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With these angles use trig to nd the coordinates of

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Unformatted text preview: ss •  Find the stress state at an orientaRon rotated by angle θ relaRve to the original orientaRon: •  The state of stress at this orientaRon is given by sx’, sy’ and txy’. •  Sign convenRon: s is posiRve outward, and t is posiRve along posiRve axes on posiRve faces. •  Next we’ll find the relaRonship of sx’, sy’ and txy’ to sx, sy and txy. Plane Stress TransformaRon EquaRons •  Repeated here, are the stress transformaRon equaRons: •  These allow us to find the stresses on a plane element rotated by an arbitrary angle θ relaRve to the original orientaRon. Principal Stresses •  The two principal stresses are: •  Where we always let s1 >= s2 algebraically. •  At principal plane angles θp1 or θp2 the shear stress is: •  This means that on an element rotated to align with principal stresses, there is zero shear stress. Principal Stresses •  θp1 is the angle that rotates the x- axis to the direcRon of s1 •  θp2 is the angle that rotates the x- axis to the direcRon of s2 •  θp1 and θp2 always differ by 90°. On your calculator: •  If •  If Maximum In- Plane Shear Stress •  The max in- plane shear stress is: •  At max in- plane shear plane angles θs1 or θs2 the average normals stress is: •  This means that on an element rotated to align with the maximum in- plane shear stress, the normal stress is equal to the average normal stress on all faces. Maximum In- Plane Shear Stress •  θs1 is the angle that rotates the x- axis to the direcRon of s1 •  θs2 is the angle that rotates the x- axis to the direcRon of s2 •  θs1 and θs2 always differ by 90°. On your calculator: •  If •  If Mohr’s Circle •  The graph of Mohr’s circle is fro...
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