April 29, 2015
Understanding staged structural failure analyses
By Bill Yao, P.Eng.
HVAC equipment is generally installed on top of the flat roofs of industrial, commercial, and institutional buildings. The maintenance personnel sometimes are exposed to danger of falling if the units are close to the roof’s edges. In this case, a guardrail system is required by Ontario Ministry of Labour Regulation 851, the Occupational Health and Safety Act. The regulation also specifies a guardrail shall be constructed to meet the structural requirements for guards as set out in Ontario Building Code (OBC), which has been adopted from the National Building Code of Canada (NBC) 184.108.40.206.
Set up at the edge of the roof, these guardrail systems are laid directly on a flat roof without any anchors penetrating through. This means the stability to resist a concentrated load specified in the province’s code fully depends on its integrity and the balance weight of the base plates.
A guardrail system generally consists of three components:
Design standards for a guardrail system are specified in the 2012 OBC under 220.127.116.11. (“Loads on Guards”):
1. The minimum specified horizontal load applied inward or outward at the top of every required guard shall be,
B. A concentrated load of 1.0 KN applied at point for access ways to equipment platforms, contiguous stairs, and similar areas where the gathering of many people is improbable.
The question is, how can one be certain a guardrail system will protect those on a roof? This article suggests an analysis option to determine structural success.
A typical three-bay guardrail system is set up on a gravel protected roof. The vertical posts of the system are spaced at 2.4 mm (8 ft). The vertical posts are installed to the base plates, and a 1219-mm (48-in.) long outrigger is attached at each end to increase the system’s stability. The plan view of the guardrail system is shown below. 
In this scenario, there are the following assumptions:
For the analysis, the initial calculations were as follows:
At the beginning, the guardrail system stands there with all posts fixed. When a point load is applied and slowly increased, the first post would reach its breaking point in which the bending moment is 0.222 KN-m, or lateral shear force is 0.22 KN, then the base plate will rotate or slide. If the load increases, it will be transferred through the rails to the other base plates, which will rotate or slide—either the whole system stably stands or completely collapses.
The guardrail system will change its stability mode during the loading process. Or, in other words, the analysis model will change. Therefore, the general structural analysis is unsuitable for this situation.
Staged structural failure analysis
A special procedure for this situation is called ‘staged structural failure analysis.’ The term derives from the concept of staged construction created by Computers & Structures Inc. This is a static modelling, analysis, and design application that enables the definition of a sequence of construction stages in which structural systems and load patterns are added or removed, and time-dependent behaviours are evaluated, including creep, shrinkage, aging, and tendon relaxation.
For the example discussed in this article, one model can simulate the whole restraints that are fixed, while another simulates one restraint that is hinged or rolled. However, one should know when the first model would switch to the second model—a trial-and-error method could be adopted to determine the maximum load withstood by the specific model.
The main procedures are described below:
The detailed calculations are shown below to demonstrate the trial-and-error calculation methods step by step. The guardrail system’s three-dimensional structural analysis is conducted with SAP2000 v.15.
From this calculation table, one can obtain some helpful conclusions:
Staged structural failure analysis is a practical method that can be applied to many cases where the structural systems and loads change. When engineers sometimes have to handle this kind of problem, the so-called staged structural analysis might provide an ideal solution.
Bill Yao, P.Eng., has been a civil/structural designer for 20 years. He currently works as a structural engineer in an engineering firm in Markham, Ont. He can be reached via e-mail at firstname.lastname@example.org.
Source URL: https://www.constructioncanada.net/roof-guard-woes/
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