Backbone M-θ & Deformation Classification for Extended Endplate Connections

Column stiffeners
Column
Beam
End-plate
Bolts

Lengths in mm, stresses in MPa. fu for the column, fy for the beam, and fy for the bolt are shown for reference — the models don't use them. To use a different section table:

* For a cyclic backbone, the strength parameters should be amplified by 10-15% to account for cyclic hardening.

Connection geometry & assembly

Member lengths and end-plate edge margins are schematic. Section dimensions, bolt gauge and row pitch follow the inputs.

About: Extended endplate connection model

What this tool does

Predicts the moment–rotation (M-θ) backbone of extended endplate beam-to-column connections using the MVLR model (Ding and Elkady, 2025) or the MISO ANN, MIMO ANN and XGBoost machine-learning models (Ding and Elkady, 2026), with optional uncertainty bands for the machine-learning models. A second tab predicts the expected deformation mode with a Random Forest classifier. You can save each plot as PNG or SVG and the curve data as CSV.

Backbone with smooth transition

This optional MVLR branch starts at (θy, My), where θy = My/Ke, and meets the existing hardening line. Its stiffness is Ktrans = 0.63 Ke0.89, using stiffnesses in kN·m/rad. The intersection rotation is (Mye − Ksθye − My + Ktransθy)/(Ktrans − Ks), where θye = Mye/Ke and Ks is the slope of the existing hardening branch. Capping and post-peak branches remain unchanged. Ktrans has COV 0.23; the uncertainty option varies only Ktrans by ±z × 0.23 Ktrans, holding other parameters fixed. If the transition has no valid intersection before capping, the original curve is retained and a message is shown.

Author and contact

Developed by Dr Ahmed Elkady, University of Southampton. Email: a.elkady@soton.ac.uk · Homepage

How to cite

Disclaimer

These tools are provided for research and educational purposes only, without warranty of any kind. The predictions are estimates from the cited models and are only as reliable as those models within their validity ranges. Results should be checked independently by a qualified engineer before being used in design or assessment.

© 2026 Ahmed Elkady, University of Southampton. All rights reserved.