An L-, U-, E- or other (in plan) shaped building where two wings may oscillate out-of-phase, leading to large shear stresses in floor and/or roof diaphragms.

If the plan setback is at least 15% of both plan dimensions, then the setback is considered to form a re-entrant corner.

REC_diagram_Charleson_1

Examples of building shapes with re-entrant corners (A. Charleson, Seismic Design for Architects, Architectural Press 2008, p133 fig. 8.10)

REC_diagram_1

This diagram illustrates the principle that a 15% plan setback is required in both directions for it to be considered a re-entrant corner.

REC_FEMA454_1

Movement of the wings of an L-shaped building during an earthquake results in high shear stresses combined with a stress concentration at the re-entrant corner; this is aggravated by torsional effects which develop since the center of mass and the center of rigidity cannot coincide in this form. (FEMA 454)

REC_USA_NISEE_1REC_USA_NISEE_2

West Anchorage High School suffered extensive damage in the 1964 Alaska earthquake. Stress concentration at re-entrant corner caused damage in the concrete roof diaphragm of this reinforced concrete building. The left photo shows building damage, and floor plan drawing is shown on the right  (Courtesy of the NISEE, University of California, Berkeley)

REC_India_Brzev_1

An L-shaped building with re-entrant corner, India (S. Brzev)