Thermal gradient

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Predicting the Demand and Plastic Capacity of Axially Loaded Steel Beam–Columns with Thermal Gradients

Journal Title, Volume, Page: 
Engineering Structures Volume 58, January 2014, Pages 49–62
Year of Publication: 
2014
Authors: 
S.E. Quiel
Dept. of Civil and Env. Engineering, Lehigh University, Bethlehem, PA 18015, USA
M.E.M. Garlock
Dept. of Civil and Env. Engineering, Princeton University, Princeton, NJ 08544, USA
M.M.S. Dwaikat
Dept. of Civil Engineering, An-Najah National University, Nablus, Palestine
Current Affiliation: 
Department of Civil Engineering, Faculty of Engineering and Information Technology, An-Najah National University, Nablus. Palestine
V.K.R. Kodur
Dept. of Civil and Env. Engineering, Michigan State University, East Lansing, MI 48824-1226, USA
Preferred Abstract (Original): 

This study evaluates the adequacy of different methodologies to predict the plastic capacity and response caused by non-uniform thermal gradients through the depth of beam–columns that are loaded only axially at the centroid. Three models with different levels of complexity were used to evaluate the fire response of beam–columns under non-uniform temperature gradients: (1) code-based equations; (2) a fiber-beam element model; and (3) a shell element model that discretizes the full cross section and length and is capable of capturing local (i.e. plate) instability. The code-based equations do not predict the response satisfactorily since these equations do not properly consider temperature gradients. The fiber-beam element and shell model results correlate well to the thermal and structural response of the beam–columns tested experimentally with varying parameters. If local buckling is not expected at ambient temperature, complex shell elements are not necessary when the failure mode is fully plastic and fiber-beam elements, which are simpler and less “computationally expensive” than shells, suffice. The experiments and models also validated equations that consider thermal gradients and predict the plastic capacity and structural response of these members, which includes a moment reversal due to a shift in the section center of stiffness with increasing temperatures.

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A Simplified Approach for Evaluating Plastic Axial and Moment Capacity Curves for Beam-Columns with Non-uniform Thermal Gradients

Journal Title, Volume, Page: 
Engineering Structures, 32(5), pp.1423-1436
Year of Publication: 
2010
Authors: 
M.M.S Dwaikat
Department of Civil and Environmental Engineering, Michigan State University, United States
Current Affiliation: 
Department of Civil Engineering, An-Najah National University, Palestine
VKR Kodur
Department of Civil and Environmental Engineering, Michigan State University, United States
Preferred Abstract (Original): 
Restrained steel members, when exposed to fire develop significant forces and this transforms the behavior of a beam (or column) into that of a beam–column. The load carrying capacity of such beam–columns is determined through axial and moment capacity curves (P–MP–M curves). Codes and standards recommend the use of uniform average temperature for establishing the P–MP–M curves at elevated temperatures. This assumption, though adequate for cases where temperature in steel is uniform, such as a column exposed to fire from four sides, may not be valid for columns or beams exposed to fire from 1, 2, or 3 sides since significant thermal gradients develop across the section. These thermal gradients can cause severe distortion in the P–MP–M curves and render the capacity curves based on uniform temperature inadequate for evaluating the strength of such beam–columns. In this paper, a simplified approach is proposed for adjusting the uniform temperature plastic P–MP–M curves to account for the shape distortion resulting from fire-induced thermal gradients. The proposed method employs a two-step process in which the cross-sectional steel temperatures are calculated first, and then the distorted P–MP–M diagram is computed by adjusting the P–MP–M diagrams based on a uniform “averaged” temperature. The applicability of the proposed method to a design situation is illustrated through a numerical example. It is demonstrated that the proposed approach is well suited for predicting the capacity of beam–columns that develop thermal gradient under fire.
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A simplified approach for predicting temperatures in fire exposed steel members

Journal Title, Volume, Page: 
Fire Safety Journal
Year of Publication: 
2013
Authors: 
M.M.S. Dwaikat
Research Associate, Department of Civil and Environmental Engineering, Michigan State University, East Lansing, MI, United States
Current Affiliation: 
Department of Civil Engineering, An-Najah National University, Palestine
V.K.R Kodur
Department of Civil and Environmental Engineering, Michigan State University, East Lansing, MI., United States
Preferred Abstract (Original): 
For evaluating fire resistance of steel structural members, temperatures in the cross section of the member are required. In this paper, a simplified approach for evaluating cross sectional temperature in contour protected steel members exposed to fire is presented. The approach is derived utilizing simplifying assumptions to the general heat transfer equation for standard fire and is then extended for application under design fire scenarios. The proposed approach is applicable for both protected and unprotected steel sections. The validity of the approach is established by comparing predicted temperatures with those obtained from finite element analysis generated via ANSYS. In addition, predictions from the proposed method are also compared with the temperatures predicted by “best-fit” method. The comparisons to test data, finite element results and best-fit method indicate that the proposed simplified method gives good predictions of fire induced thermal gradient and temperature history in steel sections under any fire exposure. The simplicity of the proposed method makes it attractive for use in design situations.
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