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This paper presents the findings of an experimental research to investigate the performance of axially restrained elliptical hollow (EHS) steel columns subjected to severe hydrocarbon fire. The test programme involved 12 steel columns presenting 2 oval sections 200 × 100 × 8 mm and 300 × 150 × 8 mm and yielding 2 slenderness λ = 51 and 33. The 1800 mm columns were tested under loading ratios ranging between 0.2 and 0.6 of the ultimate strength determined using EC3 and under axial restraint degree ranging from 0 to 0.16. The obtained results of axial displacements, lateral displacements, measured restraint forces, and high temperatures are presented in the paper. It was found that introducing restraint to the columns with elliptical section produces high restraint forces which reduce the time to lose lateral stability. This is more evident in cases of lower load ratios than the higher load ratios. The numerical study presented in this paper involved building a finite element model to simulate the columns behaviour in fire. The model was validated using the test results obtained from unrestrained and restrained columns fire tests. The model demonstrated good agreement in the prediction of failure times and failure mechanisms of local and overall buckling. The FEM model was then used to conduct a parametric analysis involving factors of slenderness, restraint and loading. The conclusions drawn for this research are presented at the end of the paper.

In spite of the increasing use of elliptical hollow steel sections in buildings (due to their aesthetically pleasing shape compared to rectangular and circular hollow sections), there are limited researches carried out on the performance of columns with elliptical sections under fire conditions especially with axial restraint. The growing trend in the construction industry to use elliptical hollow steel sections in buildings requires more research investigating the performance of structural elements with elliptical sections. There is however very limited research carried out on the performance of the elliptical columns under fire conditions especially with introduction restraint boundary conditions. In recent years, research has investigated the performance of other hollow sections available (circular, rectangular and square) under loading and fire conditions. There have been some researches carried out on the performance of stub elliptical columns under loading conditions by Gardner et al. [

Twelve elliptical steel columns were tested at the FireSERT research laboratories at the University of Ulster. The rig (see figure 1) used during testing allows for loads to be applied to the columns and can provide axial restraint using the rig stiffness. The facilities also allow, measuring thermocouple temperature readings, axial and lateral displacements using LVDT’s. The test programme involved testing columns with 2 oval sections 200 × 100 × 8 mm (EHS-A) and 300 × 150 × 8 mm (EHS-B) of length = 1800 mm, yielding 2 slenderness λ = 51 and 33. The columns were tested under loadings levels of 0.2, 0.4 and 0.6 of the ultimate strength for the hollow elliptical section EC3 [_{k} ranging from 0 to 0.16. The degree of axial restraint α_{k} is defined as:

α k = K s K c (1)

where K_{s} is the stiffness of the surrounding structure (rig), K_{c} is the axial stiffness of the column

K c = A E L (2)

where A is the column section area; E is the Young modulus and L is the length of the column. The loading imposed on columns was increased gradually in equal time steps to allow the column to settle and to get stable readings. Once the load level was reached the burner was ignited subjecting the columns to a hydrocarbon fire Ali et al. [

The testing rig is shown in

The data of axial and lateral displacements obtained from the tests are shown in

By comparing the two sets of data, it can be seen that the columns responded to heating in a similar way as the axial displacement increased linearly as the time increased. When the column reached the maximum axial displacement it started to fail slowly at first (due to degradation in the steel properties under high temperatures), then the deformation started to increase more rapidly towards complete failure. This can be observed more clearly in the load levels of 0.6 of the ultimate loading as there are approximately 30 seconds between the peak deformation and the columns failure where as it takes the 0.2 loaded columns between approximately 1min 30 secs to 2mins. The results show that the

two sections demonstrated the same fire resistance time for each of the different loading levels regardless of the size of the section.

In the case of the restraint tests the same load ratios of 0.2, 0.4 and 0.6 were applied to the columns as in the unrestrained tests. The restraint provided during the tests was imposed by the stiffness of the testing rig with the addition of rubber springs which help to provide a range of rig stiffness (

The displacements obtained during the tests show that the EHS-AR (slenderness λ = 51) failure time (due to loosing lateral stability) decreases with the increase of loading level from 10mins for 0.2, to 8 mins for 0.4 and to 6 mins for 0.6 (

The same relationship can be seen in the larger EHS-BR (slenderness λ = 33) section, 10 mins for 0.2, to 9 minutes for 0.4 and to 8 minutes for 0.6 (

The results indicate that the failure by losing lateral stability of the EHS-BR tests occurs gradually when the load ratio increases if compared with the smaller EHS-AR section. This can be attributed to the high frictional forces being generated at the half moon supports for the larger sections as the load applied is greater than that of the smaller section. As both of the sections were subjected to relatively the same axial restraint then this may be a feasible reason for this observation.

