How to Calculate Forces in Bridge Points?

In summary, the problem is to calculate the forces at points A, B, C, D, and E in a bridge with a length of 200m that has the ability to expand horizontally for thermal expansion. The masses of the beams are small compared to the car's mass of 1360kg. The calculated forces are Na = 11.0kN, Ne = 3.67kN, Fab = Fde = 7.35kN, Fac = Fce = 6.37kN, Fbc = Fcd = 4.24kN, and Fbd = 8.49kN. The homework equations involve static equilibrium and parallel forces, but the ability for the bridge
  • #1
Mister V
7
0

Homework Statement



The problem statement:

Bridge of length: 200m
Construction can expand horizontally to allow thermic expansion
Masses of beams: small in comparison to the car
Mass of the car: 1360 kg.

The answers: Na= 11,0 kN, Ne= 3,67 kN, Fab = Fde = 7,35 kN, Fac = Fce = 6,37 kN, Fbc=Fcd= 4,24 kN, Fbd = 8,49 kN

Question: Calculate the forces in points A,B,C,D,E

brug1.jpg



Homework Equations



We've already solved a similar bridge, but there was not the possibility of horizontal expansion.

In the similar bridge we stated that, as the beams were in static equilibrium, the forces should be parallel to the beams, either pointing outwards or inwards:

brug3.jpg



The Attempt at a Solution




My problem is I haven't got a clue how to incorporate the ability to move horizontally. Do I have to allow the forces to be non parallel to the beams?
What I find hard to understand is the fact that the normal force in point A (Na) is different form the normal force in point E (Ne)? I thought that, since the massa is equally distributed along the bridge, the normal forces would be the weight of the car divided by 2.

I have made a drawing with the forces, knowing that when I found a negative force, I assumed the wrong direction.

brug2.jpg


I thought to calculate Fab by saying that there are only forces having a vertical component, so those two should be zero when added.

I stated Fn is = 6670,80. , so Fab . sin(40°) = - 6670,80, Fab = -10377 N, which apparently is wrong ?
 
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  • #2
Mister V said:
[
In the similar bridge we stated that, as the beams were in static equilibrium, the forces should be parallel to the beams, either pointing outwards or inwards:
That's correct, as long as you have a pure truss with loads applied at the joints.
My problem is I haven't got a clue how to incorporate the ability to move horizontally. Do I have to allow the forces to be non parallel to the beams?
No, this just means that there can be no horizontal reactions at A and E, under the vertically applied load.
What I find hard to understand is the fact that the normal force in point A (Na) is different form the normal force in point E (Ne)? I thought that, since the massa is equally distributed along the bridge, the normal forces would be the weight of the car divided by 2.
me too.
I have made a drawing with the forces, knowing that when I found a negative force, I assumed the wrong direction.

I thought to calculate Fab by saying that there are only forces having a vertical component, so those two should be zero when added.

I stated Fn is = 6670,80. , so Fab . sin(40°) = - 6670,80, Fab = -10377 N, which apparently is wrong ?
Looks right to me. The answer key looks wrong.
 
  • #3
Thanks for helping me out!
 

1. How do you calculate the weight of a bridge?

To calculate the weight of a bridge, you must first determine the weight of each individual component, such as the deck, beams, and cables. Then, you can add these weights together to find the total weight of the bridge. It is important to account for any additional factors, such as traffic and weather conditions, that may affect the weight of the bridge.

2. What forces act on a bridge?

The main forces that act on a bridge are compression, tension, and shear. Compression is the force that pushes inward on a structure, while tension is the force that pulls outward. Shear is the force that acts parallel to the surface of the bridge. These forces can be caused by the weight of the bridge itself, as well as external factors such as wind and traffic.

3. How do you calculate the load capacity of a bridge?

The load capacity of a bridge is determined by calculating the maximum amount of weight that the bridge can support without collapsing. This calculation takes into account the materials used, the design of the bridge, and the forces that act on it. Engineers use various mathematical equations and computer simulations to accurately determine the load capacity of a bridge.

4. What is the difference between static and dynamic forces in a bridge?

Static forces are constant and do not change over time, while dynamic forces are constantly changing. In a bridge, static forces may include the weight of the bridge and the force of gravity, while dynamic forces may include wind, traffic, and vibrations. It is important for engineers to consider both types of forces when calculating the stability and safety of a bridge.

5. How do you determine the stability of a bridge?

To determine the stability of a bridge, engineers use various methods such as structural analysis, computer simulations, and physical testing. They consider factors such as the weight of the bridge, the forces acting on it, and the design of the structure. By analyzing these factors, engineers can determine if a bridge is stable and able to withstand the forces that may act upon it.

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