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T13.3 Stress due to Shear

T13.3 Stress due to Shear - Stress due to Shear Force Part...

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Stress due to Shear Force Part II: “The Second Path” T13.3 Do you recall t =V/A? That was Part I
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Internal Resultant & Stress Pairings P V T M t normal stress [F/L 2 ] shear stress [F/L 2 ] Force [F] Moment [F-L] 1 normal component 2 tangential components 1 normal component 1 normal component 2 tangential components 2 tangential components Internal resultant Internal resultant
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Why Not t =V/A? 4 boards NOT glued together 4 boards glued together
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Kinematics
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Using to Calculate t L/4 L/2 L/4 P P P P P P P 0 -P V M 0 PL/4 pure bending flexure flexure
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Shear Flow, q
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Shear Flow, q dx ' ' ' ( , ) 0 cut x L R A A A F dA dA y z dsdx t
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Fundamental Quantities
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Shear Flow, q & Shear Stress, t ' ' ' ' ' ' 0 ( ) 0 1 0 L R A A A A A A dA dA qdx My M dM y dA dA qdx I I dM dM ydA qdx q ydA I I dx ' y ' y V
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Discussion s glue V V
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V A B d d Discussion What are the shear stresses @ A and B?
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Example Determine the shear stress distribution for a beam with a rectangular cross-
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