Luke (an avid bridge blog reader and UW graduate student) suggested that I learn how to put a link in the blog so that readers could find past posts during the design and model building phase that relate to the real construction now going on. So here goes.
If the link works it should take you to the blog post of Feb. 22, 2011 that was titled - "When do we get to work?" In this post I am working on building the camber into the 3/8 scale model truss. Reading and studying this past post may be helpful to understanding the thinking.
Feb 22, 2011 post When do we get to work
One of my biggest fears would be to build a bridge and then have the dead weight load of the bridge itself cause the bridge to sag. Looking at the design of flat bed semi trailers one can see the arch or camber built into them and this is what I thought would be needed in a bridge. Bridge #1 was supported with knee braces. The bridge deck was jacked up and the braces installed. For 24' long Bridge #2 the bottom chord was arched. The center was 2" higher and then pulled down 1/2" per each "vertical" in the truss. This rate of drop was linear and not a true arc but did the job. Bridge #3 (also 24' long) was a mortise and tenon design and there was no reasonable way I could see cutting a camber into the joinery. Just doing it straight would be enough trouble for me and the students!
Milton's book described the camber in two of his bridges. The 140' Union Street had 12" of camber and the 240' long Zehnder's bridge in Frankenmuth, Michigan had 14" of camber. This worked out to between .342" and .233" per 4' interval of the truss. The 32' long South Wayne bridge with 8 - 4' intervals at .342" each would come to 2.75" of camber. I rounded it up to 3"so there should be plenty of camber.
This time I wanted the points for arc of the camber to follow the true arc and not be linear. I would be working with the chord of a circle that would form the camber. The length of the chord would be 32' and the rise at the midpoint would be 3". That was the easy part. Finding what the radius for drawing this circle would be a dandy math problem! Then doing the calculations to determine the rise from the chord to the arc at 4' intervals would be a killer. However, using the CAD program was the easy way out and worked like a charm. Next was to determine if the arc for the top chord used the same center point (were the circles concentric just increased by the height if the bridge truss)?Again the CAD program made quick work of this and I determined that the top and bottom chord arcs had to be identical. Keep in mind that the top chord would be 40' long because of the angle and way the lattice continues at each end of the truss.
In the end the measurements for the camber, going from the center of the truss to the end in 4' intervals are: 3.000" to 2.875" to 2.250" to 1.375" to 0.000" in the deck to -1.750" in the top chord.
Interval drop #1 = .125" #2 = .625" #3 = .875 #4 = 1.375 (deck total = 3" ) plus #5 = 1.750"
Puzzler - On page 85 of Milton's book he states, "The base intersections of the lattice having been laid out for 4' on centers, a radius is projected from the extreme intersections to the top of the fourth chord. A measurement along the top chord will determine the amount of excess to be added to each 4' multiple without the inaccuracy of projecting additional radii." What did this mean?
Tech Vocab - Perpendicular, Perpendicular bisector, Arc, Radius, Chord, Circumference