The following is a summary of the conclusions drawn from this research:
(1) Column flexural stiffness reduction factor (τN) and beam flexural stiffness reduction factor (τM),
applicable to stainless steel members with compact cold-formed RHS and SHS, are developed. The proposed τN depends on the maximum internal first order axial force within a member (Pr1). The proposed τM depends on the maximum internal first order moment within a member (Mr1) and material properties (E,
fy, and n). The results of verification study show that GNA coupled with the developed stiffness reduction factor (τN and τM) reaches the accuracy of GMNIA. The slight discrepancy between the developed stiffness reduction factor (τN and τM) and the actual stiffness reduction factor will be considered in the development
of the approximate expression of stainless steel beam-column stiffness reduction factor (τMN) expression.
(2) Flexural stiffness reduction factor (τMN) formulation applicable to the in-plane stability design of
stainless steel beam-columns is proposed through analytical and numerical study. The proposed beam- column flexural stiffness reduction factor (τMN) accounts for deleterious influence of spread of plasticity,
residual stresses and member out-of-straightness of 0.001. Two main aspects of developing τMN are: (1) Develop analytical expressionof τMN through extending formulations that evaluate second order effects of beam-columns. These formulations are extended to determine maximum second order inelastic moment of beam-columns by incorporating τMN into elastic critical buckling load. (2) Based on numerical study of beam-columns, the approximate expression of τMN is developed by fitting relevant variables to analytically determined expression.
The soundness and accuracy of τMN determined by analytical expression are verified through comparison
of maximum bending moments within members determined through GNA-τMN against those obtained from GMNIA. It is observed that predicted results from GNA-τMN are in very close agreement with those provided by GMNIA. Besides developing flexural stiffness reduction factor (τN, τM , τMN) formulations that are applicable to stainless steel members. Moreover, it is worth pointing out that the formulations of evaluating second order elastic effects are extended to determine inelastic maximum second order moment within beam-columns, through incorporating τMN into elastic critical buckling load. Furthermore, since in
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practical design Mr2 is not known in advance, an approximate expression of τMN, which is assumed to be a function of relevant variables, is proposed by fitting variables to the analytically determined expression. For the purpose of developing the approximate expression of τMN, column flexural stiffness reduction factor (τN) and beam flexural stiffness reduction factor (τM) are derived from stainless steel column strength curves
and from the moment-curvature relationship, respectively.
(3) The accuracy of GNA coupled with flexural stiffness reduction factor (determined by the approximate expression) for the in-plane stability design of stainless steel frames is verified. The maximum bending moment and Demand-Capacity ratio within a member determined by GNA-τMN and GNA-τN are compared against those determined by GMNIA. It is found that predicted results of GNA-τMN are in close agreement with those provided by GMNIA. In some cases, GNA-τN gives unsafe predictions for the frames that are very sensitive to second order effects, one possible explanation is the adopted stiffness reduction factor 0.8τN underestimates actual reduced stiffness, and therefore underestimates additional second order effects
resulted from material non-linearity. Both GNA-τMN and GNA-τN are safe for predicting the ultimate capacity (member-based) of the studied frames that are not sensitive to second order effects. Compared to GNA-τN, GNA-τMN with lower deviation from predicted results of GMNIA, provides improved estimation of internal moments and Demand-Capacity ratios for most members. This is due to the reason that τMN can accurately capture stiffness reduction caused by spread of plasticity through cross-section and along members. As a consequence, GNA-τMN produces more reasonable distribution of internal force and moment, and well captures additional second order effects due to material non-linearity.
(4) The stiffness reduction factor formulations, applicable to stainless steel elements and frames with compact sections, are extended to account for local buckling effects and initial localized imperfection (ω).
Local buckling effects and influence of initial localized imperfection are accounted for by means of reducing the gross section resistance using a factor ρ. The factor ρ, determined by the Direct Analysis
Method, depending on cross-section slenderness, is adopted. The accuracy of GNA with extended stiffness reduction factor for in-plane stability design of stainless steel elements (columns, beams and beam-columns) with non-compact and slender sections is verified. Predicted results by GNA with stiffness reduction (using shell element) are in close agreement with those determined by GMNIA using shell element.
(5) The effect of uncertainty in ω on the ultimate capacity of cold-formed stainless steel columns and beam-
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coefficients of variation and the maximum value of absolute error for the predicted results increases as cross-sectional slenderness increases. This is due to the reason that columns with larger cross-sectional slenderness are sensitive to initial localized imperfection, and consequently the change in the value of modelled localized imperfection can lead to much discrepancy in the ultimate compressive strength. Therefore, the effect of uncertainty in ω on the columns with larger cross-sectional slenderness should be
considered in practical design. For the studied beam-columns, the mean value of the ultimate end moment obtained from GMNIA in which ω is modelled randomly, is very close to the ultimate end moment obtained from GMNIA in which ω is modelled as local buckling mode times 0.185. It also shows uncertainty in ω
result in prediction errors for GNA-τMN-ρ to some extent, but ignoring uncertainty in ω won’t lead to significant errors for GNA-τMN-ρ.