Problem 1: Stress analysis of a lamina using experimental data from a strain rosette The strain rosette used to measure failure strains at a point yielded the following ratio between the

strains in the lamina coordinate axes: &1= n₂/₁2=0 E2 The lamina was loaded by tensile stresses and ₂. Compare the results obtained by the maximum stress, Tsai-Hill and Tsai-Wu criteria to determine the failure stress. Which of these criteria prescribed the safest stress combination? &c Eb 60° Y 60° 30° QU X 45⁰ Figure 1. Typical strain gauge rosettes (eFunda.com). (a)/nNotes: The ratio of strains: See Table 1 for your variant. Material: See Tables 2 and 3 for your variant. Table 1. The strain ratio measured in the lamina at failure. Variant 1 n Variant 10 1.3 n 1.5 Variant 19 1.4 n 2 1.1 11 1.6 20 0.75 3 1.2 12 1.15 4 0.8 13 0.7 5 2.0 14 0.5 6 1.7 15 1.5 7 0.6 16 1.2 8 0.9 17 0.4 9 0.75 18 1.6 1/nTable 2: Material in Problem 1 (see Table 3 for properties) Var. 1 Material 1 Var. 10 Material 1 Var. Material 19 1 2 1 11 1 20 1 3 1 12 1 4 2 13 2 5 2 14 2 6 2 15 2 7 3 16 3 8 3 17 3 9 3 18 3/nTable 3. Composite materials for problems 1 and 2 (material number in your variant refers to the material in Table 1.1 below) From Table 1.1 Typical properties of unidirectional composites E.J. Barbero, "Introduction to Composite Materials" Density ( Longitudinal Model E Tven Mode GP Inplane Shear Modulus G₁ GP P's Radio Longitudinal Tessile Strength F₁, [MPa] Transverse Tensile Strength PMP Inplane Shear Strength (MP Longitudinal Compressive Strength F₁, [MPa] Transverse Compressive Strength F (MP) elaminar Shear Strength (For Fy) [MPa] Longitudinal Tessile Strain 3, 1963 Longitudinal CTE o [10/C) Transverse CTE [10/ Longitudinal moisture Transserse mistare expansice P Fiber Volume Fract V Void Content V. [] Fiber Misalignment Material number E-Glass S-Class Epoxy Epoxy 2.076 12 55 30 0 55 16 0.2 60 82-85SBASERE 0.19 0.28 10:20 1630 40 60 630 140 60 23 37 Jalalalalalalal 16 60 6.90 140 80 29 32 02 60 2 *** 982-30*****338-3822M E-Glas Kevlar Epery ophtal Polyester 1.85 113 40 40 357 24 6.5 3.53 1.380 75.8 5.5 934 13800 34.5 441 586.0 138.0 48.69 1.8 -1.0 60 0.01 02 60 4 Carbo Carbon/ Carbon Carbon Epoxy Epoxy Epey ASA/35-6 T80/1960-2 1551 ASAPCE PEEK 1.58 142 10.3 7.2 0.27 1830 57 71 1096 228 1.29 -49 27 0 02 60 n 1558 19 5.14 0.3 2608 168 0.0095 0.321 151 9.0 5.6 0.3 L64 57.3 DI 1.6 138 102 5.7 0.3 2000 85 186 1360 400 150 1.45 0.5 30 61 6 2 Carbo Polid ASU Avi Note: Carbon/epoxy, Kevlar/epoxy and boron/epoxy (to a smaller extent) are used in aerospace applications, while less expensive glass/epoxy and glass/polyester are preferred by shipbuilders and in civil engineering. 110 83 37 63 1000 0.5