Answer Happy

Tay T Og 1- Consider the element of material shown in the figure subject to biaxial direct and thear stresses. For each of the cases given below. draw the Mohr circle: determine the principal stresses and their direction, as well as the maximum shear stress and its direction. (a) 0 -6 N/mm², oy=8 N/mm3 N/mm? (Ans. 6=10.2, 02-3.8 at -36", Tmax=32) (b) = -5 N/mm², o=7 N/ mm. tx4 N/mm2 (Ans0,=8.2.0--6.2 at -16.8°, Tm=72) (c) =10 N/mm?, gy-6 N/mm² 1,4 Nimm? (Ans. 0,=11, 0=-7 at 13.3", Ima=9) 6 TT, 120 N/mm 30 N/mm2 30 N/mm 2- For the rectangular stressed piece of material shown, draw the Mohr circle and determine the direct and shear stress on the plane shown for: (a) a = 30° (b) a = 45°(c) = 60° (Ans.: (a) o=116 -=-37 (b) =90 r=-80 (e) a=56cm-87) 30 N/mm 30 N/mm2 Tizo Nimo tos 3. For the element shown opposite, determine the maximum and minimum values of the vertical direct stress for which the maximum shear stress present in the block is kept below 35 N/mm² (Ans.: Oymar=97.4 N/mm², Omn=-17.4 Nimm”) 20 N/mm 40 N/mm2 Т" Tos 45 45 75 75 I 45 45 4- A steel plate is subject to two mutually perpendicular stresses, one compressive of 45 MN/m², the other tensile of 75 MN/m², and a shearing stress, parallel to these directions, of 45 MN/m2 (a) Find the principal stresses. (b) Find the strains in the horizontal and vertical axes taking E = 200 GN/m² and ys 0.3 (c) Find the principal strains. (Ans.: (a) 90 MN/m? and - 60 MN/m2 (c) 5.4 104 and 4.35 109) TAS 45