Example The axial loading P produces the state

Example: The axial loading P produces the state of stress in the material. Draw Mohr’s circle for this case. P Dr. Ali Al-Gadhib P 1

Solution: F A( , 0) C D E y' x Dr. Ali Al-Gadhib 45 o x' 2

Example: The torsional loading T produces the state of stress in the shaft. Draw Mohr’s circle for this case. T Dr. Ali Al-Gadhib T 3

Solution: A(0, - ) D C B x Dr. Ali Al-Gadhib 45 o x' 4

Example: Due to the applied loading, the element at point A on the solid cylinder is subject to the state of stress shown. Determine the principal stresses acting at this point. A M Dr. Ali Al-Gadhib P T 12 MPa 6 MPa 5

Solution: 12 A 8. R= D 6 49 6 B (MPa) C 2. 49 MPa 14. 5 MPa x' Dr. Ali Al-Gadhib 22. 5 o x (MPa) 6

Example: The state of plane stress at a point is shown on the element. Determine the maximum in-plane shear stresses and the orientation of the element upon which they act. 90 MPa 60 MPa Dr. Ali Al-Gadhib 20 MPa 7

Dr. Ali Al-Gadhib Solution: 8

Example: The state of plane stress at a point is shown on the element. Represent this state of stress on an element oriented 30 o counterclockwise from the position shown. 12 MPa Dr. Ali Al-Gadhib 8 MPa 6 MPa 9

Dr. Ali Al-Gadhib Solution: 10

Dr. Ali Al-Gadhib Example: The beam is subjected to the distributed loading of w = 120 k. N/m. Determine the principal stresses in the beam at point P, which lies at the top of the web. Neglect the size of the fillets and stress concentrations at this point. I = 67. 4 (10 -6) m 4. 11

Solution: 35. 2 MPa Dr. Ali Al-Gadhib 45. 4 MPa 12

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