1108402材料力学作业

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Abstract:Usebasicassumptionsofmechanicsofmaterialsstraightbeam

andhooke’slawtodeducethecalculationformulaofnormalstressinpurebendingofcurvedbeam.Underthecircumstancesofde ningtherelativeerrorεr,outsideandinsidediameterratioα,wegettherangewhichcanuseformulatoreplacetheelasticmechanics:1.295≤α≤1.521or1<α≤1.257.Andvalidateitbyusingstraightbeamformula.Whentheradiusofcurvatureofthecurvedbeamcentroidaxistendstoin nity,theformulaturnintoanormalstressstraightbeamformula.Sowecangetnormalstressofcurvedbeamformulawithsmallerror.

KeyWorld:curvedbeam¶normalstress

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Äk3α=1.001→10.001 m£Xã2.2.1¤§¿b éØ 3εr≤5% ± ɧ µ

Xã2.2.2Úã2.2.3§KXJ éØ ¦32.3%≤max{εr}≤5%§ …= 1.295≤α≤1.521½1<α≤1.257â ±^ í úªCqO“ 5åÆúª"

XJ éØ ¦3max{εr}≤2.3%§ …= 1<α≤1.257â ±^ í úªCqO“ 5åÆúª§ α→1,Ø "Xã2.2.2µ α=1.001,max{εr}=5.469×10 7§ @ üúª "

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