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Find the slope and vertical deflection at point A using the Method of Superposition. Use E = 31,000 ksi and I = 246 in4. 3 kip B 2 kip/ft 3 ft 3 ft A

Find the slope and vertical deflection at point A using the Method of Superposition. Use E = 31,000 ksi and I = 246 in4. 3 kip B 2 kip/ft 3 ft 3 ft A

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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Find the slope and vertical deflection at point A using the Method of Superposition. Use E= 31,000 ksi and I = 246 in4. 3 kip B 2 kip/ft 3 ft- 3 ft A
Transcribed Image Text:Find the slope and vertical deflection at point A using the Method of Superposition. Use E= 31,000 ksi and I = 246 in4. 3 kip B 2 kip/ft 3 ft- 3 ft A
EQUATIONS FOR DEFLECTIONS OF SIMPLY SUPPORTED BEAMS SIMPLY SUPPORTED BEAMS LENGTH, L A y A A M Y dy dx dy dy dx Max L/2 dy dx L/2 F 'YM₂ Max 9 b U/2 F dy dx Y Mas dy (3). L/2 dx dx B dia dy dx CANTILEVER BEAMS LENGTH, L dy dx/u win dy dx B B An Yst *7 % LENNET Ум Mo (dy Уми SLOPE dx/Max dy -Fab(L+b) (dx 6EI L (dy) dx dy (dx) dy dx/ dy dx/ dy dx = dy dx = Fab(L+a) 6EI L =-- dy 3q, L' dx), 128EI dy 7q,1 (dx) 384E1, (dy dx -FL² 16EI dy ML 6EI, = = 9.L² dx 45EI, ML ЗЕІ, a Max 9.1.² 24EI, Ma SLOPE Max -79 L' 360EI X dy =9,L¹ dx/stas 6EL, dy -FL² dx SEI, Max -FL² 2EI, ML EI, 9.L² 48EI -Fx y= (3L²-4x²) 48EI Уми EQUATIONS FOR DEFLECTIONS OF CANTILEVER BEAMS y= Умак y= y= Y 6EL,L у" DEFLECTION EQUATIONS -Mx y=- -(x²-3Lx+21²) 6EI,L -ML-² √243EI atx=0.4226L -9x(x²-2Lx² +1²) 24EI, Умит Уман |y= -Fbx 6EI,L Ума y= -FL² 48EL, y=(16x-24Lx² +9L') 384EI -9.L 384E1, +17L²x-L¹) L/2≤x≤L -Fba (1-b²-a¹) 360EI,L (L-b²-x²) 0≤x≤a Уман y=- 0≤x≤L/2 -Sq₂L¹ 384EI, (8x³-24Lx¹ -6.563x10¹q L EI, -9x(3x-10L²x² +7L') -Fx². 6EI -6.52 x 10 ³q,L* EI, Mechanics of Materials - 455 0≤x≤L/2 DEFLECTION EQUATIONS -FL² ЗЕІ, -(3L-x) -9₁x² 24EI, Y = at x= 0.4598L -Fx² y= - (2-x) 6EI, y=-9₁x²x² 24EI у -FL² 3x-1-1) 24EI y = at x 0.5193 -9,L¹ SEI (x²-4Lx+6L²) Mx² 2EI₂ -9²²² (₁ ML² Уми "2EI, x²-21x4 + 0≤x≤L/2 L L/2≤x≤L 0≤x≤L/2
Transcribed Image Text:EQUATIONS FOR DEFLECTIONS OF SIMPLY SUPPORTED BEAMS SIMPLY SUPPORTED BEAMS LENGTH, L A y A A M Y dy dx dy dy dx Max L/2 dy dx L/2 F 'YM₂ Max 9 b U/2 F dy dx Y Mas dy (3). L/2 dx dx B dia dy dx CANTILEVER BEAMS LENGTH, L dy dx/u win dy dx B B An Yst *7 % LENNET Ум Mo (dy Уми SLOPE dx/Max dy -Fab(L+b) (dx 6EI L (dy) dx dy (dx) dy dx/ dy dx/ dy dx = dy dx = Fab(L+a) 6EI L =-- dy 3q, L' dx), 128EI dy 7q,1 (dx) 384E1, (dy dx -FL² 16EI dy ML 6EI, = = 9.L² dx 45EI, ML ЗЕІ, a Max 9.1.² 24EI, Ma SLOPE Max -79 L' 360EI X dy =9,L¹ dx/stas 6EL, dy -FL² dx SEI, Max -FL² 2EI, ML EI, 9.L² 48EI -Fx y= (3L²-4x²) 48EI Уми EQUATIONS FOR DEFLECTIONS OF CANTILEVER BEAMS y= Умак y= y= Y 6EL,L у" DEFLECTION EQUATIONS -Mx y=- -(x²-3Lx+21²) 6EI,L -ML-² √243EI atx=0.4226L -9x(x²-2Lx² +1²) 24EI, Умит Уман |y= -Fbx 6EI,L Ума y= -FL² 48EL, y=(16x-24Lx² +9L') 384EI -9.L 384E1, +17L²x-L¹) L/2≤x≤L -Fba (1-b²-a¹) 360EI,L (L-b²-x²) 0≤x≤a Уман y=- 0≤x≤L/2 -Sq₂L¹ 384EI, (8x³-24Lx¹ -6.563x10¹q L EI, -9x(3x-10L²x² +7L') -Fx². 6EI -6.52 x 10 ³q,L* EI, Mechanics of Materials - 455 0≤x≤L/2 DEFLECTION EQUATIONS -FL² ЗЕІ, -(3L-x) -9₁x² 24EI, Y = at x= 0.4598L -Fx² y= - (2-x) 6EI, y=-9₁x²x² 24EI у -FL² 3x-1-1) 24EI y = at x 0.5193 -9,L¹ SEI (x²-4Lx+6L²) Mx² 2EI₂ -9²²² (₁ ML² Уми "2EI, x²-21x4 + 0≤x≤L/2 L L/2≤x≤L 0≤x≤L/2
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