Inputs
Example Data Table
| Scenario | Lo | Tributary Area (At) | Slope | R1 | R2 | Reduced Load (Lr) |
|---|---|---|---|---|---|---|
| Small residential member | 20 psf | 60 ft² | 8:12 | 1.000 | 0.800 | 16.0 psf |
| Large post-frame member | 20 psf | 300 ft² | 4:12 | 0.900 | 1.000 | 18.0 psf |
| Very large tributary area | 20 psf | 700 ft² | 2:12 | 0.600 | 1.000 | 12.0 psf (bounded) |
Formula Used
Reduced roof live load: Lr = Lo × R1 × R2
Tributary area factor (R1):
- R1 = 1.0 for At ≤ 200 ft²
- R1 = 1.2 − 0.001At for 200 < At < 600 ft²
- R1 = 0.6 for At ≥ 600 ft²
Slope factor (R2): with F = inches of rise per foot of run.
- R2 = 1.0 for F ≤ 4
- R2 = 1.2 − 0.05F for 4 < F < 12
- R2 = 0.6 for F ≥ 12
Bounds: for ordinary roofs, the reduced value is typically limited to 12 ≤ Lr ≤ 20 (psf), and reductions are not applied when the specified unreduced roof live load exceeds 20 psf.
How to Use This Calculator
- Select your unit system to match your drawings.
- Pick an unreduced roof live load, or enter a custom value.
- Choose tributary method: compute span × spacing, or enter At.
- Enter roof slope as rise/12 or degrees.
- Optionally enter plan area to estimate total roof live force.
- Click Calculate to see results above this form.
- Download CSV or PDF to attach in submittals.
Professional Notes on Roof Live Load
1) Why roof live load matters
Roof live load represents temporary actions such as workers, tools, and short-term maintenance materials. It can move and concentrate on one bay, so a sound design pressure supports safe member sizing, connection detailing, and serviceability checks across framing zones. Use it to screen alternatives before detailed analysis.
2) Common reference pressures
Typical reference values are 20 psf for ordinary roofs and 12 psf for limited maintenance. You can use these presets or enter a project value. If the unreduced value exceeds 20 psf, reductions are disabled for a conservative outcome.
3) Tributary area as a design driver
Tributary area converts pressure into member force. For many joists or purlins, a practical estimate is span × spacing (horizontal projection). Larger tributary areas can justify reductions because full loading across a large area is less likely for maintenance-type traffic. Document assumptions early to avoid redesign later.
4) Area reduction thresholds used here
The area factor R1 is 1.0 up to 200 ft², then R1 = 1.2 − 0.001At between 200 and 600 ft², and 0.6 for 600 ft² or more. These breakpoints mirror common reduction frameworks and stay easy to audit.
5) Roof slope and maintenance behavior
Slope is represented as F (inches of rise per foot). The slope factor R2 is 1.0 for F ≤ 4, then R2 = 1.2 − 0.05F for 4 < F < 12, and 0.6 for F ≥ 12. Steeper roofs typically discourage sustained temporary loading and equipment staging.
6) Bounding the reduced pressure
For ordinary roofs, reduced roof live load is often limited to 12 ≤ Lr ≤ 20 psf. This avoids unrealistically low design pressures and keeps detailing consistent across roof zones. The calculator applies Lo × R1 × R2, then enforces the minimum and maximum limits.
7) Turning pressures into totals
After computing Lr, the force on a member’s tributary area is Lr × At. If you enter a plan area, the tool also estimates total roof live force for that footprint, which helps quick load summaries. Metric reporting uses 1 psf ≈ 0.04788 kN/m² for comparisons.
8) Practical checks before you finalize
Verify tributary area near edges, hips, valleys, and irregular framing. Confirm roof access frequency, concentrated equipment loads, and any local requirements that override reductions. Export CSV or PDF outputs to document inputs, assumptions, and results for submittals.
FAQs
1) What is the difference between Lo and Lr?
Lo is the unreduced roof live load pressure you start with. Lr is the reduced design pressure after applying tributary-area and slope effects, then enforcing the minimum and maximum bounds for ordinary roofs.
2) When should I choose “Light maintenance”?
Use it when roof access is limited to occasional inspection and minor servicing, with no expectation of storage or frequent worker presence. Always confirm the correct category with the governing project requirements.
3) Why does a larger tributary area reduce the load?
Large areas are less likely to be fully occupied by temporary loads at the same time. Many standards allow statistical reductions using area-based factors, which this calculator models with the R1 thresholds.
4) How do I enter roof slope correctly?
Use rise per 12 run for common roof notation (for example, 6 means 6:12). If you only have degrees, enter the angle and the tool converts it to an equivalent rise per foot.
5) Why is my reduced load “bounded” at 12 or 20?
Many provisions prevent overly low reduced pressures by setting minimums, and they cap the reduced value at the unreduced reference pressure. Bounding keeps design assumptions realistic and consistent.
6) What does “Total load on At” represent?
It is the live load force on the selected member’s tributary area, computed as Lr × At. It helps translate roof pressure into a single-member design load for checks and sizing.
7) Is this output a substitute for code compliance?
No. It is a calculation aid. Always verify that the selected roof live load category, reduction eligibility, and any local amendments match the governing standard and your engineer’s design criteria.