## Calculate the design loads

*How much load does Beam RB-3 support?*

Calculating the loads on the beam is the first step in our exercise. Consider four basic loads on the structure:

- Dead loads from permanent weight
- Live loads from use and occupancy
- Snow loads from climate and roof geometry
- Wind loads from climate and building height

*Seismic loads, dynamic analysis, temperature effects, and temporary construction loads are also important loading considerations. Assess them at a later stage in the project. We limit our exercise’s scope to the four basic loads.*

Part 4 of the *National Building Code of Canada 2015* (NBCC 2015) describes the method to calculate each load. The national code is a minimum standard. Be aware that local codes may dictate other projects. In our exercise, we use design values and equations from NBCC 2015.

Calculate each load as a uniformly distributed load (UDL) on the roof area. Convert the UDL to a line load using the tributary area for Beam RB-3. We will use the line loads in Step Two.

### Dead loads from permanent weight

Figure 3 illustrates a cross-section of a conventional built-up roofing system. Roof components are layered on top of open-web steel joists (OWSJ). The OWSJ also carries load from the fire protection, mechanical ductwork, electrical systems, and suspended ceiling. Estimate the weight of each roof component. Use the data tables in Part 7 of the Canadian Institute of Steel’s *Handbook of Steel Construction*.

Joist suppliers list the self-weight of the OWSJ on their data sheets. Add the OWSJ self-weight into the dead load calculation. Use the expected beam depth to estimate the self-weight of the roof’s steel structure. Add an allowance (between five and ten percent) for connections and secondary framing. Table 1 presents the total dead load calculation for our exercise.

Make the dead load estimate accurate. Use established tables and manufacturer specifications. A conventional built-up roof has a dead load between 1.0 and 2.0 kPa.

*Small conservative allowances are appropriate, but do not overestimate the dead load. The dead load acts to reverse the uplift wind load. So an accurate dead load will prevent underestimating the net uplift on the roof.*

### Live loads from use and occupancy

Table 4.1.5.3 (NBCC 2015) indicates the live loads from use and occupancy. Roofs require a 1.0 kPa minimum live load.

### Snow loads from climate and roof geometry

Equation 1 calculates the basic snow load described in Article 4.1.6 (NBCC 2015). Climatic data is available in Appendix C (NBCC 2015), indicating the snow (*So*) and rain (*Sr*) values for the site location. Determine the remaining coefficients using the roof geometry.

The roof in our exercise also has large parapet where snow drift accumulates. Commentary G (NBCC 2015) discusses how to calculate the snow drift. The basic snow load is 1.46 kPa for our exercise. Around the parapet, the snow drift reaches a maximum load of 2.51 kPa.

### Wind loads from climate and building height

Equation 2 calculates the internal and external wind load described in Article 4.1.7 (NBCC 2015).

We use the 1-in-50 hour maximum pressure (*q*) value found in Appendix C (NBCC 2015). Calculate the exposure coefficient (*Ce*) using the building height. The remaining coefficients account for pressure and gust effects. Follow the procedure in Commentary H (NBCC 2015).

We calculate the external and internal wind load separately with Equation 2. Determine the uplift on the roof by adding the external and internal wind components.

The lateral wind load acts in three directions:

- In the East-West direction, applying a weak-axis bending moment force on Beam RB-3
- In the North-South direction, applying an axial compression load on Beam RB-3
- In both directions simultaneously, applying a weak-axis bending effect and axial load on Beam RB-3

Commentary H covers the analysis of each wind load direction. Let’s use simplified wind loads for our preliminary design exercise:

- An uplift wind of 1.42 kPa on the roof surface
- An East-West lateral wind of 1.00 kPa
- An North-South lateral wind of 1.00 kPa

*Exercise your curiosity: Calculate the wind load on each building surface according to Commentary H. What assumptions do you need to make to complete the full calculation? What critical information is missing? Does our simplified wind load overestimate the load?*

Refer back to the plan view drawing in Figure 2. Beam RB-3 has a tributary width of 2500 mm. Multiply the tributary width with each UDL to calculate the line loads on the beam. Summarize the design loads in a table. Then proceed to Step Two.