A cantilever bracket is bolted to a column using three M12

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

1. 332
2. 321
3. 322
4. 330

Correct Option: A

P = 9 kN, e = 250 mm
Primary shear force

P^'_p =P^'_q = P^'_r =	p	=	q	= 3kN
	3		3

Secondary shear force:
By symmetry C.G lies at the centre of bolt Q.
∴ r_p = 30 mm
r_r = 30 mm
r_q = 0

C =	Pe
	r²_p + r²_q + r²_r

=	9000 × 250	= 1250
	30² + 0² + 30²

P^"_p = P^"_r = C

P^"_p = Cr_p = 37.5 kN
P^'_r = Cr_r = 37.5 kN
P^"_q = 0
Resultant shear force
Due to symmetry stress in P Q R will be equal in magnitude
P_p = P_r = √(3)² + (37.5)²
= 38.5648 kN

τ =	P
	A

=	38.5648
	π/4(0.012)²

= 332 MPa ≃