A single self-energizing long shoe drum shoe uses a molded lining of friction coefficient 0.45 and maximum allowable pressure of 150 psi as the friction material. If the angle subtended by the shoe is 120°, with θ1 = 0, find the face width required for the shoe to stop a torque of 3800 lb. in. The drum diameter is 12-in.

A = 10.83 in² ,  w = 3.29 in

Explanation:

For this exercise we must use the rotational equilibrium condition

        Σ τ = 0

in this case they give us the external torque τ = 3800 lb in.

        τ - τ’= 0

        τ = τ'

where τ‘ is the torque exerted by the brake shoe that is given by the friction force

      τ’ = fr r sin θ

indicates that θ= 120º and the radius is half the diameter of the drum

      r = 6 in

the friction force is given by the expression

       fr = μ N

substitute

        τ = μ N r sin θ         (1)

to find the normal let's use Newton's second law on the perpendicular pressure axis

        Σ F = 0

        N - f = 0

        N = f

The applied force can be found using the definition of pressure

         P = f / A

where A is the area of the footing

         f = P A

let's substitute

          N = P A

let's substitute in 1

         τ = μ P A r sin θ

let's calculate

          A = 3800 / (0.45 150 6 sin 120)

          A = 10.83 in²

to find the size of the shoe we must assume a specific shape, suppose the shoe is square

          A =w²

          w = √A

          w = 3.29 in

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hope this ! : )