For a prismatic bar loaded in tension by an axial force P, the elongation of the bar can be determined as Suppose the bar is loaded at one or more intermediate positions, then equation (1) can be readily adapted to handle this situation

**Deformation of compound bars under axial load**

For a prismatic bar loaded in
tension by an axial force P, the elongation of the bar can be determined as
Suppose the bar is loaded at one or more intermediate positions, then equation
(1) can be readily adapted to handle this situation, i.e. we can determine the
axial force in each part of the bar i.e. parts AB, BC, CD, and calculate the
elongation or shortening of each part separately, finally, these changes in
lengths can be added algebraically to obtain the total charge in length of the
entire bar.

When
either the axial force or the cross -
sectional area varies continuosly along the axis of the bar, then equation (1)
is no longer suitable. Instead, the elongation can be found by considering a
deferential element of a bar and then the equation (1) becomes i.e. the axial
force Pxand area of the cross - section Ax must be
expressed as functions of x. If the expressions for Pxand Ax are not too
complicated, the integral can be evaluated analytically, otherwise Numerical
methods or techniques can be used to evaluate these integrals.

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Civil - Mechanics Of Solids - Stress, Strain And Deformation Of Solids : Deformation of compound bars under axial load |

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