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2/1 DIRECT SHEAR

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). Angle  = /L. Area A. V. . . Original. L. . V. Shear Force V. Shear Stress  = V/A

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2/1 DIRECT SHEAR

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  1. 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)

  2. Angle  = /L Area A V   Original L  V Shear Force V Shear Stress  = V/A Shear Strain  = /L 2/2 EQUALITY OF STRESSESDEFINITION OF STRAIN y z x

  3. 2/3 EQUALITY OF MOMENTS • But that block is not in EQUILIBRIUM • It will rotate • There must be a matching pair of shears

  4. 2/4 SHEAR COUPLES Angle /2 = /2L Area A V  Original L  V Shear Force V Shear Stress  = V/A Shear Strain  = /L

  5. 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?

  6. -Fx Fx 2/6 Sign for Force and Stress Y Negative X Face Area A Z Positive X Face Area A x = -Fx/-A = +Fx/+A X

  7. Vxy Direction Face -Vxy Vxy 2/7 Sign for Shear Force & Stress Y Negative X Face Area A Z Positive X Face Area A  = -V/-A =+V/+A X

  8. 2/8 Sign for Moments and Rotations Y Y z,Mz Z X X

  9. 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

  10. 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

  11. 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

  12. 2/12 BOLT IN SINGLE SHEAR

  13. 2/13 BOLT IN SINGLE SHEAR

  14. 2/14 PIN IN DOUBLE SHEAR 2V V V V ave=V/A

  15. 2/15 Shear failure of wood block in compression

  16. 2/16 OTHER CAUSES OF SHEAR • Shear also appears in torsion

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