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Unformatted text preview: oint bend test demo (INSTRON): hFps://www.youtube.com/watch?v=zeyqcPiUFPs 3 point bend test photoelasLc image of stress field: hFps://www.youtube.com/watch?v=bowEGwD0TWE 3 point bend test (ADMET): hFps://www.youtube.com/watch?v=veVwA3- Vpmg 2/18/13 M. Mello/Georgia Tech Aerospace 5 4PB loading configura=on P/2 x1 P/2 s RA L RB STEP 1: DETERMINE REACTIONS RA, RB FROM FREE- BODY DIAGRAM OF THE ENTORE BEAM X FV = 0 RA + R B P /2 P /2 = 0 R A + RB = P RA = P RA = P RA = MA = 0 P P x1 ( x1 + s ) = 0 2 2 P RB = (2x1 + s) 2L RB L RB P (2x1 + s) 2L P (2L 2L 2/18/13 X 2x 1 s) M. Mello/Georgia Tech Aerospace 6 4PB loading analysis (0 < x < x1) STEP 2: DRAW AND ANALYZE FREE- BODY DIAGRAM OF EACH DISTINCT REGION P/2 x1 P/2 X s Fv = 0 V + RA = 0 RA L x c V RA M FREE- BODY DIAGRAM: (0 < x < x1) RB V = RA recall, RA = V ( x) = X P (2L 2L P (2L 2L 2x 1 2x 1 s) s) (0 < x < x1) Mc = 0 M = RA x M ( x) = 2/18/13 M. Mello/Georgia Tech Aerospace Px (2L 2L 2x 1 s) (0 < x < x1) 7 4PB loading analysis (x1 < x < s+x1) P/2 x1 P/2 s X P + RA = 0 2 P V = RA 2 P V= (2L 2x1 s) 2L V RA RB L x P/2 x1 c M V RA Fv = 0 X FREE- BODY DIAGRAM: (x1 < x < s+ x1) V ( x) = P (L 2L 2x1 s) P 2 (x1 < x < s+ x1) Mc = 0 P ( x x 1 ) RA x = 0 2 P M= ( x x 1 ) + RA x 2 P Px M= ( x x1 ) + (2L 2 2L 1 x1 s P x1 )x + 2 L 2L 2 P P x1 M ( x) = ( L 2x 1 s ) x + 2L 2 M+ 2/18/13 M = P( 2x 1 s) M. Mello/Georgia Tech Aerospace 8 The 4 point bend test NEXT, Consider under what condi=on M(x) = constant P P x1 ( L 2x 1 s ) x + 2L 2 V (x) = P (L 2x1 s) (x < x < s+ x ) 1 1 2L Centered loading span P/2 M ( x) = x1 P/2 s x1 Note: if, L 2 x 1 = s 0 RA RB L P x1 = constant then, M (x) = 2 P (L s) or: M (x) = = constant Constant bending moment within the interior span 4 0 P ALSO... Note what happens to the shear force: V (x) = ( L 2x 1 s ) = 0 2L Hence, there is a constant bending- moment and no shear force within the interior (centered) loading span (x1 < x < s+ x1). THIS IS KNOWN AS PURE BENDING AND SERVES AS THE BASIS FOR THE CLASSIC 4 POINT BEND TEST. 2/18/13 M. Mello/Georgia Tech Aerospace 9 The 4 Point Bend (4PB) Test s s L 4 point bend test •  •  •  ²་  Photoelas=c image of transparent beam under 4 point bend loading. Fringes correspond to stress contours within the body. ²་  Parallel and equi- spaced interference fringes within the loading span (s) region...
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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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