Compound Normal & Shear Stresses

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Presentation transcript:

Compound Normal & Shear Stresses Lecture # 25 Compound Normal & Shear Stresses Problem… Find the state of stress at point A, B and C, which are contained in a plane 100in from the free end, Show stress over an element. y 40N C 30N A B z 12mm x Free End 100mm 6mm

Internal forces and moments Solution… Internal forces and moments x y z 40N 30N 30 4000 60 40 3000 y Summary: N = 0 Mz = 4000 My = 3000 Vz = 30 Vy = 40 T = 60

Compound Normal Stress…

Compound Shear Stress…

2 3  x-plane 4 5 6  y-plane 7 8 9  z-plane y 69.4 0.833 0.625 z 41.6 0.269 0.625 0.833 2 1 3 6 4 5 9 7 8 2 3  x-plane 4 5 6  y-plane 7 8 9  z-plane

Stress Transformation Objective: To be able to find the maximum stress and the maximum shear stress and their orientation.

Plane, Stress Transformation + Fx’ = 0; + Fy’ = 0;

Principal Normal Stress

Maximum Shear Stress

Mohr's Circle

R = distance between A and C max = C + R min = C – R max =  R min A (x, xy) R 2P 2S R = distance between A and C max = C + R min = C – R max =  R min 2S + 2P = 90o

The enD