Truss Bridge Design and Analysis: Warren Truss with 20 Joints and 37 Members

[mathsgeek]

Truss urgent Help

Homework Statement

We must design a truss bridge that we will then build from spaghetti. The chosen design is a warren with vertical supports. It has 20 Joints and 37 members. (Bridge is 64.8cm long and 10.2cm high)

Homework Equations

I am trying to calculate the forces and need to determine if it is statically determinate using the equation 2J=M+R but the thing is that we will just place the bridge (won't be fixed to it) on blocks at each end and the rest will be resting on nothing. Will that mean R = 2 because of only 2 reactions forces being vertically upwards? if it is, that means 40 = 39 which means it is statically indeterminate and where do i go from there? Also, do i use the method of joints or sections to calculate the forces in each member as i don't know which is better/easier to use/best for a structure that is structurally determinate etc? Thank you (Please answer asap as urgent)

The Attempt at a Solution

 

[mathsgeek]

Also is warren the best design when building it out of spaghetti? Thanks

 

[PhanthomJay]

A Warren truss with vertical members from the apex of the equilateral triangles to the mid point of the horizontal compression chords should work out well. The structure is externally determinate and should be also internally determinate unlress you've added additional members somewhere. Your aim is to minimize the weight for the given loads, and keep the compression members with as small loads and/or short lengths as possible.

 

[mathsgeek]

Phantom, is this what you mean?
http://g.imagehost.org/view/0861/Untitled_1

Also, they aren't equilateral triangles, 2 sides are 115mm and the other is 108mm. Is this design the most efficient or should i remove some evrtical members? Also, how am i supposed to make the compression members have small loads, please explain? Thank you

 

[mathsgeek]

AN URGENT Q!
If I am using the method of joints to calculate forces, i consider all cases at each join t of thee roadway where it meets the joint in the bridge BUT do i also consider when the cart is in the middle of the section of the roadaway where there isn't a joint in the roadway but one in bridge (IE not force from the roadway at this point but there will b force from the cart) or does this not go with the method that assumes force is only applied at the joints? One last thing, when calculating the moment from a certain point, do the measurements have to be in metres or wat because mine are in mm and also, in an example they actually do the force x distance/overall distance of the bridge, is this incorrect or correct because most other examples I've seen don't do this? Thanks

 

[PhanthomJay]

They aren't equilateral triangles, 2 sides are 115mm and the other is 108mm.

They're pretty close to equilateral...do you have a height requirement?

Is this design the most efficient or should i remove some evrtical members?

The vertical members are good, especially if you are going to be applying loads at the bottom (tension) chord. The vertical members to the top (compression) chord will reduce the lengths of top members between joints, providing greater strength with lighter members against buckling failure. But I'd make the spans symmetric, I don't like those end panels. All triangles should be identical, even if it means adding a few members.

Also, how am i supposed to make the compression members have small loads, please explain?

The greater the angle of the diagonals, the less the loading in those diagonals, but you'll need more of them. The smaller the angle, you'll need less of them, but the lengths increase and buckling strength decreases. It's a tradeoff. Think equilateral symmetry. Your design looks pretty good with some slight mods.

AN URGENT Q!
If I am using the method of joints to calculate forces, i consider all cases at each join t of thee roadway where it meets the joint in the bridge BUT do i also consider when the cart is in the middle of the section of the roadaway where there isn't a joint in the roadway but one in bridge (IE not force from the roadway at this point but there will b force from the cart) or does this not go with the method that assumes force is only applied at the joints?

You should assume all loads will be applied at joints only and not in between joints, as this will likely bust the spaghetti into 2. The road surface should be framed into the joints.

One last thing, when calculating the moment from a certain point, do the measurements have to be in metres or wat because mine are in mm and also, in an example they actually do the force x distance/overall distance of the bridge, is this incorrect or correct because most other examples I've seen don't do this? Thanks

You can leave it in mm when summing moments, it won't make any difference, but its OK to convert to meters if you want. You get the same answer for the end reactions.

 

[mathsgeek]

They're pretty close to equilateral...do you have a height requirement? The vertical members are good, especially if you are going to be applying loads at the bottom (tension) chord. The vertical members to the top (compression) chord will reduce the lengths of top members between joints, providing greater strength with lighter members against buckling failure. But I'd make the spans symmetric, I don't like those end panels. All triangles should be identical, even if it means adding a few members.

Yes, i do have the height requirement which is why they are equilateral but they are close enough to being equilateral triangles anyways.

