A 25 m flagpole that is not guyed is made of 6061T6 aluminum

A 25 m flagpole that is not guyed is made of 6061-T6 aluminum with an outside diameter of 100 mm and an inside diameter of 80 mm. Assuming that a person at the top of the pole may apply the force due to his mas axially, what is the maximum mass of person that may be supported at the top of the pole? 1. Determine the square cross section of a copper column 15 feet long if it is to carry an axial load of 440 pounds and both ends are fixed. Use a safety factor of 3 2.

Solution

1.Solution:-

E = 70*10³ N/mm² for Aluminium

For pole one end fixed and other is free

L_eff = 2L

      = 2*25000 = 50000 mm

I = /64*(D₀⁴ –D_i⁴)

= /64*(100⁴ – 80⁴ ) = 2.898119 *10⁶ mm⁴

P_c = ²EI/(L_ff)²

  = ² * 70*10³*2.898119*10⁶/(50000)²

   = 800.89 N

Mass of person = 800.89/9.8

                            = 81.72 Kg Answer

(2) Solution:-

Given L =15 feet = 4572 mm

L_eff = 0.5L (for both end fixed)

= 0.5 * 4572 = 2286 mm

E = 120 *10³ N/mm² (for copper)

Axial load = 440 pound

                = 440 * 4.448 = 1957.12 N

Ultimate Axial load = factor of safety * 1957.12

                                    = 3* 1957.12 = 5871.36 N

P_u = ²EI/(L_eff)²

5871.36 = (²*120*10³*(b⁴/12))/(2286)²

b = 23.61 mm

d = 23.61 mm

Size of column = 23.61mm * 23.61mm Answer