Question

The stresses on element A are as shown. Using Mohrs circle: a) Determine the stresses on element B and show these on a sketch of a properly oriented element. b) Determine the principal stresses and show these on a sketch of a properly oriented element. c) Determine the maximum and minimum shear stresses and associated normal stresses and show these on a sketch of a properly oriented element. у Y1 4.0 MPa 2.0 MPa A B 35° 1 1.0 MPa X1

Answer 1

4mpa 2 mpa A B 235 Impa 55. Tmax= 3-16mpa JI G (2,1) A Ampa E 0 3 amipa 20=708 (-1,0) (-4,-1) A Plan an B. Emlin=-3-16mpa Center of circle (0) = 2+(-a) = LO) 2 Radius of ciocle JBc² + BR² = √3² + 12 = 3.16 1 PARTA) ZB CF. tan o = => 0 - fan-'(V3) - 18.43 3 so, CJCB = 70-18-439 : 51:57 Now, JH., feasts sin 56-57 = JH JC-→ Radius of circle JH = 3.16 * sin 51:57 TH=2.47 mpa.

Now, HC, -> HC - COSS.57 * 316 COS S1.57 = HC JC HC = 1.96mpa $ CI= 1.96 mpa KI = 2.47 mpa Stress, 6 = OI CI-CO 1.96-1 x = 0.96 mpa by : @HO - HC + CO -1.96+1 by = 2.96 mpa • 2-96mpa TE JH = 2.47 mpa 2.47mpa В 0-96 mpa (PART-B) CE-CO (3.16-1) Acompa 6 = 2.16 mpa 2-16 53 - OA = AC + Co 3-16+1 3= -4.16 mpa at=0=18.43 = 9.21° 2 Maximum shead stress - Radius of Monics circle 3-16 mpa Minimum shego stress = 3:16 mpa. •3. lompa Noomal stress = -1 mpa.&- 1 mpa. PART-C Impa IImpa