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. 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

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 V V Original Shear Force V L   Area A Angle  /2 =  /2L 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. 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

7. 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

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

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 V V 2V 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