Determine the stresses set up in the brass, Civil Engineering

Determine the stresses set up in the brass:

A compound bar is constructed from three bars 50 mm wide by 12 mm thick fastened together to form a bar 50 mm wide by 36 mm thick. The middle bar is of aluminum alloy for which E = 70 GN/m2 and the outside bars are of brass with E = 100 GN/m2. If the bars are initially fastened at 18°C and the temperature of whole assembly is then raised to 50°C, determine the stresses set up in the brass and the aluminium.

For computation purposes, take following values:

αbrass = 18 × 10-6 K-1 , and αaluminium = 22 × 10-6 K-1

Solution

Let the stress in aluminium bar be σa and that in each brass bar be σb. Then for equilibrium

Force in brass = Force in aluminium

σb × 50 × 12 × 2 = σa × 12 × 50

or        2 σb = σa

and from extension considerations, we get

a/Eα) L + (σb/Eb) L = L(αa - αb) ΔT

∴          2σb/70 ×109 + σb/100 ×109 = (22 -18) ×10-6 × (50 - 18)

or        27σb = 4 × 10-6 × 32 × 700 ×  109

or        σb = 3.32 N/mm2    (T)

and     σa = 6.64 N/mm2    (C)

Posted Date: 1/30/2013 6:00:32 AM | Location : United States







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