Purpose of Mohr’s Circle Visual tool used to determine the stresses that exist at a given point in relation to the angle of orientation of the stress element. There are 4 possible variations in Mohr’s Circle depending on the positive directions are defined.

Sample Problem A particular point on the part Some Part y x sy = -2 ksi Some Part sx = 6 ksi txy = 3 ksi x & y  orientation

Mohr’s Circle t (CW) sy = -2 ksi x-axis y-axis (6 ksi, 3 ksi) 6 3 sx = 6 ksi (-2 ksi, -3 ksi) 2 3 txy = 3 ksi s Center of Mohr’s Circle

Mohr’s Circle (savg, tmax) t (CW) sy = -2 ksi x-face sx = 6 ksi (6 ksi, 3ksi) txy = 3 ksi s s2 s1 savg = 2 ksi (-2 ksi, -3ksi) y-face (savg, tmin)

Mohr’s Circle (savg, tmax) t (CW) (2 ksi, 5 ksi) sy = -2 ksi x-face sx = 6 ksi (6 ksi, 3ksi) R 3 ksi txy = 3 ksi s s2 s1 4 ksi y-face s1 = savg + R = 7 ksi s2 = savg – R = -3 ksi (savg, tmin) (2 ksi, -5 ksi)

Mohr’s Circle (savg, tmax) t (CW) (2 ksi, 5 ksi) sy = -2 ksi x-face sx = 6 ksi (6 ksi, 3ksi) 3 ksi 2q txy = 3 ksi s s2 s1 4 ksi y-face (savg, tmin) (2 ksi, -5 ksi)

Principle Stress Element (savg, tmax) (2 ksi, 5 ksi) t (CW) s2 = -3 ksi x-face (6 ksi, 3ksi) q = 18.435° 3 ksi s1 = 7 ksi 2q s Principle Stress Element s2 s1 4 ksi Rotation on element is half of the rotation from the circle in same direction from x-axis (savg, tmin) (2 ksi, -5 ksi)

Maximum Shear Stress Element (savg, tmax) (2 ksi, 5 ksi) t (CW) x-face savg = 2 ksi f = 26.565° (6 ksi, 3ksi) 2f tmax = 5 ksi 3 ksi 2q s savg = 2 ksi s2 s1 Maximum Shear Stress Element 4 ksi y-face (savg, tmin) (2 ksi, -5 ksi)

Relationship Between Elements savg = 2 ksi tmax = 5 ksi sy = -2 ksi savg = 2 ksi f = 26.565° sx = 6 ksi q = 18.435° s2 = -3 ksi txy = 3 ksi s1 = 7 ksi q + f = 18.435 ° + 26.565 ° = 45 °

What’s the stress at angle of 15° CCW from the x-axis? y A particular point on the part V x s = ? ksi Some Part s = ? ksi U 15° x t = ? ksi U & V  new axes @ 15° from x-axis

Rotation on Mohr’s Circle (savg, tmax) Rotation on Mohr’s Circle t (CW) (sU, tU) x-face 30° s s2 s1 savg = 2 ksi y-face 15° on part and element is 30° on Mohr’s Circle (sV, tV) (savg, tmin)

Rotation on Mohr’s Circle (savg, tmax) t (CW) Rotation on Mohr’s Circle (sU, tU) x-face R sU = savg + R*cos(66.869°) sU = 3.96 ksi sV = savg – R*cos(66.869°) sV = 0.036 ksi tUV = R*sin(66.869°) tUV = 4.60 ksi 66.869° s s2 s1 savg = 2 ksi y-face (sV, tV) (savg, tmin)

What’s the stress at angle of 15° CCW from the x-axis? y A particular point on the part V x sV = .036 ksi sU = 3.96 ksi Some Part U 15° x t = 4.60 ksi