An approach for evaluating fire resistance of high strength Q460 steel columns

Abstract

To develop a methodology for evaluating fire resistance of high strength Q460 steel columns, the load bearing capacity of high strength Q460 steel columns is investigated. The current approach of evaluating load bearing capacity of mild steel columns at room temperature is extended to high strength Q460 steel columns with due consideration to high temperature properties of high strength Q460 steel. The critical temperature of high strength Q460 steel column is presented and compared with mild steel columns. The proposed approach was validated by comparing the predicted load capacity with that evaluated through finite element analysis and test results. In addition, parametric studies were carried out by employing the proposed approach to study the effect of residual stress and geometrical imperfections. Results from parametric studies show that, only for a long column (slenderness higher than 75), the magnitude and distribution mode of residual stress have little influence on ultimate load bearing capacity of high strength Q460 steel columns, but the geometrical imperfections have significant influence on any columns. At a certain slenderness ratio, the stability factor first decreases and then increases with temperature rise.

Keywords

high strength Q460 steel / load bearing capacity / temperature

Introduction

The material that we know as steel today has evolved from ancient iron-making techniques. Writings from China and India indicate that the material saw practical applications in these countries at least as early as 2000 BC, although it cannot be confirmed that the materials were man-made [1]. Nevertheless, it is clear that iron and subsequently steel have played major roles in the history of mankind. Modern construction would not have been possible without steel as a primary material.

High strength steel is a specific class of steel with enhanced mechanical properties. The beauty of high strength stele is large elastic strength and high strength steel is most efficient when it is allowed to develop the full yield stress. However, there is no corresponding increase in the elastic modulus as the yield stress increases, which may bring some problems of serviceability of structures. For all that, because of the favorable ratio between high load capacity and cost, in the past few years, steel contractors have placed an emphasis on the use of high strength steel members in construction. The production of this new family of constructional steels is a result of breakthroughs in steel making technologies, particularly the thermo-mechanical control process that controls rolling and cooling within the steel plate production process to generate fine microstructures. Using the high strength steel in buildings, the overall weight of structures can be significantly reduced, resulting in savings in fabrication, erection, transportation to the site and smaller foundations. Lightweight and thin elements are also desirable for architecture and creative design of aesthetic members and structures [2]. The reduction of the structural sections means less consumption of steel in construction as well.

High strength Q460 steel is a new kind of high strength steel and widely used in Far East counties. The fire resistance provisions for steel structures in current design standards are based on conventional structural steel properties and does not account for high temperature properties of high strength steel. However, high strength steel is increasingly used in columns of high rise buildings. Further, these high strength steel columns are more sensitive to local buckling due to thinner plate under fire conditions.

The behavior of steel members subjected to axial compressive force at elevated temperatures has been widely studied. Although considerable work has been carried out in this area for mild structural steel columns, but there is only few literatures for high strength steel columns at elevated temperatures. High strength steel columns with nominal yield strength of 690 N/mm² has been studied by Rasmussen and Hancock [3,4] at room temperature. Material properties of high strength BISPLKATE80 steel at elevated temperature and the behavior and design of high strength BISPLKATE80 steel columns at elevated temperatures have been carried out by Chen et al. [5,6]. Up to date, there is still lack of information for the fire resistant design of axial loaded columns fabricated with high strength Q460 steel. Therefore, it is important to investigate the behavior of high strength Q460 steel columns at elevated temperatures. Due to the fact that experimental tests of columns at elevated temperatures are rather expensive, and numerical and analytical methods have been used in the area of steel structures at elevated temperatures in recent years.

In this paper, an analytical method and a numerical method to predict the load bearing capacity and critical temperature for axially loaded high strength Q460 steel columns at elevated temperatures are presented. The influences of residual stress and geometry imperfection on the fire resistance of high strength Q460 steel columns are investigated through parametric studies. The validation of proposed methods was established through finite element modeling and experimental data.

Material properties of high strength Q460 steel

A series of tensile coupon material tests to measure the yield stress using steady-state test method and a series of vibration test to measure elastic modulus using impulse excitation of vibration method at elevated temperatures on high strength steel Q460 has been performed and the test results are tabulated in Table 1. Based on the test results, the equations to predict the yield strength and elastic modulus for high strength Q460 steel at high temperature (20-800°C temperature range) was proposed, as shown in Eqs. (1) and (2). It is shown that the proposed equations agree well with the test results (shown in Fig. 1).

