Question

Determine the displacement of end A with respect to end D if the diameters of each segment are dAB = 0.85 in ., dBC = 1.1 in ., and dCD = 0.45 in . Take Ecu= 18(103)ksi.

Answer 1

Answer / Step-by-step explanation:

It should be noted that the question is incomplete due to the fact that the diagram has not been provided. However, the diagram has been complementing the question has been provided below.

To solve the question in the narrative, we recall the equation used in solving for displacement:

Thus, δₙₐ = Σ pL/AE

Where:

P is applied axial force.

E is the young's modulus of elasticity.

A is the area of cross-section.

L is length of the bar

Therefore,  -8 (80) ÷ π/4 ( 0.85)² (18) (10³) +  2(150) ÷ π/4 (1.1)² (18) (10³) + 6(100) ÷ π/4 (0.45)² (18) (10³)

Solving further,

we have,

-8 (80) ÷ 0.7853( 0.85)² (18) (10³) + 2(150) ÷ 0.7853(1.1)² (18) (10³) + 6(100) ÷ 0.7853 (0.45)² (18) (10³)

= -640÷ 0.7853( 0.85)² (18) (10³) + 300 ÷ 0.7853(1.1)² (18) (10³) + 600 ÷ 0.7853 (0.45)² (18) (10³)

Solving further, we arrive at 0.111 in answer.

The positive sign indicates that end A moves away from end D.