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902_Mechanics Homework Mechanics of Materials Solution

# 902_Mechanics Homework Mechanics of Materials Solution -...

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Unformatted text preview: PROBLEM ’7.C1 7.61 A state of plane stress is deﬁned by the stress components a", 0“,, and 1-,, associated with the element shown in Fig. P7.C1a. (a) Write a com- yl puter program that can be used to calculate the stress components 0-,, 03:, and a 11),: associated with the element after it has rotated through an angle 0 about y“ the z axis (Fig. new). (5) Use this program to solve Probe. 7.13 through Try 7.16. SOLUTION 29c: abs/«1 F25440m1~5 Etﬁf-Jﬁ'ﬂoNS (T-fﬁ‘ .. “E‘J'FLtq‘ 01’ (ﬁt-rd}, _ (Ty—T8 Ea: (7.9) Pew: ca; 39 + 7% \$3129 519(7- V), rm: 0*. = cos 26-" 2:35.?»29 S 2 2 (a) _ (7—0“ . a 7.4 (/27: r.- 7‘ 5 y, 9 y z- ! )4! 75.3. 2 5/»25+7;360\$?9 [#753 GQJWBK 7;: AND 6 paw/7“ WALES“ GE WWW—‘0 FOR RUTSUG'ND 7&3: Problem '7 . 13a Problem 7 . 13b Sigma x = -40 MPa Sigma 3: =2 —40 MPa Sigma y a 60 MPa Sigma y = 60 MPa Tau xy = 20 MPa Tau xy = 20 MPa Rotation of element Rotation of element (+ counterclockwise) (+ counterclockwise) theta = ~25 degrees theta = 10 degrees Sigma x' = —37.46 mm Sigma x‘ = -30.14 MPa Sigma 17' = 57.46 MPa Sigma y' a 50.14 MPa Tau x'y' a -25.45 MPa Tau x'y' = 35.89 MPa Problem '7 .143 Problem 7 .141) 80 Mpa Sigma 3: = 0 MPa Sig-ma x = 0 MPa Sigma y a -80 MPa Sigma y = -80 MPa Tau xy = -50 MPa Tau xy = -50 MPa Rotation of element Rotation of element (+ counterclockwise) (+ counterclockwise) theta a —25 degrees theta = 10 degrees 50MP a Sigma x' a 24.01 MPa Sigma x' = -19.51 MPa Sigma 31' a -1o4.01 MPa Sigma y' a: -60.49 MPa Tau x'y' a —1.50 MPa Tau x'y' a -60.67 MPa CONTINUED ...
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