Figure 3 shows a vertical structural member, with a rectangular cross-sectional area, made of an aluminium alloy. The member, which is fixed at its upper end with its lower end unconstrained, is intended to bear a maximum vertical tensile load of F = 20 kN at the centre of its free end. The design specification for the member also indicates that the nominally ‘vertical’ load may be inclined to the vertical by up to 3° in any direction.
Figure 3 Vertical structural member
• a.
i. Calculate the longitudinal stress in the member when it is subject to the purely vertical maximum design load.
• a.
i. Calculate the longitudinal stress in the member when it is subject to the purely vertical maximum design load.
ii. Write down the two-dimensional stress tensor for stresses in the x–y plane. What is the stress state in the member when loaded purely vertically?
• b. Determine the resolved horizontal and vertical forces at the free end of the member when the 20 kN load is inclined at 3° to the vertical.
• c. Calculate the maximum longitudinal tensile stress in the member when the 20 kN load is inclined at 3° to the vertical such that bending occurs about the z-axis only.
you will need to treat the member as a cantilever beam and sum the longitudinal stress due to the axial load with the longitudinal bending stress.
you will need to treat the member as a cantilever beam and sum the longitudinal stress due to the axial load with the longitudinal bending stress.
• d. Repeat the calculation in (c), this time for the case where the 20 kN load is inclined at 3° to the vertical such that bending occurs about the y-axis only.
• e. If the same member was subjected to a purely vertical compressive force of 20 kN at the centre of its free end, determine whether buckling failure would be likely to occur. Assume E = 70 GPa for the aluminium alloy.
