The double riveted butt joint shown in the Figure connect two plates, which are each 2.5 mm thick

Question: The double riveted butt joint shown in the Figure connect two plates, which are each 2.5 mm thick, the rivet has a diameter of 3mm. If the failure strength of the rivets in shear is 370 N/mm2 and the ultimate tensile strength of the plate is 465 N/mm2 determine the necessary rivet pitch if the joint is to be designed so that failure due to shear in the rivets and failure due to tension in the plate occur simultaneously. Calculate the joint efficiency.

Solution:

Given that:
Thickness = 2.5 mm
Diameter = 3 mm
Tensile strength = 465 N/mm^2
Shear strength = 370 N/mm^2
Shearing of rivets can be calculated as below:
Ps = nπ/4 * d^2 * τ * 2 (double shear)
where
τ = shear strength
n = no of rivets pen pitch length = 2
d = 3
Now substitute in above

Ps = 2 π/4 * 3^2 * 370 * 2
Ps= 10461.5 N

Tearing resistance of plate:
Pt = (P-d)tθt
d = 3 mm
t = 2.5 mm
θt = 465 N/mm^2

Pt = (P – 3) * 2.5 * 465
As given question shearing resistance of rivet = tearing resistance of plate
that is
Ps = Pt
(P-3)2.5465 = 10462
(P-3) * 1162.5 = 10462
P – 3 = 10462/1162.5
P – 3 = 8.999
P = 8.99 + 3
P = 11.99
P = 12
Now the strength of the unriveted on solid plate pen pitch length
P = Ptθt
t = 2.5 mm
P = 12
θt = 465
Now substitute those value’s then
P = 122.5465
P = 13950N
where P= pitch of revert
Now to determine the efficiency of the joint we know that the
efficiency of joint = least of Ps,Pt/P
Now substitute those values
Ps = 10462N
P = 13950
= 10462/13950
= 0.749
Efficiency of joint = 74.9%