Message-Id: <3.0.1.32.19970430221109.006b41a8@skypoint.com>
Date: Wed, 30 Apr 1997 22:11:09 -0600
To: baidarka@lists.intelenet.net
From: wayne steffens <wsteffen@skypoint.com>
Subject: Gunwales/ Stiffness/strength of wood.
In-Reply-To: <199610091603.JAA00408@ns1.intelenet.net>
I think I found the post Eric was referring to. I didnt realize I had it
till he jogged whats left of my memory. I thought the new folks might find
it helpful, others will find it redundant.
At 11:00 AM 10/9/96 CDT, Wolfgang wrote:
> >Well, I have finally dug up the formulas and plugged some
>numbers into them and turned the crank and here is what
>came out:
>
>The following information is derived from the
>Wood Handbook: Wood as an Engineering Material
>USDA Forest Products Laboratory
>Forest Service
>Agriculture Handbook No. 72
>for sale by Superintendent of Documents
>US Government Printing Office
>Washington DC 20402
>
>Here's the magic formula that ties together
>deflection, load, length, depth and width of a rectangular
>wooden beam:
>
> k 12 F l**3
>D = -----------------------
> E w h**3
>
>k is some arbitrary constant
>F is the force applied to the beam
>l**3 is the length of the beam cubed
>E is the modulus of elastictiy
>w is the width of the beam
>h**3 is the height of the beam cubed
>
>The next formula is the same thing for a beam of circular cross section
>
> k 20 F l**3
>D = -----------------------
> E d**4
>
>all symbols have the same meaning except that
>d**4 is the diameter of the beam to the fourth power
>
>Here's what this all means:
>D is basically how much a piece of wood will bend for a given amount
>of force F applied to it. Twice the force, twice the deflection.
>E, the modulus of elasticity is basically a measure of stiffnes.
>The stiffer the wood, the less the bending. For instance, white oak
>will have a greater E than white pine. So twice as big an E means
>half the deflection.
>
>The amazing part is of course the nonlinear terms. l**3 means
>that if a piece of wood is twice as long, it will bend 8 times
>as much.
>
>Taking a 17 foot piece of wood as a base, for instance, and assuming
>that we apply a force that deflects it 1", here is how much the
>same force will deflect pieces of wood of different length but
>the same cross section:
>
>length 15' 16' 17' 18' 19' 20'
>deflection .68 .83 1 1.19 1.4 1.63
>
>So this little chart tells us that a 20 foot piece of wood will
>bend twice as much as a 16 foot piece of wood.
>
>Conversely, if you double the depth of a piece of wood in the
>direction of bending, the deflection is cut by a factor of 8.
>However, doubling the width of the piece of wood only cuts the
>deflection in half.
If I understand this, making my gunnels thicker than .75 inch wont help
compensate for the stiffness lost by having 1.5 inch gunnels, which is what
Eric was telling me I believe.
I think I'll keep shopping for the right slab of wood.
Wayne
>Or to look at it yet another way, the ratio of 20 to 16 is 1.25, so
>if you want your 20' piece of wood to be as stiff as your 16' piece,
>you have to increase its depth by a factor of 1.25.
>
>If we take the second formula for circular cross section wood and
>apply it to ribs, we get the following results:
>
>diameter 5/16 3/8 7/16 1/2
>deflection 2.07 1 .53 .32
>
>Hard to believe, but a 1/2 inch diameter circular rib is
>3 times as stiff as a 3/8 inch diameter rib.
>
>For rectangular ribs of fixed width, here's how stiffness varies
>with thickness (inverse cube)
>
>diameter 1/4 5/16 3/8
>deflection 1 .5 .3
>
>But remember flexibility of ribs goes up with the cube of the
>boat's width.
>
>And don't take these formulas as absolute gospel. They make certain
>assumptions that you can read all about in the wood handbook, but
>you get the general idea about how wood behaves.