Wood Design Shortcut – Beam Stability Factor (and Column Stability Factor)

Introduction

If you have studied or have done some wood design, you certainly have came across the “beam stability factor”.

It looks something like this ((NDS Equation 3.3–6):

Now, I am not going to go into details about all the variables; I mainly just wanted to talk about the final C_L factor.

As you already know, once you obtained F_bE and F_b^*, calculating C_L is merely plug-and-chug. It is very straightforward yet tedious…

I can’t remember the number of times that I accidentally plugged in the wrong numbers or made a silly mistake when punching the numbers into a calculator. The result, as you guessed it, is usually not pretty (depending on how early I find out about the mistake).

So I came up with a simpler way to avoid doing all of these tedious “plug-and-chug”.

Introducing – Tabulated Table For Beam Stability Factor:

Wood CL Tabulation

1 file(s) 291.59 KB

Download

This table not only helped me avoid making arithmetical errors, it also saved me quite some times during the SE exam (which you know, every second counts!) And before I knew it, life was good again (ok that might be exaggerating a little but you get the idea).

How To Use The Tabulated Table for Beam Stability Factor

Since C_L only depends on [F_bE / F_b^*], I figured if I have a table that lists out all of the possible [F_bE / F_b^*] and its corresponding C_L, I’ll never have to use a calculator to “plug-and-chug” again.

So the way to use it is very simple:

1. First, determine the [F_bE / F_b^*] ratio up to 2 or 3 decimal points.
2. Then, find your C_L.

Example 5.3 (SERM)

Let’s test this out using Example 5.3 of the Structural Engineering Reference Manual (SERM).

1. [F_bE / F_b^*] = 2.83 from the example.
2. 2.83 falls in between 2.54 and 3.42; therefore, use C_L = 0.97.

Calculate C_L Using Tabulated Table (Example 5.3)

And we are done! (Although the actual C_L is 0.974, a difference of 0.004 will not make much difference to your design 99% of the time.)

Example 5.4 (SERM)

Let us do another one using Example 5.4.

1. [F_bE / F_b^*] = 1.06.
2. For this part, we first match 1.0 to the first column then we find 0.06 in the top row. The result is C_L = 0.840. Done!

Calculate C_L Using Tabulated Table (Example 5.4)

Imagine doing this simple two-step process using the table versus hand calculating the following using a non-graphical calculator…

See the difference? I hope so because it sure helped me quite a bit.

Next: Tabulated Table for Column Stability Factor

Similar to the Beam Stability Factor, Column Stability Factor also requires you do the same thing – tedious plug-n-chug (NDS Equation 3.7-1):

In this case, besides [F_cE / F_c^*], there is one more variable, c, which can be 0.8, 0.85, or 0.9 depending on the type of lumber.

No problem, I’ll just create 3 more tables.

Example 5.7 (SERM)

We’ll test this out using again, the example from SERM. From example 5.7:

1. [F_cE / F_c^*] = 0.333 and c = 0.8.
2. 0.33 corresponds to C_P = 0.304… and done.

Calculate C_P Using Tabulated Table (Example 5.4)

Again, by using the table, you avoided having to do this during the exam:

Thoughts?

That’s it for now. Do you find this helpful? Let me know in the comments below.

Thank you for reading and good luck studying!