MadSci Network: Engineering

Re: Re: An old query on truss bridges

Date: Mon May 30 13:50:39 2005
Posted By: C.H. 'Chas' Hague, PE SE, Senior Project Engineer
Area of science: Engineering
ID: 1115082671.Eg

Hello, Christina!
Every year, I attend the awards ceremony for the bridge building contests 
run by the Illinois Institute of Technology.  Some of the bridges these 
kids have made are fantastic -- a few grams of wood supporting 60-70 
kilos!  Many of the winners were girls, too.
But they've been building bridges all semester, and your class is just 
doing this for fun at the end of the year.  So, a "crash" course in how 
bridges work:
First, like you said, a bridge is a machine that takes a load from where 
it is and puts it somewhere else, that is, out at the ends.  A bridge with 
no supports under the roadway is called a "simple" bridge.  
All bridges work by "compression" and "tension" in their members, 
compression being when the material is being pushed together, and tension 
being when it's pulled apart.  A piece of string under load is in tension; 
a stack of blocks held horizontally is in compression. 
The loads on an arch bridge are pretty much uniform all the way across.  (the bottom picture 
is not an arch bridge!)
 This puts the entire arch in compression.  If the load is applied in the 
center only, the shoulders of the arch (with nothing to hold them down) 
will flex upwards and fail. 
If the load is placed only in the center of the span, the best supporting 
structure would be what's called a kingpost 
(Also see drawing)  The two diagonal members are in compression; the 
horizontal member is in tension, keeping the bottom end of the diagonals 
from flying out.  
Now the thing with compression members is that they fail by buckling.  
Push down (carefully) on one of your wood pieces.  At some point, it will 
bow sideways.  Try this with a long and a shorter piece, and you will see 
that the longer the member is, the smaller the load it can support before 
it bows.  And, due to the geometery of the triangle, the more acute the 
angle between the strut and the load vector is, the less load there will 
be on the strut -- that is, a strut supporting a load at 45 degrees will 
have to work harder to support it than when the load is at 30 degrees.
So there's the design problem:  The longer the compression struts, the 
more acute the angle between them and the load, so the less load on each 
strut.  But, the longer they are, the more likely they are to buckle.  
Adding bracing from the bottom chord to the struts reduces what engineers 
call the unbraced length, but it adds weight to the truss.
I shouldn't make an out-and-out recommendation as to what kind of bridge 
you should build. But, the simplest structure would be a kingpost truss in 
the form of a four-sided triangle, with the load applied at the apex, two 
long horizontals spanning the gap, and the other two sides the width of 
the "roadway."  The angle of the struts to the bottom chord should be on 
the order of 45 to 60 degrees.  Use bracing struts to reduce the unbraced 
length of the compression members. One more bit of advice:  be very 
careful in making your joints.  That is the most likely point of failure.
When you and your friends break your bridges,  I strongly recommend that 
you not only record the weight of the bridge and how much load it 
carried.  Also record the location and type of failure that each bridge 
experienced.  Then, you can build another bridge with the broken part 
strengthened and other parts lightened.  Load that one, and see where the 
new version breaks.  Keep trying, and you may end up with a bridge the 
equal of the design contest prizewinners!

Good Luck!
C.H. "Chas" Hague, PE SE 

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