The force will be applied at the top chord, so are any changes that can be made to make the vertical members as efficient if the load was placed at the bottom?

How would i fix the end panels without changing their length, could you draw a possible solution please? Thank you

About the load applied at the joint, it will be applied at the joint in the bridge but not the roadway, but i don't do this though do i because it doesn't fit with my assumption cause a roadway joint would also have to be there? here's a pic to explain wat I am thinking of doing:
http://img407.imageshack.us/img407/5200/88552026.jpg

 

[PhanthomJay]

Instead of breaking the bottom chord into 3 members @ 108mm and 2 @162mm, try 6 equal length members @108mm. If your bridge is to be loaded at the top joints only, the vertical members such as BL and DN are zero force members, and since the bottom chord, to which they would be attached will be in tension, they are not critical to the design. However, it might be a good idea to leave them in, for some stability in the event of horizontal construction or handling loads. The roadway should be supported by beam members which frame into the joints between the 2 top chords, and horizontal beam members should be placed between the joints of the bottom chords as well.

 

[mathsgeek]

Instead of breaking the bottom chord into 3 members @ 108mm and 2 @162mm, try 6 equal length members @108mm. .

If i do that tho, the joints in the roadway wouldn't be located directly over the joints of the standard triangles located at the top of the bridge. This would result in the upper horizontal members of the truss would be subjected to vertically downward forces along their entire length and this would ultimately result in the bridge failing under relatively small forces. Isn't this correct?

 

[mathsgeek]

Double Post

 

[mathsgeek]

Phantom, would u PLEASE b e able to have a look at these calculations as i don't know if I've done it right cause for one of the beams, i get to different values. (Highlighted in yellow). It would be greatly appreciated if you could have a look as i am stuck.

http://uploading.com/files/YU95JWLI/Document1.doc.html

Thankyou very much

 

[PhanthomJay]

If i do that tho, the joints in the roadway wouldn't be located directly over the joints of the standard triangles located at the top of the bridge. This would result in the upper horizontal members of the truss would be subjected to vertically downward forces along their entire length and this would ultimately result in the bridge failing under relatively small forces. Isn't this correct?

I don't know what the givens or requirements or rules are for your design. You definitely don't want your loads to be applied between the joints of the top chord. So you adjust your roadway support beams such that they frame into the joints and not in between them. This will result, for case 1, in 6 concentrated loads applied at the top chord instead of 5. The first load will be applied 54 mm from the bridge abutmentm, at a joint. Where are the loads coming from? One load is much greater than the others. Were the loads given to you?

 

[PhanthomJay]

Phantom, would u PLEASE b e able to have a look at these calculations as i don't know if I've done it right cause for one of the beams, i get to different values. (Highlighted in yellow). It would be greatly appreciated if you could have a look as i am stuck.

http://uploading.com/files/YU95JWLI/Document1.doc.html

Thankyou very much

I haven't checked all your numbers, but your analysis looks very good. You've correctly identified the end reactions, and the zero force members; correctly noted that all the top chord members are in compression, and that all the bottom chord members are in tension. And that the diagonals alternate between tension and compression, typical of a Warren truss. Note that the largest load is compressive in the very first diagonal...and it has the longest length...you'll need a lot of spaghetti for that one, the one i didn't like!

 

[mathsgeek]

I don't know what the givens or requirements or rules are for your design. You definitely don't want your loads to be applied between the joints of the top chord. So you adjust your roadway support beams such that they frame into the joints and not in between them. This will result, for case 1, in 6 concentrated loads applied at the top chord instead of 5. The first load will be applied 54 mm from the bridge abutmentm, at a joint. Where are the loads coming from? One load is much greater than the others. Were the loads given to you?

The roadway placed ontop is 0.9kg and is made up of 6 sections, i did sum simple maths then divided by 2 because 2 sides of the bridge to get 0.74N acting on these joints, which leads back to the initial assumption. The 5.15N is a combination of the 0.74N from the roadway and 4.41N from a 0.9kg trolley that will move across the bridge (its forced was also halved due to to sides to the bridge).

Also, is anybody able to help me with my problem because on member KJ i calculated compression forces of both 3.75N and 3.22N? Is there a technical error, or should this jiust be ignored due to the small value of it? Thankyou, all your guys help is appreciated.

 

[mathsgeek]

Quick q, the cart that is moving across the bridge is pushed from one side which is inclined at a slope of 7.9 degrees. What calculations can i do to calculate the force that will act on the bridge when the cart hits the bridge cause this force broke one the other team's bridges so i can determine gow much to reinforce this area? Thanks