Determine change in length of the bar:
A steel bar is subjected to loads as shown the given figure. Determine change in length of the bar ABCD of 18 cm diameter. E = 180 kN/mm2.
Sol.:
As d = 180mm
E = 180 × 103 N/mm^{2}
L_{A}_{B} = 300mm
L_{B}_{C} = 310mm
L_{C}_{D} = 310mm
From the given figure
Load on portion AB = P_{A}_{B} = 50 × 103 N
Load on portion BC = P_{B}_{C} = 20 × 103 N
Load on portion CD = P_{C}_{D} = 60 × 103 N
Area of portion AB = Area of portion BC = Area of portion CD = A = Πd^{2}/4
= (180)2/4 = 25446.9 mm^{2}
By using relation l = Pl/AE
δL_{a}_{b} = (50 × 103 × 300)/( 25446.9 × 180 × 103) = 0.0033mm ---------------- Compression
δL_{b}_{c} = (20 × 103 × 310)/( 25446.9 × 180 × 103) = 0.0012mm ---------------- Compression
δL_{c}_{d } = (60 × 103 × 310)/( 25446.9 × 180 × 103) = 0.0041mm ---------------- Compression
As net change in length = - δ L_{a}_{b} - δ L_{b}_{c} - δ L_{cd}
= - 0.0033 - 0.0012 - 0.0041
= - 0.00856 mm
Decrease in length = 0.00856mm .......ANS