Question

An aluminium bar 600mm long1 with diameter 40mm, has a hole drilled in the centre of the bar. The hole is 30mm in diameter and is 100mm long. If the modulus of elasticity for the aluminium is 85GN/M^2 Calculate the total contraction on the bar due to a compressive load of 180KN

Answer 1

To calculate the total contraction on the aluminium bar, you need to consider the change in length of the bar and the change in length of the drilled hole. The change in length can be calculated using the formula ΔL = F * L / (A * E), where ΔL is the change in length, F is the compressive load, L is the original length, A is the cross-sectional area, and E is the modulus of elasticity.

Step-by-step explanation:

To calculate the total contraction on the bar, we need to consider the change in length of the bar and the change in length of the drilled hole. The change in length of the bar can be calculated using the formula: ΔL = F * L / (A * E), where ΔL is the change in length, F is the compressive load, L is the original length, A is the cross-sectional area, and E is the modulus of elasticity. The change in length of the drilled hole can be calculated using the same formula, but with the cross-sectional area and original length of the hole. Then, we can subtract the change in length of the hole from the change in length of the bar to find the total contraction.

First, let's calculate the change in length of the bar:

ΔL_bar = (180 * 10^3 N) * (600 * 10^-3 m) / ((π * (20 * 10^-3 m)^2) * (85 * 10^9 N/m^2))

Next, let's calculate the change in length of the hole:

ΔL_hole = (180 * 10^3 N) * (100 * 10^-3 m) / ((π * (15 * 10^-3 m)^2) * (85 * 10^9 N/m^2))

Finally, we can find the total contraction by subtracting the change in length of the hole from the change in length of the bar:

Total contraction = ΔL_bar - ΔL_hole

Answer 2

Total contraction = 1.2277 mm

Step-by-step explanation:

the solution is given in the picture below and it is more explanatory