Author: Adisorn Owatsiriwong, D. Eng.

🔍 Problem Statement

In modern seismic design, shear walls are critical lateral force–resisting elements. Traditional design workflows distribute shear forces using simplified assumptions: uniform distribution, tributary areas, or hardcoded templates.

But what if:

The wall is non-rectangular?
Composed of multiple inclined or disconnected legs?
Subjected to both global shear and torsion?

These complexities demand a more general and physically correct approach.

💡 Our Approach: FEM-Inspired Shear Solver Using Rigid Diaphragm Constraints

We developed a shear distribution solver that:

Works for any wall shape (I-shaped, L-shaped, zigzag, diagonal)
Uses leg geometry only — no mesh, no shell
Honors global equilibrium for shear and torsion
Produces transparent force outputs leg-by-leg

🧱 The Formulation

We treat the wall system as a rigid diaphragm–connected group of shear elements. Each wall leg is:

A discrete shear spring
Oriented in its actual inclined axis
Assigned a shear stiffness:
ki = G⋅Ai/Li

🧠 Displacement Transformation

For each leg at centroid (xi,yi), the displacement due to rigid body motion is:

[uxuy]=[1 0−yi ; 0 1 xi] [UVΘ]

Where:

U,V = global translations
Θ = in-plane rotation (torsion)
u_leg = projection onto leg axis direction (via angle α)

🔄 Global Equilibrium

All shear legs contribute to resisting:

Horizontal shear: Vx, Vy
Torsion: T

We assemble:

Kglobal=∑T1T⋅T2T⋅ki⋅T2⋅T1

Then solve:

[VxVyT] = Kglobal⋅[UVΘ]

And finally back-calculate individual leg shear force:

Vleg=ki⋅uleg

✅ Advantages of This Method

Generalizable: works for any shape
Physically consistent: honors stiffness, geometry, and equilibrium
Code-transparent: fully written in MATLAB
FEM-inspired: but requires no mesh or commercial engine

📊 Applications

This solver is already integrated into our WALLCHECK platform to:

Perform shear check per ACI 318
Combine direct + torsional shear in a single step
Output detailed per-leg reports (Vu, φVc, Vs, Asv/s)

🚀 What’s Next?

With this solver in place, we are now building a graphical interface to:

Import forces directly from ETABS
Visualize shear demand distribution
Enable one-click reporting

Soon, anyone can verify their shear wall design with clarity, control, and confidence.

🧠 From Theory to Practice: General FEM-Based Shear Distribution for Complex Shear Walls