Question

wise 5. An element in pure shear is subjected to stresses thy 32 MPa, as shown in the figure. Using Mohr's circle, determine: (a) The stresses acting on an element oriented at a counterclockwise angle 0 = 75' from the x axis. (b) The principal stresses. Show all results on sketches of property oriented elements. Vertical 3MPa 32 MPa Horizontal

Answer 1

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Sol. Given data, Element is under pure shear ) -( 32mpa B nes *(5,9) A 32mpa. = 9xy. the A, B are vertical and Horizontal planes on which Shear stress is acting center For Mohr circle: 10 to ( 5499, ] = (0,0) (: oy= Jy zo] only shear is present Radius R = Ty-Ty - VO 32. Mpa t Tay Ray Mohr The extremities of circle along X- direction Represents Max and Min. principal Stresses . coordinater of A (0,32) BC 0,.-32) clockwise Shear is taken the and cow as ve.

2 *. The distance b/w A and B gives diameter of Mohr Circle. ñ 1 (0,39). C. 9 Go vi B(0, -32) A. A 15 50 The plane will be inclined at an angle of 25° in ew direction wort Vertical or Y- axis. or from plane A. then it If in the component then 'A the Mohr circle. from point "c'plane. will be it is 150 30° in the il C-(0,9) ; o= R. coet 60 32.co860 = 16 mpa. sta Rsin to = 32 Singo - 27.7 MPa - 27.7 16 MPa 16 Mpa. a 87.7

from Mohr circle. 5, 32 Mpa T2= 32 MPa. 90° incw from 'A' in Mohr circle the plane of 'si' is So, in the the component it will be 45° from CA AU in cu. 6r 9 bri be will zero as shear stress element on this on ,2 are X- axie. T.,82 both see We can