| doi:10.3850/978-981-08-6218-3_SS-Fr028 |
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RELIABILITY-BASED LIMIT STATE DESIGN OF STEEL SUPPORT SCAFFOLD FRAMES
J. Reynolds, A. Trouncer, H. Zhang and K. J. R. Rasmussen
Civil Engineering, University of Sydney, NSW 2006, Australia
Second-order inelastic analysis (advanced analysis) can predict accurately the ultimate loadcarrying capacity of steel support scaffold frames, making it possible to design scaffolds with direct system capacity check. However, despite the advances in the analysis method, structural strengths and loads remain uncertain due to their inherent random nature. Steel scaffold frames are characterized by the large variations of geometric and mechanical properties, notably joint stiffness, initial geometric imperfections, and load eccentricity. These uncertainties give rise to risk of structural failure. Modern limit state design requires these uncertainties, along with the finite element (FE) modeling uncertainty to be accounted for in the analysis and design process, using a rational probabilistic approach. Aiming to develop a system reliability-based limit state design method, the researchers at the University of Sydney have investigated the load carrying capacity of steel scaffolds using experimental tests, advanced analysis and probabilistic study. This paper presents some of the research results and introduces system reliability-based design equations for designing steel scaffold frames using advanced analysis. The scope of the work is limited to the steel support scaffold frames with cuplok joints.
The design equation proposed in this work has an LRFD-type of format, i.e. φRn ≥ ∑Υi Qni, in which Rn is the nominal system strength computed by advanced analysis, Qni are the nominal loads, φ is the (system) resistance factor, and Υi are the load factors. It must be noted that the design equation is applied at the system level, with R representing the load carrying capacity of the system rather than of an individual member. Developing such a formula for system check involves the following tasks: 1) identify the appropriate system limit states; 2) develop the statistics of system capacity; 3) estimate the statistics of loads supported by scaffolds; and 4) quantify a system reliability target.
For steel scaffolds, the system limit state is violated when the applied load exceeds the ultimate system strength (ultimate load-carrying capacity). The ultimate strengths of steel scaffold systems are predicted using advanced analysis. Fifteen full-scale multi-story steel scaffold frames with cuplok joints were tested at the University of Sydney. These tested frames were used as calibration models to develop a three dimensional advanced analysis model. The ratios of test capacity and analytical prediction for the fifteen frames have a mean of 1.0 with a COV (coefficient of variation) of 0.1, suggesting that the advanced nonlinear analysis used in this study is an “unbiased” and good predictor of the “true” strength of scaffold systems. Therefore, this study assumes that the modeling uncertainty is a lognormal with a mean of 1.0 and a COV of 0.1.
The researchers at the University of Sydney have acquired the statistic data for the cuplok joint stiffness, out-of-straightness (of the standards) and load eccentricity through field measurements and laboratory tests. Using these statistical data, probabilistic studies were performed to investigate the effects of these uncertain properties on the strength of four typical steel scaffold frames. Three values of jack extensions were considered, i.e., 100 mm, 300 mm and 600 mm, covering the possible range encountered in construction practice. Monte Carlo simulations were conducted to generate sample distributions of the system strength. The effect of modeling uncertainty was taken into account by introducing a random “correction factor” applied to the simulated results. The Monte Carlo simulation results showed that the ratio of nominal strength (Rn) to mean strength (Rm) and COV (VR) for the system strength appear to vary with the jack extension, but are relatively independent of system size. The following representative values of strength statistics were obtained through the simulations: Rm/Rn = 1.0, VR = 0.1 for systems with 600 mm jack, Rm/Rn = 1.05, VR = 0.11 for systems with 300 mm jack, and Rm/Rn = 1.17, VR = 0.12 for systems with 100 mm jack. Probability distribution for R is assumed to be lognormal.
The design of scaffolds is often governed by vertical loads. Thus only the vertical load combination ΥDDn + ΥLLn is considered. Vertical loads on scaffold systems consist of dead and live loads. The weight of formworks and freshly-placed concrete are regarded as dead load. The probability distribution of the construction dead load is assumed to be similar to that of occupancy dead load. The live load supported by formworks includes the weight of workers, equipment, stacked material and impact. The survey data for construction live loads are very scarce. A statistical load model for the construction live loads supported by scaffolds, particularly during concrete placement, is not yet available. In this paper, the statistics of maximum construction live load on scaffold systems is assumed to be a Type I extreme distribution, with a mean-to-nominal value Lm/Ln = 0.9 and a COV of 0.6. This appears a reasonable and conservative assumption to the writers.
Probabilistic limit state design is based on “target” reliability as a quantitative measure of structural safety. Structures are deemed safe if the probability of failure is below the target level. In this paper, the target reliability index for steel scaffolds is estimated using the available data of statistics of societal risks and observed building failure rate. The target reliability for steel scaffold systems is estimated to be 2.55. This β-value of 2.55 corresponds to a 5.4 x 10-3 /yr probability of failure. Future research is required for the determination of a more rational reliability target, with inputs from all community stakeholders.
With statistics for system strength and loads available, the system resistance factor and load factors can be determined using the first-order reliability method to achieve a prescribed target reliability index. The values of resistance and load factors are dependent on the liveto- dead load ratio which, in practice, varies in a range. To make the design equation applicable to the most general case, the resistance and load factors were selected to minimize the term Σ(β∗i −β0)2Pi, in which β0 is the established target reliability index (2.55 in this case), β∗i is the actual reliability index for the i-th load situation, and Pi is the relative weight assigned to the i-th load situation. The load factor for dead load is fixed as ΥD =1.2, a value recommended in ACI 347. Also, for operational convenience, it is desirable to choose a constant live load factor ΥL independent of the jack extensions. Through optimization, the design equation is obtained as φRn ≥ 1.2Dn +2.0 Ln, in which
