Problem Statement: Determine the strength and efficiency of a double cover butt joint, consisting of a 16mm thick plate jointed with a 10mm thick cover plate using 20mm diameter power driven shop rivets. The steel used for both the plate and cover plate is IS 226-1975 with a permissible tensile strength of 150MPa. The joint pitch is 9cm.

Solution:
To determine the strength and efficiency of the joint, we need to consider the following factors:

Strength of the Joint:
The strength of the joint is determined by the strength of the rivets used. We can calculate the strength of the joint using the following formula:

Strength of Joint = (Total area of rivets) x (Shear strength of rivet)

Total area of rivets = (Number of rivets) x (Area of one rivet)
Area of one rivet = π/4 x d^2
where d is the diameter of the rivet

Number of rivets = (Length of joint) / (Pitch)
Length of joint = (2 x plate thickness) + cover plate thickness
Pitch = 9cm = 90mm

Substituting the values in the above formula, we get:

Area of one rivet = π/4 x 20^2 = 314.16 mm^2
Number of rivets = (2 x 16) + 10 / 90 = 0.44
Total area of rivets = 0.44 x 314.16 = 138.35 mm^2

Shear strength of rivet = 0.5 x Permissible tensile strength
= 0.5 x 150 = 75 MPa

Strength of Joint = 138.35 x 75 = 10376.25 N

Efficiency of the Joint:
The efficiency of the joint is the ratio of the strength of the joint to the strength of the plate without the joint. We can calculate the strength of the plate using the following formula:

Strength of Plate = (Area of plate) x (Permissible tensile strength)

Area of plate = (Length of joint) x (Width of plate)
Width of plate = Diameter of rivet + 2 x diameter of rivet hole
Diameter of rivet hole = 1.5 x diameter of rivet

Substituting the values in the above formula, we get:

Diameter of rivet hole = 1.5 x 20 = 30mm
Width of plate = 20 + 2 x 30 = 80mm
Length of joint = (2 x 16) + 10 = 42mm
Area of plate = 42 x 80 = 3360 mm^2

Strength of Plate = 3360 x 150 = 504000 N

Efficiency of Joint = (Strength of Joint / Strength of Plate) x 100%
= (10376.25 / 504000) x 100%
= 2.06%

Therefore, the strength of the joint per pitch of 9cm is 10376.25 N and the efficiency of the joint is 2.06%.