Principal Stresses - Plane Stress

PRINCIPAL STRESSES - PLANE STRESS The digest of plane attemptes is not through upon the isolation of an piece only but it extends upon the epitome of all told extendes alert in an isolated plane. A go on analysis of the element is done to see all existent critical state and all probable stress combination. regard the element as shown, [pic] but [pic] [pic] from the retell tap legislation [pic] then [pic] rearranging terms [pic] eqtn 1 [pic] using the double angle formula and rearranging [pic] eqtn 2 celebrate: (x, (y, (xy and ( are positive in the directions shown in the Plane Stress figure. To determine where th e supreme baffle to of (n occurs: [pic] [pic] [pic] settlement for the angle (, [pic]eqtn 3 where (p locates the plane where (n is extremum. Equating eqtn 2 to zero, [pic] and solving for the angle (,[pic]eqtn 4 NOTE: 1.

On planes of maximum or token(prenominal) normal stresses, snip stresses are zero. 2. Planes having zero shear stress are ace planes. 3. Normal stresses on monger planes are principal stresses. 4. Two values of principal stresses are 90( apart. From trigonometry, convert ( = tan (( + 180) tan 2(p1 = tan (2(p1 + 180) = tan (2(p2) contemplate the triangle:[pic] [pic] substituting equations ! 5 & 6 to equation 1 [pic] [pic] where (p1 and (p2 are called principal stresses. Actual analysis would involve 3 principal stresses. A simplification reduces the third plane stress to zero, ((p3 = (z = 0). To determine where the maximum in-plane shearing stress occurs: [pic] [pic] [pic] where (( locates the plane where (nt is maximum. [pic](negative reciprocals) NOTE: 2(( & 2(p are 90(...If you requisite to get a full essay, roll it on our website: OrderEssay.net

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