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Basic Stress Equations - Fairfield University

Dr. D. B. WallaceBasic Stress EquationsInternal Reactions:6 Maximum(3 Force Components & 3 Moment Components)Normal Force) () (Shear ForceszxyPVyVxTorsional Moment) () (Bending MomentszxyTMyMxor TorqueForce ComponentsMoment Components"Cut Surface""Cut Surface"Centroid ofCross SectionCentroid ofCross SectionNormal Force:Axial ForcezxyPCentroid Axial Stress "Cut Surface" =PAl Uniform over the entire cross Axial force must go through Forces:Cross SectionyAaPoint of interestLINE perpendicular to V through point of interest= Length of LINE on the cross section= Area on one side of the LINE Centroid of entire cross sectionCentroid of area on one side of the LINE= distance between the two centroids= Area moment of inertia of entire cross sectionabout an axis pependicular to V. VbAayI"y" Shear ForcezxyVy"x" Shear ForcezxyVx = VAyIbabgNote: The maximum shear Stress for common cross sections are:Cross Section:Cross Section:Rectangular: max= 32 VASolid Circular: max= 43 VAI-Beam or H-Beam:webflange max=VAwebThin-walledtube: max= 2 VABasic Stress EquationsDr.

Basic Stress Equations Dr. D. B. Wallace Bending Moment in Curved Beam: Geometry: r r e rn r σ σo i centroid centroidal neutral axis axis o i y nonlinear stress distribution M c ci o ρ r A dA e r r n area n = = − z ρ A = cross sectional area rn = radius to neutral axis r = radius to centroidal axis e = eccentricity Stresses: Any Position ...

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