Answer :

Solution :

e = 3√7a, P = 10 kN, 2a = 100 mm

permissible shear stress, τ = 50 MPa

r = a = 50, e = 3√7 × 50

Primary forces :

F_p = P/2 = 5 kN

Secondary forces :

Pe = F_s (r₁² + r₂²)/ r₁

here r₁ = r₂ and F_s at both the rivet is also equal

F_s = $\frac{Pe}{2r}$ = (10 × 3√7 × 50)/(2 × 50)

F_s = 39.68 kN

Since the revet is critical at 1 &2

Resultant force R = $\sqrt{5^2+{39.68}^2}$ = 40 kN

To avoid failure : 

${\tau }_{per}\ge \frac{Force}{Area}$

50 ≥ 40 × 10³\ A

A = 800 mm²