### 1. Introduction

### 2. Residual Strength versus Damage Index Diagram

### 2.1 Fire Load Identification

### 2.2 Characterization of Fire Damage Variables

### 2.3 Credible Fire Damage Scenarios

### 2.4 Calculation of Damage and Residual Strength for the Scenarios

*r*/

*b*) was determined by the ratio of the flame radius (

*r*) and the breadth of the plate (

*b*). Candidate methods (numerical, analytical, and experimental methods) are able to calculate the residual strength. In this study, numerical methods were most commonly applied to structural analysis as they have been found to be the most efficient (Kim et al., 2014). Once the fire damage index and the ultimate strength were simulated for the selected fire damage scenarios, the diagram was expressed in form of Fig. 4. R-D diagrams can be used to predict the residual strength with fire exposure damage.

### 3. Applied Examples

### 3.1 Definition of Structure Characteristics

*a*= 4000 mm between the transverse stiffeners and

*b*= 800 mm between the longitudinal stiffeners. This study considered T-bars as both longitudinal and transverse stiffeners. Fig. 6 and Table 1 show the cross sections of the longitudinal and transverse stiffeners (Paik and Thayaballi, 2003).

*w*for plating between stiffeners and

_{opl}*w*and

_{osx}*w*for x- and y-stiffeners, respectively. The stiffened plate panel may also have welding-induced residual stresses. Fig. 7(b) shows the typical idealization of residual stresses in plating between stiffeners. The simplified residual stresses are considered uniform compressive residual stresses, which are denoted by

_{osy}*σ*rsx and

*σ*rsy for x- and y-stiffeners, respectively. In this study, both initial deflection and residual stress were considered.

### 3.2 Characterization of Fire Damage Parameters

### 3.3 Selection of Fire Damage Scenarios

### 3.5 Calculation of Damage Index for Selected Fire Damage Scenarios

*T*) and surface (

_{g}*T*) of the steel structural element with an exposed side. Radiation, convection, and heat loss should be considered for the unexposed side. In the case of shell elements in LS-DYNA, the temperature was uniform (

_{s1}*T*=

_{s1}*T*) in the steel thickness direction. In this study, the coefficient of convection was

_{s2}*h*= 25 W/m

_{c}^{2}K, and the emissivity of carbon steel was

*ε*= 0.7 (Franssen and Real, 2010). The temperature-dependent specific heat and thermal conductivity of carbon steel shown in Fig. 12 were considered to result in an accurate heat transfer analysis. Fig. 13 shows a typical temperature distribution of fire position A after 10 minutes.

_{s}### 3.6 Calculation of Residual Strength

### 4. Development of R-D Diagram

### 4.1 R-D Diagram Based on Residual Strength

*σ*) under a compressive axial load at fire position A was formulated as follows:

_{rxu}*k*= Buckling coefficient (It can be approximated to

*k*= 4)

### 4.2 Development of Design Formulae Based on Residual Ultimate Strength

*R*) is proposed to estimate the ultimate strength of a steel stiffened plate panel under longitudinal axial compression with varying area and duration of fire exposure. The residual ultimate strength reduction factor can be defined by a polynomial equation in terms of flame radius and plate aspect ratio as follows: where

_{xu}