### ASCE’s Live Load Model

#### by briancpotter

*(Thanks to Dr. Ross Corotis for help in obtaining some of these original papers.)*

The live load on a structure consists of the weight of people, pets, furniture, and anything else that has weight and can be moved around. Despite how heavy concrete, steel, and masonry are, it’s often the magnitude of the live load which governs a structure’s capacity. However, unlike other loadings, live loads are extremely difficult to model accurately. They depend on how people decide to live and where they decide to go, and are thus not very amenable to the sort of mathematical modeling building codes like to be rooted in.

But that hasn’t stopped the codes from trying.

In fact, an attempt at basing live loads on solid, statistical ground can be traced to the update to the 1972 ANSI A58 code. However, at the time of the update, statistical models of live load weren’t developed enough to be used as a basis for the code. Therefore, the loads were instead updated based on a survey of 25 experts that was performed using the Delphi Method.

While this survey was being conducted, however, a probabilistic model of live load was being developed that would ultimately find it’s way into the code. In fact, this same model has been a part of ASCE 7, unmodified, for nearly 25 years.

The basic live load model the code uses is somewhat simple. Live load is broken into two parts – a sustained load, based on the people and furniture that normally occupy a space, and a transient or extraordinary load, based on parties, gatherings, and other less frequent events. The sustained load changes at a certain rate – for example, on average every 2 years a tenant may move out and a new one may move in. The extraordinary load also occurs at a certain rate – there may be a huge gathering on average once a year or so. Each of these processes are modeled as probability distributions with a mean and a standard deviation, and they get “sampled” at various times throughout the lifetime of the structure. The live load to be designed for is simply a value that will exceed the maximum of these samples.

In this model, the sustained load values are based on actual data gathered on the loading patterns in various buildings. Reliable (if somewhat long in the tooth) data has been collected for a large variety of occupancy types, from schools to offices to homes to libraries to hotels. The extraordinary load, on the other hand, has almost no available data. This shouldn’t be surprising – by it’s very nature, an extraordinary load occurs infrequently and unpredictably, making it difficult to study. Instead of survey data, values for the extraordinary load are based largely on theoretical models of how large and how often parties, gatherings, remodeling, and other extraordinary events will occur.

The ASCE 7 has included a description of this model in the commentary of every version since it first took over from ANSI in 1988. In fact, it even copies a table of simulation and model data more or less directly from the paper where this model is developed[1]. Based on this, you’d expect that it, well, actually uses the model – that the prescribed loads are based on it.

But in fact, what the prescribed loads are based on is the same old Delphi expert survey that was intended to be a stopgap until a proper theory was developed. The model is briefly described as providing “suitable design values”, but isn’t actually used beyond a point of comparison for a handful of cases. No equations are given, and it’s not described in enough detail to recreate – not only is it not used, but there’s no way for anyone else to actually use it.

So, despite a desire to base the code in accurate statistical models and reliability theory, it hasn’t yet happened. And given the fact that these portions of the code and commentary are almost identical to what they were 25 years ago, there doesn’t seem to be much likelihood that this will change any time soon.

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The full theoretical model used to predict maximum loads is somewhat involved. However, the model was verified using simulations, which should be easy enough to recreate.

The input data for the simulations can be found below, as well as the output of the simulation compared to the theoretical model. The sustained load and extraordinary load are each sampled from a Gamma distribution, with an occurrence rate based on a poisson (exponential) distribution.

My own attempts at running this simulation have so far been unsuccessful – for reasons I haven’t been able to figure out yet, my output data doesn’t resemble that given in the table. However, if you’d like to use it as a starting point (or point out my mistakes!), the python script can be found here.

References:

[1]: Chalk, P. L., and Corotis, R. B. (1980). “Probability model for design live loads.” J. Struct. Div., 106(10), 2017–2033.

Other Sources:

ASCE Standard 7-10: Minimum Design Loads for Buildings and Other Structures

ASCE Standard 7-88: Minimum Design Loads for Buildings and Other Structures

Corotis, R. B., Harris, J. C., and Fox, R. R. (1981). “Delphi methods: Theory and design load application.” J. Struct. Div., 107(6), 1095–1105.

Harris, M. E., Bova, C. J., and Corotis, R. B. (1981). “Area-dependent processes for structural live loads.” J. Struct. Div., 107(5), 857–872.