Elastic Analysis of Straight Members at Elevated Temperatures

Abstract

The inherent expense of conducting full-scale experiments on steel members at elevated temperatures reinforces the need for accurate and reliable theoretical modelling, in order to assess their structural response under fire loading. The behaviour of steel members at elevated temperatures is quite complex and often counter-intuitive, and hitherto advanced finite element packages have been preferred over more generic or analytical solutions. Because of this, the significance of some parameters that influence the behaviour greatly may be lost. This article presents a generic modelling of the behaviour of a restrained beam member in a compartment fire, using the philosophy of a sub-assembly approach in lieu of a global modelling of the structure, which is allowed by the Eurocode standard. The analysis is elastic and therefore ignores yielding and the catenary effects that result at higher temperatures, and is based on the theorems of virtual work which allows for the prescription of governing differential equations of equilibrium and of the static boundary conditions. The equations of equilibrium are solved for some specific cases of restraint, and it is shown how the analytical solutions lead directly to prescriptive modelling of the structural behaviour, and importantly these equations lend themselves readily to codification in fire engineering design.

Keywords

analytical model elasticity fire engineering nonlinearity steel virtual work

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References

ABAQUS (2001). Standard User's Manual, Hibbitt, Karlsson and Sorensen Inc., Pawtucket, Rhode Island.

Leston-Jones

L.C.

Burgess

I.W.

Lennon

and Plank

R.J.

(1997). “Elevated temperature moment-rotation tests on structural steelwork”, Proceedings of the Institution of Civil Engineers, Structures and Buildings, Vol. 122, pp. 410–419.

Liew

J.Y.R.

and Ma

K.Y.

(2004). “Advanced analysis of 3D steel framework exposed to compartment fire”, Fire and Materials, Vol. 28, No. 2–4, pp. 253–267.

Liu

T.C.H.

and Davies

J.M.

(2001). “Performance of steel beams at elevated temperatures under the effect of axial restraints”, Steel and Composite Structures, Vol. 1, No. 4, pp. 427–440.

Liu

T.C.H.

Fahad

M.K.

and Davies

J.M.

(2002). “Experimental investigation of the behaviour of axially restrained steel beams in fire”, Journal of Constructional Steel Research, Vol. 58, pp. 1211–1230.

Y.L.

and Bradford

M.A.

(2004). “In-plane strength and design of fixed steel I-section arches”, Engineering Structures, Vol. 26, No. 3, pp. 291–301.

Usmani

A.S.

Chung

Y.C.

and Torero

J.L.

(2003). “How did the WTC towers collapse: A new theory”, Fire Safety Journal, Vol. 38, No. 6, pp. 501–533.

Usmani

A.S.

Rotter

J.M.

Lamont

Sanad

A.M.

and Gillie

(2001). “Fundamental principles of structural behaviour under thermal effects”, Fire Safety Journal, Vol. 36, pp. 721–744.

Trahair

N.S.

and Bradford

M.A.

(1998). The Behaviour and Design of Steel Structures, 3rd Australian edn., E&FN Spon, London.

10.

Trahair

N.S.

and Chan

S.L.

(2003). “Out-of-plane advanced analysis of steel structures”, Engineering Structures, Vol. 25, No. 13, pp. 1626–1637.

11.

Wang

Y.C.

(2002). Steel and Composite Structures: Behaviour and Design for Fire Safety, Spon Press, London.

12.

Yin

Y.Z.

and Wang

Y.C.

(2004). “A numerical study of large deflection behaviour of restrained steel beams at elevated temperatures”, Journal of Constructional Steel Research, Vol. 60, pp. 1029–1047.

13.

Yin

Y.Z.

and Wang

Y.C.

(2005a). “Analysis of catenary action in steel beams using a simplified hand calculation method, Part 1: Theory and validation for uniform temperature distribution”, Journal of Constructional Steel Research, Vol. 61, pp. 183–211.

14.

Yin

Y.Z.

and Wang

Y.C.

(2005b). “Analysis of catenary action in steel beams using a simplified hand calculation method, Part 2: Validation for nonuniform temperature distribution”, Journal of Constructional Steel Research, Vol. 61, pp. 213–234.

15.

H.X.

and Liew

J.Y.R.

(2005). “Considering catenary action in designing end-restrained steel beams in fire”, Advances in Structural Engineering, Vol. 8, No. 3, pp. 309–324.