Thermal buckling of a heat-exposed, axially restrained composite column

doi:10.1016/j.compositesa.2005.04.006

Composites Part A: Applied Science and Manufacturing

Volume 37, Issue 7, July 2006, Pages 972-980

https://doi.org/10.1016/j.compositesa.2005.04.006 Get rights and content

Abstract

The response of composite columns under axial compressive loading, and in which a non-uniform temperature distribution through the thickness exists, is investigated. This non-uniform temperature distribution can develop when one side of the structures is exposed to heat flux. In this paper, we assume that this distribution is linear, which corresponds to a steady state temperature profile due to heat conduction. The degradation of the elastic properties with temperature (especially near the glass transition temperature of the matrix) is accounted for, by using experimental data for the elastic moduli. Furthermore, the formulation includes transverse shear and it is done first for the general non-linear case and subsequently linearized. Due to the non-uniform stiffness and the effect of the ensuing thermal moment, the structure behaves like an imperfect column, and responds by bending rather than buckling in the classical Euler (bifurcation) sense. Another important effect of the non-uniform temperature is that the neutral axis moves away from the centroid of the cross-section, resulting in another moment due to eccentric loading, which would tend to bend the structure away from the heat source. Simple equations for the response of the column are derived and results are presented for the variation of the deflection with the heat flux, as well as for the combined effects of the applied load and heat flux. It is found that the thermal moment would tend to bend the structure away from the heat source for small temperatures (small heat fluxes) but towards the heat source for large temperatures. On the contrary, the moment induced due to the eccentric loading would always tend to bend the structure away from the heat source. Results indicate the combined influences of these moments and that of axial constraint.

Introduction

Fiber-reinforced polymeric composites are used extensively in aerospace, marine, infrastructure and chemical processing applications. In these applications, events creating a heat flux (e.g. due to fire), and their resulting effects on the structural integrity, are of considerable concern. In addition to the implications for design, quantitative information regarding the nature of the strength loss is required to make decisions regarding, for example, the seaworthiness of a ship that has sustained fire damage.

Many of the thermal properties of composites related to fire have been thoroughly studied and are well understood, including ignition times, heat release rates, smoke production rates and gas emissions [1], [2], [3], [4], [5], [6], [7]. Also, some recent work into the post-fire residual properties has been conducted, for example, a preliminary investigation into the effect of fire damage on the edgewise compression properties and failure mechanisms of sandwich composites [7] showed large reductions to the edgewise compression properties of phenolic-based sandwich composites despite having good flame resistance. However, one important gap in the understanding of composites is their response and structural integrity due to the combined effect of mechanical loading and thermal loading due to fire. This paper addresses this issue as far as compressive loading, which in an otherwise purely mechanical loading (no fire) would lead to bifurcational (Euler) buckling.

One important characteristic of fiber-reinforced polymeric composites is that increases in temperature cause a gradual softening of the polymer matrix material with a significant effect near the glass transition temperature, T_g. Recent experiments on E-glass vinyl ester composites, conducted by Kulkarni and Gibson [8] can be used as a basis for including the resulting non-uniform stiffness distribution.

When heat flux is applied on one side of a column/plate, a non-uniform temperature develops through the thickness. Since the modulus of elasticity of polymeric composites depends on temperature, this non-uniform temperature results in a non-uniform distribution of stiffness through the thickness. In addition, a thermal moment is developed, which causes bending of the column from the very start of heat exposure when only the slightest change of temperature occurs. An additional ‘eccentricity moment’ is created since the non-uniform temperature induces a shift of the neutral axis away from the centroid of the cross-section. Thus, the column bends like an imperfect beam (even if it is initially straight) and cannot buckle in the classical Euler (bifurcation) sense. In this paper, we investigate the general bending response of such a column that is pinned at both ends, with an applied axial force. In simple terms, the column is subjected to both (1) an axial force that can cause buckling at the Euler load if it is large enough; (2) a thermal moment that causes bending immediately; and (3) an ‘eccentricity moment’ induced by the neutral axis moving away from the centroid of the cross-section, resulting in eccentric loading. The details of the formulation are outlined in Section 2.

Section snippets

Formulation

Let us assume a symmetric cross-section of thickness h. First, we derive the temperature distribution through the thickness. Assuming steady state, the temperature, T, satisfies the heat conduction equation $\frac{d^{2} T}{d y^{2}} = 0; - \frac{h}{2} < y < \frac{h}{2} .$

At the side of the fire, y=−h/2, a constant heat flux, Q, is supplied by the fire: $- K \frac{d T}{d y} = Q at y = - h / 2,$ and at the other side, y=h/2, we have a ‘radiation’ boundary condition to the air at room temperature, T₀: $- K \frac{d T}{d y} = H (T - T_{0}) at y = h / 2.$

In these equations, K is the thermal

Conclusions

The thermal buckling of a composite column under external heat flux and compressive load is investigated based on a linear temperature distribution. We considered two cases: one is a constrained pinned column (immovable ends) under an external heat flux and the other is the same pinned column, but with the ends of the column free to move axially and subjected to both an applied compressive load and an external heat flux. For the constrained column, the variations of the axial constraint force P

Acknowledgements

The financial support of the Office of Naval Research, Grant N00014-03-1-0189, and the interest and encouragement of the Grant Monitors, Dr Patrick C. Potter and Dr Luise Couchman is gratefully acknowledged.

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Thermal buckling of a heat-exposed, axially restrained composite column

Abstract

Introduction

Section snippets

Formulation

Conclusions

Acknowledgements

Improved fire safety of composites for naval applications

Fire Mater

Materials and fire threat

SAMPE J

Flammability of GRP for use in ship superstructures

Fire Mater

Fire performance studies on glass-reinforced plastic laminates

Fire Mater

Fire performance of composite panels for large marine structures

Plast Rubber Compos Process Appl

Reinforcement and matrix effects on the combustion properties of glass reinforced polymer composites

Composites