Torsional capacity of reinforced concrete U-shaped walls
Introduction
Reinforced concrete (RC) walls provide the primary lateral resistance from wind and earthquakes in RC buildings internationally. There are many geometrical shapes used for RC walls, generally dictated by architectural requirements, as well as those requirements from an engineer. For example, RC U-shaped walls are popular in construction practice as, from the perspective of an architect, they enclose elevator and stair shafts or toilets and increase the net lettable area, while, from the standpoint of an engineer, the non-planar wall provides stiffness in all directions. Further demand for more efficient use of the building, which is particularly warranted by architects, can result in the RC U-shaped core walls being placed on the periphery (Fig. 1a). This type of RC building configuration with an asymmetric core wall is particularly common in regions of low-to-moderate seismicity, such as Eastern North America [42], Australia [22], and Hong Kong [45]. Furthermore, one of the primary methods of strengthening older buildings is to add RC walls to the periphery [32]. The RC wall is typically much stiffer than other structural elements in the building, which creates plan asymmetry due to the offset of stiffness from the center of mass. Thus, these building configurations have the potential to create a torsional response (i.e., twist) when subjected to earthquake ground motions. In fact, even for symmetric structures, accidental loading and mass eccentricities are inevitable and can trigger critical, unforeseen torsional responses. An example of a torsional response of a symmetric structure is the Atwood building, located in a highly seismic area of Alaska, which has repeatedly shown dominant, twisting actions from moderate-to-large earthquake events [9], [23]. Furthermore, in low-to-moderate seismic regions, it is common to find just a single, peripheral core wall, which alone needs to resist the twisting actions of the building [22]. In these regions, it is possible that the additional stresses induced in the wall from the twisting actions will result in a premature and brittle failure. This building typology is similar to the CTV building in Christchurch, which catastrophically collapsed on 22 February 2011 during a moment magnitude (Mw) 6.2 earthquake event, tragically taking the lives of 115 people [25]. A shown in Fig. 1b, the peripheral core wall to its North creates in-plan asymmetry, which was likely to have led to an increase in building deformations during the 2011 earthquake event due to the torsional rotation of the building [13], [35].
It is possible that the additional stresses induced in a RC wall due to the twisting actions result in a premature and brittle failure, unless it has been designed and sufficiently detailed for such actions. However, even in regions of high seismicity, building codes do not cater for the design of open-section walls (e.g., U-shaped) subjected to torsion. For example, the torsional behavior of elements governed by circulatory torsion under monotonic loading have been simulated to an acceptable degree of accuracy using truss models [24]) and the design requirements for torsion in most structural concrete building codes [e.g., [1]] are based on these models. However, the torsional performance and capacity of open sections that are governed by warping torsion and subjected to highly nonlinear cyclic demands, such as RC U-shaped walls under earthquake loading, are difficult to quantify and cannot be confidently designed using current building codes [36]. Importantly, if the U-shaped core wall does not have the required reinforcement detailing for the torsional demand, extensive damage will occur to structural (and non-structural) elements. Damage to RC walls results in large post-earthquake retrofit costs or more often requiring demolition of the entire building, assuming that the worst-case scenario of catastrophic building collapse did not occur.
There is a very limited amount of research that has focused on the torsional performance of RC walls. Some torsion related experimental research has been conducted on RC U-shaped beams [10], [27], [58] due to the wide application of these elements in rail viaduct engineering [59]. However, the experimental results from beam specimens cannot be extrapolated to determine the expected performance on walls given the differences in: (i) boundary conditions and restraints, (ii) reinforcement detailing, (iii) confinement effects, (iv) axial load, and (v) loading conditions. To the knowledge of the author, only two experimental campaigns have ever focused on the torsional capacity of RC walls: Peng and Wong [44] tested half-scale wall units subjected to pure torsion. However, these specimens were all rectangular in cross-section, whereas RC core walls typically have non-planar sections (i.e., U-shaped). Some core walls specimens with H-shaped cross-sections were tested for torsion in Maruta et al. [36], however a highly-contentious scale factor of 1:12 was employed. While there has been some recent testing on RC U-shaped walls [5], [17], only a small twist was applied to these specimens at different loading stages to provide information on the torsional stiffness rather than determine the torsional capacity.
