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#1




questions: strength of plywood
Imagine a rough table made of a single 4 x 8 sheet of plywood, with a
leg (4x4) at each corner. Imagine a weight placed exactly in the center of this table. The preliminary question is, how much will the plywood sag under the weight? I should think that it would depend on (a) how thick the sheet is and (b) how heavy the weight is. (Also possibly relevant might be the area occupied by the weight; would a 100lb weight on a 36 sq. in. base cause more sag than the same weight distributed over, say, 324 sq. in.?) My real question is this: is there a formula or rule of thumb to calculate how thick the plywood sheet needs to be to support a given weight without sagging beyond a certain limit? I know I could prevent sagging altogether by putting a fifth leg in the center, but the space beneath the table needs to be completely open. Thanks in advance for any insights you might have. cheers, Henry 
#2




questions: strength of plywood
Henry wrote: Imagine a rough table made of a single 4 x 8 sheet of plywood, with a leg (4x4) at each corner. Imagine a weight placed exactly in the center of this table. The preliminary question is, how much will the plywood sag under the weight? I should think that it would depend on (a) how thick the sheet is and (b) how heavy the weight is. (Also possibly relevant might be the area occupied by the weight; would a 100lb weight on a 36 sq. in. base cause more sag than the same weight distributed over, say, 324 sq. in.?) My real question is this: is there a formula or rule of thumb to calculate how thick the plywood sheet needs to be to support a given weight without sagging beyond a certain limit? This can be calculated fairly easily. I don't have time now but perhaps this evening will. What is the type of plywood? The parameter needed is Young's modulus, or modulus of elasticity. The remaining just depends on the dimensions of the surface. Phil I know I could prevent sagging altogether by putting a fifth leg in the center, but the space beneath the table needs to be completely open. Thanks in advance for any insights you might have. cheers, Henry 
#3




questions: strength of plywood

#4




questions: strength of plywood
I've probably got the matnamatical answer to that here somewhere in my
reference library but I'd avoid the whole question by either building the top of the table top as a torsion box assembly or provide a skirt and leg base for the table along with additional cross pieces in the middle.  Mike G. Heirloom Woods www.heirloomwoods.net "Henry" wrote in message ... Imagine a rough table made of a single 4 x 8 sheet of plywood, with a leg (4x4) at each corner. Imagine a weight placed exactly in the center of this table. The preliminary question is, how much will the plywood sag under the weight? I should think that it would depend on (a) how thick the sheet is and (b) how heavy the weight is. (Also possibly relevant might be the area occupied by the weight; would a 100lb weight on a 36 sq. in. base cause more sag than the same weight distributed over, say, 324 sq. in.?) My real question is this: is there a formula or rule of thumb to calculate how thick the plywood sheet needs to be to support a given weight without sagging beyond a certain limit? I know I could prevent sagging altogether by putting a fifth leg in the center, but the space beneath the table needs to be completely open. Thanks in advance for any insights you might have. cheers, Henry 
#5




