An aluminum tube of 90-mm outer diameter is to carry a centric load of 120 kN. Knowing that the stock of tubes available for use are made of alloy 2014-T6 and with wall thicknesses in increments of 3 mm from 6 mm to 15 mm, determine the lightest tube that can be used.

9mm tube

Explanation:

Given data:

Outer diameter = 90-mm   therefore outer radius ( R ) = 90/2 = 45-mm

centric load = 120kN

wall thickness of tubes = 3mm from 6 mm to 15 mm

length of column = 2.25 m

Inner radius ( r )  = 45 - 6 = 39-mm

Determine the lightest tube to be used

we calculate the area of the column = 1.593 * 10^-3 m^2

next we determine the moment of Inertia = 1.4036 * 10^-6 m^4

determine radius of Gyration = 0.02977 m

slenderness ratio = 75.57

Allowable stress = 65.14

Allowable load = ( allowable stress * Area ) = (65.14 * 10^6 * 1.583 * 10^-3) = 103.12 kN

Attached below is a detailed solution

In order to make the right choice the given value Pall will be greater than 120Kn hence we will use 9mm thickness as the lightest tube

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