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Fig 3 attachedFigure 3...

Fig 3 attachedFigure 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.

• a.

o i.Calculate the longitudinal stress in the member when it is subject to the purely vertical maximum design load.

o ii.Write down the two-dimensional stress tensor for stresses in the x minus 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.

• 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.

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