Deep Beam Theory 1

[PaulMarkham]

I am trying to design a temporary foundation using 9"x3" timbers in cantilever. The bending capacity of the timbers results in a short member (about 16"), when I use simple bending theory.
Is there a deep beam theory applicable to timber? This should allow a longer cantilever and thus be more economic.
I have done a web search and found deep beam theory relating to concrete but nothing for timber.

 

[pmkPE]

How are the foundation beams to be loaded? i.e. how do you arrive at a foundation member length of only 16"?

 

[PaulMarkham]

This is a temporary foundation for a mobile crane. The load is spread by a grillage of timber beams. I am referring to the bottom layer, in contact with the ground, and have calculated the cantilever distance using simple beam theory. The 16" length is limited by the bending strength of the timber.
I am reluctant to apply deep beam theory for concrete but thought that similar theory might exist for timber.
Any ideas?

 

[pmkPE]

I have not been able to locate any deep beam theory for timbers/wood. Looking at the deep beam theory for concrete I find examples using either grillage of steel (horizontally) in the depth of the beam or tie-and-strut models where there is sufficient steel to model a truss within the concrete beam. Timber is never going to be able to compare with such composite materials.

Your evaluation for 16" lengths is most likely the best that you can get, depending on the weights of the crane and allowable soil bearing capacity. I found in one of my old reference books: Kidder/Parker, Architects' and Builders Handbook a recommended approach for timber foundations for buildings. If you are interested in the formula let me know and I will type it in - its probably similar to what you used.

 

[PaulMarkham]

Yes, please send the formula. If it's easier than typing you could scan it in and send it to paul.markham@interserveprojects.co.uk.

 

[pmkPE]

PaulMarkham:
From the above referenced book, eighteenth ed.,1946; John Wiley & Sons, Inc.

"Foundations, section 25. Timber Footings for Temporary Buildings
Timber Footings. For buildings of moderate height timber may be used to give the necessary spread to the footings, provided water is always present.The footings should be built by covering the bottom of the trenches, which should be perfectly level, with 2-inch planks laid close together and longitudinally with the wall. Across these planks heavy timbers should be laid, spaced about 12 inch on centers, the size of the timbers being proportional to the transverse stress. On top of these timbers again should be spiked a floor of 3-inch planks, of the same width as the masonry footings which are laid upon it. All of the timber-work must be kept below low-water mark, and the space between the transverse timbers should be filled with sand, broken stone or concrete. The best woods for such foundations are oak, long-leaf pine and Norway pine."
Now here is the part you are interested in:
"Calculations for the sizes of the cross-timbers. The sizes of the transverse timbers should be computed by the following formula:
Breadth in inches = (2XpXc^2Xs)/(d^2XA). p represents the bearing resistance of the foundation-bed in pounds per sq. ft., c the projection of the transverse timbers beyond the 3-inch planks, in feet, s the distance on centers of the timbers in feet, and d the assumed depth of the beam in inches. A is the constant for strength. The values recommended (in 1946) for "A" are 88.9 for long-leaf yellow pine, 66.7 for white oak, and 61.1 for common white pine or spruce."

The part about keeping the timbers below the low water mark is naturally to ensure long term use. As your project is for temporary service I would disregard.

Good Luck with your project!

 

[tincan]

Try treating the system as similar to rails over ties. An elastic foundation analysis should work. Try Roark for formulas and theory of beams on elastic foundation.