Question

Example: 1.2 A wrench is made of steel (E=210 GPa, v=0.3) with elastic constants of strain components for a state of plane stress at a critical point in the structure are calculated as 6, 50 x 10 = -75x10* 1 = 150 x 10"rad. a) Determine the complete strain and stress matrices in this state of stress, b) Determine the in-plane state of stress with rotating current coordinate system an angle of 45 degrees clockwise by applying either the transformation equations of plane stress, and c) Show this stress state on such oriented element. Part 2: Principal Stresses and Maximum Shear Stress Example 1.3: Given the stress matrix of 3-D state of stress at a point in a structure as shown O, 1, 1 100 - 2000 [ol-, , 400 O (MPa) 1. Synom. 01 Determine a) the principal stresses and the oriented angle associated with the direction of each principal stress using the transformation equations of plane stress and b) the absolute maximum shear stress at the point according to this stress matrix.

Answer 1

I LUI TO (6) = 1100-2000 - 400 o on = lookpa, og o yoo upe, Iny: 200 hpa ng og ne Principal strey og o digagajati Ingi = 100f 4 to floorkoog F42001 - - 250 + $ 150127120012 . - 250¢ 25. ! - 500, o ma Joonga (Feniled an area an 20. złny takip a 2x (-200) - 100-400 yoo 23.00 y 200 - 53.130 .11 De 226.560 or 116.560 - Absolute mor han strey Ever gegaan Scanngd: with , Cams Farner — Sompe

Dale 4-0.3.? selama CAH2) En = 50x100 Gy = -75x16t, Yay 150 x16 nd E= 210X10 Tipa Weknow that a E Contuty) 1. g. & (ft min) Trg Giling 10x10° (soxio" + (0-38 (+75410937 10.3 j2 21681031508106_2301067 210X10% [ 28X104) 2 576 Mga 210 X109 (-7881667 0.36507106) Q1OX 10.3 x 0.91 Çin 1-(63) S 1 210x108x167" x[=75..15) OX 0.91 210x10x660) 0.91 og = 73.846 Mpa Eny Coling FE=2lite) . 2108103 2x Lito) al 80176X103 cs Scanned with CarScanner ! ! Trys 80.76 *10*x 150 x 100 = 12:11 mpa.