Why Do Edge Springs on a Simulated Suspension Bridge Show Higher Tension?

[pratikpatel]

So I'm working on assignment dealing with creating a simulation of a bridge made with springs and masses. **THIS IS NOT A HOMEWORK PROBLEM (I just want some explanation)**

When I calculate the tension on each of the springs, I find that the springs towards the middle have the least tension on them, while the springs towards either ends have a higher tension. Why is that? (Unless I'm doing calculations wrong.)

Also, when I "place" more mass (people) on the bridge at particular locations the springs around the mass have 0 tension! (and tensions on all the other springs increase).

I have attached a screenshot of the bridge where I have placed some mass (people) on the 12th mass of the bridge and also one of the tension in each of the springs observed.

I would love to hear an explanation/correction. I will be happy to post the code if anyone wants to look at it. The simulation was created using EJS.

 

[PhanthomJay]

So I'm working on assignment dealing with creating a simulation of a bridge made with springs and masses. **THIS IS NOT A HOMEWORK PROBLEM (I just want some explanation)**

It appears you are modeling a cable suspension bridge by placing a series of uniformly closely spaced equal masses connected by massless springs, to simulate a parabolically shaped cable under uniform loading from the load it supports? Is this correct?

When I calculate the tension on each of the springs, I find that the springs towards the middle have the least tension on them, while the springs towards either ends have a higher tension. Why is that? (Unless I'm doing calculations wrong.)

That is correct, the tension is lowest at the midpoint (horizontal tension at the low point), increasing to a maximum at the end points, at which points the cable tension is the vector sum of the horizontal tension and 1/2 the bridge's weight (from equilibrium considerations).

Also, when I "place" more mass (people) on the bridge at particular locations the springs around the mass have 0 tension! (and tensions on all the other springs increase).

All tensions should increase due to the increase in load, I don't see how you would get zero tension anywhere...perhaps it is in the modeling of the extra point load (people load applied at a point) at the 12th mass, which is fouling up your computer model.

I have attached a screenshot of the bridge where I have placed some mass (people) on the 12th mass of the bridge and also one of the tension in each of the springs observed.

I would love to hear an explanation/correction. I will be happy to post the code if anyone wants to look at it. The simulation was created using EJS.

I wouldn't know what to do with the code, since I am not familiar with the software program..

 

[pratikpatel]

Yup. Massless springs, and it's parabolic with no people on the bridge. Also, it's not only the 12th mass that gives 0 tension. Anywhere I place people the tension goes to zero. I'm reviewing my code right now to see what can be changed. Thanks a lot for your help! I'll keep you updated.

 

[PhanthomJay]

It's parabolic with no people on the bridge, but only if your initial point masses uniformly spaced represent bridge dead loading. If your initial point masses are supposed to represent the cable weight, then you could be getting large errors, because the cable takes on the shape of a catenary involving the hyperbolic functions, and due to your large sag-span ratio, the parabolic curve will not closely approximate the catenary under such a large sag-span ratio. But regardless, you should not be getting zero tension at the people load appication points. You don't get any zero' tensions when using your original equal spaced mass point loads, do you?

 

[rwisz]

This is a very interesting assignment and it's great that you are seeking clarification on the results you are getting. From a scientific standpoint, the tension on a suspension bridge can be affected by a number of factors, such as the weight and distribution of the load, the material and design of the bridge, and external forces like wind and temperature.

In the case of your simulation, it appears that the tension on the springs is directly related to the weight and distribution of the masses on the bridge. This is consistent with the concept of tension, which is the force exerted on an object due to a pulling or stretching force. As you add more mass to the bridge, the springs closest to the mass will experience the highest tension because they are supporting the most weight. This is why the springs towards the middle of the bridge have less tension - they are supporting less weight compared to the ends of the bridge.

As for the observation that the springs around the mass have 0 tension, this could be due to the way your simulation is set up. It's possible that the mass is not actually resting on the springs, but rather is being supported by the surrounding springs. This would result in the springs directly under the mass having 0 tension, while the surrounding springs experience an increase in tension to support the added weight.

In terms of the code, it would be helpful to see it in order to provide a more specific explanation or correction. However, from a scientific standpoint, it seems that your simulation is accurately representing the tension on a suspension bridge. I hope this helps and good luck with your assignment!