questions: strength of plywood
"Henry" wrote in message ... Imagine a rough table made of a single 4 x 8 sheet of plywood, with a leg (4x4) at each corner. Imagine a weight placed exactly in the center of this table. The preliminary question is, how much will the plywood sag under the weight? I should think that it would depend on (a) how thick the sheet is and (b) how heavy the weight is. (Also possibly relevant might be the area occupied by the weight; would a 100lb weight on a 36 sq. in. base cause more sag than the same weight distributed over, say, 324 sq. in.?) My real question is this: is there a formula or rule of thumb to calculate how thick the plywood sheet needs to be to support a given weight without sagging beyond a certain limit? I know I could prevent sagging altogether by putting a fifth leg in the center, but the space beneath the table needs to be completely open. Thanks in advance for any insights you might have. cheers, Henry Deflection with a uniform load is determined by the formula 5wL^4/384EI w = weight per unit length L = length E = modulus of elasticity of the material used I = the bending moment of the member being considered. Here you can see that since the length is to the 4th power that as the member gets longer the deflection gets much much greater. Make your sheet of plywood 20 feet long and it is likely to touch the ground in the middle under its own weight. People have advocated using steel because the modulus of elasticity (stiffness basically) is much higher than plywood so you can get some advantage there, however the most effective way to minimize defiection is to work on I, the bending moment. The bending moment is based on the geometry of the member. For a rectangular member the formula is bh^3/12 where b is the width and h is the height. As the height is cubed you can see that a small change in h means a big change in deflection. This is why a thin deep apron would add more strength than doubling the thickness of the plywood. To maximize the bending moment putting most of the material at the top and the bottom is most effective. This is why steel beams are shaped like an I. You can do the same thing by taking two thinner pieces of plywood and running a series of 1x2 ribs between them. The result will be a strong light top. Maximize the depth of your top and you minimize the bending. Double the thickness and the deflection is decreased by a factor of 8 (2 cubed) Triple it and it decreases by a factor of 27. A sandwich of 1/2" plywood with 1x2s on edge (every 8 inches or so) inside will be strong enough to hold several hundred pound with minimal deflection. Jack 
#6




questions: strength of plywood
JackD wrote:
Deflection with a uniform load is determined by the formula 5wL^4/384EI w = weight per unit length L = length E = modulus of elasticity of the material used I = the bending moment of the member being considered. etc. Thanks, Jack! Exactly what I needed to know. cheers, Henry 
#7




questions: strength of plywood

#8




questions: strength of plywood
On 12Aug2003, "JackD" wrote:
I = the bending moment of the member being considered. Nitpick: I is the moment of inertia of the cross section. A bending moment is a force (what most people would think of as torque). Mike 
#9




questions: strength of plywood
On 12Aug2003, Tom Watson wrote:
D = 0.1563wl^4 _____________ Ebh^3 Whe D = deflection (in inches) w = load per lineal inch of span l = span (length) E = modulus of elasticity b = base (width) h = depth (thickness) Actually, this is likely to be a lower bound to the deflection. Since the sheet is significantly wide and fairly flexible, there will be some sagging resulting from bending in both directions (plus or minus anticlastic curvature effects). The deflection of a plate is a lot more complex than that of a beam. You'll never get better than a rough estimate from basic elastic theory, since wood in general (including plywood) is not a nice isotropic material. You really want to reinforce this plywood sheet, as so many have pointed out. Wood will be more weight efficient that steel angles. Tables are made like tables for a good reason. The torsion box is a nice alternative. Mike 
#10




questions: strength of plywood
On Tue, 12 Aug 2003 22:22:33 GMT, "Michael Daly"
wrote: On 12Aug2003, Tom Watson wrote: D = 0.1563wl^4 _____________ Ebh^3 Whe D = deflection (in inches) w = load per lineal inch of span l = span (length) E = modulus of elasticity b = base (width) h = depth (thickness) Actually, this is likely to be a lower bound to the deflection. Since the sheet is significantly wide and fairly flexible, there will be some sagging resulting from bending in both directions (plus or minus anticlastic curvature effects). The deflection of a plate is a lot more complex than that of a beam. You'll never get better than a rough estimate from basic elastic theory, since wood in general (including plywood) is not a nice isotropic material. You really want to reinforce this plywood sheet, as so many have pointed out. Wood will be more weight efficient that steel angles. Tables are made like tables for a good reason. The torsion box is a nice alternative. Mike I should have referenced this formula in my original post. It comes from the AWI spec book and they got the formula and the field testing from the University of West Virginia wood sciences people. My own estimates of the deflecting strength of a table are more rough and tumble. If I've a question about a table's strength, I stand in the middle of it. If it adequately resists my two hundred pounds, distributed through two size eleven shoes, I figure it'll hold up the grits. I miss the old days of American engineering, where three times theory was the norm. Regards, Tom Tom Watson  Woodworker Gulph Mills, Pennsylvania http://users.snip.net/~tjwatson 
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