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Behavior of Slender RC Columns Bent in Single and Double Curvature at Elevated Temperatures

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Abstract

In this study, a numerical model for tracing the behavior of eccentrically loaded slender reinforced concrete (RC) columns bent in single and double curvature, and subjected to elevated temperatures is presented. The developed model incorporates the high-temperature material properties, the nonlinear behavior of concrete sections, time dependent effects, and the nonlinear responses of slender RC columns. Based on Newton–Raphson method, an iterative technique, wherein strain and curvature are concurrently iterated, is used to find the strain distribution on the cross-section. By proposing a simple and reliable calculation procedure, the lateral deflection is calculated using numerical and searching techniques. The compatibility between forces and deformations at a joint in the column is established by another iterative technique, which involves the analysis of the whole column. The validity of the analytical model is established by comparing its predictions with results obtained from laboratory tests found in literature. A parametric study is conducted to investigate the effect of end eccentricity conditions on columns bent in single and double curvatures. It was found that lateral deflection plays an important role on column responses when subjected to fire. This finding confirms the usefulness of lateral deflection as a powerful tool in validating eccentrically loaded slender RC columns. It was also found that unwinding at elevated temperature has detrimental effect on columns bent in double curvature. It was observed that for all columns, there exists a critical eccentricity after which column responses to fire change.

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Abbreviations

\(b\) :

Column width (cross-section) (mm)

\(c\) :

Depth of natural axis (mm)

\(d_{t}\) :

Depth form extreme compressive fiber to extreme tensile bars (mm)

\(E_{cT}\) :

Concrete modulus of elasticity at elevated temperature (MPa)

\(E_{cT}^{h}\) :

Concrete strain hardening modulus at elevated temperature (MPa)

\(E_{sT}\) :

Steel modulus of elasticity at elevated temperature (MPa)

\(e\) :

End eccentricity, representative eccentricity (mm)

\(f^{\prime}_{c}\) :

Concrete compressive strength at ambient temperature (MPa)

\(f^{\prime}_{cT}\) :

Concrete compressive strength at elevated temperature (MPa)

\(f_{c}\) :

Concrete compressive stress at ambient temperature (MPa)

\(f_{cT}\) :

Concrete compressive stress at elevated temperature (MPa)

\(f_{sT}\) :

Steel stress at elevated temperature (MPa)

\(f_{y}\) :

Steel yield strength at ambient temperature (MPa)

\(f_{yT}\) :

Steel yield strength at elevated temperature (MPa)

\(h\) :

Column height (cross-section) (mm)

\(L\) :

Column length (mm)

\(M\) :

Bending moment (kN m)

\(M_{500}\) :

Bending moment for 500 × 500-element mesh (kN m)

\(n_{x}\) :

Number of elements in x-direction (cross-section)

\(n_{y}\) :

Number of elements in y-direction (cross-section)

\(P\) :

Axial load (kN)

\(P_{500}\) :

Predicted axial load for 500 × 500-element mesh (kN)

\(P_{pr}\) :

Predicted axial load (kN)

\(P_{t}\) :

Test axial load (kN)

\(Q\) :

Shear force (kN)

\(R_{f}\) :

Fire resistance (min)

\(R_{f}^{critical}\) :

Fire resistance at critical eccentricity (min)

\(t\) :

Time of fire exposure (min)

\(T\) :

Temperature (°C)

\(y_{c}\) :

Distance between the compression face and the center of concrete element (mm)

\(y_{s}\) :

Distance between the compression face and the center of steel element (mm)

\(\alpha\) :

Inclination angle (radian)

\(\delta\) :

Lateral deflection (mm)

\(\theta\) :

Deflection slope (radian)

\(\varepsilon\) :

Strain, effective strain

\(\varepsilon_{0}\) :

Ultimate strain at ambient temperature

\(\varepsilon_{0T}\) :

Ultimate strain at temperature T

\(\varepsilon_{c}\) :

Mechanical strain, effective strain of concrete at ambient temperature

\(\varepsilon_{cr}\) :

Basic creep strain of concrete

\(\varepsilon_{cT}\) :

Mechanical strain, effective strain of concrete at temperature T

\(\varepsilon_{cr}^{c}\) :

Basic creep strain of concrete

\(\varepsilon_{cr}^{s}\) :

Basic creep strain of steel

\(\varepsilon_{sT}\) :

Mechanical strain, effective strain of steel at temperature T

\(\varepsilon_{th}^{c}\) :

Free thermal strain of concrete

\(\varepsilon_{th}^{s}\) :

Free thermal strain of steel

\(\varepsilon_{tot}^{c}\) :

Total strain for concrete

\(\varepsilon_{tot}^{s}\) :

Total strain for steel

\(\varepsilon_{tr}\) :

Transient creep strain of concrete

\(\psi\) :

Curvature

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  1. Civil Engineering Department, Faculty of Engineering, Assiut University, Assiut, 71518, Egypt

    Khaled Ahmed Mahmoud

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Correspondence to Khaled Ahmed Mahmoud.

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Mahmoud, K.A. Behavior of Slender RC Columns Bent in Single and Double Curvature at Elevated Temperatures. Fire Technol 57, 1313–1363 (2021). https://doi.org/10.1007/s10694-020-01057-y

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