The Reliability Margin of the Direct Strength Method Prediction Model for Cold-Formed Steel Members
Thesis (MEng)--Stellenbosch University, 2016.
ENGLISH ABSTRACT: SANS 10162-2, the South African standard for structural purpose cold-formed steel, allows for design of members to resist loading of compression, bending and combinations of these among others. The focus of this research is to determine the reliability of member strength design according to the standard, following the Direct Strength Method (DSM) for beams and columns. The DSM is an empirical design prediction model that has been developed through testing and from prediction curves based on the Effective Width Method (EWM). Member strength from the DSM is dependent on three dominant buckling modes. The design failure capacity considers local, distortional and global (exural, torsional or torsional-exural) buckling. For the local and distortional buckling cases some post buckling reserve consideration is incorporated by the DSM. To attain the reliability margin for the design of members using the DSM, the First Order Reliability Method (FORM) was implemented in combination with the semi-empirical Finite Strip Method (FSM). The FSM allows prediction of the elastic buckling loads, which are necessary for the capacity prediction, as well as buckling modes and shapes. A FSM model can therefore be used to numerically determine the directional derivatives of the limit state function necessary for the FORM and allows for a unique approach to conventional FORM. Based on literature, probabilistic parameters that form part of the investigation presented are: the yield stress, the thickness and the model factors for the prediction curves. The integrated DSM-FORM procedure was used to determine the reliability margin for various member lengths with idealised pin-pin ended boundary conditions. A typically used lipped C-section, which conforms to the geometric limitations of the DSM, was investigated for the design of concentric axial compression and pure laterally unrestrained bending. Normal probability distributions were used for the thickness and model factor variables. A lognormal distribution and a design yield strength of 300MPa was assumed for all members. Discrete member lengths ranging from 0:1m to 4m were investigated to determine the reliability across multiple failure modes. For the members designed in compression, reliability indices as low as R = 1:31 were obtained relating to local buckling capacity prediction. A minimum reliability index of R = 1:32 was found by the FORM for compression members failing due to global buckling. No reliability index was found as a result of the distortional buckling failure mode, since the lipped C-section analysed does not fail from this buckling mode. Members designed for uniform laterally unrestrained bending were analysed for failure from all buckling modes, depending on member length. A minimum reliability index of R = 1:69 was found for members designed to resist distortional buckling failure. From the local-global buckling interaction assumed in the DSM bending capacity equations, a minimum reliability index of R = 1:45 was obtained for both failure modes as a result of the analyses. The findings of this thesis show that the level of reliability achieved by the DSM is not consistent across all modes of failure. This is largely attributed to the fact that one partial factor is used in the design process, to ensure reliability across all failure modes of the design resistance. It may be more appropriate to apply different partial factors to the three failure modes. Also, the reliability indices across all modes of failure were shown not to conform to the targeted reliability from calibration. The assessed reliability indices in addition do not conform to the conservative resistance based target of tR = 2:4 for the South African structural design standard. Due to the South African loading code not covering the sensitivity of the resistance targeted by the currently provided partial factors for the DSM, lowering of the partial factors is recommended.
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