(1)f_{y,T}/f_y=-\mathrm{5.59}\times {\mathrm{10}}^{-\mathrm{14}}{T}^{\mathrm{5}}+\mathrm{1.}3\mathrm{8}\times {\mathrm{10}}^{-\mathrm{10}}{T}^{\mathrm{4}}-\mathrm{1.21}\times {\mathrm{10}}^{-\mathrm{7}}{T}^{\mathrm{3}}+\mathrm{4.}18\times {\mathrm{10}}^{-\mathrm{5}}{T}^{\mathrm{2}}-\mathrm{4.}6\mathrm{7}\times {\mathrm{10}}^{-\mathrm{3}}T+\mathrm{1.07},

(2)E_T/E=-\mathrm{1.38}\times {\mathrm{10}}^{-\mathrm{9}}{T}^{\mathrm{3}}+\mathrm{7.}4\mathrm{0}\times {\mathrm{10}}^{-\mathrm{7}}{T}^{\mathrm{2}}-\mathrm{3.69}\times {\mathrm{10}}^{-\mathrm{4}}T+\mathrm{1.01},

where f_{y,T} is yield strength at temperature T; f_y is yield strength at room temperature; E_T is modulus of elasticity at temperature T; E is modulus of elasticity at room temperature.

From the Figs. 2-3, we can easily conclude that the strength and stiffness of high strength steel degrade slowly that that of mild steel and this may be due to the more kinds and amount of alloys in high strength steels. Also, for different high strength steel (Q460steel and BISPLATE80 steel), the yield strength is still quite different during temperature range 200 - 500°C.

Load bearing capacity of high strength Q460 steel columns

For the mild steel columns, there are some assumptions adopted to calculate the load bearing capacity of steel columns at elevated temperatures, for high strength Q460 steel columns, same assumptions are utilized as follows.

1) The initial geometry imperfection of a steel column can be represented as a half sine wave;

2) The temperature distributions across the section and along the columns are both uniform;

3) The distribution of residual stress over cross-section of the columns at high temperatures is the same as that recommended for ambient design.

Two methods, namely Critical Stress Method (simplified method or analytical method) and Inverse Calculation Segment Length Method (numerical method) are frequently used to calculate the load bearing capacity for mild steel columns at ambient temperature. The former one is simple to use but only applicable for special type of steel and section shape. The latter one is versatile and feasible to any steel and any section shape but too complicate and needs lots of calculation. Actually, the former one is the simplified results of a great amount data obtained by the latter method for some frequently used steel type and section shape.

For high strength Q460 steel, the two methods are extended by taking the high temperature properties of Q460 steel into consideration.

Critical stress approach

Similar to the calculation for critical stress of mild steel columns at room temperature, the critical stress for high strength Q460 steel columns at elevated temperatures can be expressed [9]

(3){\sigma }_{crT}={\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}\{(\mathrm{1}+e_{\mathrm{0}}){\sigma }_{ET}+f_{y,T}-\sqrt{{[(\mathrm{1}+e_{\mathrm{0}}){\sigma }_{ET}+f_{y,T}]}^{\mathrm{2}}-\mathrm{4}{f}_{y,T}{\sigma }_{ET}}\},

where f_{y,T} is yield strength of high strength Q460 steel at elevated temperatures, which can be determined by Eq. (1); {\sigma }_{ET}={\mathrm{\pi }}^{\mathrm{2}}{E}_T/{\lambda }^{\mathrm{2}}; E_T is modulus of elasticity at elevated temperature, which is determined by Eq. (2); \lambda is slenderness ratio of the column; e_{\mathrm{0}} is ratio of equivalent initial eccentricity; for welded H-shaped and Box section with flame-cut flange edges, which can be obtained by e_{\mathrm{0}}=\mathrm{0.300}\overline{\lambda }-\mathrm{0.035}, (\overline{\lambda }=\lambda /\mathrm{\pi }\sqrt{f_{y,T}/E_T}).

The stable factor of high strength Q460 steel columns can be determined by

(4){\phi }_T={\sigma }_{crT}/f_{y,T}.

From the Eq. (3) (4) and (1), the stable factor can be obtained at different temperature and different slenderness ratio as shown in Fig. 4. As can be seen from Fig. 4, with the increase of temperature, the stable factor almost keeps constant. At temperatures of 200°C and 500°C, the stable factor is a little lower than that at room temperatures. However, at temperature higher than 600°C, the stable factor is a little higher than that at room temperatures. This is due to that the stable factor at high temperature has great relation with the ratio of elastic modulus to yield strength (as can be seen from the Eqs. (3) and (4)), and when the temperature is at range of 200°C and 500°C, the ratio of elastic modulus to yield strength is lower than that at room temperature. For the temperature is high than 600°C, the ratio is higher (as shown in Fig. 5).

It is also shown that with the increase of slenderness ratio, the stable factor decreases and during the slenderness ratio 50 through 100, the decrease of stable factor is more significant than other slenderness ratio.

To conveniently use in practice, the stable factor of Q460 steel columns at room and elevated temperature was presented in Table 2. After obtaining the slenderness ratio and temperature, one can find the stable factor by looking up the table.

