Calculating Minimum Thickness for Aluminum Alloy Tube Supporting Steel Rod

[mit_hacker]

(Q) An aluminum alloy (E=73GPa) tube A with an outer diameter of 75mm is used to support a 25-m-diameter steel (E=210GPa) rod B, as shown (in the attachement). Determine the minimum thickness t required for the tube if the maximum deflection of the loaded end must be limited to 0.40 mm.

I understand if the length of the working puts you off. In that case, can someone please tell me:

(a) What deformation compatibility equation to use?
(b) How is it that for the steel, the load is 35 kN and the length, area and extension are all given? What I mean is that if we calculate the Young's Modulus using those figures, it does not come out to be 200 GPa. In that case, what force do we use?
(c)What is the force on each of the aluminum alloy bars?

 

[Astronuc]

The total displacement of the loaded end of the steel bar is to be limited to 0.4 mm.

Excluding the deflection of the horizontal bar, there are two dimensional changes to consider: 1) the steel bar will stretch under tension, which will include the 35 kN load and its own weight, and 2) the contraction of the Al tube(s) under compression. One has to determined the length increase in the steel rod and subtract that from the 0.4 mm, and that result will be used to determine the minimum thickness of the Al tube using the appropriate stress/strain relationship.

This appears to be a homework problem, thus it should be posted in the Homework forums.

 

[ravenprp]

To calculate the minimum thickness required for the aluminum alloy tube, we can use the following formula:

t = (3FL^3)/(8EI)

Where:
t = minimum thickness
F = maximum load (35 kN)
L = length of the tube (25 m)
E = Young's Modulus (73 GPa)

To answer your questions, the deformation compatibility equation that can be used is the one mentioned above. This equation takes into account the maximum load, length, and Young's Modulus to determine the minimum thickness required for the tube.

For the steel rod, the load of 35 kN is given as the maximum load that the tube must support. The length, area, and extension are given to provide information about the material properties of the steel rod. The Young's Modulus of 210 GPa is the material property of the steel and is used in the calculation of the minimum thickness for the aluminum alloy tube.

The force on each of the aluminum alloy bars can be calculated by using the formula F = E*A*ΔL, where:
F = force
E = Young's Modulus (73 GPa)
A = cross-sectional area of the bar (calculated using the given outer diameter of 75mm)
ΔL = extension of the bar (calculated using the maximum deflection of 0.40 mm).

I hope this helps clarify any confusion and helps you in your calculations. It is important to use the correct equations and values in order to accurately determine the minimum thickness required for the aluminum alloy tube to support the steel rod.