Question

3. A20-t-tall thin hollow tapered tube of a uniform wall thickness of j in. is used for a light pole in a parking lot,as shown in Figure P3 The mean diameter at the bottom is 8 in, and at the top it is 2 in. The weight of the lights on top of the pole is 80 Ib. The pole is made of aluminum alloy with a specific weight of O.1 lbin, a modulus of elasticity E 11,000 ksi, and a shear modulus of rigidity G 4000 ksi. Determine (a) the maximum axial stress; (b) the contraction of the pole. (Hint: Approximate the cross-sectional area of the thin-walled tube by the product of circumference Tapered pole Figure P3.

Answer 1

Tiven Data Height of the tube, h 20ft 240 in Uniform wall thickmess, in Mean diameter at the top, d 2in Mean diameter at the bottom, d 8in Weight at the top, F-801b Specific weight of the mateial 0lb/in a) Considera section of the pole at a distance y fiom thetop end. Write the expression for the mean diameter for the that section. d-d d-d Substitute the given values in the above expression

d-2 6 У 240 240 d=- v + 2 40 Write the expression for the moment of the area. 40 40 64 64 40 64 40 Write the expression for the buckling load 240 π EI nv 240 Since the pole is fixed at both the ends so, Substitute the given values

21.8 40 12 0 ny+2-1.8 40 64 =0.174x- 7 Substitute the corresponding values and solve the above expression. F=0.174x-x11000 14836.5 kips Calculate the stress Calculate the area of the cross section of the pole -Tx2x1.8 = 11.309 in

Substitute the given values in the above expression. 14836.5 11.309 1311.91 ksi b) Write the expression for the concentration of pole rd =0.174 64 d 2.372 in Substitute the given value in equation (1). 2.372--y +2 40 у 14.88 in Thus, the concentration of the pole is at 14.88 in from the top end