Question

2.3 6/6 points (graded) Brass has a Young's Modulus of E = 97GPa, shear modulus of G = 37GPa and a Poisson's Ratio of v = 0.31. A block of isotropic, linear elastic brass is subjected to an in-plane stress as shown in the figure, where 0, 120MPa, 0y = 110M Pa, Ozy 75 MPa, o, = Ozz = y2 = 0. a) Give numerical values for all strain components. 6 03 Oy os 0 0 ere to search O

Answer 1

Toy = Txy = 7smpa = 120mpa Oy=11ompa 02-0 2 = 0.31, E = 97 GPA G=37 GPa As we know that from Strain formula En 203) =hlox - uloto) E Eus (120- 720-_- 6313 10) 97710 Ex = 0.88X10 Ex= 8.35 X 10 1 Answers =) ty= /[oy-re (ox) ] =) ty= [ 110 -- 0.31x120) 974103 Ey = 7,50X109 3 Anvers +2= 1 1 [ Oz - M(extoy) Ez = 1 [ 0 – 0.31*(120+110)] 97X10 -Answer 62=-7. 35X10a we know that G = Tony ray 2 Shear strain 75 37x10 I Try 2.0 270 X10 Vay = for ry, z o racz=0 Frey = -0.00202 Answer
c
b principal stresses 012 = betes era + try 072 = 1207110 + √ (120-11 (120+10)2 + (7533 02= is 1 75. 16 0 = 190.16 MPa d = 39.84 mpa Strain energy perunit volume + trop +03 - 2 28/0702) VE 12 f 190.76 + 39.897–280.311190.316839.84]] 0 2x97x109 U = 170,365.70 J/m3 | Answer