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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 • σ z – Direct stress (due to bending moments or bending action of shear loads) 2200 τ – Shear stresses due to shear loads or torsion loads (for closed section) • σ s – Hoop stress, usually zero (nonzero due to internal pressure in closed section beams) τ zs = τ sz = τ shear flow; shear force per unit length q = τ t (positive in the direction of s) Force equilibrium (cont’d) • From force equilibrium considerations in zdirection: • Force equilibrium in sdirection gives Stress Strain Relationships • Direct stress: σ z and σ s strains ε z and ε s • Shear stress: τ strains γ (= γ zs = γ 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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