DEPARTMENT OF MECHANICAL AND MANUFACTURING ENGINEERING UNIVERSITY OF NAIROBI DEPARTMENT OF MECHANICAL AND MANUFACTURING ENGINEERING ENGINEERING DESIGN II FME 461 PART 10 GO NYANGASI January 2007

DISTORTION ENERGY THEORY IN BIAXIAL (PLANE) STRESS SITUATION

PRINCIPAL STRESSES IN BIAXIAL STRESS SITUATION In plane stress situation, the principal stresses are given by the expression

EQUIVALENT STRESS With plane stress, EQUIVALENT stress is

EQUIVALENT STRESS Equivalent stress then becomes

PRINCIPAL STRESS IN TERMS OF PLANE STRESS ELEMENTS Becomes

EQUIVALENT STRESS IN TERMS OF PLANE STRESS ELEMENTS Consequently

EQUIVALENT STRESS-BI-AXIAL STRESS IN TERMS OF STRESS ELEMENTS

EQUIVALENT STRESS IN TERMS OF STRESS ELEMENTS

EQUIVALENT STRESS-BI-AXIAL STRESS IN TERMS OF STRESS ELEMENTS

DISTORTION ENERGY THEORY When Yielding occurs in any material, The distortion strain energy per unit volume At the point of failure Equals or exceeds When yielding occurs in the tension test specimen.

DISTORTION ENERGY THEORY PLANE STRESS SITUATION Design equation becomes

PLANE STRESS SITUATION WITH ONE NORMAL STRESS This situation of plane stress With one normal stress only Arises in the loading of shafts with combined torsion, bending, Shafts with combined torsion and axial loads.