Mechanical Engineering Material: Composite bars:

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Saturday, March 24, 2012

Composite bars:

A composite bar may be defined as a bar made up of two or more materials joined together in such a manner that both are extended or contracted as a single unit. The main considerations while solving a composite bar problem is
1) strain in all the materials is same. This is because elongation or contraction is same in the composite bar.
2) total load on the composite bar is sum of loads on each bar
Consider a composite bar shown in the figure. And let P-total load on the bar
A1,A2-area of bars (1) and (2)
E1,E2-youngs modulus of the bar (1)and(2)
P1,P2-load carried by the bar (1) and (2)
L,§l-length,Location of the composite bar

From the problem we can say that-
P=P1+P2
Stress in bar(1) p1=P1/A1
Strain in bar (1) = e1=p1/E1=P1/A1E1
:. Elongation §l=P1l/A1E1
similarly §l=P2l/A2E2
In composite bars §l1=§l2
=> P1l/A1E1=P2l/A2E2
Deducing them we get
P1=P*A1E1/(A1E1+A2E2)
AND P2=P*A2E2/(A1E1+A2E2)

Mechanical Engineering Material