Q. 203.5( 13 Votes )

# Two strips of met

Answer :

Now here the metal strips are riveted together so the stress in the rivet would be shearing stress since force would be perpendicular to surface area of rivet and stress is the restoring force per unit area, restoring force is same as applied force in equilibrium condition, the rivet joints and force on them are as shown in the figure Now we know shearing stress is given as

𝝈s = F/A

Where 𝝈s is the shearing stress F is the Shearing Force and A is the surface area

So, we get maximum force that can be applied to a rivet as

F = 𝝈s/A

There are four rivets and We are given diameter of each rivet as d = 6.0 mm

So, radius of each rivet is

r = d/2 = 6.0mm/2 = 3.0 mm

or r = 3 × 10-3m

since rivet is circular in shape area is given as

A = πr2

So, area of each rivet is

A = π × 3 × 10-3m×3 × 10-3m = 28.27 × 10-6 m2

So, area of each rivet is

A = 2.827 × 10-5m2

Now we know shearing stress is given as

𝝈s = F/A

Where 𝝈s is the shearing stress F is the Shearing Force and A is the surface area

So, we get maximum force that can be applied to a rivet as

F = 𝝈s × A

We are given maximum shearing stress that can be applied to a rivet as

𝝈s = 6.9 × 107 Pa

Putting value of 𝝈s and A we get maximum shearing force each rivet can with stand as

F = 6.9 × 107Nm-2 × 2.827 × 10-5m2 = 19.50 × 102 N

So each rivet can withstand a force of

F = 1.95 × 103 N = 1.95 KN

Now each rivet is to carry one-quarter of the load i.e 1/4 th of the total load so total load that can be applied or maximum tension that can be exerted is four timed of that can be applied on each rivet i.e. the maximum tension

Tmax = 4 × F

So Tmax = 4 × 1.95 KN = 78 KN

So, the maximum tension that can be exerted by riveted strip is 78 ×103 N or 78 KN

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