Question

The hollow thin-walled hollow section of aluminium alloy illustrated below is 1200 mm long. It has one free end and the other is built into a solid wall. At the free end, the following loads are applied in the directions illustrated and distributed evenly over the perimeter of the section:- A central, axial compressive load, P = 10 kN; and A torque, T = 0.2 kN.m. Properties of the aluminium alloy are given as E = 72 GPa and = 0.32.

Answers given: (a) 16 MPa (compressive); (b) 23.57 MPa; (c) sketch; (d) 0.696 deg; (e) 96.16 and 106.26

a) Calculate the normal stress on section due to the axial load P;

b) Calculate the shear stress on the section at the location of the surface element shown due to the torque T; c) Draw a sketch of the surface element and the x-axis direction as indicated in the figure and show the normal and shear stresses on this element;

d) Determine the angle of twist of the thin -walled hollow section over its full length due to the torque T. Express the angle of twist in degrees.  Assuming the axial load is the only load acting at the free end, determine the critical buckling load, Pcr for the configuration shown.

surface element 1200 109 110 75

Answer 1

Calculate the normal stress on section due to the axial load P 10x103 (110x 80)-(75x109) 16MPa Calculate the shear stress on the given section. Tr Tr (0.2×10°)(112) 80×110°-75×109")+ー( 1 1 0x80°-109×75° 12 12 - 6.70 MPa Draw a sketch of the surface element.

mar mar Calculate the angle of twist of the thin -walled hollow section. TL TL GJ 0.2x106 (1200 72x10 2(1+0.32) (80x1103-75x1093)+12(110x803-109 x 753) 12 0.005364 0.3070