Question

Problem #2 150 pointsl: Gere 7.7-19 During a test of an airplane wing, the strain gage readings from a 45 rosette (see figure) are as follows: gage A, 520 x 10-6, gage 8,360 x 106, and gage C,-80 x 10-6. Determine the principal strains and maximum shear strains, and show them on sketches of properly oriented elements. [Hint: see Gere Example 7-9. Understanding this will help with this problem.) a. b. Draw Mohr's circle for plane strain. Show points A, B, and C(li.e. 0. 45, 909) 459 45

Answer 1

Sigma _x = sigma_A = omega 0 times 10^-6 sigma _y = sigma_c = -80 times 10^-6 alpha _xy = 2 sigma _B - sigma A - sigma c r xy = 2 (360) - 520 - (-80) r max/2 = 331 times 10^-6 r max = 662 times 106-6 rxy = 280 times 10^-6 thetaS_1 = theta p_1 - 45 = - 32 5 principal strains sigma 1 2 = sigma x + sigma 4/2 plusminus squareroot sigma x -sigma y/2)^2 + (r xy/2)^2 theta s_2 = theta s_1 + 90 = 57 5 rmin = -662 times 10^-6 sigma _1 2 = 520 -80/2 plusminus squareroot (520 +80/2)^2 + (280/2)^2 sigma_avg = sigma x + sigma y/2 = 220 times 10^-6 sigma 1 2 = 220 times 10^-6 plusminus 331 times 106-6 sigma _avg = 220 times 106-6 sigma_1 = 551 times 10^-6 sigma _2 = -111 times 10^-6 tan 2 theta p = r xy/sigma - sigma y = 280/5