September 2013 · Index · May 2014

Treefort Bridge

Scary Bridges · Issue 3

Note: The calculations on this page were neither calculated nor certified by a licensed engineer. All calculations for discussion purposes only. While this page is intended to be educational, students should refer to their text and professors to verify their calculations.

Built: Circa 1995
Destroyed: 10 May 2000
Length 9ft (estimated)
Type: Simple Wooden Beam
Location: Los Alamos, NM
Reason for listing: Substantial lack of planing and design, poor construction quality, and a noteworthy lack of safety measures.

Photo of

The author is not without fault when it comes to design and construction of scary bridges. Indeed, by the close of 7th grade he had designed and executed his very own scary bridge. Admittedly, in this context "designed" means "Decided that some of the 2x4s salvaged from the landfill could be spliced together and used to connect the main fort to the treefort. And wood from some old pallets would make excellent decking for said endeavor." And "executed" means "Took a saw, hammer, and nails. And used them to fasten said wood together into a bridge and install it between his two forts."

Once the bridge was installed the author was, at the time, very pleased with the result. The resulting functionality was well worth the investment. Oddly, all others refused to cross the bridge more than once. It remains unclear why anyone would, even just once, let a 7th grader talk them into crossing a bridge of his own design and construction without first insuring that it passed inspection.

Other than the lack of hand railings (and lack of a warning sign), the obvious safety question is "Even under good conditions, can this bridge hold a reasonable load?" Due to the later destruction of the bridge it is not possible to determine exact design values, nor to conduct much needed destructive testing. However, a rough estimate of the bridges strength can be made.

As with the prior bridge, page number references refer to pages in Structural Design in Wood, ISBN 0-412-10631-0.

Bridge Specifications and Assumptions:

Adjustment Factors
Factor Notes
Size factor: Already incorporated into Fb (p394) The size factor adjusts for the increased possibility of hidden defects in larger beams.
Wet service factor, CM: 0.85 (P394) The wet service factor accounts for the decreased strength of the wood due to wet use.
Beam stability factor, CL: 1, based on depth to thickness ratio (p100). The beam stability factor accounts for the tendency of tall & narrow beams to easily buckle.

Moment due to self weight
Calculation Notes
vb = 2(1.5in*3.5in) = 10.5in2 per inch of bridge Volume of the 2 x 4 support beams
vd = 1in*16in = 16in2 per inch of bridge Volume of the decking
ws, = volume * specific gravity * mass of water Equation for finding the self weight.
Specific gravity of southern pine: 0.55 (p420) This, times the weight of water, will convert volume to weight.
Water is 62.4lbs/ft3, or 0.36 lb/in3
w = 26.5in2 * 0.36lb/in3 * 0.55 per inch of bridge Adding vb and vd gives 26.5in2. Then use above info to find weight per inch.
w = 0.485lb per inch of bridge
M (Moment) = wl2/4, where w=weight and l=length. Equation to find the moment from an evenly distributed load on a simple span.
M = (0.485lb/in * 108in2)/4
M = 1,415in*lb
  • 707.5in*lb per beam
This gives us the moment induced by the self weight of the bridge. The remaining strength can be used to support any payload foolish enough to cross.
Beam Capacity
F'b= allowable bending stress * adjustment factors F'b is the adjusted allowable bending stress, or the strength of the beam times the aforementioned adjustment factors. This is how much bending stress the beam can safely handle, assuming all the assumptions and calculations are correct. Since the goal is to find that greatest stress that it will handle, F'b should always be a value slightly below the result of that found by a destructive test.
F'b = 1350psi * 0.85 * 1.0
  • Self weight does not dominate, so we use 1.0 as the load duration factor.
Multiply the bending strength by the adjustment factors. If the self weight dominated it would change the calculation.
F'b = 1147.5psi
Mmax = Sx * F'b The maximum allowable moment is the section modulus times F'b.
Mmax = 3.06in3 * 1147psi Sx was listed above.
Mmax = 3511 in*lb
Mp3,511in*lb-708in*lb = 2,803in*lb Subtracting the moment due self weight tells us how much is left to support the payload, Mp.
M = Pl/4, where P=load and l=length Equation for the moment caused by a point load at the center of a simple span.
P = 4Mmax/l M and l are known; solve for P
P = 4(2,804in*lb)/109in By putting in Mp the allowable payload is found.
P = 103lbs
Estimated Bridge Strength

This gives us a maximum bridge strength of 206lbs if both beams are evenly loaded. However, a walking person could easily place all their load on one side or the other. The larger load duration factor for short duration loads (1.6 for 10min loads, 2.0 for impact) suggests that the bridge would not immediately break due to a 150lb person crossing it - but repeated use by a 150lb person could result in a failure.


The bridge likely would not break under occasional use of a 7th grader, provided that no extra load is carried. However, the bridge can not be considered to have adequate capacity for normal safe operation. Additionaly, due to the lack of the warning sign, this bridge fails on all counts of Don Lawson's Safety of Engineering Hierarchy.

Final Note

The eventual destruction of the bridge was indeed accidental in nature. As hard to believe as it may be, that destruction was not due to any design defect, nor was it in any way the fault of the author. Had the bridge (and fort) been properly engineered & constructed the bridge would still have been accidentaly destroyed at the same time and in the same way.

September 2013 · Index · May 2014

Last Update: This page was last updated on March 2014; reformatted, minor content updates.

Photo © Alice Lacelle, 1995
Other content © David C. Hunter, 2013-2014
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