00:01
Length of the bar capital l equals to 6 feet and thickness t equals to 0 .75 inch and it is subjected to a force p equals to 20 kilo newton at the end and the width of the bar varies from b1 equals to 4 .0 inch to b2 equals to 6 .0 inch and the larger end to the larger end okay and we have also e equals to 25000 ksi so now for the diagram is this okay this is the diagram of the question so now in which we can take an element this is an element okay small element which is at x distance from one end and it element has a width of d x now this is b1 and this is b2 and this is total length l and this force is p and this is the thickness okay this is the thickness okay now for this element we can write the value of b here so b will be equals to b1 plus b2 minus b1 divided by l multiplied by x okay so elongation in this element will be d -dl, this will be given by p -dl -d -x divided by b -t multiplied by e.
01:34
Okay, so this will be the elongation from the young's modellus of elasticity.
01:39
So from here we get del equals to this is a small elongation and this is complete elongation.
01:44
So integration of p -d -x divided by b -t multiplied by e.
01:50
So now substituting values in this equation we get dl equals to p by te and integration from 0 to capital l.
02:01
Substituting value of b here so dx divided by b1 plus b2 minus b1 divided by capital l multiplied by x.
02:11
Okay, so now from here after integrating this we get dl equals to p by t e multiplied by ln and b1 plus b2 minus b1 by l multiplied by x and this complete divided by b2 minus b1 divided by l okay and the limits are from 0 to l okay these are the limits so now solving further after substituting these limits we will get that elongation dell will be equals to p l p l divided by t e and b2 minus b1 and ln b2 by b1.
02:56
Okay, this will be the final result after substituting these limits...