Bridge design conceptual questions

[giacomh]

Homework Statement

I'm designing a Pratt Bridge (http://www.garrettsbridges.com/photos/pratt-truss-bridge/attachment/pratt-truss-bridge-2/). It must be able to hold 10,000 lbs at pins every 5 feet and be 40 feet long.

2. Homework Equations / 3. The Attempt at a Solution

I know how to approach this problem, I'm just looking for an explanation of the concepts behind this problem...

So, I have the upward y-force (Ay) from the support on one end up the bridge (along with an x force which is just 0), and just an upward force from the roller at the other end (Py). I use 5000 as the weight in the y direction, because I'm only considering one side of the bridge.

ƩFy=0=Ay+Py-5000
ƩM=0=-5B-10C-15D-20E-25F-30G-35H-40I+40Py

Depending on which two pins the 5000 lb weight is distributed on (2500 per pin), I solve for Py, and in turn solve for Ay.

Basically, as the weight moves farther from the support (closer to the roller), Py increases, and it in turn increases (or decreases if you consider the negative) the value of Ay. Also, the tension in the trusses is often much greater than 5000 lb. Some trusses (verticals) are always 0, and only have tension when the weight is on their respective pin.

My questions:

How is it possible that the tension in the tresses is significantly higher than the only force in the negative y-direction?

Is it possible for a truss to have 0 tension on a bridge (not literally 0, but in a hypothetical case study, where we are neglecting the weight of the bridge)?

Also, if Ay is a negative value, should I use this negative in future calculations that involve Ay, or is it just indicating that the tension is compressive? So I should use the absolute value?

 

[CWatters]

How is it possible that the tension in the tresses is significantly higher than the only force in the negative y-direction?

Consider a horizontal rope such as that used to hang washing on to dry. What's the tension in the rope if you hang a weight in the middle? The answer depends on how much the rope sags. What's the tension if you try to pull it so tight it doesn't sag at all?

 

[pongo38]

point 1: "It must be able to hold 10,000 lbs at pins every 5 feet and be 40 feet long." You seem to be interpreting "every" as each. Not quite the same thing.

point 2: Not sure what you mean by the symbols B through to I in the moment equation.point 3: "as the weight moves farther from the support (closer to the roller), Py increases, and it in turn increases (or decreases if you consider the negative) the value of Ay." What are the circumstances in which Ay is negative?

point 4 :"How is it possible that the tension in the tresses is significantly higher than the only force in the negative y-direction?"
This is the lever principle. The external moments from loads and reactions have relatively small forces and large distances. The internal forces that balance these applied loads are principally in the horizontal top and bottom members, which are relatively close together. Balance of moments makes the internal forces inevitably larger than the applied loads. For the same reason, in a solid beam like a timber floor board which is say only 3/4 of an inch thick, the internal forces are much much greater than the weight of the person standing on the board. The Pratt truss is just an efficient form of solid beam, but there's no escape from the large internal forces unless the height of the truss is comparable to its span.

point 5: "Is it possible for a truss to have 0 tension on a bridge"
Only theoretically. In practice there are many load cases, including assymmetrical loadings, wind, and forces during construction that need to be considered. All members contribute to buckling resistance from compression and torsion effects.

point 6: "Also, if Ay is a negative value..." I have already raised this above. I think the answer is that you shouldn't believe your calculations without doing a check. For example, if you have determined Py from your two equations, then check equilibrium by taking moments about ANY other point (the roller will do nicely). The moment should be zero. If Ay is negative you have made a mistake. Hence my request for you to describe the meanings of B C D etc.

 

[giacomh]

Oops. Messed up equation for the moment. Also, should the members be in symmetry?

 

[giacomh]

Actually, I guess what I'm asking is: how can I verify that my tensions are correct?

 

[pongo38]

There is more than one answer to your latest question. In the method of sections you cut the structure through the member of interest and complete the cut through the rest of the structure, hopefully intersecting not more than 3 members in total. Then for one half of the structure, use equations of equilibrium to solve for the 3 forces 'exposed' by the cut. including the tension force in which you are interested. To check it, do the same for the other half of the structure on the other side of the cut.