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Unformatted text preview: Who wants to win a million dollars ? Who wants to drop the lowest score of his/her HW ? • $ 10,000 question • $ 100,000 question • $500,000 question • $1,000,000 question • $10,000 question • $100,000 question • $500,000 question • $1,000,000 question Lecture 21 Shearing Stresses in Beams and ThinWalled Members Shear Stress in Beams Introduction ( ) ( ) M y M dA F dA z M V dA F dA z y M dA F x z xz z x y xy y xy xz x x x = − = = = = = − = = = − = = = ∫ ∫ ∫ ∫ ∫ ∫ σ τ σ τ τ τ σ • Distribution of normal and shearing stresses satisfies • Transverse loading applied to a beam results in normal and shearing stresses in transverse sections. • Longitudinal shearing stresses must exist in any member subjected to transverse loading. • When shearing stresses are exerted on the vertical faces of an element, equal stresses must be exerted on the horizontal faces Shear Stresses in Beams of Rectangular Cross Section • In these cases, both normal and shear forces are developed in the beam. • Normal stresses are calculated with the Flexure Formula. • We will now look at the Shear Stresses Vertical Shear Stresses • Consider a beam of rectangular cross section subjected to a positive shear force. How the shear force is being passed in a beam ? Vertical & Horizontal Shear Stresses • Consider a cantilever beam made up of planks that are not bonded and subjected to transverse loading. • Each individual plank will be subjected to slip at the interfaces. • Plane sections before deformation do not remain plane after deformation. Vertical & Horizontal Shear Stresses • If the planks are bonded together to form a single beam, longitudinal...
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 Spring '08
 PAPADOPOULOS
 Statics, Force, Shear Stress, Shear, shear stresses

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