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|| 16 to 24 inches high <<BR>> Water saturated silt loam <<BR>> 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:raisedbed480.png]]|| <<EmbedObject(raisedbed480.swf,play=true,loop=true,width=480,height=360)>> || || 16 to 24 inches high <<BR>> Water saturated silt loam <<BR>> 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-8hoop.pov]]|| {{raisedbed480.png}} ||

Raised Bed Design

16 to 24 inches high
Water saturated silt loam
1.83 g/cm3, 114 lb/ft3, 1830kg/m3
18 kN/m2 per meter depth
2.6 psi per meter depth, 0.794 psi per foot depth

source:raisedbed-8hoop.pov

raisedbed480.png

Summary: 2 stacked 8x12x2 (96 x 11.5 x 1.5 inch) cedar board sides, less than 1/8 inch differential bulge

  • 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

  • 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

RaisedBed (last edited 2022-03-14 23:56:02 by KeithLofstrom)