EngineeringMechanics

20xx-x-xInstructor:WANGZHONG

MarineengineeringShandongtransportvocationalcollegeGeneralStateofStressataPoint(3D)Module5LearningOutcomes?Definethestateofstressforatapointinthreedimensions(3D)?Definethesignconventionforthestateofstressatapointin3D?For

morecomplicatedstructuralmembers,

the

stress

distributions

maynot

be

uniformonarbitraryplanes?Foraninfinitesimally

small

point,

the

stressdistribution

approachesuniformity?Aninfinite

numberor

planescan

be

passedthrougheach

point.?But,it

can

be

shownthatthree

mutually

perpendicular

planes

is

sufficienttocompletelydescribethestateofstressatany

point

for

any

orientation.(Hencewewill

useacubeto

representthestateofstressat

a

point.)General

3DState

ofStress

at

a

Point(Arbitrarily

Loaded

Member)Fig.5.1Fig5.25.2(a)5.35.3,Fig5.2Units.

Sincestressrepresentsaforceperunitarea,intheInternationalStandardorSIsystem,themagnitudesofbothnormalandshearstressarespecifiedinthebaseunitsofnewtonspersquaremeter(N>m2).Thiscombinationofunitsiscalledapascal(1Pa=1N>m2),andbecauseitisrathersmall,prefixessuchaskilo-(103),symbolizedbyk,mega-(106),symbolizedbyM,orgiga-(109),symbolizedbyG,areused

in

engineeringtorepresentlarger,morerealisticvaluesofstress.*GeneralStateofStress.

Ifthebodyisfurthersectionedbyplanesparalleltothex–zplane,Fig.5.3b,andthey–zplane,Fig.5.3c,wecanthen“cutout”acubicvolumeelementofmaterialthatrepresentsthestateofstressactingaroundachosenpointinthebody.Thisstateof