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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.

= is perpendicular to axis ⋅ = = ⋅ 3 2 12 6 I D R Z I c D R = ⋅ = ⋅ = = ⋅ = ⋅ π π π π 4 4 3 3 64 4 32 4 Parallel Axis Theorem: I = Moment of inertia about new axis I = I +A ⋅d 2 centroid d new axis Area, A I = Moment of inertia about the centroidal axis A = Area of the region d = perpendicular distance between the two axes ...

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