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Mechanics of Solids Lecture 5 by Dr Emre Erkmen Lecturer, School of Civil and Environmental Engineering, The University of Technology Sydney Office: 2.520 Phone:9514 9769 Email: [email protected] Lecture hours: Tuesdays 11:00-14:00, Wednesdays 15:00-18:00 Office hours: Tuesdays 15:00-17:00 1
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Mechanics of Solids - Lecture 5 Outline - Shear stress - Shear flow 2 - Built-up sections
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Mechanics of Solids - Lecture 5 Effect of longitudinal Shear stress 3
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Mechanics of Solids - Lecture 5 Effect of longitudinal Shear stress 4 Slip between the unbonded boards When boards are bonded together
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Mechanics of Solids - Lecture 5 Member under general loading The system of forces that may exist at a section of a beam include: SHEARING FORCE BENDING MOMENT 5 M V FBD x R A
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Mechanics of Solids - Lecture 5 Relation between moment and shear force Consider a segment Δ x isolated from a beam: M + M q 6 x A B x x M V + V V Since the segment is in equilibrium Σ M A = 0 A B
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Mechanics of Solids - Lecture 5 Relation between moment and shear force Δ x M M + M V + V V q By simplifying and neglecting the infinitesimals of higher order, the equation can be reduced to: ( ) ( ) 0 2 x M M M V V x q x Δ + Δ + Δ Δ − Δ = V x = Δ 7 Shear depends on the difference between the bending moments on the adjoining sections. If no shear acts at the adjoining sections of a beam, no change in the bending moment occurs. M Δ M V x Δ = Δ dM dx = 0 x Δ →
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Mechanics of Solids - Lecture 5 Longitudinal Shear stress V V+ V M+ M t σ t t + Δ q t t t + Δ q F s My I = − y 8 x b b + Δ b
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