Answer Happy

A [+45/0₂] s graphite-reinforced plate is subjected to a biaxial loading such that the stress resultant in the y direction is opposite in sign to and one-half the magnitude of the stress resultant in the x direction. Call the stresses resultant in the x direction N; the loading is given by Nx = N Ny = -0.5N Nxy = 0 (a) Use the Tsai-Wu criterion to compute the value of N to cause failure. (b) What layers control failure? (c) Use the contribution to unity of each term in the criterion to estimate the failure mode. To answer these questions, construct a table similar to Table 10.4. (d) Compare the results with the predictions of the maximum stress criterion, Exercise 2 in the Exercises for Section 9.2.
02 Torsion T12 Axial load 01 FIGURE 10.10 Cylindrical specimen for determining F12 in the Tsai-Wu criterion Pressure
TABLE 10.4 Summary of loads P (kN) to cause failure in [±20/03] tube: Tsai-Wu criterion* +20° layers -20° layers 0° layers P = -198 P = +350 P = -198 P = +350 P = -156.0 -758 1340 -758 1340 -743 01, MPa σ2, MPa 712, MPa 26.3 -51.9 0 0 F101 0.101 -0.179 0.101 -0.179 0.099 -0.196 F202 0.334 -0.590 0.334 -0.590 0.394 -0.779 F₁10² 0.306 0.958 0.306 0.958 0.295 1.149 F2202/2 0.049 0.155 0.049 0.155 0.069 0.269 F66712 0.087 0.271 0.087 0.271 0 0 -√F11F220102 0.123 0.385 0.123 0.385 0.143 0.556 Total 1.000 1.000 1.000 1.000 1.000 1.000 *The maximum stress failure criterion predicts failure with a positive axial load of P = +315 kN; failure is due to tensile stresses in the fiber direction in the 0° layers. Failure with a negative axial load occurs when P = -262 kN and is due to compression stresses in the fiber direction in the 0° layers. 22.2 29.4 -39.3 -52.1 22.2 29.4 -39.3 -52.1 P = +308 1467