Essential structural considerations in roof design

How loads are specified
Nothing in safety, resistance, or loads for structural design is cut and dry. Most of the variables shown in this article can vary, and each variable has a probability distribution. For example, roof snow loads S = Sr + Cw Cb Ca Cs Ss Cw Ca Cs are educated approximations while for Sr, Cb, Ss can be modelled using probability distributions.

Considering the period building codes have been used, snow loads have been specified in the National Building Code of Canada (NBCC) since 1953. Technology has advanced exponentially while more environmental data has been collected. The improvement in computing capability has allowed loads and safety to be addressed in a more sophisticated manner than in earlier years.

The following is a brief history on the development of loads, but first, here are some terms that will be used that need explanation:

  • Specified load—load set so the probability of exceeding the specified load is only between one and 10 per cent. The load is usually set with a two per cent chance of exceedance.
  • Characteristic or nominal resistance—resistance set so the probability of the nominal resistance is only between one and 10 per cent. The resistance is usually set with a five per cent chance of being less.
  • Accidental (rare) load—load the structure must support during the life of the structure.
  • Ultimate (factored) load level—a combination of loads the structure must support during the life of the structure.

Step 3: Limit States design approach allowed loads to be combined in a manner that provided a more consistent margin of safety than allowable strength design.1

Step 4: With the additional environmental data, the accidental (rare) load could be better defined. Use of the accidental load captures unique situations that were not caught by using a specified load with a load factor. For example, on the coastal areas of the U.S., there are significant spring snow falls. The effect of these storms was not accounted for previously but are now. The 2020 snow study increased the design snow loads two to three times in some coastal areas. This change reflected local knowledge of snow loads for those municipalities.

Step 5: Is an exciting development, it shows multiple probability distributions can be used to establish design loads, where in the past, only one probability distribution was used for each load type.

  1. Loads were first estimated and if they were used in combination with material design standards of the time, they produced safe, robust, and durable structures, for example, U.S. minimum roof loads.
  2. In the 1960s, statistics were used to calculate specified loads. Usually, these were set so the probability of the loads would only exceed two per cent of the time over a year. With Allowable Stress Design, a factor of safety would be used to arrive at a member size. For example, Canadian snow loads.
  3. In the 1980s, Canada used Limit States design. So, instead of using a Factor of Safety, the loads were increased by a load factor and the resistance was reduced by a Resistance Factor. The term Factor of Safety was replaced with Margin of Safety.
  4. Over the past 10 years in the U.S., instead of using the specified load set at two per cent, it was set as an accidental load. For example, U.S. wind loads.
  5. In 2022, the U.S. design snow load was set based on the consistent probability of failure (where the load value exceeds the resistance capacity). It considers both Cb and Ss probability distributions.


1 For more on Limit States Design in Canada, read the paper “Safety and Limit States Design for Reinforced Concrete” by J.G. MacGregor published in the Canadian Journal of Civil Engineering, V. 3, No. 4, Dec. 1976, pp. 484-513.

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