Question

Figure 4 shows an element experiencing several stress components. Determine the following: 1. The stress components Oxvxr. Oysy, and T xuy, acting on the element oriented at a counter clockwise angle = 40° from the horizontal x axis 2. The principal stresses, the maximum shear stress and their associated angles For each of the stress state calculated in parts 1 and 2, show all results on sketches of properly oriented elements. Note: Solutions MUST be obtained using Mohr's circle ONLY. If you solve with stress transformation equations, you will receive zero marks. The Mohr's circle, workings to calculate all the stress components, and angles must be shown in the scanned pdf. Scanned solutions without any workings will also receive zero marks. 108 MPa 30 MPa 52 MPa

Answer 1

Detailed answer of above asked question is solved as below.

→ Given 108mpa 30MPa 52 mpo le 6xx'= -52 MPa (compression) by y'= 108 MPa (Tensile) Zxy = 30 MPO put 1 cm = 2ompa 6xx' = -52npa byy=108rpa D Zmax bn 2002 -Zx'y = 30MPO P O 2011 B c20 А lot Bn2 = minor DY bri= major principal principal stress. Stress 10 - steps ) select origine o Toke lcm = 20mpa, Take os= 108 = 5.4 cm. op= -52/20 = 2.6cm, 2 Draw perpendicular. from pands such that PR =P Q = 30120= 1.5cm 3) jorn RQ and mark c as centre of circle where segment RQ interseed x-axis 4) Draw circle with radius. ca 5) Mark point A4 B. on horizontal axis when circle cut the axis. 6) Principal stress in = oAyscale 5:8X20 - 116 MPa (Tensile) In2= OBXscale: -209%20--58 Mpd (compressive) ON CR

7) orientation of principal plane. 20p1= L Q CS = 20° 2 P2 = LACR = 200 " ☺ pi= 100 Op2 = 9oo. 0 8) Maximum shear stress Zmax=CD x scale = 4.4 X20= 88 MPa g) Draw line CH ot angle. 20 = 2X40° 80' worot Horizontale in 4th quadrant (for antrelockwise) 10) Draw perpendicular from it to x-axis & mark it point e 11) Normal stres on=oExscale = 2.2x200 = 44 MPa Tongential stress=&t= EH x Belle = 48x200 = 86 MPa.