a: 1 The state of plane stress at a point P is shown on the element in Figure be

Question

a: 1 The state of plane stress at a point P is shown on the element in Figure below. 12 ksi 6 ksi 6 ksi (a) Draw neat Mohn's circle to a proper scale by choosing proper sign convention. (b) Show the reference line from where the angle measurement is made. (c) Determine the state of plane stress at point p acting at an angle 70 degrees. (d) Draw the FBD of the element showing the stresses acting on it. (e) Find the Principal plane Angle and its value. (f Find the value of Principal shear stress (g) Draw the FBD of the element showing all shear stresses with proper sign convention (h) Find the value of normal principal stresses (i) Draw the element configuration showing all signs for principal stresses. Verify the above results by theoretical calculations

Explanation / Answer

tan2p = 2xy/(x-y) = 0.6667 p = 18.42 deg or 108.42 deg

s = p-45 = -26.58 or s = p+45 = 63.42 deg (These two represents physically the same FBD)

1=(x+y)/2+(x-y)/2cos2p1 + xysin2p1 = -7.80 ksi

2=(x+y)/2+(x-y)/2cos2p2 + xysin2p2 = 13.80 ksi

s=-(x-y)/2cos2s1 + xysin2s1 = -10.381 ksi

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