(e) Based on limit state design determine the cross-sectional area of a high yield steel cable which supports a total dead load of 5.0 kN and a live load of 4.0 kN. The characteristic yield stress of the high yield steel is 460N/mm^2 factors of safety for the dead load=1.5, live load=1.7 and steel strength=1.15 (3 marks)

To determine the cross-sectional area of the high yield steel cable, we need to use the limit state design method. The limit state design method is a method of designing structures based on the limit states that the structure is expected to withstand.<br /><br />The first step is to calculate the factored loads. The factored dead load is calculated by multiplying the total dead load by the factor of safety for the dead load:<br /><br />Factored dead load = Total dead load x Factor of safety for dead load<br /> = 5.0 kN x 1.5<br /> = 7.5 kN<br /><br />The factored live load is calculated by multiplying the live load by the factor of safety for the live load:<br /><br />Factored live load = Live load x Factor of safety for live load<br /> = 4.0 kN x 1.7<br /> = 6.8 kN<br /><br />The factored steel strength is calculated by multiplying the characteristic yield stress of the high yield steel by the factor of safety for steel strength:<br /><br />Factored steel strength = Characteristic yield stress x Factor of safety for steel strength<br /> = 460 N/mm^2 x 1.15<br /> = 529 N/mm^2<br /><br />The total factored load is the sum of the factored dead load and the factored live load:<br /><br />Total factored load = Factored dead load + Factored live load<br /> = 7.5 kN + 6.8 kN<br /> = 14.3 kN<br /><br />The cross-sectional area of the high yield steel cable can be calculated using the formula:<br /><br />Cross-sectional area = Total factored load / Factored steel strength<br /> = 14.3 kN / 529 N/mm^2<br /> = 27.05 mm^2<br /><br />Therefore, the cross-sectional area of the high yield steel cable is 27.05 mm^2.