Upper-bound yield-line rigid-plastic plane-stress analysis of core coupling-beams in tall buildings
Authors: Gurley C. 
Published: March 2011

Cores in tall buildings sub-divide and fire-separate vertical riser services such as lifts, stairs, air-conditioning systems, utilities and rooms requiring access to plumbing. This paper addresses the structural design of load-bearing concrete cores as distinct from framed structural steel cores fire-protected by gypsum plasterboard. Concrete cores are much more resistant to abnormal events such as earthquake, terrorist attack and disproportionate collapse, and also provide huge increases in structural stiffness and damping. Concrete cores seem to be universal for tall buildings in Australia perhaps because of local experience in the construction of wheat silos. A decision for a concrete core leaves open the decision to use concrete or structural steel for floor and façade framing. Concrete core-walls are penetrated by vertical families of openings for doors to stairs, lifts and other spaces. These openings separate the core as a whole into a number of sub-cores linked by coupling-beams (the residual strips of concrete core-wall above and below openings). Coupling-beams can be thought of as large-scale shear connectors providing composite action between distinct sub-cores. First yield will often occur in coupling-beams and spread vertically. The span/depth ratio of these beams is determined by architects and lift engineers and is often well into the ‘deep-beam' range prone to brittle behaviour. American seismic design practice, based on experimental research at the University of Canterbury, New Zealand, requires complete ‘X-reinforcement' consisting of tied rebar cages (as for columns) on both diagonals of coupling-beams. X-reinforcement can definitely improve the ductility of otherwise brittle elements. It does, however, create practical construction problems: ties are closely spaced (for Bauschinger buckling) and the crossing X-cages together with the ‘basketing' reinforcement (to avert injuries from falling concrete chunks) can amount to six to eight (or ten) layers of reinforcement across the thickness of a wall, which may also require 40 mm cover for fire-rating. Walls of 250 mm thickness are barely possible and 300 mm thick walls present difficulties. For regions of lower earthquake risk, such as the UK and Australia, one wonders whether there are reasonable alternatives to X-reinforcement, particularly when the beam size provided by lift engineers is large and only minimal rebar is required. Minimal rebar is not much more than the basketing reinforcement required with X-bars, and in some cases may be ample without large reliance on ductility. In New Zealand, more recent codes do permit buildings of limited ductility with stronger elements. In any case, the rigid-plastic collapse mechanisms provided and discussed here are quite capable of including X-bars and the present approach just provides the simplest first-pass treatment. The analyses presented here seem to agree with the conclusion reached by the late Professor Tom Paulay from experimental work at Canterbury beginning in 1967: that the bending ‘compression' rebars may be highly stressed in tension and this does reduce strength and ductility. The paper studies a range of in-plane yield-line mechanisms, starting with an almost conventional bending mechanism and then considering three shear mechanisms before arriving at a combined (bending/shear) mechanism which seems to be ‘exact'. One aim is to exemplify the variability of upper-bound analysis where, in this case, the highest bound is 2·6 times the ‘exact' result.