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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
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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Using the method of superposition and the table provided, find the deflection at b, the slope at b

ๆ | 1 2 3 5 A Beam and Loading Elastic Curve A 7 6 W |-| A W -L- a W P b M M B B 0 A Mc = A L L→ a wL² 6 →ymax L -X b Lymax X fymax ymax Уmax Ymax Bx Ymax B x For the cantilever beam and loading shown, determine (a) the deflection at B, (b) the slope at B. Maximum Deflection PL³ 3EI WLA SEI ML²2 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 EI PL² 16EI 0₁A== OB = + wL³ ± 24EI 0₁ = + 0B == OB Pb(L²-b²) 6EIL Pa (L² - a²) 6EIL ML 6EI ML 3EI Equation of Elastic Curve sm y = y = y y = P 6EI (x³ - 3Lx²) V= W 24EI For x < a: V= M 2EI For x ≤L: P y = ; (4x³ - 3L²x) 48EI For x = a: (x² - 4Lx³ + 6L²x²) Pb -[x³ - (L² - b²)x] 6EIL W 24EI 2 M 6EIL y = Pa²b² 3EIL (x² - 2Lx³ + L³x) (x³ - L²x)
Transcribed Image Text:ๆ | 1 2 3 5 A Beam and Loading Elastic Curve A 7 6 W |-| A W -L- a W P b M M B B 0 A Mc = A L L→ a wL² 6 →ymax L -X b Lymax X fymax ymax Уmax Ymax Bx Ymax B x For the cantilever beam and loading shown, determine (a) the deflection at B, (b) the slope at B. Maximum Deflection PL³ 3EI WLA SEI ML²2 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 EI PL² 16EI 0₁A== OB = + wL³ ± 24EI 0₁ = + 0B == OB Pb(L²-b²) 6EIL Pa (L² - a²) 6EIL ML 6EI ML 3EI Equation of Elastic Curve sm y = y = y y = P 6EI (x³ - 3Lx²) V= W 24EI For x < a: V= M 2EI For x ≤L: P y = ; (4x³ - 3L²x) 48EI For x = a: (x² - 4Lx³ + 6L²x²) Pb -[x³ - (L² - b²)x] 6EIL W 24EI 2 M 6EIL y = Pa²b² 3EIL (x² - 2Lx³ + L³x) (x³ - L²x)
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