{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

LECTURE+28+COE-3001-A

# Min principal stresses are known s 2

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

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: as either σ1 or σ2 (by comparing to values obtained using (6- 17)) 3/25/13 M. Mello/Georgia Tech Aerospace 6 Resolving the double angle ambiguity: method 2 y Method 2: •  The only angle that sa]sﬁes BOT(6- 13a) AND (6- 13b) is Θp1 (maximum principal stress direc]on) •  Sign combinaJon of Cosine and Sine uniquely determine the quadrant cos 2✓p1 = sin 2✓p1 x y (6- 13a) 2R ⌧xy = R 1 cos ✓ 0 0 cos ✓ 1 0 sin ✓ 1 (6- 13b) 1 cos ✓ 0 1 sin ✓ 0 0 sin ✓ 1 x 0 cos ✓ 1 1 sin ✓ 0 ²་  The 3rd principal stress: •  Finally, note that there is a 3rd principal stress which we tend to overlook when focusing on 2D plane stress. •  We should also strictly include the normal stress ac]ng on the z- face of the element (for plane stress σ3=0) •  However in some instances we my have σ3=k (constant). •  This is then classiﬁed as generalized plane stress •  END RECAP OF LECTURE 27 3/25/13 M. Mello/Georgia Tech Aerospace 7 BEGIN LECTURE 28 x1 = x y1 = x + 2 + 2 ⌧x 1 y 1 = y + y y x y 2 (6- 5a) cos 2✓ (6- 5b) 2 2 x cos 2✓ + ⌧xy sin 2✓ y x ⌧xy sin 2✓ sin 2✓ + ⌧xy cos 2✓ Resta]ng the transforma]on equa]ons here for the sake if convenience and easy recall (6- 6) ²་  Determine planes of maximum shear stress: Diﬀeren]ate (6- 6) and set equal to zero! ²་  maximum shear stress (with respect to Θ) and how to determine the direc]on of maximum shear stress: x y tan 2✓s = (6- 20) 2⌧xy ²་  DEFINES ORIENTATION OF PLANES OF MAX, POS. AND NEG. SHEAR STRESS ²་  (6- 20) yields one angle between 0° and 90° and a second angle between 90° and 180° 3/25/13 M. Mello/Georgia Tech Aerospace 8 DETERMINING PLANES OF MAXIMUM SHEAR STRESS ²་  maximum shear stress and how to determine the direc]on of maximum shear stress: x y tan 2✓s = 2⌧xy •  DEFINES ORIENTATION OF PLANES OF MAX, POS. AND NEG. SHEAR STRESS •  (6- 20) yields one angle between 0° and 90° and a second angle between 90° and 180° x y 2⌧xy tan 2✓s = (6- 11) ⌧ WITH tan 2✓p = ²་  COMPARE: (6- 20) 2 xy x y 1 tan ✓s = (6- 21) tan ✓p ✓s = ✓p ± 45 (6- 22) •  Planes of maximum shear stress occur at 45° to the principal planes deﬁned by Θp1, Θp2 3/25/13 M. Mello/Georgia Tech Aerospace 9 PLANES OF MAXIMUM...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online