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LECTURE+17+COE-3001-A

# Bending moment within the interior span 4

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Unformatted text preview: which conﬁrm the region of constant bending moment within the beam. Composite beam under 4- point bending: hFps://www.youtube.com/watch?v=e9uxNBqW4Z4 1:35 Microelectronics applicaLon 4 point bend test demo (ADMET): hFps://www.youtube.com/watch?v=x0zGYJiGAPU 4 point bend test photoelasLc image of stress ﬁeld: hFps://www.youtube.com/watch?v=7Hqc8ki4a2A 2/18/13 M. Mello/Georgia Tech Aerospace 10 PROBLEM 4.3- 11 “DISTRIBUTED LIFT LOAD ACTING ON AIRPLANE WING” FREE- BODY DIAGRAMS/STATIC CALCULATIONS: 1600N/m M c V DETERMINE: (A)  SHEAR FORCE AT INBOARD END OF WING (B)  BENDING MOMENT AT INBOARD END OF WING SOLUTION: X 2.6m 2.6m 1m Fv = 0 V + 0.5(1600 V= 900N/m 900)(2.6) + (900)(5.2) + 0.5(900)(1) = 0 6.04kN (minus sign means guessed wrong sign for shear force) X Mc = 0 M + 0.5(700)(2.6)[2.6/3] + (900)(5.2)[5.2/2] + 0.5(900)(1)[5.2 + 1/3] = 0 M = 1.54 ⇥ 104 N m 2/18/13 M. Mello/Georgia Tech Aerospace 11 PROBLEM 4.3- 18 “THE ARCHER’S BOW” DETERMINE: BENDING MOMENT AT MIDPOINT OF THE BOW SOLUTION: FREE- BODY DIAGRAMS/ STATIC CALCULATIONS: Tx T a 70 T P = 130N X X P = 2Tx Ty c T Fx = 0 X = 0.35m Y = 0.7m a M Mc = 0 M + Tx (0.7m) + Ty (0.35m) = 0 Tx = 65N M + (65N )(0.7m) + (65N ) tan 70 (0.35m) = 0 tan 70 = Ty /Tx M = 108Nm Ty = (65N ) tan 70 2/18/13 M. Mello/Georgia Tech Aerospace 12 PROBLEM 4.3- 15 “CENTRIFUGE ROTATING WITH CONSTANT ANGULAR ACCELERATION ” w dm = dr g b ↵ Free- body diagram: dF = GIVEN: •  Centrifuge rota=ng in a horizontal (xy) plane. •  constant angular accelera=on (α) •  w = weight per unit length of each arm •  W=2wL (weight at each end) DERIVE: •  MAX. SHEAR FORCE IN THE ARMS •  MAX . BENDING- MOMENT IN THE ARMS •  (ASSUME b=L/9, c=L/10) 2/18/13 c ²་  Bar rota=ng counter- clockwise with constant angular accelera=on (α). ²་  Each mass element (dm) experiences an iner=al reac=on force (dV). V dm r M ↵ “weight per unit length/g = mass/length” w ↵r g L+b Iner=al reac=on force V (r ) = Z r L+b ✓ ◆ w ↵⇠ d⇠ g M. Mello/Georgia Tech Aerospace ²་  Integrate the iner=al reac=on force of all mass elements to the right of the mass element (dm) to determine shear force at any radial posi=on (r) within the arm 13 PROBLEM 4.3- 15 “CENTRIFUGE ROTATING WITH CONSTANT ANGULAR ACCELERATION ” (cont.) w↵ ⇠ 2 V (r ) = g2 V (r ) = ↵ L+b r w↵ ((L + b)2 2g r2 ) Shear force at any radial distance (r) Maximum shear force from arm...
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