Simple estimation of the maximum elastic roof displacement of a slender cantilever RC wall accounting for dynamic effects

Abstract

This article presents a simple method for estimating the maximum elastic roof displacement of a slender cantilever reinforced concrete RC wall, accounting for dynamic effects, named δ. The formulation computes δ as a function of an equivalent concentrated lateral load, acting at an equivalent height hν . The dynamic effects are included by calculating the equivalent height of a load pattern representative of the first mode of vibration, h1 , and reducing it to be consistent with a lateral load distribution that imposes a deformed shape representative of higher modes upon the wall. This is executed when dividing h1 by the dynamic amplification factor ων , previously defined for capacity-based shear design. The displacement δ is obtained by imposing nominal yielding conditions at the critical cross-section of the wall, for the lateral load acting at the reduced height hν . Including well-established expressions for the nominal yielding curvature of RC cross-sections, a new formula for computing the maximum elastic top lateral drift ratio of the wall as a function of dimensionless numbers associated to the wall geometry, topology, and reinforcing steel is proposed. Using an example, it is shown that the novel expression provides more conservative results compared to those obtained with classical and recently proposed formulas, noting that this results into larger extensions of horizontal boundary confinement elements of a wall, for the same ultimate roof displacement. To conclude, the formulation is presented in a way suitable for its implementation within the Chilean code, and in simplified versions useful for quick hand calculations.