Mohr's Circle - Application Example: The axial loading P produces the state of stress in the material. Draw Mohr’s circle for this case.  P

Solution: D F C E   A(, 0) y' x' x 45o

Example: The torsional loading T produces the state of stress in the shaft. Draw Mohr’s circle for this case.  T

Solution: D C B   A(0, -) x' x 45o

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. M 6MPa 12MPa T P A

Solution: A D B (MPa) C 2.49 MPa x' 14.5 MPa (MPa) 22.5o x 12 R=8.49 6 R=8.49 A x' x 22.5o 2.49 MPa 14.5 MPa

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 20 MPa

Solution:

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

Solution:

Example: The beam is subjected to the distributed loading of w = 120 kN/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) m4.

Solution: 45.4 MPa 35.2 MPa

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