Inverse calculation segment length method

In 1970s, Chen and Atsuta [10] proposed CDC method to calculate the defection of steel column at a certain load and boundary conditions. In 1980s, based on the CDC method, Li et al. [11] proposed a numerical method named inverse calculation segment length method to calculate relationship of axial load, moment and curvature, under consideration of initial flexure, residual stress on the section and also transverse load action. In this paper, the inverse calculation segment length method was extended to obtain the load bearing capacity of high strength Q460 steel columns at elevated temperatures. The flowchart of extended inverse calculation segment length method for high strength Q460 steel at elevated temperature is shown in Fig. 6.

Based on the steps and flowchart of inverse calculation segment length method, a computer program was designed and employed to calculate stress-slenderness relations for high strength Q460 steel columns at different temperatures.

Comparison of the two methods

The curves of stable factor and slenderness ratio for high strength Q460 steel at temperatures 400°C and 800°C obtained by critical stress method and extended inverse calculation segment length method were compared in Fig. 7. As can be seen from Fig. 7, the two methods agree well with each other, especially for the slenderness ratio more than 100. For the slenderness ratio less than 100, there is some difference and only about 10% departure from the average value of the results. From the comparison, we can conclude that the two methods are feasible to calculate the load bearing capacity of high strength Q460 steel columns at elevated temperatures.

As mentioned above, the critical stress method is simple to use and has implicit expression. The inverse calculation segment length method is versatile and feasible to any residual stress distribution and initial flexure ratio. Hence, in the following sections, the critical stress method is utilized to deduce the critical temperature of high strength Q460 steel columns and the inverse calculation segment length method is employed to perform parametric study on the initial flexure and residual stress.

Critical temperature

At the elevated temperature, critical temperature is a key parameter used to represent the fire resistance for steel members. For an axially compressed steel column with a serviceability load N, the yield strength of steel reduces with the increase of temperature. When the yield strength declines to global stability critical stress, the failure occurs. The critical temperature T_{\mathit{c}\mathit{r}} is defined as the temperature at which the yield strength equals to the global stability stress [9]. Therefore, the critical temperature can be found by solving

(5){\displaystyle \frac{N}{{\phi }_{T}A}}=f_{y,T}.

Equation (5) can be rewritten in the following form

(6){\displaystyle \frac{N}{\phi Af}}={\gamma }_R{\displaystyle \frac{f_{y,T}}{f_y}}\cdot {\displaystyle \frac{{\phi }_T}{\phi }},

where \phi is the stable factor of steel column at room temperature; f is the design strength of steel at room temperature, which is equivalent to f_y/{\gamma }_R; {\gamma }_R is the resistance factor of steel, can be approximately adopted as in Section 1.1.

The left item of Eq. (6) is the load ratio R, which is defined as the ratio of serviceability load N to the stability load bearing capacity at room temperature and has no relation with temperature. Given a certain load ratio, the critical temperature of high strength Q460 steel column with axial load may be obtained by solving Eq. (6), which is a function of critical temperature T_{\mathit{c}\mathit{r}}.

Figures 8-9 present the critical temperature calculated for \lambda = 30 ~ 250 and R = 0.3 ~ 0.8 for high strength Q460 steel columns. From Fig. 8, it can be observed that the critical temperature slightly increase with the increase of the slenderness ratio when the load ratio is lower than 0.7. However, the critical temperature becomes decrease with the increase of the slenderness ratio when the load ratio is higher than 0.7. It is shown that in Fig. 9, the critical temperature almost linear reduces with the increase of load ratio. By comparing the critical temperature with EC3 [12] as shown in Fig. 9, at the same load ratio, the critical temperature of high strength Q460 steel columns is much higher than mild steel columns. Therefore, the critical temperatures for mild steel columns given In EC3 are not applicable to high strength Q460 steel columns.

Parametric study

For a compressed steel column, the load bearing capacity mostly depends on the global instability. At room temperature, in addition to the slenderness ratio, the residual stress and geometric imperfection have obvious influence on the global instability. At elevated temperature, the influence of residual stress and geometric imperfection is unknown. To understand the influence of residual stress and geometry imperfection on load bearing capacity of high strength Q460 steel columns at elevated temperatures, the parametric study is carried out on the initial flexure and residual stress distribution.

Residual stress

In the middle of 20th century, the Fritz laboratory of engineering structure in Lehigh University [13] comprehensively studied the distribution of residual stress in cross section of steel members and influence of residual stress on the buckling capacity of steel columns and found that the residual stress is a key factor in determining the load bearing capacity of steel columns. As to now, few literatures focus on the residual stress of high strength steel columns at elevated temperatures. At room temperature, the residual stress on the section of steel columns induced by weld or rolling is simplified to triangle or rectangle distribution. For high strength Q460 steel, same distribution modes are used to study the influence of residual stress value and distribution mode on the load bearing capacity. For one distribution mode, two factor values 0.3 and 0.5 are considered. The two distribution modes and relevant factor values are shown in Fig. 10. The factor α means the ratio of the maximum residual stress to yield strength f_y.

