机器设计-综合方法p0565.pdf

MACHINEDESIGN-AnIntegratedApproach,4thEd.5-65-1

PROBLEM5-65

Statement:Adifferentialelementissubjectedtothestresses(inksi):=10,=-5,=15.Thematerialis

xyxy

unevenandhasstrengths(inksi)ofS=50,S=40,andS=90.Calculatethesafetyfactorand

utyuc

drawaa-bdiagramshowingtheboundaryforeachtheorywiththestressstateandloadline

using:

(a)Coulomb-Mohrtheory,and

(b)ModifiedMohrtheory.

Given:Stresscomponentsσx10ksiσy5ksiτxy15ksi

MaterialpropertiesS50ksiS40ksiS90ksi

utyuc

Solution:SeeFigure5-65andMathcadfileP0565.

1.Calculatethenonzeroprincipalstressesusingequation4.6a.

2

σσσσ

xyxy2

σaτxyσa19.3ksi

22