LECTURE+11+COE-3001-A

Zl zl t dx d

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: t(x)] per along the axis of the per unit distance ZL T ( x) = t(x)dx 0 ²་  Determine shear stress: ⌧ ( x) = ²་  Determine total angle of twist: Z = o L T ( x ) ⇢( x ) Ip ( x) Z d = L 0 T (x)dx GIp (x) t( x ) (3- 22) NOTES/LIMITATIONS: ²་  Analysis in case of nonuniform torsion valid for linear elasVc materials with circular cross secVons, (solid or hollow). ²་  EquaVons also only apply to bars with varying cross secVons characterized by gradual diameter changes (taper angle < 10°). ²་  Stress calculaVons are valid in regions away form stress concentraVons (such as where diameter abruptly changes or where concentrated torques are applied) ²་  Stress concentraVons have very likle effect on twist angle (φ) 2/1/13 M. Mello/Georgia Tech Aerospace 5 STRESSES AND STRAINS IN PURE SHEAR STRESSES ACTING ON A STRESS ELEMENT CUT FROM A BAR IN TORSION ELEMENT IN STATE OF PURE SHEAR ²་  only stresses are shear stress τ on the four side faces ²་  lengths of the sides of the element do not change NOTE/RECALL ORIGINAL SIGN CONVENTON: ²་  ⌧ > 0 shear force acts in posiVve direcVon on a posiVve face (a posiVve face has unit normal directed along posiVve direcVon of a coordinate axis) ²་  ⌧ < 0 shear force acts in negaVve direcVon on a posiVve face ²་  In the case above, all shear stresses acVng on the stress element are posiVve ²་  DirecVon of torques chosen so that resultant shear stresses are posiVve. ²་  THIS IS ALL ABOUT TO CHANGE 2/1/13 M. Mello/Georgia Tech Aerospace 6 STRESSES ACTING ON INCLINED PLANES X Y ⌧✓ A0 sec ✓ Free body diagram ELEMENT IN PURE SHEAR STRESSES ON TRIANGULAR STRESS ELEMENT FORCES ON TRIANGULAR STRESS ELEMENT ²་  REMEMBER THAT THE ELEMENTS ARE REALLY 3D A0 / cos ✓ = A0 sec ✓ NO STRESS ON FRONT A0 AND REAR (Z) FACES ²་  NOW RESET SIGN CONVENTON FOR NORMAL AND SHEAR STRESSES ON INCLINED SURFACES •  Different than sign convenVon for ordinary shear stresses (τ) that act on sides of rectangular elements oriented to a set of xy axes. •  NORMAL STRESSES (σΘ > 0) IN TENSION •  SHEAR STRESSES (τΘ >0) IF TENDENCY IS TO ROTATE ELEMENT CCW 2/1/13 M. Mello/Georgia Tech Aerospace 7 STRESSES ON INCLINED SURFACES FOR AN ELEMENT IN PURE SHEAR (cont.) X Y X 0...
View Full Document

Ask a homework question - tutors are online