Question

4. (a) Find the normal and shear stresses on the plane indicated on the element. (6) Sketch Mohr's circle. (b) Determine the principal planes and the principal stresses using Mohr's circle approach. Sketch the results. (25 points) .80 M Pa 120 MPa •40 MPa

Answer 1

لهه OB Plane 8ompa 0=+25° plane AO 120MPa Jy YO MPa Jo = 120MPa 80MPa Tay Yompa let two points on moka cercle be A, B A = (120,40) Ja, Try) B = 180,-40) (5g, - Txy) o center of mahr's wrele Diameter (x2-x)²+(92-4.)? AB- Scale :- 1 unit 3 MPa ' AB - 40 Emase 03 20 с o' O D B -Tmax

Distance between a points queen by re-o)² +92-y,,? r AB = Dia (120-89+(40=(,0))? 407+802 - -- AB = 4055 MPa = 89.49 m Pa = 89.44 MPa 2 " Tmax = 44.20 MPa -A00B = cadius of motore circle = 89:44 = 44.72 m Pa radius of make circle now IB c = 40 MPa 1o B = 44.72 MPa oc JOB²-BC² :: Oca 164.73) * + 40% و oc=20 MPa we know that oc=80MPa o'o=80720 loompa .. = 100+44.72 = 144.77 MPa nlow o,= (o'o + radius Ta = 100 - radius) Ja = 100-44.72 = 55.28 MPa Pa = .. mayor frenapal stress T = 144.72 MPa mayor principal plane (ou) plane Minor principal stress 55.28 MPa Minor principal planee - (cz) plane max. shear stress 44.22 MPa mos shear stress plane O Times mas

. : 0,= tan / 40 20 Jueen state - major principal plane angle from on plane -> o 0, - tan" ( 50,- 63.43 This O, is twice angle on moke circle, so in the of stress diagram 0, = 63143 = 02= 0, +180 = 63.43.+ 180 = 243.43° ( cw) O2> angle of munor principal stress & in diagram 102=121-77° 3). 21 اراک) plow 03 angle of mas shear stress plane from of plane 03 = 90-0, 03-90-63.43 ::-03 = 26.57° (CCW) & on diagram 03= 13.285° rlow stress at 0= as" on diagram from plane of in ..oon moka arde = 20 = 50° plane OE CW 0 10,-20) – (63. 43-50) - (13:43) do to A cas 10,-80) To = OA Sin (6-20) To = (4.78 * 0.232) 1.-Jo 100 + 43.5 To 10.38 MPa To = 143.5 MPa