An element in a strained body is subjected to a tensile...

An element in a strained body is subjected to a tensile stress of 150MPa and a shear stress of 50MPa tending to rotate the element in an anticlockwise direction. Determine: (i) The magnitude of the normal and shear stresses on a section inclined at 40° with the tensile stress. (ii) The magnitude and direction of the maximum shear stress that can exist on the element.

Transcript

00:01 According to the question we have an element this is the element upon which the shear stress act as 50 mpa while the tensile strength or stress act as 150 mpa.

00:13 Now consider we can take this as an right angle triangle these would be the pointers a, b and c marked the shear stress would be acting this way as 50 as this way as 50 again and in this direction it would be tensile stress that is 150 mpa this is already given to us.

00:36 Now we would be using mohr circle that the center given to us c should be 75 and 0 the coordinates are given as these.

00:55 So the radius of the circle should be radius should be equal to under root 75 square plus 50 square that should be equal to 90 .18 mpa.

01:17 Now understanding this with the circle diagram we have these are the axis, axis y and x.

01:28 Now this is the circle drawing the circle upon the axis then lines would meet at certain points on both the axis.

01:42 Let's mark this point as a and this point as c the center as b joining this with a the x axis this point would be mark as c dash while this point can be marked as a dash.

02:01 Now this is point b we have both these angles let to be q while this is of 80 degrees.

02:13 Now the coordinates for this point is 150, 50 while the coordinates for point a would be 0 minus 50.

02:24 This is the diagram according to this we would be taking tan q or tan theta this can be also taken as theta that is just a demarcation of the angle tan theta is equal to now what will be the value that will be 50 divided by 75 that would give us the value of q or theta q would be equal to 33 .7 degrees...

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