A3 - Yilei

• Free Body Diagram & Calculations

     By using the "Method of Joints", the analysis of the truss bridge is showed below. The bridge has a span of 24", a height of 8" and a load of 15 lb at point C.

• The overall forces can be seen below.

• The  same results of analysis in The Bridge Designer's version. 

       The online Bridge Designer is a program allows to design a virtual truss, and then put a load on it. It will calculate the tensions and compressions of each members itself. 

       When I did this program, I had to use the same scale of all members and angles to correspond the results of my hand analysis.  I made each grid be 2"so that the length should be 12 grids. And the height should be 4 grids. Then I picked up the middle node of the length to put a load on, which was 15 pound in this case. Consequently, I got the most approximating forces equaling the ones calculated by hand.   

• The results of analysis of our two foot span bridge in Bridge Designer program.

        Might because of our design, it was hard to computed via the Bridge Designer program. Our two foot span bridge has a bottom truss. So when I completed the adding process and pressed the calculate button, there's an error came out. It said that we had to followed stable structure is M + 3 = 2*N , where M is the number of members and N is the number of nodes. The simulation will not calculate forces unless this condition is met. Thus, we changed our K'Nex design a lot. Besides, we did looked the K'Nex joint test page and it showed the tension would increase if the bridge is symmetrical. So we did the bridge symmetrically.

        That type analysis of the K'Nex truss bridge can find out the strong and weak parts of the bridge by using the average strength of each joint. So we can change our design to reach the proper number. That can make the bridge more stronger.    

week 8 -Yilei Jiang

       I learnt the "Method of Joints" during last lab which is s a way to find unknown forces in a truss structure. This method also would be used in completion of the A-3 assignment.The method of joints consists of satisfying the equilibrium equations for forces acting on each joint. In the lab, we also discussed some ideas of our next three foot span bridge. We agreed that we would use the new method we learnt to calculate our new design to get the most serviceable design.  


       After the amounts of calculating, I think this method of analysis, the "Method of Joints," is not sufficient for a real bridge for some reasons.  First, a real bridge should be tested and analyzed in many more ways than just testing a downward force on a connection joint. Even this method shows the tension and suspension of every members, a real bridge could not be built of this simple databases. Secondly, A real bridge is not only hold its own weight but also deals with dynamic loads and the things like side pushing from the side and even up drafts from underneath. "Method of Joints" does not show that side.  
    
      I am not saying that the "Method of Joints" is completely useless because it at least shows the force when a truss bridge is under a special circumstance, which is  in equilibrium. If a truss is in equilibrium, then each of its joints must be in equilibrium. That's how this method works. This method is one of many methods that are used to analyze bridges. Of course there should have more different calculation for a real bridge. 
      
      There's one thing I'd like to further analyze, which is the accurate breaking point of the K'Nex gussets when they are   experiencing forces. I think that this information would be useful at our next assignment, which is designing a three foot span bridge.
      
      For next week, we will working on our new bridge and complete the comp2.

week8 - xue bai

Last week in class we start work on the basic calculation of the force that on each member. We learn how to use free body diagram and trigonometry to get the force that is one each member, but it need a lot of calculation. The bridge design is the next thing we learn that could help calculation the force. It was very quick and useful. It is better the calculation by hand. I believe we can do a better job on our second bridge.

Next week we would start to work on our second bridge. By the experience we had on our first bridge and the ability of analyze the tension and compression of each member we can design our second bridge in a better way and made it more effective.

The ability of analyze is very helpful but it also have a lot of limited. Analyze we learn just calculate the force form one side but not all the side. The structure in the middle also can be affecting the finial load. In the first test our bridge is fall down because of the twister. The bridge design did not count the chance of bridge twister. The other part that is also very important is the joins. K’net has a very weak join. It fall apart very easily even the member can support the loads the joins could fall apart and made the bridge fall down. It better to know the limit for the join and how much force is do on it. That could help a lot.  

A3 - XUE

 Free Body Diagram

Angle Calculations

Calculations

Replication of Analysis in Bridge Designer

In order to make sure results of the hand analysis correspond to online Bridge Designer I use every square as a two time two square. The length of the bridge is 36’’. That meant that I use 18 little squares as my base and my high is 10’’. That made my bridge has 5 squares high. So my hand analysis has same angle as the online bridge. Same angle is very important in the calculation. That make sure I have a correct number in my online bridge designer. The online bridge designer also is a tool to make sure my calculation is right. My number of calculation is mostly match to the online one, so my calculation should be right.

We change our bridge a lot to follow the ruler of member add 3 equal twice the nodes. The online Bridge Designer cans only calculation particular member and nodes. That made the calculation it give did not match the number the number we get in the text. But I try my best to get it as close as possible. I put 35 pounds load on the bridge. It should that some member get a lot of forces in other hand some member did not get any of the force. I do not know is that number come out because my changer of the structure or our bridge have this problem in the first time. However get to know force on each member is very helpful in future design. We can improve our design and made it became more effective by that way. Such as cut up the member in the place that have less force or do not have force at all. Add more members to the place, which has a lot of force. In the picture shows that middle has a lot of force. We may add some member in the middle. The online bridge design was very helpful. I hop we can made a better bridge next time. 

