Reliability-based analysis and design of steel frames with different supports
Authors: Aderinlewo Olufikayo , Ayodele Alade Gabriel 
Published: February 2014

Purpose
– The behaviours of four indeterminate frame-support combinations namely Type I (with fixed supports), Type II (with pinned supports), Type III (with fixed-pinned supports) and Type IV (with fixed-roller supports) frames under the exposure conditions and loads as existing on site were simulated. Two categories of these combinations (I and II) were studied namely single storey-single bay and multiple storey-single bay frames, as illustrated in the case studies treated. A procedure for determining the probability of failure at different sections along the frame types, the range between the probability of failure bounds and the reliability ratings of the frame types were developed based on the kinetic method of plastic moment analysis, minimum weight design method, piecewise method of moment analysis and first order-second moment (FOSM) methods. The analysis results of the Category I frames showed that the Type I frame was most reliable (with the lowest probability of failure range of 0.3269), while the Type II frame was least reliable (with the highest probability of failure range of 0.4918). These results were consistent with those of the Category II frames. The paper aims to discuss these issues.

Design/methodology/approach
– Collapse mechanisms were generated for four frame-support types and the corresponding plastic moments were determined using both the kinematic plastic analyses and minimum weight design methods. The members were designed and the plastic moments were distributed at sections of constant interval along the frame length to generate corresponding envelopes. A similar process was carried out to determine the elastic moment variables due to the loads. The reliability index and the corresponding probability of failure at each frame section were determined. Then, the probabilities of failure bounds for the frames were then compared to determine the most reliable.

Findings
– It was observed that there existed a wide margin between the elastic and plastic moments indicating that design of steel structures at the elastic limit does not take full advantage of its strength. Hence, the design can be carried out beyond the elastic limit and within the safety margin given in equation (3). However, the safety of the entire frame is assessed on the basis of range of values between the highest and the lowest probability of failure bounds. The lower this range is (not exceeding 0.5 or 50 per cent), the more reliable the frame is.

Research limitations/implications
– The equations developed in this study can only be directly applied to multi storey-single bay frames. However, the reliability-based analysis and design procedure developed can be extended to other types of frames.

Practical implications
– A practical approach for analysing steel frames with different supports with the overall goal of producing safe and economical designs has been developed and presented in this paper.

Originality/value
– The procedure adopted is very original and can be backed up by existing literature. The piecewise method for analysing moments at various sections along a frame is also innovative. The whole concept can be adopted to determine the reliability of other types of frames such as multiple bay-multistorey frames with different support types.