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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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This note was uploaded on 01/30/2014 for the course EMCH 210 taught by Professor Osama during the Winter '08 term at Penn State.
 Winter '08
 OSAMA

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