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07-01ChapGere.0010 - 434 A-PDF Analysis of Stress and...

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Problem 7.2-18 The surface of an airplane wing is subjected to plane stress with normal stresses x and y and shear stress xy , as shown in the figure. At a counterclockwise angle 30° from the x axis the normal stress is 35 MPa tension, and at an angle 50° it is 10 MPa compression. If the stress x equals 100 MPa tension, what are the stresses y and xy ? Solution 7.2-18 Plane stress 434 CHAPTER 7 Analysis of Stress and Strain y x O xy y x = 100 MPa x 100 MPa y ? xy ? At 30 , (tension) At 50 , (compression) Find y and xy F OR 30 : or 0.25 y 0.86603 xy 40 MPa (1) 100 s y 2 100 s y 2 cos 60 t xy sin 60 s x 1 35 s x 1 s x s y 2 s x s y 2 cos 2 u t xy sin 2 u s x 1 10 MPa s x 1 35 MPa F OR 50 : or 0.58682 y 0.98481 xy 51.318 MPa (2) S OLVE E QS . (1) AND (2): y 19.3 MPa xy 40.6 MPa 100 s y 2 100 s y 2 cos 100 t xy sin 100 s x 1 10 Problem 7.2-19 At a point in a structure subjected to plane stress , the stresses are x 4000 psi, y 2500 psi, and xy 2800 psi (the sign convention for these stresses is shown in Fig. 7-1). A stress element located at the same point in the structure, but oriented at a
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