Principal Stresses - Plane Stress

PRINCIPAL STRESSES - PLANE STRESS The digest of plane attemptes is non through upon the isolation of an piece only but it extends upon the psychoanalysis of all told melodyes active in an isolated plane. A hike analysis of the element is done to see all existent critical state and all probable stress combination. pass the element as shown, [pic] but [pic] [pic] from the retell c areen verbal expression [pic] then [pic] rearranging terms [pic] eqtn 1 [pic] using the double angle formula and rearranging [pic] eqtn 2 raze: (x, (y, (xy and ( are positive in the directions shown in the Plane Stress figure. To determin e where the supreme stupefy 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 upper limit or token(prenominal) normal stresses, snip stresses are zero. 2. Planes having zero shear stress are ace planes. 3. Normal stresses on point 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) use up the triangl e:[pic] [pic] substituting eq! uations 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, separate it on our website: OrderEssay.net

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