The given cantilever system consists of a beam with a pin connection, and is hel

Question

The given cantilever system consists of a beam with a pin connection, and is held up by two wires connected as shown in the diagram. One wire is aluminum with a cross-sectional Area (Aa) of 0.2 in^2. and a modulus of elasticity value (Ea) of 10 X 10^6 psi. The other wire is steel with a cross-sectional area (As) of 0.2 in^2 and a modulus of elasticity value (Es) of 30 X 10^6 psi. Given this system, find:

a) What are the two equations of equilibrium from statics?

b) How is the deflection at C related to the deflection at B?

c) What are the three equations that must be solved to find Fa, Fb, and Fc?

d) What are Fa, Fb, and Fc?

e) What is the stress in each wire?

Explanation / Answer

a) Fb+Fc+Fa(y) = 1000 lb Fa(y) = y-component of Fa Fa(x) = 0 b) Deflection at C = 2 * Deflection at B c) Strain at wire at C = 2 * Strain at wire at B ==> Stress of Steel/K1 = 2*Stress of Al/K2 ==> Fc = 6 Fb Moment about A = 0 ==> (10/12)*Fb + (20/12)*Fc = (20/12)*1000 Moment about B = 0 ==> (10/12)*Fa(y) - (10/12)*Fc = -(10/12)*1000 d) Fa = -76.9 Fb = 153.84lb Fc = 923.1lb e) Stress in Al = Fb/ area = 769.2 Stress in Steel = Fc/Area = 4615.5

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