How Do You Calculate Forces in Truss and Suspension Bridges?

[Alpha[X]²]

How will I calculate the forces involved in a truss and suspension bridge, my teacher did not explain this fully and I'm confused as hell.

 

[radou]

How will I calculate the forces involved in a truss and suspension bridge, my teacher did not explain this fully and I'm confused as hell.

Depends on the geometry and the loads applied to your bridge. If would be great if you posted a pic.

Basically, all you have to do is apply the equations of equilibrium to your system. I can't be any more specific with the given data.

 

[Alpha[X]²]

Erm, let's just say a 100 metre bridge with trusses with an angle of 60 degress. The bridge weights 20 000 N.

 

[Pyrrhus]

Well, a picture and your attempt will be a good start.

 

[Alpha[X]²]

I don't have anything because I don't know how to calculate the forces.

 

[radou]

Do you know how to calculate the support reactions? Your bridge must have some supports. Did your teacher explain this? It's the first step.

 

[radou]

Well, after calculating the support reactions, you can calculate the force in every truss element by analyzing every node separately. Start with the node(s) where you have only two (out of three) unknown forces.

 

[Alpha[X]²]

How did it come up with those calculations though?

 

[radou]

How did it come up with those calculations though?

Which calculations? Do you mean, the calculation of the reaction forces at the supports?

 

[Alpha[X]²]

Yes, the numbers on the members in the diagram.

 

[radou]

Yes, the numbers on the members in the diagram.

I assume the numbers represent the forces in the members, and the colors represent compression/tension. As I said, you can calculate every force by looking at every node separately. Imagine you "cut out" the leftmost node. You have two unknown and forces and one familiar force. Set up two equations of equilibrium, one for the "y-direction", and one for the "x-direction". You can calculate the forces in the members from these equations.

 

[Alpha[X]²]

But, that looks like an equilateral triangle, why is there different calculations?

 

[Alpha[X]²]

Also, I the program used a matrix to solve the forces, what would the matrix calculation formula be?

 

[radou]

What matrix are you talking about?

The calculations seem wrong. For example, I got ~28.87 for the leftmost blue truss element.

 

[AlephZero]

The triangles are not equilateral in the drawing.

The answers are correct (to 2sf) for the shape as it is drawn. I get 30.05 for the force in the leftmost blue truss.

 

[radou]

The triangles are not equilateral in the drawing.

The answers are correct (to 2sf) for the shape as it is drawn. I get 30.05 for the force in the leftmost blue truss.

Of course, for some reason, I totally ignored the mesh.

Alpha[X]^2, sorry for causing eventual confusion.

 

[dfx]

Read up on "pin-jointed analysis of trusses". The "matrix" is probably just Cramer's method to solve simultaneous equations for the member forces.