Project ForgeA 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.
Explanation
Primary (direct) shear per rivet: F_p=P/2=5kN (vertical). Secondary shear from the moment M=Pe: since U,V lie on a single vertical line each at distance a from the centroid, Σr²=2a², so F_s=M·a/Σr²=Pe/(2a)=10×3√7a/(2a)=15√7≈39.69kN (horizontal, perpendicular to the vertical line UV). Since F_p and F_s are perpendicular on each rivet: F_R=√(5²+(15√7)²)=√(25+1575)=√1600=40kN. Required area A=F_R/τ_allow=40000/50=800 mm².
Source: GATE ME 2022 Session 1 (ME-1) (2022)
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