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Proposed design methodology for laterally unrestrained monosymmetric I-beams in fire

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Abstract

Occasionally steel structures are exposed to fire hazard during its lifetime. As temperature rises, the material characteristics of steel rapidly deteriorate, resulting in a loss in the flexural resistance of the beam members. For laterally unrestraint beams, lateral–torsional buckling (LTB) may predominate in design strength calculations. Beams may fail prematurely due to a rapid loss in capacity at elevated temperatures. Previous research has focused on employing a single equation to determine LTB design curves at elevated temperatures, with reduction factors. These curves may result in a very conservative design that might change with the loading patterns and can sometimes predict unsafe design strengths. The present manuscript carries out a parametric study using a validated numerical model. The robust computational software ABAQUS is used for simulating a total of 2940 elastic and inelastic beam models. A new proposal is recommended for predicting the design capacity for the uniform moment, moment gradients, point load at mid-span and uniformly distributed load considering monosymmetric sections at elevated temperatures. Further, a statistical study is conducted to ascertain the accuracy of the present proposal, and only 0.045 root mean square error is observed for new proposal. The resulted data are also compared with the available literature. The results show that the current proposal provides economical, safe and less scattered predictions with R2 > 0.95.

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Abbreviations

\(a, \, b, \, c\) :

New proposal constants

\(b\) :

Width of the section

\(B_{{\text{c}}} , \, B_{{\text{t}}}\) :

Top and bottom flange widths

\(\alpha\) :

Imperfection factor

\(E_{{\left( {20} \right)}}\) , \(E\) :

Elastic modulus at ambient temperature 20 °C

\(T_{{\text{c}}} , \, T_{{\text{t}}}\) :

Top and bottom flange thickness

\(f_{{{\text{y}},{ }\left( {20} \right)}}\), \(f_{{\text{y}}}\) :

Yield stress at ambient temperature 20 °C

\(l\) :

Span length

\(W_{{y,{\text{pl}}}}\) :

Section’s plastic modulus

\(M_{{b,{\text{fi}},t}} ,_{{{\text{Rd}}}}\) :

LTB resistance moment

\(h\) :

Section’s height

\(I_{{{\text{ZC}}}}\), \(I_{{{\text{ZT}}}}\) and \(I_{Z}\) :

Second moment of area about the section z-axis of the top flange, bottom flange and the whole section

\(\gamma_{{{\text{m}},{\text{fi}}}}\) :

Material partial safety factor in fire

\(\Psi\) :

Moment gradients

\(f\) :

Modification factor for \(\chi_{{{\text{LT}}}}\)

\(\beta\) :

Severity factor

\(k_{{\text{c}}}\), \(k_{{{\text{c}}1}}\) :

Correction factors for moment distribution

\(\lambda_{{{\text{LT}}}}\) :

Non-dimensional slenderness for LTB

\(\chi_{{{\text{LT}}}}\) :

Reduction factor for lateral–torsional buckling

\(M_{{{\text{cr}}}}\) :

Elastic critical moment for lateral–torsional buckling

\(\chi_{{{\text{LT}}\,{\text{fi}}}}\) :

The reduction factor for lateral–torsional buckling in the fire design situation

\(\rho\) :

Degree of monosymmetry

\(\lambda_{{{\text{LT}}\,{\text{fi}}}}\) :

Non-dimensional slenderness for LTB in fire

\(\lambda_{{{\text{LT}}\,0}}\) :

Plateau length of LTB curves for hot-rolled steel sections

\(\phi_{{{\text{LT}}}}\, \phi_{{{\text{LT}}\,{\text{fi}}}}\) :

Value to determine the reduction factor \(\chi_{{{\text{LT}}}}\)

\(k_{{{\text{y}}\, \left( \theta \right)}}\),\(k_{{{\text{E}}\,\left( \theta \right)}}\), \(k_{{{\text{p}}\,\left( \theta\, \right)}}\) :

The reduction factor for the yield strength, elastic modulus and proportional limit of steel at the steel temperature \(\theta\)

\(f_{{{\text{y}}\,{ }\left( \theta \right)}}\), \(f_{{{\text{p}}\,{ }\left( \theta \right)}}\),:

The effective yield strength, proportional limit of steel at the steel temperature \(\theta\)

\(f_{{{\text{p}}\,{ }\left( {20} \right)}}\) :

Proportional limit of the steel at ambient temperature 20

\(E_{{{ }\left( \theta \right)}}\),:

Proportional limit of the steel temperature \(\theta\)

\(M_{{{\text{ult}}\, {\text{FEM}}}}\) :

Ultimate moment obtained from FEM

\(M_{{{\text{ult}}\, {\text{Analytical}}}}\) :

Ultimate moment obtained from various formulations

\(n\) :

Number of samples

\(\overline{\chi }\) :

Mean of data

\(\chi_{i}\) :

Ratio for comparing FEM to analytical values

\(\chi_{{{\text{LT}}\,{\text{Analytical}}}}\) :

The reduction factor for LTB from analytical data

\(\chi_{{{\text{LT}}\,{\text{EC}}3}}\) :

The reduction factor for LTB from Eurocode 3 formulations

\(\chi_{{{\text{LT}}\,{\text{ref}}}}\) :

The reduction factor for LTB from reference formulations [28]

\(\chi_{{{\text{LT}}\, {\text{New}}\;{\text{proposal}}}}\) :

The reduction factor for LTB from new proposal formulations

\(\chi_{{{\text{LT}}\, {\text{FEM}},{\text{i}}}}\) :

The reduction factor for LTB from FEM individual data

\(\overline{\chi }_{{{\text{LT}}\,{\text{ FEM}},{\text{i}}}}\) :

The reduction factor for LTB from FEM mean of individual data

\(\chi_{{{\text{LT}}\,{\text{Analytical}},{\text{i}}}}\) :

The reduction factor for LTB from analytical individual data

\(\chi_{{{\text{LT}}\,{\text{ FEM}}}}\) :

The reduction factor for LTB from FEM data

\(\chi_{{{\text{modified}}\, {\text{fi}}}}\) :

Modified reduction factor

\(\chi_{{{\text{LT}}\, {\text{fi}}\,{\text{New}} {\text{proposal}}}}\) :

LTB curve reduction factor for new proposal

\(\chi_{{{\text{modified}}\, {\text{fi}}\,{\text{New}} {\text{proposal}}}}\) :

Modified reduction factor calculated from \(\chi_{{{\text{LT}}\, {\text{fi}}\,{\text{New}} {\text{proposal}}}}\)

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Funding

The authors gratefully acknowledge the support and funding for the doctoral research work of the first author by Indian Institute of Technology Patna, India.

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  1. Department of Civil and Environmental Engineering, Indian Institute of Technology Patna, Patna, Bihar, 801106, India

    Saurabh Suman & Avik Samanta

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  1. Saurabh Suman
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Correspondence to Avik Samanta.

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Suman, S., Samanta, A. Proposed design methodology for laterally unrestrained monosymmetric I-beams in fire. Innov. Infrastruct. Solut. 7, 367 (2022). https://doi.org/10.1007/s41062-022-00972-z

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