**Find increase in the length of bar:**

**Q: Find increase in the length of bar of uniform section because of self weight.**

**Sol.: **Take a bar of cross sectional area A and length l hanging freely under its own weight as shown in figure

Let attention be focused on a small element of length dy at distance *x *from the lower end. If ' ω ' is specific weight (weight per unit volume) of bar material, then total tension at section m-n equals weight of bar for length y and can be given by

*P *= *Ay*

As a result of which load, the elemental length *dx *elongates by small amount *Ax*, and

The total change in length of bar because of self weight is worked out by integrating above expression between limits *y *= *a *and *y *= l. Thus,

The total change in length of bar because of self weight is worked out by

integrating the above expression between limits y = a and y = l. Thus,

If W is total weight of bar (*W*= *wAl*), then *w *= *W*/*Al*. In that case, the total extension of the bar

Figure

Thus total extension of bar because of self weight is equal to the extension that would be produced if ½ of the weight of bar is applied at its end.