By employing the computer program designed in Section 2.2, the load bearing capacity for H shaped high strength Q460 steel columns are performed, respectively bending around strong and weak axis. The dimension of cross section for the Q460 steel column is H200 × 200 × 12 × 8 and the initial flexure is 1‰ length of column. The stable factor of high strength Q460 steel columns with distribution mode 1 and 2, residual stress value 0.3 and 0.5 are shown in Fig. 11-12.

As is shown in Fig. 11, for distribution mode 1, the residual stress value has almost no influence on the stable factor when the slenderness ratio is bigger than 75. However, when the slenderness ratio is lower than 75, with the increase of residual stress value, the stable factor decrease. The same conclusion can be drawn for both strong axis and weak axis. For distribution mode 2, the similar trend can be observed from Fig. 12. Therefore, the residual stress value has significant influence on the stable factor for the short and medium columns (slenderness ratio is less than 75), and for long column (slenderness ratio is more than 75), the influence is negligible.

The comparison of two distribution modes for residual stress is shown in Fig. 13. It is easy to find that at the same residual stress value, the distribution mode has very little influence on stable factor around strong axis. However, around weak axis, the stable factor of steel column under rectangle distribution (mode 2) is higher than triangle distribution (mode 1) for short and medium columns. For the long columns, the distribution mode has no influence on the stable factor.

Initial flexure

In a realistic steel column, the geometric imperfection always exits and the shape of initial flexure is various. It is proved that the initial flexure can be represented as a half sine wave [14]. Through a large numbers of test data on the steel columns, the maximum initial deflection (1‰ length of column) is often adopted at the mid-span of the column. For some columns, the initial flexure may be larger than 1‰ length of column. At elevated temperature, the non-uniform temperature distribution along the cross section also results in additional flexure of the column.

To study the influence of initial flexure on the stable factor for high strength Q460 steel columns, the computer program designed in Section 2.2 is adopted to obtain the stable factor at two different initial flexure value 1‰ and 3‰. The stable factor for high strength Q460 steel columns with different initial flexure are shown in Fig. 14. As can be seen from Fig. 14, at high temperatures, the initial flexure has very significant influence on the stable factor. With the increase of initial flexure, the stable factor reduces obviously both for bending around strong and weak axis.

Finite element analysis and experiment validation

To validate the method presented in Section 2, the finite element analysis was performed on global stability. The software ANSYS was employed to conduct the analysis. The comparison between global stability analysis result from ANSYS and predicted results by critical stress method was made to validate the critical stress method.

The ultimate load bearing capacity for 6 high strength Q460 steel columns at elevated temperatures were preformed by using element BEAM188. The section dimension of the column is H200 × 200 × 12 × 8 and the initial flexure is 1‰ length of column. The residual stress is adopted as left one distribution shown in Fig. 10(a). Three kinds of slenderness ratio 50,100 and 150, two temperatures 300°C and 600°C were considered in the analysis.

Figure 15(a) shows a typical stress distribution along high strength Q460 steel columns at temperature 600°C. Figure 15 (b) shows a typical load-displacement curve at temperature 300°C and the load bearing capacity is defined as the peak point of the curve. The analysis results were compared with the critical stress method and are shown in Fig. 16. From the comparison we can find that the finite element analysis results agree well with critical stress results. Therefore, the method proposed in this paper is validated to predict the load bearing capacity for high strength Q460 steel columns at elevated temperatures.

As to now, the test result on load bearing capacity of Q460 steel column at elevated temperature was not found. However, there is some data for Q460 steel column at room temperature [15]. As presented above, the critical stress approach can also be used to calculate the stable factor of Q460 steel columns at room temperature. To validate the method by experiment, the comparison of stable factor was made between test results and analytical results (as shown in Table 3). Form the comparison, it is shown that the results agree well and only 7 percent difference between them.

Conclusions

The fire resistance study on high strength Q460 steel column was carried out and an approach to evaluate the load bearing capacity was proposed. A computer program was designed to compute the relationship between stable factor and slenderness ratio for high strength Q460 steel column at elevated temperature by extending the inverse calculation segment length method at room temperature. The approach was validated by finite element analysis and based on the study presented, some conclusion can be drawn:

1) The strength and stiffness of high strength Q460 steel degrade slowly that that of mild steel and exhibit good fire resistance.

2) The critical temperature of high strength Q460 steel column is much higher than mild steel columns at the same load ratio.

3) The residual stress value and distribution mode has little influence on the load bearing capacity for the long column that the slenderness ratio is bigger than 75.

4) The initial flexure of high strength Q460 steel column has significant effect on the load bearing capacity at elevated temperatures.

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