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Unformatted text preview: AERSP 301 Shear of beams (Open Crosssection) Jose Palacios Shear of Open and Closed Section Beams Megson Ch. 17 Open Section Beams Consider only shear loads applied through shear center (no twisting) Torsion loads must be considered separately Assumptions Axial constraints are negligible Shear stresses normal to beam surface are negligible Near surface shear stress = 0 Walls are thin Direct and shear stresses on planes normal to the beam surface are const through the thickness Beam is of uniform section Thickness may vary around c/s but not along the beam ThinWalled Neglect higher order terms of t (t 2 , t 3 , ) Closed Section Beams Consider both shear and torsion loading Force equilibrium: General stress, Strain, and Displacement Relationships S the distance measured around the c/s from some convenient origin z Direct stress (due to bending moments or bending action of shear loads) 2200 Shear stresses due to shear loads or torsion loads (for closed section) s Hoop stress, usually zero (nonzero due to internal pressure in closed section beams) zs = sz = shear flow; shear force per unit length q = t (positive in the direction of s) Force equilibrium (contd) From force equilibrium considerations in zdirection: Force equilibrium in sdirection gives Stress Strain Relationships Direct stress: z and s strains z and s Shear stress: strains (= zs = zs ) Express strains in terms of displacements of a point on the c/s wall v t and v...
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 '09
 GANDHI,FARHANLESIEUTRE,GEORGE

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