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Normal Stress

Example: While stopping a car the driver exerts a force, P, of 10 lb on the brake pedal at C

as shown below. The brake rod is pinned normal to the brake pedal ABC at B. d = 2 in. and

e = 10 in. The diameter of the brake rod is 3/16 in. Find the normal stress in brake rod BD.

Strategy: Construct a free body diagram of the brake pedal. Use equilibrium to find the

force exerted by the brake rod on the brake pedal. Then the normal stress in the brake

rod is just the force it carries divided by the cross-sectional area of the brake rod.

The free body diagram of the brake pedal, ABC, is:

Apply the equation of equilibrium ΣM_A = 0. R(d) – P(d+e) = 0, R = P(d+e)/d

R = 10(2+10)/2 = 60 lb x-sectional area, A, of brake rod = π(3/16)²/4 = 0.0276 in²

The force in the brake rod is equal and opposite. So the normal stress in the brake rod is:

σ = R/A = - 60/0.0276 = - 2170 psi Note: The brake rod is in compression. (result)

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