## Check the code requirements

*How do we select a trial beam size for Beam RB-3?*

We calculated the strong-axis moment force in Step Two. The moment force determines the required moment resistance of our beam. We use moment resistance to select trial beam sizes in preliminary design.

The Canadian Institute of Steel Construction (CISC) publishes the *Handbook of Steel Construction*, pictured in Figure 4. The eleventh edition of the *Handbook* incorporates requirements from S16-14, the standard for steel design published by the Canadian Standards Association (CSA). Design tables included in the *Handbook* help organize beams to simplify design. Figure 5 is an excerpt of the Beam Selection Table found in Part 5 of the *Handbook*.

The Beam Selection Table organizes beam sizes by moment resistance. Bolded sizes indicate economical choices, based on a weight-to-resistance ratio. Values for shear resistance, moment of inertia, flange width, and unbraced length, are also listed.

Scan the Beam Selection Table and select a trial beam size based on moment resistance. Once we find a trial beam size, inspect the shear resistance and moment of inertia values listed on the left side. Beams that meet all three criteria are reasonable trial sizes. Select a trial size and inspect the beam using Clause 13 in the *Handbook*. We discuss the relevant requirements below.

### Moment resistance

A beam’s section class determines whether we use the plastic (*Z*) or elastic (*S*) section modulus in the moment resistance equation. Use Clause 11 to determine the beam’s section class. Calculate the beam’s moment resistance using Clause 13.5.

Clause 13.5 assumes continuous lateral support on the beam to prevent lateral-torsional buckling. In our exercise, the OWSJ frames onto the top flange of the beam at 1500 mm spacing intervals. The spacing interval defines the unbraced length of the beam’s top flange — the compression flange. We use the unbraced length to check Clause 13.6. Verify whether the joist spacing is adequate to provide continuous lateral support. If the joist spacing is too wide, Clause 13.6 reduces the beam’s moment resistance to account for lateral-torsional buckling.

Check the weak-axis moment resistance with Clause 13.5. Use the appropriate weak-axis properties for the selected trial beam size. Find the geometric properties for beams in Part 6 of the *Handbook*.

### Shear resistance

Under uniformly distributed building loads, shear resistance rarely governs steel beam design. However, if the building has concentrated point loads, check the beam and verify the shear resistance at the loading points.

Calculate the beam’s shear resistance using Clause 13.4. Shear resistance relies on the geometry of the web.

### Axial compression resistance

Calculate the beam’s axial compression resistance using Clause 13.3. Compression resistance requires:

- Cross-sectional area based on the beam geometry
- Yield strength based on the steel grade
- Buckling length based on the lateral support conditions

The OWSJ provide lateral support to the top flange, there is no lateral support to the bottom flange. Use the full beam length as the buckling length in Clause 13.3. If the resistance is exceeded, we can reduce the buckling length by specifying a tie joist is required at midspan.

### Strength and stability resistance

Axial compression and moment force act simultaneously in the ULS load combinations calculated in Step Two. Calculate the strength and stability resistance using the axial-moment interaction ratios in Clause 13.8.

*Strength and stability is the most critical code requirement. The maximum load effects from moment and compression are multiplied by stability factors and added together. The analysis is beyond the scope of our exercise.*

Let’s consider two trial beam sizes for Beam RB-3:

- W310x33
- W250x39

Both beam sizes meet design requirements for resistance and deflection. Figure 6 illustrates the different geometry of the trial beam sizes. This is a critical factor when considering the connection style, as we will discuss in Step Four.