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Published byLeon Carroll Modified over 9 years ago
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2/1 DIRECT SHEAR Scissors Shear stress still Force/Area but different area Strain still deflection over length but angular distortion at right angles =angle in radians (for small strains)
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2/2 EQUALITY OF STRESSES DEFINITION OF STRAIN V V Original Shear Force V Area A L Angle = /L Shear Stress = V/A Shear Strain = /L x y z
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2/3 EQUALITY OF MOMENTS But that block is not in EQUILIBRIUM It will rotate There must be a matching pair of shears
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2/4 SHEAR COUPLES V V Original Shear Force V L Area A Angle /2 = /2L Shear Stress = V/A Shear Strain = /L
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2/5 Sign Conventions What is a positive direct stress? What is a positive shear stress? What is a positive moment? What is a positive force? What is a positive BENDING moment?
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2/6 Sign for Force and Stress X Z Y FxFx -F x Positive X Face Area A Negative X Face Area A x = -F x /-A = +F x /+A
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2/7 Sign for Shear Force & Stress X Z Y V xy -V xy Positive X Face Area A Negative X Face Area A V xy Face Direction = -V/-A =+V/+A
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2/8 Sign for Moments and Rotations X Z Y X Y z,M z
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2/9 SIGN CONVENTION +ve faces – outward normal pointing towards +ve direction -ve faces – pointing towards origin +ve shear stress – acts on a +ve face in a +ve dirn or a –ve face in a –ve dirn +ve shear strain – when angle between two +ve or two –ve faces is reduced. +ve shear stresses give +ve shear strains
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2/10 PURE SHEAR No normal stresses Pure shear means no change of length Can only apply in one direction Pure shear produces (implies) Diagonal Tension Diagonal Compression
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2/11 SHEAR TESTS Stress–strain diagram in shear ( vs ) Hooke’s Law in shear = G. G = Shear Modulus of Elasticity Same units as E (Pa), steel = 75GPa G = E/(2[1+ ]) G,E and not independent elastic props 0< <0.5 so E/3<G<E/2
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2/12 BOLT IN SINGLE SHEAR
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2/13 BOLT IN SINGLE SHEAR
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2/14 PIN IN DOUBLE SHEAR V V 2V V ave =V/A
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2/15 Shear failure of wood block in compression
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2/16 OTHER CAUSES OF SHEAR Shear also appears in torsion
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