LECTURE 28 COE-3001-A

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Unformatted text preview: ctly to the magnitudes of 1 , 2 ) = 92.4M P a + ( 32)2 AND 2 84 + ( 30) = 2 2 = s✓ 84 ( 30) 2 ◆2 This is R = τmax compute and store it in calculator memory Perfectly consistent with what We obtained on the previous page + ( 32)2 38.4M P a 3/25/13 M. Mello/Georgia Tech Aerospace 18 EXAMPLE 6- 3: Element in plane stress subjected to σx = 84MPa, σy = - 30MPa, τxy = - 32MPa (cont.) •  DETERMINE PRINCIPAL ANGLES USING (6- 13A) AND (6- 13B): x cos 2✓p1 = sin 2✓p1 = R= s✓ y 2R (6- 13a) ⌧xy (6- 13b) R x y 2 ◆ 2 + ⌧xy = ⌧max 84 ( 30) = 0.8720 2 · 65.36 32 = = 0.4895 65.36 cos 2✓p1 = THE ONLY ANGLE THAT CAN SATISFY BOTH OF THESE RELATION IS ✓p1 (max principal stress direction) R= s✓ 84 ( 30) 2 ◆2 + ( 32)2 = 65.36M P a Now must be careful with calculators, Matlab, etc.. 3/25/13 1 (0.8720) 2✓p1 = cos 1 2✓p1 = sin sin 2✓p1 2✓p1 = cos (0.8720) ! 29.3081 1 ( 0.4895) ! M. Mello/Georgia Tech Aerospace 29.3081 19 EXAMPLE 6- 3: Element in plane stress subjected to σx = 84MPa, σy = - 30MPa, τxy = - 32MPa (cont.) y 1 cos ✓ 0 0 sin ✓ 1 Min principal stress direc]on 90° away from max princ. Stress direc]on 0 cos ✓ 1 0 sin ✓ 1 ✓p2 = 75.36 x ✓p1 = 165.35 It’s got to be in here 1 cos ✓ 0 1 sin ✓ 0 0 cos ✓ 1 1 sin 0 2✓p1 = cos 1 2✓p1 = sin 1 (0.8720) ! 29.3081 ( 0.4895) ! 29.3081 thus, 2✓p1 = 360 29.3081 = 330.69 and ) ✓p1 = 180 29.3081 2 = 165.35 This angle must be linked to the algebraically larger principal stress. ✓p2 = ✓p1 ± 90 ✓p2 = 165.35 3/25/13 M. Mello/Georgia Tech Aerospace 90 = 75.36 20 Example 6- 3 (cont.) SOLUTION: (b) MAXIMUM SHEAR STRESSES s ✓ x y ◆2 2 •  USE ⌧max = + ⌧xy (6- 25) 2 •  SUBSTITUTE σx = 84MPa, σy = - 30MPa, τxy = - 32MPa s✓ ◆2 84 ( 30) ⌧max = + ( 32)2 = 65.4M P a 2 •  OBTAIN ANGULAR ORIENTATION Θs1 OF MAX SHEAR STRESS PLANE •  USE ✓ s1 = ✓ p 1 45 (6- 24) ✓s1 = 165.3 45 = 120.3 •  Minimum nega]ve shear stress acts plane for which ✓s2 = 120.3 90 = 30.3 •  Normal stress ac]ng on planes of max shear stress: 84 + ( 30) aver 3/25/13 = 2 = aver = 27M P a M. Mello/Georgia Tech Aerospace x + 2 y (6- 27) 21...
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This note was uploaded on 09/19/2013 for the course CEE 3001 taught by Professor Zhu during the Spring '09 term at Georgia Institute of Technology.

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