A3 - Kyle Hayes

Ends

   ΣF_X = 0:   F_AX = 0

   ΣF_Y = 0:   -10lbs x 1ft + F_EY x 2ft = 0

F_EY = 10/2 = 5lbs

F_EY = 5lbs

F_AY = -10lbs + F_EY = 0:   F_AY = 5lbs

F_AY = 5lbs

Joint A

   ΣF_Y = 0:   T_AB sin(45) + F_AY = 0:   T_AB = -5/sin(45) = -7.07lbs

                T_AB = -7.07lbs

   ΣF_X = 0:   T_AB cos(45) + T_AC = 0:   T_AC = 7.07 cos(45) = 5lbs

                T_AC = 5lbs

Joint B

   ΣF_Y = 0:   -T_AB sin(45) + T_BC sin(45) = 0:   T_BC = -T_AB sin(45) / sin(45) = 7.07lbs

                T_BC = 7.07lbs

   ΣF_X = 0:   -T_AB cos(45) + T_BC cos(45) + T_BD = 0:   T_BD = -7.07 cos(45) - 7.07 cos(45) = -10lbs

                T_BD = -10lbs

Joint C

   ΣF_X = 0:   T_BC sin(45) + T_CD sin(45) -10lbs = 0:   T_CD = [10 – 7.07 sin(45)] / sin(45) = 7.07lbs

                T_CD = 7.07lbs

   ΣF_Y = 0:   -T_AC – T_BC cos(45) + T_CD cos(45) + T_CE = 0:   T_CE = 5 – 7.07 cos(45) – 7.07 cos(45) = -5lbs

                T_CE = -5lbs

Joint D

  ΣF_Y = 0:    -T_CD sin(45) – T_DE sin(45) = 0:   T_DE = -7.07 sin(45) / sin(45) = -7.07lbs

                T_DE = -7.07lbs

 

Joint E

   All tensions around joint E are already solved for.

My Analysis Diagram

Bridge Designer Analysis



To make sure the hand analysis corresponds to the Bridge Designer, the lengths of the members and the angles must scale to each other. So that all angle are the same between the hand and Bridge Designer analysis. For the members it is just important the relative size to one another is kept the same. If two pieces are the same length as each other than those two corresponding pieces on the Bridge Designer must be the same length. If one is twice the size of the other, than the corresponding piece on the Bridge Designer must be twice the size of the other.



K'NEX

Bridge Designer Analysis

The K’NEX joint test page showed that the pull out for required to remove a member from a joint increase with the more members attached to that joint, it also increase more if it is symmetrical. This test tells us that the average max limit of tension of a member can be 37lbs before the connecter is almost guaranteed to fail, useful information as any member nearing this tension amount must be adjusted and will most likely fail first. We can use the fact the more members per connector increases the tension required to remove the member to strengthen our connection. Where ever there is a spot nearing this maximum tension amount we can add a member that will have a vector force in the same direction as the member nearing the max tension to increase capacity. To explain a bit more clearly, the example only had three of the five slots of the connector use, the other to slots, the ones on the end would not contribute to increasing the strength though as they were only in the x direction and thus can only hold and x direction vector force, but the three that were used either only had a y vector or had a component of them that was in the y direction. This is why adding members increases the tension needed to pull it out, because it is not just that member being pulled in the y direction but some of the pull is being sent to the other member whose vector is in both the x and direction.

    - Kyle Hayes

Week 8- Kyle Hayes

Last week we practiced how to calculate the force on each member of the truss using method of joints by calculating it for a low load simple 7 member bridge. After doing the calculations and following the video tutorial we verified it using Bridge Designer online, and then we used Bridge Designer on our K’NEX design to help analyze the tension and compression of each member which will be used to improve our design as we near the final weeks.

I feel that this method is good for calculation basic tension, but must less reliable when there are many loads that are always moving and changing value rather than fixed to just one joint. Also like many of the other method we used this only calculates for perfect conditions, no live load, no wind or other force, and the members and gussets are perfect fit and perfect condition. So yes, it is a useful tool but not sufficient enough and reliable enough to count for a real bridge.

The one other thing I would like to analyze is the tension of the gussets. What is the max strength of the member-gusset connection, and the strength limit of the two grooved gussets stuck together as they seem much weaker and tend to fail more often than the member-gusset connection in my experience.

This week in class we will be using the data collected from Bridge Designer for our K’NEX bridge and fix our design based on adjusting high and low tension points of our design.

Week 7 - Yilei Jiang

       Last week, we finally tested our bridge and it loaded 34-pounds of sand. At first, the bridge wasn't long enough to fit in a two foot long span. Therefore, we decided to add an extra 2.125" long chord on the base. By doing this, the bridge became symmetrical.
       The bridge started to twist when we added weights because of the structure of our bridge design. We added an extra 5' long chord on the top truss to make the bridge more stable. However, the 5" long chord was beyond the width of the bridge, so it didn't fit too well with the gussets. When we added the load, the bridge started to twist lightly. There were two groove gusset plates in the middle which pulled apart, at first. Then two members from the support points could not hold the load any more, so the bridge collapsed. We planned to fix these problems on our next three-foot bridge design.
        For K'NEX numbers, I would like to know the accurate tension of every piece truss members during the bridge loading. That would help me to design a more serviceable bridge by calculating some trigonometry functions with those databases.
       Next week, we will start designing the three-foot long bridge on the basis of previous designs.

- Yilei Jiang