In each of the tests the lateral displacements of the columns were recorded using

quartz rods connected to the LVDTs. The columns are deemed to have failed laterally when the column has deflected by more than L/300, according to the EC3 [

In general the restrained columns demonstrated lower fire resistance than the unrestrained columns and the results are shown in

When comparing the overall buckling and local buckling failure mechanisms shown in

The elliptical columns were modelled using the finite element method and the software Diana TNO [

Section | Load Ratio | Load (kN) | Time to Failure (mins) | Maximum Axial Displacement (mm) | |
---|---|---|---|---|---|

Axial | Lateral | ||||

200 × 100 × 8 EHS-A | 0.2 | 212 | 13 | 11 | 9.94 |

0.4 | 424 | 10 | 10 | 7.31 | |

0.6 | 616 | 8 | 7 | 5.31 | |

300 × 150 × 8 EHS-B | 0.2 | 354 | 13 | 12 | 7.61 |

0.4 | 701 | 10 | 9 | 5.36 | |

0.6 | 1053 | 8 | 8 | 4.81 |

Section | Load Ratio | Degree of Axial Restraint α_{k} | Load (kN) | Time to Failure (mins) | Maximum Axial Displacement (mm) | Maximum Restraint Force (kN) | |
---|---|---|---|---|---|---|---|

Axial | Lateral | ||||||

200 × 100 × 8 EHS-AR | 0.2 | 0.12 | 209 | 10 | 8 | 5.04 | 257.032 |

0.4 | 411 | 8 | 7 | 4.04 | 186.066 | ||

0.6 | 637 | 5 | 5 | 2.47 | 100.745 | ||

300 × 150 × 8 EHS-BR | 0.2 | 0.16 | 348 | 10 | 9 | 3.93 | 378.191 |

0.4 | 697 | 9 | 8 | 3.27 | 305.585 | ||

0.6 | 1052 | 8 | 8 | 2.04 | 191.431 |

response of the columns, a transient heat transfer analysis was performed using a three-dimensional steady-state heat flow derived for the Law of Conservation of Energy:

δ δ x ( k δ T δ x ) + δ δ y ( k δ T δ y ) + δ δ z ( k δ T δ z ) + Q − ρ c δ T δ t = 0 (3)

where: k is the thermal conductivity; T is the temperature gradient; Q is the internally generated heat per unit volume per unit time, ρ is the density of the material; c is the specific heat of the material and t is time. Solution of equation (3) is governed by the boundary condition:

− k δ T δ n = h c ( T s − T f ) + h r ( T s − T f ) (4)

where: n is the direction of heat flux; h_{c} is the heat transfer coefficient; T_{s} is the temperatures of the solid surface, T_{f} is the temperatures of the fluid and h_{r} is the radiation heat transfer coefficient calculated using Stefan-Boltzmann equation.

The Galerkin method was used by determining {T} as a function of time and expressed as the first order differential equation:

[ k ] { T n } + [ c ] { T n } = { F n } (5)

where: [k] is element heat conduction/convection matrix; [c] is element heat capacity matrix; {T_{n}} is element nodal temperature vector; {F_{n}} is element nodal heat input vector and defined at boundary nodes using Equation (6):

− k [ δ T δ x l 1 + δ T δ x m 1 ] = h c [ T e − T r ] + ε e σ [ T e 4 + T r 4 ] (6)

where: T_{e} = temperature of emitting surface; T_{r} = temperature of surface; s = Stefan-Boltzmann coefficient; l_{1}-direction cosine of n relative to x = cosθ; m_{1} = direction cosine of n relative to y = sinθ; ε_{e} = emissivity of the surface.

After completing the thermal analysis, the model undergoes structural analysis to evaluate the effect of temperatures on the column behaviour. The stresses that occur under temperature are governed by the following equation:

{ σ } = [ K ] { ε − ε T } (7)

where: {σ} = stress vector; [K] = stiffness matrix; ε_{T} = thermal strain vector.

In order to calculate the stiffness matrix [K] in Equation (7) a material model was assigned to the structural element. In the case of the elliptical section it is taken as steel material with a yield stress value 355 N/mm^{2}, and a standard stress/strain curve was adapted with the Von-mises failure criteria used. The non-linear properties of the steel are taken from EC3 (2005a, 2005b) for the change due to high temperatures.

A 3-D model was created for the two elliptical sections, 200 × 100 × 8 mm and 300 × 150 × 8 mm. The structural model consists of a 20 node of iso-parametric brick element, CHX60, TNO [

A sensitivity analysis was carried out in order to determine the size of the meshing to be used that would enable fast computational time without compromising the performance of the model. The final model created consisted of 38,845 nodes and 10,445 elements that represent the structural and temperature elements as shown in

The room temperature compressive capacity of the model was first validated using the EC3 [

In the case of considering axial restraint, the restraint was modelled using a one way spring with constant stiffness to simulate the effect of surrounding structural elements in practice. The restraint is formed by using a 0D, one node element in the form of a discrete spring/dashpot element, SP1TR, whereby the total restraint applied is the total number of nodes times the individual spring stiffness of each node.

