Comparing Bridge Forces: With & Without Trusses

[Eagle784]

I'm doing a research paper on bridges, and I'm having trouble finding an example contrasting the magnitudes of forces on a bridge with trusses as opposed to a bridge without trusses.

I understand pretty clearly how a truss works, however I need to give an example with numbers, and I'm not able to find anything useful. Thanks for your help.

 

[PhanthomJay]

I'm doing a research paper on bridges, and I'm having trouble finding an example contrasting the magnitudes of forces on a bridge with trusses as opposed to a bridge without trusses.

I understand pretty clearly how a truss works, however I need to give an example with numbers, and I'm not able to find anything useful. Thanks for your help.

When you say a "bridge without trusses" , do you mean a beam-girder span bridge, suspension bridge, cable-stayed bridge, or what? And when you say "contrast the magnitude of forces", do you mean a comparison of related stresses and member sizes for each?

 

[Eagle784]

I only need a simple example, such as perhaps a description of forces on a simple beam bridge with a large weight in the middle, contrasted with how the presence of a truss would spread the forces out.

For example, take a beam bridge with 1200N force applied on top of it's center: how concentrated would the compression force be? If this same beam bridge had a truss, how spread out would these forces be?

I've attached what I've written on trusses so far. My professor reviewed it and told me I should compare the truss example to an example of a beam bridge without trusses. (He also said I didn't explain my calculations clearly enough, if you have any tips in that regard.) Thanks for your help.

 

[PhanthomJay]

Your calcs look good and your explanation is very clear, in my opinion. Truss members have axial tension or compression forces which give rise to axial tension or compression stresses (F/A). Beams, on the other hand, have bending moments which give rise to flexural tension and compressive stresses.
Trusses tend to be lighter and with less deflection than beams designed for the same load. Are you familiar with bending moments and calculations for bending stresses in beams, and how to size the beam for those stresses?

 

[Eagle784]

I submitted the pdf I attached above, adding only a statement that the same bridge without a truss would have to be able to withstand 1200N at a single point. This is what he wrote back:
"In your calculation on page 2, you go through some of the forces acting at different points in the truss, and conclude that the forces are more spread out - but you don't calculate the forces that would be acting on the same bridge without a truss. So you really can't conclude that the forces are more spread out just yet."

I wasn't familiar with bending moments, but I looked over what they involve, and it seems outside of the scope of the class (this is an introductory physics class). Not only that, I'm afraid if I start talking about them, he'll want the analysis for a truss bridge as well, and he seems happy with it as it is.

I'm assuming he wants more than a simple beam bridge drawn with a 1200N force arrow pointing down at a point, but I really can't imagine what. Thanks for any help you can give.

 

[PhanthomJay]

I submitted the pdf I attached above, adding only a statement that the same bridge without a truss would have to be able to withstand 1200N at a single point. This is what he wrote back:
"In your calculation on page 2, you go through some of the forces acting at different points in the truss, and conclude that the forces are more spread out - but you don't calculate the forces that would be acting on the same bridge without a truss. So you really can't conclude that the forces are more spread out just yet."

I wasn't familiar with bending moments, but I looked over what they involve, and it seems outside of the scope of the class (this is an introductory physics class). Not only that, I'm afraid if I start talking about them, he'll want the analysis for a truss bridge as well, and he seems happy with it as it is.

I'm assuming he wants more than a simple beam bridge drawn with a 1200N force arrow pointing down at a point, but I really can't imagine what. Thanks for any help you can give.

I think in your truss example, if the truss extends from an abutment at A to an abutment at E, a span of 4 meters, it's probably best to show your applied forces of 400 and 800 Newtons as being applied on the bottom chord member AE, 1 meter to the right of A, and 1 meter to the left of E, respectively. But in so doing, you'll have to modify your truss configuration by adding 2 vertical members, one perpendicular to member AC from joint B, and the other perpendicular to member CE from joint D. This will not change your reactions or member forces, but will add a 400 or 800N force on the newly added members.

The reason why I suggest this change, is so that now you can look at the alternate beam bridge, a single beam AE, 4 meters long, with a load of 400N 1 meter from A, and a 800N load 1 meter from E. You will get the same reactions at A and E as you did for the truss example.

Now here's where I'm not sure what your professor is looking for. In the truss example, you end up with axial compression or tension stresses in the members. In the beam example, you end up with vertical shear loads and flexural bending stresses from the bending moments. I don't know what to tell you about the distribution of these stresses along the beam if you are not familiar with this process of calculating shears and moments along the beam. yet. The truss might end up being made up of multiple small size members, whereas the beam is on heavy member, probably heavier than the sum of the truss members, depending on calculating out the numbers.

 

[Eagle784]

Thanks for the suggestion on the design of the truss, that does provide a nice comparison.

I began looking into bending moments and shear forces (read the wikipedia articles about them). They seem to talk about determining how much load a beam could withhold; how can I use these concepts to show how spread out the force would be? If there are any good resources you know of on this subject, please let me know. Thanks for all your help.

 

[PhanthomJay]

Thanks for the suggestion on the design of the truss, that does provide a nice comparison.

I began looking into bending moments and shear forces (read the wikipedia articles about them). They seem to talk about determining how much load a beam could withhold; how can I use these concepts to show how spread out the force would be? If there are any good resources you know of on this subject, please let me know. Thanks for all your help.

You might want to google on "Shear and Bending Moment Diagrams" to see how these forces and moments distribute along a beam for specific examples, and then google on "Strength of Materials" for what stresses are induced in the beam under these forces and moments, but this is a course unto itself. Maybe someone else has a good reference.