Closed‐Form Critical Buckling Load of Coupled Shear Walls With Local Shear Deformation: An Independent‐Subsystem Decomposition for Generalized Continuous Models

The global stability of coupled shear walls under distributed axial loading remains without a closed‐form solution when local wall shear deformation is simultaneously considered. Existing closed‐form solutions are restricted to concentrated loads applied at the top, and existing distributed‐load solutions exclude local wall shear deformation. No explicit non‐iterative expression has previously been derived for the distributed‐load case in any of the three generalized continuous models reported in the literature (MSB, GCTB, and GSB). This paper derives such expressions through a decomposition into independent subsystems of the sixth‐order differential equation governing the behavior of each generalized continuous model. The decomposition partitions the total vertical load into two components whose associated subsystem equations are treated as uncoupled: the first is structurally identical to the classical sandwich beam subjected to distributed loading and directly recovers the reference critical load; the second takes the form of the classical sandwich beam under a concentrated top load with an effective negative load, whose analytical solution quantifies the stiffness reduction attributable to the local shear deformation of the wall. The total critical load is expressed compactly as the product of the classical critical load and a reduction factor characteristic of each model, evaluated explicitly without iteration. For the MSB and GCTB models, this factor involves the combined shear stiffness, whereas for the GSB model it depends exclusively on the local shear stiffness, reflecting the distinct kinematic coupling topology of each formulation. Validation against equivalent‐frame finite element models developed in SAP2000, covering an asymmetric single‐bay wall system and a three‐bay configuration, confirms that, for buildings of 10 stories or more, the signed relative errors remain below the 5% threshold commonly accepted in structural engineering practice. The GSB model consistently provides the closest agreement with the finite element results. A sensitivity analysis of this reduction factor reveals a monotonic decrease with increasing coupling beam depth and an asymptotic convergence toward unity as local shear effects vanish in the high‐slenderness limit. The resulting expressions are fully explicit, require the evaluation of only five dimensionless parameters per model, and constitute a practical analytical tool for the preliminary design and global stability assessment of coupled shear wall systems. The proposed method is valid for both single‐bay and multi‐bay configurations, though larger error margins should be expected in the latter.