00:01
Hello students, in this question we have given first sigma for x 0 and sigma for y is minus 50 mpa and tau for xy is 30.
00:12
Now as we know that standard convention is that the angle of the plane should be from vertical plane and it anticlockwise manner.
00:22
So we can write 20 plus theta is 90.
00:25
This is from figure given in the question.
00:28
So from here we can find theta and that is 70 degree.
00:32
Now first for normal stress.
00:37
So for normal stress sigma n will be sigma x plus y upon 2 plus sigma x minus y upon 2 cos of 2 theta plus tau for xy sin 2 theta.
00:55
Now we can find sigma and that is 0 minus 50 upon 2 plus 0 plus 50 upon 2 cos of 140 plus 30 sin of 140.
01:11
Now from here we can find the value of sigma that is minus 24 .867 pascal.
01:21
Now shear stress.
01:28
So using the formula that is x minus y upon 2 sin of 2 theta minus tau xy cos of 2 theta.
01:39
Now substituting the values after substituting we get 0 minus 50 upon 2 sin of 140 minus 30 cos of 140.
01:53
Now from here we can find the value that is 6 .911.
01:59
Now next for maximum normal stress normal stress.
02:12
So d sigma upon d theta is equal to 0.
02:17
So we can write d by d theta of x plus y upon 2 plus x minus y upon 2 cos of 2 theta plus tau xy sin of 2 theta is equal to 0.
02:33
Now from here sigma x minus y upon 2 minus 2 sin of 2 theta plus 2 tau of xy cos 2 theta is equal to 0...