Determine an equation for shear-stress distribution over the cross section of a rod that has a radius c. by what factor is the maximum shear stress greater than the average shear stress acting over the cross section?

Explanation:

Lets take

d= diameter of rod

T=Applied torque on the rod

τ=Shear stress on the rod

We know that shear stress in the rod is varying with radius r of the rod.Shear stress is zero at center of the rod and maximum at the outer most section of the rod.

From Torque-Stress

So we can say that shear stress is varying linearly with radius of rod.

We know that

And for maximum shear stress r=R

So we can say that shear stress due to torque

If we consider that only shear force acting on the rod  then maximum shear stress is 4/3 times more than average shear stress.

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2