This research focuses on the torsional capacity of RC U-shaped walls. A mechanical model is introduced, which was originally developed to determine the torque-rotation behavior of RC U-shaped beams under pure torsion and is further extended here for RC U-shaped walls. A validated finite element modelling program is used to find the torque-rotation behavior for a range of RC U-shaped walls subjected to pure torsion, the results of which are compared to the estimates provided by the mechanical model. A parametric study is undertaken using the mechanical model to find the ultimate torque capacity for RC U-shaped walls with a large range of typical design values. A nonlinear regression analysis is used to develop an expression that can readily determine a reasonable estimate of the torque capacity of RC U-shaped walls.
Section snippets
Mechanical model
According to the theory proposed by Vlasov [55], three types of internal forces simultaneously exist when a thin-walled section is subjected to pure torsion: warping torque [Tω, Fig. 2a(ii)], warping moment (Mω) which is a result of the warping torque, and circulatory torque [Tc, Fig. 2a(iii)] which is a result of the circulatory torque. For closed-boxed sections, circulatory torsion governs the behavior and the effects due to warping torsion are negligible. However, for an open section, such
Finite element modellng with vector3
VecTor3 [15] is a state-of-the-art nonlinear finite element modelling (FEM) program used for RC 3-dimensional solids and using the Disturbed Stress Field Model (DSFM) [53]. The DSFM improves the prediction of the behavior of RC elements [14]) relative to its predecessor, the Modified Compression Field Theory (MCFT) [54]. VecTor3 has been used in previous research investigations for modelling and predicting the seismic performance of U-shaped walls [18], [20], [21] and H-shaped walls [43]. The
Parametric study
A low-rise (LR) RC U-shaped core wall is used as the “master” wall for the proposed parametric study, where the design parameters of this wall will be varied one at a time to observe their dependency on the torsional capacity. The size of the LR wall was determined by using the internal dimensions of a 500 kg, 6-person elevator car from RLB [49]. The corresponding wall web length (Lw), flange length (Lf), and thickness (tw) are 2000 mm, 1500 mm, and 200 mm respectively. Two layers of evenly
Future research
The behavior of RC U-shaped walls subjected to earthquake ground motions is complex due to the effects of bending (flexural) moments, shear, axial loads, and torsion, as well as frame-wall or slab-wall interactions. Experimental research is currently being proposed by the author focusing on testing large-scale RC U-shaped wall specimens subjected to a combination of flexure and torsion, which will help to further validate the work undertaken here. Future numerical research will also focus on
Conclusions
RC U-shaped walls are popular in construction, providing large lateral resistance in all directions while enclosing elevators or stair shafts. In regions of low-to-moderate seismicity, it is not uncommon to find these structural elements acting as peripheral core walls, where an offset of structural stiffness from the center of mass would cause a large torsional response in the event of an earthquake. Given the paucity of research that has focused on this topic, this paper investigates the
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
References (60)
- et al.
Impact of bi-directional loading on the seismic performance of C-shaped piers of core walls
Eng Struct
(2020) - et al.
Experiments and calculation of U-shaped thin-walled RC members under pure torsion
Eng Struct
(2016) - et al.
Behaviour of U-shaped RC walls under quasi-static cyclic diagonal loading
Eng Struct
(2016) - et al.
Generalized thin-walled beam models for flexural-torsional analysis
Comput Struct
(1992) - et al.
Nonlinear seismic modeling of reinforced concrete cores including torsion
Eng Struct
(2017) - et al.
Behavior of reinforced concrete walls subjected to monotonic pure torsion—An experimental study
Eng Struct
(2011) A numerical approach to the complete stress-strain curve of concrete
Cem Concr Res
(1973)- et al.
Analysis of core wall structure subjected to applied torque
Build Sci
(1973) - et al.
Parametric study on mixed torsional behavior of U-shaped thin-walled RC girders
Adv Civ Eng
(2018) Building Code Requirements for Structural Concrete (ACI 318–14) and Commentary (ACI 318R–14)
(2014)