## Analyze the beam

*How does Beam RB-3 react with loads applied?*

The loads on the beam transfer through connections to the column. Connections are classified as fixed or simple depending on the amount of rotation they allow at the beam end. The classification determines the equations we use for analyzing moment force, shear force, and deflection.

Fixed connections are rigid. They allow moment, shear, and axial force to transfer to the column. Less rotation occurs at the connection because there is continuity between the members. The beam also deflects less. Analyzing fixed connections is more complex and fabricating the connection is more expensive.

Our exercise uses simple connections. Shear and axial force transfer at each beam end. Moment force is not transferred to the column. The beam is free to rotate at each end.

Also, consider how the beam is laterally supported. Continuous lateral support to the beam’s top flange prevents lateral-torsional buckling — a critical beam failure method. Joists frame onto the top flange of Beam RB-3 at 1500 mm intervals, as indicated in Figure 2. The joists provide lateral support to the top flange.

### Calculate the moment and shear force

We take each line load (*w*) from Step One and combine them in load combinations for ultimate limit states (ULS) and serviceability limit states (SLS). The load combinations appear in Article 4.1.3.2 (NBCC 2015). ULS load combinations check strength and stability under factored loads. Use Equation 3 to calculate maximum moment force (*M*). Use Equation 4 to calculate maximum shear force (*V*).

In our exercise, lateral wind load applies weak-axis moment force. We use a tributary wall height of 2500 mm, equal to half the storey height to determine the wind line load in the East-West direction. Calculate the weak-axis moment force using the wind line load on Beam RB-3 and Equation 3.

### Calculate the axial compression force

In the North-South direction, the wind load applies an axial compression load (*P*) on Beam RB-3. Multiply the tributary wall width with the tributary wall height to calculate the tributary area (*A*). Calculate the axial compression load using Equation 5. Multiply the tributary area with the North-South wind load on Beam RB-3.

*Our exercise’s limited scope assumes that the lateral resistance system of the building is a core wall on a nearby gridline. Beam RB-3 transfers the wind load to the core wall. Confirm this simplification with the actual building design.*

### Calculate the moment of inertia

Moment of inertia (*I*) is a geometric property that determines a beam’s stiffness. Stiffness determines how a beam deflects under load. Equation 6 calculates the deflection of a beam with simple connections.

We express the deflection limit (*∆*) as a ratio of the length. Table D1 in the Handbook defines typical deflection limits for structures. For roofs, the deflection limit is L/360. Rearrange Equation 6 and solve for *I*. Determine the required moment of inertia that will limit beam deflection.

Determine the design criteria using the load combinations from NBCC 2015. Equations 3, 4, 5, and 6 calculate the design values required for Beam RB-3. We use the design criteria in Table 2 to continue through the next steps in our exercise. In Step Three we will check the code requirements and select trial beam sizes based on strength, stability, and deflection.