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| Describe RaisedBed here. | = Raised Bed Design = || 16 to 24 inches high <<BR>> Saturated silt loam, 1.83 g/cm^3^, 114 lb/ft^3^, 1830kg/m^3^ <<BR>> 18 kN/m^2^ per meter depth <<BR>> 2.6 psi per meter depth, 0.794 psi per foot depth <<BR>><<BR>>source:[[attachment:raisedbed.pov]]||<<EmbedObject(raisedbed.swf,play=true,loop=true,width=480,height=360)>> || * 8 foot long, 23 inches high, two boards, 1.522 psi at bottom . w = 4.38 lbf (pounds force) per lineal inch top board . w = 13.13 lbf per lineal inch bottom board * cedar modulus: E = 1M psi [[http://www.wrcea.org/technical-specifications/engineering_data.htm | Table 9]] * 3 point, end and center post support - see [[http://civilengineer.webinfolist.com/str/prob72.htm]] . L = 96 inch, w = 4.4 lbf/in top, 13 lbf/in bottom, EI tbd . wL = 420 lbf top, 1260 lbf bottom . deflection of two point supported board, distributed load d = 5 w L^4^/384EI . deflection of two point supported board, point load R in middle d = R L^3^/48EI . therefore, R = -(5/8)(wL) . top . . . : 79 lbf both ends, 262 lbf middle . bottom : 236 lbf both ends, 788 lbf middle * deflection for uniformly loaded beam: y = ( w x / 24 EI ) ( L^3^ - 2 Lx^2^ + x^3^ ) * deflection for center point loaded beam: y = ( R x / 48 EI ) ( 3 L^2^ - 4 x^2^ ) ... 0 < x < L/2 . see [[http://en.wikipedia.org/wiki/Deflection_(engineering)]] * compound force deflection: y = ( w / 384 EI ) ( L^3^ x - 12 L x^3^ + 16 x^4^ ) . test, x=L/2 : ( L^4^/2 - 3/2 L^3^ + L^3^ ) = 0 deflection at center . max deflection, first derivative = 0 = L^3^ -36Lx^2^ + 64x^3^, x=0.210767582704314 L . max deflection = 3.3851E-4 ( L^3^ (wL) / E I ) * I = w t^3^ / 12 for beam width w, thickness t * I = 3.23 in^4^ for '''11.5 x 1.5''' inch side board . (3.3851E-4*96^3^/(3.23*1E6)) ( wL ) = 9.2E-5 in/lb * (W/L) * 8 foot bed deflection '''0.042 inch top, 0.127 inch bottom''' * I = 0.404 in^4^ for 11.5 x 0.75 inch side board . (3.3851E-4*96^3^/(0.404*1E6)) ( wL ) = 7.4E-4 in/lb * (W/L) * 8 foot bed deflection 0.311 inch top, 0.934 inch bottom . (3.3851E-4*72^3^/(0.404*1E6)) ( wL ) = 3.13E-4 in/lb * (W/L) * 6 foot bed deflection 0.144 inch top, 0.432 inch bottom |
Raised Bed Design
16 to 24 inches high |
- 8 foot long, 23 inches high, two boards, 1.522 psi at bottom
- w = 4.38 lbf (pounds force) per lineal inch top board
- w = 13.13 lbf per lineal inch bottom board
cedar modulus: E = 1M psi Table 9
3 point, end and center post support - see http://civilengineer.webinfolist.com/str/prob72.htm
- L = 96 inch, w = 4.4 lbf/in top, 13 lbf/in bottom, EI tbd
- wL = 420 lbf top, 1260 lbf bottom
deflection of two point supported board, distributed load d = 5 w L4/384EI
deflection of two point supported board, point load R in middle d = R L3/48EI
- therefore, R = -(5/8)(wL)
- top . . . : 79 lbf both ends, 262 lbf middle
- bottom : 236 lbf both ends, 788 lbf middle
- L = 96 inch, w = 4.4 lbf/in top, 13 lbf/in bottom, EI tbd
deflection for uniformly loaded beam: y = ( w x / 24 EI ) ( L3 - 2 Lx2 + x3 )
deflection for center point loaded beam: y = ( R x / 48 EI ) ( 3 L2 - 4 x2 ) ... 0 < x < L/2
compound force deflection: y = ( w / 384 EI ) ( L3 x - 12 L x3 + 16 x4 )
test, x=L/2 : ( L4/2 - 3/2 L3 + L3 ) = 0 deflection at center
max deflection, first derivative = 0 = L3 -36Lx2 + 64x3, x=0.210767582704314 L
max deflection = 3.3851E-4 ( L3 (wL) / E I )
I = w t3 / 12 for beam width w, thickness t
I = 3.23 in4 for 11.5 x 1.5 inch side board
(3.3851E-4*963/(3.23*1E6)) ( wL ) = 9.2E-5 in/lb * (W/L)
8 foot bed deflection 0.042 inch top, 0.127 inch bottom
I = 0.404 in4 for 11.5 x 0.75 inch side board
(3.3851E-4*963/(0.404*1E6)) ( wL ) = 7.4E-4 in/lb * (W/L)
- 8 foot bed deflection 0.311 inch top, 0.934 inch bottom
(3.3851E-4*723/(0.404*1E6)) ( wL ) = 3.13E-4 in/lb * (W/L)
- 6 foot bed deflection 0.144 inch top, 0.432 inch bottom