7 1d calculate the normal stress

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Unformatted text preview: PLE 7- 2(d) cont. x1 = y1 x = x + 2 y + 2 + y 2 y x y 2 cos 2✓ + ⌧xy sin 2✓ y cos 2✓ pr (3 cos 2✓) 4t pr = sin 2✓ 4t ⌧x 1 y 1 ⌧xy sin 2✓ y (6- 5b) A 2 x (6- 6) sin 2✓ + ⌧xy cos 2✓ = x1 (6- 5a) 1 2 x ⌧x 1 y 1 = x x1 = 47.8M P a ↵ = 55 B ⌧x1 y1 = 16.9M P a ✓ = 35 Finally, invoke the 1st invariant to obtain 2 x 1 + 2 = + x2 x2 = x2 = 72M P a + 36M P a 4/3/13 1 + x1 2 x ✓ = 90 ↵ = 90 55 = 35 x1 47.8M P a = 60.2M P a M. Mello/Georgia Tech Aerospace 15 EXAMPLE 7- 2(d) cont. (⌧max )z = 18M P a Solve part (d) using Mohr’s circle •  What horizontal and verNcal normal stresses do we know? •  From part (a) 1 2 = = h (800 ⇥ 103 P a)(1.8m) = = 72M P a 0.020m L (800 ⇥ 103 P a)(1.8m) = = 36M P a 2(0.020m) They just happen to be the principal stresses.. Max. shear stress τmax = 18MPa (72=36)/2=54 R = (72- 36)/2 = 18 2 1 A (Θ=0°) O C B (Θ=90°) x1 x Need to idenNfy point A = the point on Mohr’s circle corresponding to the stress along =0 within in the physical body 4/3/13 36 72 M. Mello/Georgia Tech Aerospace No shear stress along principal plane 16 EXAMPLE 7- 2(d) cont. ⌧w = 16.9M P a ✓ = 35 w =? ⌧w =? w = ✓ 1 2 2 ◆ R cos 2✓w w = 54 ⌧w = 18 sin 70 ⌧w = R sin 2✓w 18 cos 70 ⌧w =? A (Θ=0°) O B (Θ=90°) x1 C 2✓ = 70 x 4/3/13 D’ (Θ=35°) R =? Need to idenNfy point A = the point on Mohr’s circle corresponding to the stress along Θ=0 within in the physical body = 47.8M P a ⌧w = 16.9M P a (72=36)/2=54 w w 36 72 M. Mello/Georgia Tech Aerospace D (Θ=35°) 17 EXAMPLE 7- 2(d) finish Obtain this normal stress Component parallel to the weld From D’ on the previous page w w = ✓ 1 2 2 ◆ w =? + R cos 2✓w = 54 + 18 cos 70 = 60.2M P a ⌧w =? 4/3/13 M. Mello/Georgia Tech Aerospace 18 What about absolute max shear stress? Radius of larger (red) Mohr’s circle the absolute max shear stress: (⌧max )x = 36M P a 45 1, in the plane of rotation 3 R (⌧max )x = 36M P a (72=36)/2=54 D’ (Θ=35°) 1 A (Θ=0°) O 2 2✓ = 70 x Need to idenNfy point A = the point on Mohr’s circle corresponding to the stress along Θ=0 within in the physical body B (Θ=90°) x1 C 36 72 D (Θ=35°) (⌧max )y = 18M P a 4/3/13 M. Mello/Georgia Tech Aerospace 19 Combined loadings EXAMPLE 1: Combined bending and axial load EXAMPLE 2: Cylindrical pressure vessel supported as a beam EXAMPLE 3: Shap in combined torsion and bending...
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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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