God is in the detail

24 Tuesday Apr 2012

Tags

geometric method, Maxwell diagram, truss

In the design of structural engineering, sometimes a small change can make a huge difference in the results. Engineers have to find out these beneficial changes and make the design as perfectly as possible. One such example is the figure 2.46 in Timoshenko’s book Theory of Structures.

In this figure, there are two trusses, which have similar dimensions and load patterns. The only difference is the direction of diagonal web members. As we can see, the first one is a simple truss and can be solved by relatively easier method. In contrast, the second is a complex truss and has to be divided into separate portions before the calculation.

So what is the conclusion? Although the two trusses look similar, but their axial forces are quite different. It is obvious that the second one has smaller internal forces. Consequently, smaller axial forces will lead to a smaller amount of materials that are used in the trusses.

The formula $V=\sum l_{i}A_{i}=\sum l_{i}\frac{F_{i}}{\sigma }$ can be used to estimate the amount of material needed in these two trusses. Then, the amount of materials in the first truss would be $\frac{700}{\sigma _{c}}+\frac{520}{\sigma _{t}}$ and the second one would be $\frac{540}{\sigma _{c}}+\frac{362}{\sigma _{t}}$ .

The amount of materials of the first one is at least 30 percent more than the second one. If they were made of the same material, the second truss would be a better design.When considering the stability of these compression bearing members, the second design is still better. The compression forces are smaller and the compression bearing members are comparatively shorter.

The famous architect Mies van der Rohe once said:”God is in the detail.” Although he was talking out the detail of architecture design, it still makes sense in the field of engineering. Some details are very important, even crucial to the whole project. As in this case, only changing the direction of the diagonal members could make such a difference in the final results. In real projects, there are so many factors that need to be modified. Some may affect the final results greatly, while others might only cause minor or even negligible changes. As structural engineers, our value is to figure out the most important factors and improve the design as much as possible.

3 thoughts on “God is in the detail”

Pranjal said:

2012-04-24 at 18:33

Hello

Nice to read your blog once again. However, I have a few comments-

1. First of all, you can not make a sound conclusion about which truss is better unless you specify the loading conditions. In your case study, you have disregarded the effect of suction forces i.e if the loads are applied in the reverse directions, in that case the lower chord will go under compression and so on. I would be interested to see your conclusions when you carry out this additional study.

2. Secondly, I am not sure from where this formula for estimating the material used in the trusses originate, but still from my opinion it is better to have as many elements working in tension as possible. Not only it makes the structure light but even more efficient.

You have made an argument in the favor of second truss althought the diagonals are acting in compression,” the compression is small and members have comparatively smaller lengths”. I have to disagree with this beacuse from your study(which is again incomplete in my opinion untill you take into account loading in both directions), still you might have less compression forces in the diagonal members but they have longer out of plane buckling lengths, you can not disregard this and when you’ll actually begin to size these members, in my opinion you’ll end up being more heavier than the first truss.

Again, these are my opinions, let me know your views.

Pranjal

Reply
- Gao Nan said:
  
  2012-04-25 at 21:36
  
  Dear Pranjal
  
  Thanks for your comments.
  
  Since it is a practice question from the book Theory of Structures, its load pattern is defined by the condition provided by the book. In short, it’s just an exercise, not a real project. So I just consider this kind of load. I should say: Under this load form, maybe the second one is a bit better. This situation is meaningful when the roof is relatively heavy and there is little wind.
  
  The formula for estimating the material is to estimate the total volume of the truss. I assume that it is made of the same kind of material. So the total volume equals the sum of all the volume of each members, which equals to the product of the length and the sectional area. In order to simplify the problem, I did not take the out of plane buckling lengths into account. In my estimation, I just assume that the sectional area equals the axial force divided by the strength of the material.
  
  I admit that this is an over-simplified solution. After all, it is an exercise. If we want to compare these two trusses, we have to consider the property of different materials. In the book, the author Timoshenko also discusses about this comparison. He states that the first truss is better if it is built of steel, since the shorter vertical members are better to bear compression than the longer diagonal members. On the other hand, if the truss is made of more than one kind of material, the second one might be better. We can use wood or concrete to bear compression and use steel to bear tension. This will be more efficient.
  
  Thanks for your comments again. And I am glad to know your opinions. It is a real pleasure to discuss with you.
  
  Yours sincerely, Gao Nan
  
  Reply
  - Pranjal said:
    
    2012-04-25 at 21:49
    
    Agreed. That was my point, the first truss should be more efficient than the second one if the material used is steel for the reason stated by the author.
    Do excuse me as most of my little experience in this field is with steel structures( except what I read about concrete and other materials at my univeristy and have already forgotten :D). Looking forward to your next case study.#
    
    Regards
    Pranjal
    
    Reply