Question

Two vertical wires are suspended at a distance apart of 500 mm as shown in figure. Their upper ends are firmly secured and their lower ends support a rigid horizontal bar which carries load W. The left hand wire has a diameter of 1.6 mm and is made of copper and right hand wire has an area of 0.8 mm and is made of steel. Both wires initially are exactly 4 m long. 

(a) Determine the position of the line of action of W, if due to W both wires extend by the same amount, and 

(b) Determine the slope of wire if a load of 500 N is hung at the centre of the bar. Neglect the weight of bar and take E for steel = 200 kN/mm² and E for copper = 120 kN/mm² .

Answer 1

(a) Let suffix s stand for steel bar and c for copper bar. 

Let P_c and P_s be the forces in copper and steel wire respectively. 

From statics P_c + P_s = W.......(1) 

Taking moment about steel wire

p₁ = \(\frac{W(500-x)}{500}\).....(2)

Taking moment about copper wire

p₂ = \(\frac{Wx}{500}\).....(3)

Since AB remains horizontal

(b) Slope of wire if W is hung in the middle of bar 

From (2)

If the \(\theta\) is the slope of the bar, we get