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 s x and s y and shear stress t xy , as shown in the figure. At a counterclockwise angle u 5 30° from the x axis the normal stress is 35 MPa tension, and at an angle u 5 50° it is 10 MPa compression. If the stress s x equals 100 MPa tension, what are the stresses s y and t xy ? Solution 7.2-18 Plane stress 434 CHAPTER 7 Analysis of Stress and Strain y x O t xy s y s x = 100 MPa s x 5 100 MPa s y 5 ? t xy 5 ? At u 5 30 8 , (tension) At u 5 50 8 , (compression) Find s y and t xy F OR u 5 30 8 : or 0.25 s y 1 0.86603 t xy 52 40 MPa (1) 5 100 1 s y 2 1 100 2 s y 2 cos 60 81 t xy sin 60 8 s x 1 5 35 s x 1 5 s x 1 s y 2 1 s x 2 s y 2 cos 2 u 1 t xy sin 2 u s x 1 10 MPa s x 1 5 35 MPa F OR u 5 50 8 : or 0.58682 s y 1 0.98481 t xy 51.318 MPa (2) S OLVE E QS . (1) AND (2): s y 19.3 MPa t xy 40.6 MPa 5 100 1 s y 2 1 100 2 s y 2 cos 100 t xy sin 100 8 s x 1 10 Problem 7.2-19 At a point in a structure subjected to plane stress , the stresses are s x 4000 psi, s y 5 2500 psi, and t xy 5 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 counterclockwise angle
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This note was uploaded on 09/20/2009 for the course COE 3001 taught by Professor Armanios during the Spring '08 term at Georgia Institute of Technology.

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