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Upper bound on the lateral stiffness of masonry walls with a new opening reinforced by a steel frame
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DOI：10.1007/s10518-026-02589-4.png)
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Abstract
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Seismic codes mandate that introducing an opening into a masonry wall shall not reduce its lateral stiffness by more than a prescribed percentage of its initial value. Compliance with this requirement typically involves installing a steel frame along the perimeter of the rough opening, anchored to the adjacent masonry to provide lateral stiffness through steel-masonry composite action. While researchers and practitioners calculate the lateral stiffness of frame-reinforced perforated masonry walls using specialized software, these numerical models have never been validated against analytical or experimental results due to a lack of published benchmark data, leaving their reliability unassessed. To provide unambiguous benchmarks, this paper presents an upper-bound analytical model. The paper also presents eight case studies demonstrating that typical openings and steel sections result in excessive stiffness reductions even under upper-bound assumptions. This finding suggests that practitioner software may significantly overestimate lateral stiffness, implying that conventionally designed frames fail to meet seismic performance targets. Furthermore, the proposed model establishes a more appropriate threshold for lateral stiffness reduction and indicates that post-cracking stiffness reduction should likewise be subject to code limits.
Keywords:
Analytical stiffness
Limiting stiffness
Relative stiffness reduction
Stiffness loss
Translational stiffness
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