An element in plane stress is subjected to stresses axx = 15, ayy = 5 and Txy = 4. Using the Mohr's circle determine: a) the stresses acting on an element rotated through an angle 0 = +40° (counterclockwise); b) the principal stresses; and c) the maximum shear stresses. Show all results on sketches of properly oriented elements. Solution:
With reference to Fig. 2.7:
1. The center of the circle is located at
2. The radius and the angle 2p are given by
tan2^ = w =0.8 = 38.66°; f3 =19.33° (2.64-b) 15 5
3. The stresses acting on a plane at 0 = +40° are given by the point making an angle of — 80° (clockwise) with respect to point X(15, 4) or — 80° + 38.66° = — 41.34° with respect to the axis.
4. Thus, by inspection the stresses on the x face are
4.23
5. Similarly, the stresses at the face y are given by oyy = 10 +6.403 cos(180° -41.34°
5.19
6. The principal stresses are simply given by a(i) a(2)
16.4
0(1) acts on a plane defined by the angle of +19.3° clockwise from the x axis, and 0(2) acts at an
angle of
with respect to the x axis.
7. The maximum and minimum shear stresses are equal to the radius of the circle, i.e 6.4 at an angle of
25.70
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