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

L_AB = 300mm

L_BC = 310mm

L_CD = 310mm

From the given figure

Load on portion AB = P_AB  = 50 × 103 N

Load on portion BC = P_BC  = 20 × 103  N

Load on portion CD = P_CD  = 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

δL_ab  = (50 × 103  × 300)/( 25446.9 × 180 × 103) = 0.0033mm ---------------- Compression

δL_bc  = (20 × 103  × 310)/( 25446.9 × 180 × 103) = 0.0012mm ---------------- Compression
δL_cd  = (60 × 103  × 310)/( 25446.9 × 180 × 103) = 0.0041mm ---------------- Compression
As net change in length  = -  δ L_ab  -  δ L_bc  - δ  L_cd

= - 0.0033 - 0.0012 - 0.0041

= - 0.00856 mm

Decrease in length = 0.00856mm                                                                        .......ANS