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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/mm2
LAB = 300mm
LBC = 310mm
LCD = 310mm
From the given figure
Load on portion AB = PAB = 50 × 103 N
Load on portion BC = PBC = 20 × 103 N
Load on portion CD = PCD = 60 × 103 N
Area of portion AB = Area of portion BC = Area of portion CD = A = Πd2/4
= (180)2/4 = 25446.9 mm2
By using relation l = Pl/AE
δLab = (50 × 103 × 300)/( 25446.9 × 180 × 103) = 0.0033mm ---------------- Compression
δLbc = (20 × 103 × 310)/( 25446.9 × 180 × 103) = 0.0012mm ---------------- Compression δLcd = (60 × 103 × 310)/( 25446.9 × 180 × 103) = 0.0041mm ---------------- Compression As net change in length = - δ Lab - δ Lbc - δ Lcd
= - 0.0033 - 0.0012 - 0.0041
= - 0.00856 mm
Decrease in length = 0.00856mm .......ANS
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