Knowing that α = 55° and that boom AC exerts on a pin C a force directed along line AC, determine

a) the magnitude of that force

b) The tension in cable BC.

Step: 1

Draw free body diagram at point C as shown:

Step: 2

From the Lami’s theorem, write the equilibrium equation of forces as follows:

…… (1)

Here, is the tension in the cable BC and is the force in the member AC.

Step: 3

(a)

Calculate the force in the member AC as follows:

From equation (1),

Here, the negative sign indicates that the original direction is opposite to that of assumed direction.

Therefore, the force in the member AC is

Step: 4

(b)

Calculate the tension in the cable BC as follows:

From equation (1),

Therefore, the tension in the cable BC is .

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