The model allows for the loading and unloading of the spring to occur (

The output from the modelling provides detailed predictions on the temperature and deformation of the sections over the period that is exposed to the fire.

The FEM results for the EHS-B are also in good agreement in failure times for the 0.4 and 0.6 load ratios whereas for the 0.2 load ratio the model slightly over predicts the failure time as shown in

The results of the lateral displacements produced by the FEM are shown in

The failure of the EHS-A in the tests was mainly due to the overall buckling of the columns with occurrence of local buckling as can be seen in

The column models were subjected to a restraining force which represents the surrounding structure which in this case is the testing rig. The summary of the

results are shown in

It was noted that the model failure occurs rather rapidly once the maximum displacement was reached in comparison to the test columns where failure was gradual. The results for the restraint case showed excellent correlation between the test and FEM in the failure time and maximum axial displacement and excellent agreement of the failure mechanism.

With the model verified by the test results a parametric analysis has been carried out. The analysis studied the effect of different load levels, of varying slenderness values 60, 90 and 120 on uniformly heated sections. The maximum load for each of the columns was calculated using EC3 method and an initial imperfection of L/360 was applied to each of the columns. The result from the analysis for λ = 90 is shown in

Section | Load Ratio | Degree of Axial Restraint | Maximum Displacement (mm) | Time of Failure (mins) | ||||
---|---|---|---|---|---|---|---|---|

Axial | Lateral | |||||||

FEM | Exp | FEM | Exp | FEM | Exp | |||

EHS-AR.0.2 | 0.2 | 0.12 | 5.62 | 5.04 | 9 | 10 | 9 | 9 |

EHS-AR.0.4 | 0.4 | 4.67 | 4.04 | 7 | 8 | 7 | 7 | |

EHS-AR.0.6 | 0.6 | 2.99 | 2.47 | 6 | 5 | 5 | 5 | |

EHS-BR 0.2 | 0.2 | 0.16 | 5.31 | 3.93 | 9 | 10 | 9 | 9 |

EHS-BR 0.4 | 0.4 | 4.48 | 3.27 | 7 | 9 | 7 | 8 | |

EHS-BR 0.6 | 0.6 | 3.30 | 2.04 | 6 | 8 | 6 | 8 |

the more slender the column is the lower the failure temperature is for the section.

The other factor investigated parametrically is the effect of restraint on the axial displacement of the columns.

The effect of restraint and loading on failure time of columns was also investigated.

column under three loading ratios. The figure shows an increase in axial restraint forces generated under low slenderness i.e. the stockier the column is the higher the axial restraint forces. The values of the axial forces increase if the applied loading is decreased. All relationships are approximately linear.

The study has demonstrated that the maximum axial displacement of columns is less in the restraint tests compared to the unrestrained column. However, the maximum restraint force generated is greater when the load ratio is low. The study demonstrated that the failure of all columns can be by combination of overall and localised buckling occurring in the steel section where failure time decreased more as the loading level was increased. This is more evident in the larger section sizes. It was observed that by using variable with temperature thermal expansion coefficient and the EC3 thermal parameters, the FE model demonstrated reasonably good agreement with the experimental values of temperatures and excellent prediction of the mode of instability. The model has shown excellent agreements in failure modes of overall and local buckling. The study also highlighted the criticalness of the effect of geometric imperfections on the ultimate failure time and the fire resistance of the EHS column. The verified finite element model was used to conduct a parametric analysis involving parameters of loading level, restraint and slenderness. The parametric analysis has shown that the more slender the column, the lower the failure temperature. The parametric study has also shown a non-linear relationship between the loading ratio and the slenderness of the elliptical columns. Increasing the loading level from 0.2 to 0.8 has reduced the maximum displacement by 47% and decreased the failure temperature by 28%. In columns’ slenderness range of 90 to 120, the effect of loading on failure temperature is less than that in the range of 60 to 90. It also showed a decrease in the axial displacements of columns if an axial restraint is imposed. The analysis has shown that increasing the loading decreases the axial displacement under fire and reduces the failure time of columns. The analysis also shows that the stockier the column is, the higher the generated axial restraint forces in fire.

The authors would like to thank the EPSRC (Engineering and Physical Sciences Research Council) UK for providing the funding grant EP/H048782/1 for this research.

Ali, F. and Nadjai, A. (2018) Effect of Severe Temperatures and Restraint on Instability and Buckling of Elliptical Steel Columns. Open Journal of Civil Engineering, 8, 41-57. https://doi.org/10.4236/ojce.2018.81004