VBA-based modeling of nonlinear P–M interaction in rectangular and T-shaped RC shear walls

Abstract

Background
Reinforced concrete (RC) shear walls provide critical lateral stiffness, strength, and energy dissipation in mid- and high-rise structures. Accurate analysis of irregular wall geometries remains challenging due to nonlinear stress distributions, complex strain compatibility, and reinforcement-layout sensitivity. The Egyptian Code of Practice ECP-203 provides the stress-block constitutive framework but does not provide design-aid interaction diagrams covering the irregular wall geometries (T-shaped) of contemporary interest.


Methods

A Visual Basic for Applications (VBA) algorithm was developed to generate axial–flexural (
P
–
M
) interaction diagrams for rectangular and T-shaped RC shear walls in compliance with ECP-203, integrating the ECP-203 equivalent rectangular stress block, plane-section strain compatibility, and sectional equilibrium with a parametric sweep on the dimensionless neutral-axis position
V
 = 
c
/
t
and an inner fixed-point iteration on the code-defined strength-reduction factors. The relative-error convergence tolerance is
ε
tol
 = 1 × 10
−3
.



Results

A fibre-discretisation study showed that a (3–9–3) bar arrangement reproduces the analytical ECP-203 interaction diagram to within ± 5%, with deviations rising to approximately 15% for the simplest (1–1–1) discretisation, confirming monotonic mesh convergence of the algorithm. Validation against SP-Column software yielded deviations within ± 5% (rectangular) and ± 7% (T-shaped); the latter is consistent with the established methodological residual between the ECP-203 equivalent stress block and fibre-based nonlinear analysis. Measured runtimes are ≈ 1.2 s per
ρ
-curve for the rectangular section and ≈ 1.8 s for the T-section on a standard desktop an order of magnitude faster than equivalent SP-Column runs.



Conclusions

The proposed VBA framework provides a transparent, computationally efficient, code-compliant tool for generating
P
–
M
interaction diagrams of rectangular and T-shaped RC shear walls. The framework is suitable for design and educational use and offers an open, accessible alternative to proprietary software, supporting performance-based RC shear-wall design under ECP-203.