Question

40 M 45 MP 50 MPA - For the given state of stress, Part A: determine analytically (using stress transformation equations): 1) the principal planes. 2) the principal stresses. 3) Sketch the stress element for the above condition 4) the orientation of the planes of maximum in-plane shearing stress, 5) the maximum in-plane shearing stress and the corresponding normal stress. 6) Sketch the stress element for the above condition Part B: Only use Mohr's circle to determine 1) the principal planes and the principal stresses. 2) the orientation of the planes of maximum in-plane shearing stress, 3) the maximum in-plane shearing stress and the corresponding normal stress. 4) Write down briefly the steps of drawing your Mohr's circle. (Show all relevant calculations) Points 50 Distribution Part A Calculation of all principal stresses and planes: 5 Sketch of the above element: 5 All required calculations for maximum shear stress criteria:5 Sketch of the above element: 5 Part B Drawing of the Mohr's Circle: 10 Determination of stresses and orientation: 15 Writing the steps of drawing: 5

Answer 1

Griven that: 46 MPа » 45 ми Go MPa parta 1) бя: Go Mpa, 68 = – 40 MP4 Tng = 45 Мра principal plane tan (20p) z 2 Try (х - бу stom (200) (245) [r - €о) = (-40] 2 ее , - 17. 4-71 Principal planer Location ді, – – 36-43°4 Јерут 51-26° Answer ). бар 2 6x +69 + 2. 2. (база)*** быз. -Кор % tea“)* 4 (45) 2

62/2 - 50 + 46.097 3.9022 MPa Ansurer 96.og 7 MPa Answer 3 fi lops) 012 Jopa Ang TE [ Princibai stress element] 62 4 Orientation in- plane of the planes of maximum shear stress - 66 Concep is pelames of preesimeem Shear stress 45° the principal planes to Hence Ast = Op+45 = 38.73+45 = 6:27 Os 2 2 90+Gr2.7 96•27) Ang Tosa = 6.27 Ang

5 Max. In plane shear stress Imad 61-62 2 Cmeia z -3.9022796•097 2 Tmax = 46.0949 Meal Ane Correspond Normal stress on Ontby (~66-40) ing 2 51 = Answer 50 MPa y AS 16 Trmica En Os Emas Stress element of Max. In plane Shear stress