00:01
Hello students here we have a stress matrix that is given as minus 2 3 minus 5 3 6 2 minus 5 2 and minus 4.
00:08
So first of all we need to calculate the principal stresses of this system.
00:14
So principal stresses so we will get first formulas as i1 equal to sigma x plus sigma y plus sigma z and i2 equal to sigma x sigma y plus sigma y sigma z plus sigma z sigma x minus tau xy square minus tau y z square minus tau zx square.
00:51
So and then i3 is the determinant of the matrix.
00:55
So we will get sigma x tau xy tau zx and tau xy sigma y and tau yz tau zx tau yz and sigma iz.
01:17
So these are the three formulas.
01:19
So first we have to calculate the i1.
01:22
So from the given matrix we will get i1 as minus 2 plus 6 minus 4 that is 0.
01:30
So i1 equal to 0 mega pascal and i2 equal to minus 2 into 6 plus 6 into minus 4 plus minus 4 into minus 2 minus 3 square minus 2 square minus of minus 5 square.
01:56
So finally we will get i2 equal to minus 66 mega pascal and we can get i3 as determinant of minus 2 3 minus 5 3 6 2 minus 5 2 minus 4...