# How does the number of braces in a balsa wood tower affect the load capacity?

I am deciding between two design ideas for a project in which I have to build a balsa wood tower that can maximize load weight and minimize structural weight (maximize efficiency). I've included a picture with the two designs I am deciding between.

I am wondering which design would be able to hold greater weight, whether increasing the number of braces changes the load capacity, and in which way it changes (linear correlation, exponential correlation, etc.).

More specifically, I'm considering a load weight of 145 N, and I am looking for the values of the internal member forces, especially those before buckling (assuming a static system).

My understanding of this subject only extends to truss calculations, considering diagonal bracing (e.g. Howe Truss), which is why I am posting on this forum. Further, if you'd be willing to give a brief explanation of these diagrams from Bracing for Stability, I'd really appreciate it.

• Build and test , but the quality of the joints will have a huge effect on the results ... – Solar Mike Mar 1 '18 at 17:38
• The cross bracing actually contributes little or nothing to the member loads. (assuming the applied load is perfectly straight down ). The loads are to a good approximation a simple force/area in the verticals and nil in the braces. The braces are there to inhibit buckling as shown in the diagram. The braces will however carry load if there is any lateral force at the top. – agentp Mar 1 '18 at 21:01
• you might want to run static analysis on some online website regarding this one so that you have a reference. – Jem Eripol Mar 1 '18 at 23:56

Elements under compression such as the vertical columns in your tower can collapse in two very different ways.

The first is via simple crushing of the member. This happens when the applied load generates an internal stress in the member which is higher than the member's strength.

The second is via buckling. In this case, infinitesimal imperfections in the structure make it "easier" for the member to bow away from the load. Get a plastic straw or a piece of paper and try to place either under compression. You'll notice they just "jump" to the side. However, once the compression is removed, the straw or piece of paper will "jump" right back into its original shape as if nothing'd happened. The theoretical equation for the buckling load (often called Euler buckling) is $$P_e = \dfrac{\pi^2EI}{(kL)^2}$$ where $E$ is the member's modulus of elasticity, $I$ is its second moment of area (aka, moment of inertia), and $kL$ is the member's unbraced length ($k$ is a coefficient which depends on the member's boundary conditions; in your case, you could conservatively assume $k=1$). Obviously, the real-world buckling load is much lower than $P_e$, since real-world imperfections are actually quite significant, not infinitesimal.

Braces aren't meant to carry any of the applied load. Their purpose is only to guarantee that the principal members (in this case, the vertical columns) do not buckle under compression. So a properly braced structure will instead collapse due to crushing or global buckling (where the entire structure buckles as if it were one member, which the braces can't help against).

To find the unbraced length for your columns, you could rework the Euler's buckling load equation to give you $L$ given the other values (which you can find online). However, given how that equation is highly theoretical (and not used directly in actual engineering), it is probably best to merely create prototypes to see at which length the parts start to buckle and then adopt that.

You need to find out structural properties of the cross-section of balsa member you use. namely at what length it is considered a short column. A short column will crush in compression rather than buckle.

This is ideally the joint height of the tower. However, practical constraints may force you to chose a compromise near that joint span.