached to a vertical column by means of two identical rivets U and V separated by a distance of 2a = 100 mm, as shown in the figure. The permissible shear stress of the rivet material is 50 MPa. If a load P = 10 kN is applied at an eccentricity e = 3√7 a, the minimum cross-sectional area of each of the rivets to avoid failure is ___________ mm².

A steel plate, connected to a fixed channel using three identical bolts $$A, B$$ and $$C,$$ carries a load of $$6kN$$ as shown in the figure. Considering the effect of direct load and moment, the magnitude of resultant shear force (in $$kN$$) on bolt $$C$$ is.

A bolted joint has four bolts arranged as shown in figure. The cross sectional area of each bolt is $$25\,m{m^2}.$$. A torque $$T = 200$$ $$N$$-$$m$$ is acting on the joint. Neglecting friction due to clamping force, maximum shear stress in a bolt is ______ $$MPa.$$

A cantilever bracket is bolted to a column using three $$M12 \times 1.75$$ bolts $$P, Q$$ and $$R.$$ The value of maximum shear stress developed in the bolt $$P$$ (in $$MPa$$) is _______________.