Twentyfive feet of steel strapping is coiled in a flat 12 in

Twenty-five feet of steel strapping is coiled in a flat 12 inch by 12 inch box. The strapping is 1 inch wide and 0.0625 inch thick. (Assume the coil can be approximated by concentric hoops with no gaps between them.) Determine Explain using complete sentences your approach to the problem. The bending moment at the outer most coil The maximum bending stress at the outer most coil The bending moment at the inner most coil The maximum bending stress at the inner most coil If the yield strength is 45 ksi, what is the minimum diameter the strapping could be coiled without causing permanent deformation?

Solution

Calculate Moment of inertia of steel

Bending moment equation

(a)

Young’s modulus of steel

Write Bending moment equation to find bending moment at the outer most coil.

(b)

Write Bending moment equation to find maximum bending stress at the outer most coil.

(c)

Write the Relation to find the inner radius of the coil

Volume of steel strapping volume of the coil

Write Bending moment equation to find bending moment at the inner most coil.

(d)

Write Bending moment equation to find maximum bending stress at the inner most coil.

(e)

Write the relation Minimum diameter strapping of coil.

Consider Factor of safety=2

Yield strength,

Safety yield strength,