Probabilistic Strength at Serviceability Limit State for Normal and SBHS Slender Stiffened Plates Under Uniaxial Compression

Abstract

Stiffened plates with high slenderness parameters show large out-of-plane deflections, due to elastic buckling, which may occur before the plates reach their ultimate strength. From a serviceability point of view, restriction of out-of-plane deflections exceeding the fabrication tolerance is of primary importance. Compressive strength at the serviceability limit state (SLS) for slender stiffened plates under uniaxial stress was investigated through nonlinear elasto-plastic finite element analysis, considering both geometric and material nonlinearity. Both normal and high-performance steel were considered in the study. The SLS was defined based on a deflection limit and an elastic buckling strength. Probabilistic distributions of the SLS strengths were obtained through Monte Carlo simulations, in association with the response surface method. On the basis of the obtained statistical distributions, partial safety factors were proposed for SLS. Comparisons with the ultimate strength of different design codes e.g. Japanese Code, AASHTO, and Canadian Code indicate that AASHTO and Canadian Code provide significantly conservative design, while Japanese Code matches well with a 5% non-exceedance probability for compressive strength at SLS.

Appendix: Required Relative Stiffness of Longitudinal Stiffeners in JSHB

According to the design provision of JSHB, the required relative stiffness for a flat longitudinal stiffener, $\gamma_{l,req}$, is given by following equations:

If $\alpha \le \alpha_{0}$,

$$\gamma_{l,req} = 4\alpha^{2} n\left( {\frac{{t_{0} }}{t}} \right)^{2} \left( {1 + n\delta_{l} } \right) - \frac{{\left( {\alpha^{2} + 1} \right)}}{n};\quad {\text{for }}t \ge t_{0}$$

(7)

$$\gamma_{l,req} = 4\alpha^{2} n\;\left( {1 + n\delta_{l} } \right) - \frac{{\left( {\alpha^{2} + 1} \right)}}{n};\quad {\text{for }}t < t_{0}$$

(8)

If $\alpha > \alpha_{0}$,

$$\gamma_{l,req} = \frac{1}{n}\left[ {\left\{ {2n^{2} \;\left( {\frac{{t_{0} }}{t}} \right)^{2} \left( {1 + n\delta_{l} } \right) - 1} \right\}^{2} - 1} \right];\quad {\text{for }}t \ge t_{0}$$

(9)

$$\gamma_{l,req} = \frac{1}{n}\left[ {\left\{ {2n^{2} \;\left( {1 + n\delta_{l} } \right) - 1} \right\}^{2} - 1} \right];\quad {\text{for }}t < t_{0}$$

(10)

In the preceding equations, the aspect ratio $\alpha = {a \mathord{\left/ {\vphantom {a b}} \right. \kern-0pt} b}$ and the critical aspect ratio $\alpha_{0} = \sqrt[4]{{1 + n\gamma_{l} }}$, where $n$ is the number of subpanels divided by the longitudinal stiffeners and $\gamma_{l}$ is the relative stiffness of the longitudinal stiffener given by

$${{\gamma_{l} = I_{l} } \mathord{\left/ {\vphantom {{\gamma_{l} = I_{l} } {\left( {{{bt^{3} } \mathord{\left/ {\vphantom {{bt^{3} } {11}}} \right. \kern-0pt} {11}}} \right)}}} \right. \kern-0pt} {\left( {{{bt^{3} } \mathord{\left/ {\vphantom {{bt^{3} } {11}}} \right. \kern-0pt} {11}}} \right)}}$$

(11)

in which $I_{l}$ is the moment of inertia for a longitudinal stiffener with respect to the base of the longitudinal stiffener and $t$ is the thickness of the panel plate. In Eqs. 7, 8, 9, 10, $\delta_{l}$ denotes the cross-sectional area ratio for the longitudinal stiffener to panel plate $\left( {{{A_{l} } \mathord{\left/ {\vphantom {{A_{l} } {bt}}} \right. \kern-0pt} {bt}}} \right)$, where $A_{l}$ is the cross-sectional area of one longitudinal stiffener and $t_{0}$ is the critical thickness of the panel plate to avoid local buckling, given by

$$t_{0} = \frac{b}{n\pi }\sqrt {\frac{{12\left( {1 - \nu^{2} } \right)\sigma_{y} }}{E}}$$

(12)

in which the notation is the same as in Eq. (1).