Determine change in length of the bar, Mechanical Engineering

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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

 

2172_Determine change in length of the bar.png

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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