Question

Three struts are pinned together at A, B, and C to form a triangular

Answer 1

Answer:

a. Fab = 3000 N tension

Fac = 1500 N compression

Fbc = 3000 N compression

b. Aluminum for AB, titanium for AC and BC.

c. Fc = 4000 N

Explanation:

a. Draw free body diagrams of the pins at A and B, assuming that all internal forces are in tension (pulling away from the pin).

Sum of the forces on A in the x direction:

∑F = ma

H − Fab sin 60° = 0

Fab = H / sin 60°

Fab = 2600 / sin 60°

Fab = 3000 N

Sum of the forces on A in the y direction:

∑F = ma

-Fab cos 60° − Fac = 0

Fac = -Fab cos 60°

Fac = -H / tan 60°

Fac = -2600 / tan 60°

Fac = -1500 N (it's negative, so it's actually in compression).

Sum of the forces on B in the x direction:

∑F = ma

Fab cos 30° + Fbc cos 30° = 0

Fbc = -Fab

Fbc = -H / sin 60°

Fbc = -3000 N (it's negative, so it's in compression)

b. AB is in tension, so it should be aluminum.

AC and BC are in compression, so they should be titanium.

c. Draw a free body diagram of the entire triangle ABC.  Assume there is both a horizontal and vertical reaction force at C, and assume they point in the +x and +y directions.

Sum of the forces in the x direction:

∑F = ma

Fcx + H = 0

Fcx = -H

Fcx = -2600 N

Sum of the forces in the y direction:

∑F = ma

Fcy − V = 0

Fcy = V

Fcy = 3000 N

The magnitude of the net force is:

Fc² = Fcx² + Fcy²

Fc² = (-2600 N)² + (3000 N)²

Fc = 4000 N