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Prediction of shear strength for squat RC walls using a hybrid ANN–PSO model

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Abstract

The squat reinforced concrete (RC) shear wall having low aspect ratio is a crucial structural component for both conventional buildings and nuclear-related structures due to the substantial role in resisting the lateral seismic loading. The prediction model for shear capacity of these walls becomes essential in ensuring the seismic safety of the building. Therefore, a model to predict the shear strength of squat RC walls has been proposed using a hybrid intelligence algorithm including the artificial neural network and particle swarm optimization algorithm (ANN–PSO). A total of 139 test results of squat walls are collected and utilized to train and test the hybrid ANN–PSO model. The performance of the proposed model has been assessed against the other shear strength models. The proposed model demonstrates good prediction capability with high accuracy for predicting shear strength of the RC walls.

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Abbreviations

h :

Thickness of the shear wall

d :

Effective depth of the cross section

S :

Spacing of the horizontal reinforcement bar

A cw :

Area of the wall bounded by the web thickness and wall length

b w :

Minimum width of the web in the tension area

A SW :

Cross-sectional area of shear reinforcement within S

z :

Lever of internal forces (z ≈ 0.9d)

A w :

Area of the web cross section

A :

Gross area of the cross section

A v :

Area of shear reinforcement within spacing S

A sh :

Total area of horizontal reinforcement

A vf :

Total area of vertical reinforcement in the wall

A cv :

Effective cross-sectional area of the concrete section

l w :

Length of the wall

f yt :

Yield strength of transverse reinforcement

f ywd :

Yield strength of shear reinforcement

\({f_{{\text{yv}}}}\) :

Yield strength of vertical reinforcement

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

Compressive strength of the cylinder concrete

\({f_{\text{t}}}\) :

Tension strength of the prism concrete (\({f_{\text{t}}} \approx 0.1{f_{\text{c}}}\))

\({f_{\text{c}}}\) :

Compressive strength of the prism concrete (\({f_{\text{c}}} \approx 0.838{f^{\prime}_{\text{c}}}\))

\({f_{{\text{ck}}}}\) :

Characteristic compressive cylinder strength of concrete at 28 days

\({N_{\text{u}}}\) :

Axial load

\({\sigma _{{\text{cp}}}}\) :

Axial compress stress

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

Moment at section

\({V_{\text{u}}}\) :

Shear force at section

\({\alpha _{\text{c}}}\) :

Aspect ratio coefficient. \({\alpha _{\text{c}}}\) equals 0.17 for an aspect ratio ≥ 2.0; 0.25 for the aspect ratio ≤ 1.5, and varies linearly within 1.5 ≤ λ ≤ 2.2

\({\rho _{\text{v}}}\) :

Vertical reinforcement ratio

\({\rho _{\text{t}}}\) :

Horizontal reinforcement ratio

\({C_{{\text{Rd}},{\text{c}}}}\) :

\(0.18/{\gamma _{\text{c}}}\)

\({\gamma _{\text{c}}}\) :

Concrete partial coefficients, equal to 0.15

k :

\(1+\sqrt {\frac{{200}}{d}} \leq 2.0\)

\({k_1}\) :

A coefficient considering the effects of axial load forces on the stress distribution, equal to 0.15

\({\phi _{\text{c}}}\) :

Resistance factor of the concrete, equal to 0.65

\({\phi _{\text{s}}}\) :

Resistance factor for non-prestressed reinforcing bars, equal to 0.18

\(\alpha\) :

Angle between the concrete compression strut and the wall axis perpendicular to the shear force. The recommended limits of \(\cot \alpha\) is from 1 to 2.5. In this paper, the value of \(\cot \alpha\) is assumed equal to 1

\(\theta\) :

Angle between the concrete compression strut and the wall axis perpendicular to the shear force. It equals 45° for the axial load ratio \(\leq 0.1;\) 35° for the axial load ratio \(\geq 0.2,\) and varies linearly for the axial load ratio between 0.1 and 0.2

\(\beta\) :

Factor accounting for the shear resistance of cracked concrete, chosen as 0.18

\(\lambda\) :

Aspect ratio coefficient which equal 1.5 for \(\lambda \leq 1.5,\) 2.2 for \(\lambda \geq 2.2,\) and varies linearly for \(1.5 \leq \lambda \leq 2.2\)

\(\lambda ^{\prime}\) :

Modification factor to reflect the reduced mechanical properties of lightweight concrete relative to normal weight concrete of the same compressive strength. It equals 1.0 in the paper

\({\gamma _{{\text{RE}}}}\) :

The seismic action coefficient, which is equal to 0.85

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Acknowledgements

The research for this paper was supported by the National Science Foundation of China under Grant no. 51478063.

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Authors and Affiliations

  1. Department of Civil Engineering, Chongqing University, Chongqing, 400044, People’s Republic of China

    X. L. Chen, J. L. Yao & J. F. Gan

  2. Department of Key Laboratory of New Technology for Construction of Cities in Mountain Area, Chongqing University, Chongqing, 400044, People’s Republic of China

    J. P. Fu

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  1. X. L. Chen
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Correspondence to J. P. Fu.

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Chen, X.L., Fu, J.P., Yao, J.L. et al. Prediction of shear strength for squat RC walls using a hybrid ANN–PSO model. Engineering with Computers 34, 367–383 (2018). https://doi.org/10.1007/s00366-017-0547-5

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