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

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.


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