Using the method of superposition and the table provided, find the deflection at b, the slope at b ๆ |1235ABeam and Loading Elastic CurveA76W|-|AW-L-aWPbMMBB0AMc =ALL→awL²6→ymaxL-XbLymaxXfymaxymaxУmaxYmaxBxYmaxB xFor the cantilever beam and loading shown, determine(a) the deflection at B, (b) the slope at B.MaximumDeflectionPL³3EIWLASEIML²22EIPL³48EIFor a > b:Pb (L²-b²)³/29√3EILat x =5wL384EIML²9√3EIL²-b²3Slope at EndPL²2EIwL³6EI±MLEIPL²16EI0₁A==OB = +wL³±24EI0₁ = +0B ==OBPb(L²-b²)6EILPa (L² - a²)6EILML6EIML3EIEquation of Elastic Curvesmy =y =yy =P6EI(x³ - 3Lx²)V=W24EIFor x < a:V=M2EIFor x ≤L:Py = ; (4x³ - 3L²x)48EIFor x = a:(x² - 4Lx³ + 6L²x²)Pb-[x³ - (L² - b²)x]6EILW24EI2M6EILy =Pa²b²3EIL(x² - 2Lx³ + L³x)(x³ - L²x)

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Y| A W W -L- H4² Beam and Loading Elastic Curve M B B M y A Mc A wL² ܐ ܝ a max +++ D Умах X Ymax x Bx Упах IB x For the cantilever beam and loading shown, determine (a) the deflection at B, (b) the slope at B. Maximum Deflection PL³ 3EI WL SEI ML² 2EI PL³ 48EI For a > b: Pb(L²-b²)³/2 9√3EIL at x = 5wL 384EI ML² 9√3EI L²-b² 3 Slope at End PL² 2EI wL³ 6EI ML ΕΙ PL² 16EI 0₁=- 0=+ ± wL³ 24EI 0₁ = + 0=- Pb (L²-b²) 6EIL Pa (L²-a²) 6EIL ML 6EI ML 3EI Equation of Elastic Curve Šm y = = 6EI y = y=- (x³ - 3Lx²) W 24EI y=. M 2EI For x ≤L: P y = (4x³ - 3L²x) 48EI For x < a: Pb y=6EIL y = For x = a: y= (x² − 4Lx³ + 6L²x²) - ·[x³ - (L²-b²)x] W 24EI M 6EIL Pa²b² 3EIL (x² - 2Lx³ + L³x) -(x³ - L²x)

Y| A W W -L- H4² Beam and Loading Elastic Curve M B B M y A Mc A wL² ܐ ܝ a max +++ D Умах X Ymax x Bx Упах IB x For the cantilever beam and loading shown, determine (a) the deflection at B, (b) the slope at B. Maximum Deflection PL³ 3EI WL SEI ML² 2EI PL³ 48EI For a > b: Pb(L²-b²)³/2 9√3EIL at x = 5wL 384EI ML² 9√3EI L²-b² 3 Slope at End PL² 2EI wL³ 6EI ML ΕΙ PL² 16EI 0₁=- 0=+ ± wL³ 24EI 0₁ = + 0=- Pb (L²-b²) 6EIL Pa (L²-a²) 6EIL ML 6EI ML 3EI Equation of Elastic Curve Šm y = = 6EI y = y=- (x³ - 3Lx²) W 24EI y=. M 2EI For x ≤L: P y = (4x³ - 3L²x) 48EI For x < a: Pb y=6EIL y = For x = a: y= (x² − 4Lx³ + 6L²x²) - ·[x³ - (L²-b²)x] W 24EI M 6EIL Pa²b² 3EIL (x² - 2Lx³ + L³x) -(x³ - L²x)

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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