Learn: Roof snow load — coefficient form
Ground snow load is not automatically the load on a roof. This teaching equation adjusts a supplied ground value for roof shape, exposure and thermal conditions to obtain one roof-load case.
What the formula is saying
Each coefficient modifies a different part of the physical model. Multiply the ground snow load by the roof shape factor and then by the exposure and thermal coefficients; none is an area.
Read the symbols in plain language
- μi
- Shape coefficient
Shape coefficient. The shape factor translates the ground load into the selected roof arrangement.
ratio / no unitA dimensionless ratio has no physical unit; 0.01 as a ratio is 1% when the percent option is selected.
- Ce
- Exposure coefficient
Exposure coefficient. These two coefficients modify the snow retained under the specified environmental conditions.
ratio / no unitA dimensionless ratio has no physical unit; 0.01 as a ratio is 1% when the percent option is selected.
- Ct
- Thermal coefficient
Thermal coefficient. These two coefficients modify the snow retained under the specified environmental conditions.
ratio / no unitA dimensionless ratio has no physical unit; 0.01 as a ratio is 1% when the percent option is selected.
- sk
- Ground snow load
Ground snow load. The shape factor translates the ground load into the selected roof arrangement.
kN/m²Use kN/m² as the base unit shown here. sk and the roof load are in kN/m². μ, Ce and Ct are dimensionless. The result is an area load, not a total force; multiply by the appropriate projected loaded area only in a separate step.
- s
- Result to find
Roof snow load — coefficient form. The result remains a load per square metre rather than the force on the whole roof.
kN/m²
Sort out the units first
sk and the roof load are in kN/m². μ, Ce and Ct are dimensionless. The result is an area load, not a total force; multiply by the appropriate projected loaded area only in a separate step.
Assumptions before calculating
All coefficients are supplied exercise data. The designer must choose them from the relevant adopted standard, design situation and National Annex; the calculator does not select a country or verify that selection.
This is a first-generation Eurocode teaching relationship or an explicitly simplified coefficient calculation. The numbers supplied here are exercise data, not a recommendation for any country. Check the adopted edition, relevant clause, National Annex, applicability conditions and all other limit states before any real design.
Let’s solve one together
Read the given values, follow each operation, then check what the result means.
Read the supplied values as one complete study case. Find s and explain the result in the stated output unit.
- μi · Shape coefficient
- 0.8
- Ce · Exposure coefficient
- 1
- Ct · Thermal coefficient
- 1
- sk · Ground snow load
- 1 kN/m²
Apply the roof-shape factor
The shape factor translates the ground load into the selected roof arrangement.
(0.8) × (1) = 0.8 kN/m²Combine exposure and thermal factors
These two coefficients modify the snow retained under the specified environmental conditions.
(1) × (1) = 1Find the roof snow area load
The result remains a load per square metre rather than the force on the whole roof.
(0.8) × (1) = 0.8 kN/m²
Does this worked answer make sense?
With all coefficients equal to 1, roof and ground loads match. Doubling sk doubles the result while leaving the coefficient selection unchanged.
A second worked example — different values
A second case uses different data. Predict which way the answer will change, then calculate it without reusing the first answer.
- μi · Shape coefficient
- 0.5
- Ce · Exposure coefficient
- 0.9
- Ct · Thermal coefficient
- 1
- sk · Ground snow load
- 1.5 kN/m²
Apply the roof-shape factor
The shape factor translates the ground load into the selected roof arrangement.
(0.5) × (1.5) = 0.75 kN/m²Combine exposure and thermal factors
These two coefficients modify the snow retained under the specified environmental conditions.
(0.9) × (1) = 0.9Find the roof snow area load
The result remains a load per square metre rather than the force on the whole roof.
(0.75) × (0.9) = 0.675 kN/m²
Now try your own values
Change a value or its unit. The same method will show your calculation, step by step.
Results update only when you calculate. The lesson example above stays unchanged.
Your turn — check your understanding
Solve this separate case yourself. Use only the values below; the two worked examples use different data. Give the requested result in the selected unit.
- μi · Shape coefficient
- 0.8
- Ce · Exposure coefficient
- 1.1
- Ct · Thermal coefficient
- 1
- sk · Ground snow load
- 2 kN/m²
Find: Learn: Roof snow load — coefficient form
A hint, not the answer
Each coefficient modifies a different part of the physical model. Multiply the ground snow load by the roof shape factor and then by the exposure and thermal coefficients; none is an area.
sk and the roof load are in kN/m². μ, Ce and Ct are dimensionless. The result is an area load, not a total force; multiply by the appropriate projected loaded area only in a separate step.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Apply the roof-shape factor
The shape factor translates the ground load into the selected roof arrangement.
(0.8) × (2) = 1.6 kN/m²Combine exposure and thermal factors
These two coefficients modify the snow retained under the specified environmental conditions.
(1.1) × (1) = 1.1Find the roof snow area load
The result remains a load per square metre rather than the force on the whole roof.
(1.6) × (1.1) = 1.76 kN/m²
Avoid the common trap
Do not confuse roof slope with the shape coefficient μ. Do not treat the sample ground snow load as valid for every altitude or location, or assume a single uniform case covers drifting.
When this method applies — and when it does not
This evaluates one coefficient set only. Drift, asymmetric loading, sliding snow, exceptional conditions, adjacent taller roofs, local effects and geographic ground-snow selection need separate rules and load cases.
For study and understanding, not approval of a real structure, site operation or design. Apply the correct standard, National Annex and professional review to actual engineering work.
One idea understood. Keep going.
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Sources & further reading
References open in a new tab and explain the underlying principles. The teaching text and examples here are SimpleFlick’s own; the source organisations have not endorsed this calculator.
Reading focus: Roof snow load — coefficient form. Action-specific reading: EN 1991-1-1 for self-weight, EN 1991-1-3 for snow, and EN 1991-1-4 for wind. National and site data are not generated by this lesson.
Lesson updated: · Both examples and the separate practice case are checked against an independent high-precision numerical implementation. This verifies arithmetic for the stated model, not engineering certification.