The analysis result shows that the interaction effect affects the distribution of shear stress, vertical stress and horizontal bending stress in the shear wall within a height equals the[r]
Introduction 1
A shear wall is a vertical structural element designed to withstand shear, moment, and axial loads caused by lateral wind forces and gravity loads from other structural components, while also providing lateral bracing for the overall structure In contrast, a transfer beam is a large, deep structural member that redistributes loads from the upper shear walls or columns to the lower framed structure, and it is categorized as a deep beam when its span-to-depth ratio is less than 2.5.
Shear wall structures have become increasingly popular in the construction of high-rise buildings, particularly for service apartments and office towers This system is recognized for its efficiency in providing structural stability for multi-storey buildings, especially those ranging from 30 to 35 storeys (Marsono and Subedi, 2000) The use of reinforced concrete shear walls is widely regarded as one of the most effective methods for ensuring lateral stability in tall buildings Notably, over the past 30 years, no tall buildings with shear wall elements have collapsed during severe wind or earthquake events (Fintel, 1995).
In tall buildings, shear wall configurations can impede access to the public lobby and car park areas at the base To address this issue, large openings at ground level are necessary, which can be facilitated by employing substantial transfer beams that gather loads from the upper shear walls and distribute them to widely spaced columns This structural arrangement effectively separates the tower into two sections: the upper portion featuring shear wall units and the lower portion typically designed as a conventional framed structure, often serving as a car park podium.
Problem Statement 2
The transfer beam-shear wall system plays a crucial role in high-rise building construction, making the stress behavior at their interaction zone a focal point for researchers Understanding these stress behaviors is essential, as inadequate analysis can result in unfeasible designs or even flawed structures, potentially leading to catastrophic failures.
The design of a transfer beam-shear wall system primarily relies on the designers' experience and structural simplifications, often modeling the beam as an equivalent grid structure.
The interaction between the transfer beam and the supported shear walls is often overlooked in structural analysis, potentially resulting in unrealistic designs for internal forces and inadequate steel reinforcement specifications.
The complexity of transfer beam usage is largely due to the interaction between the beam system and the upper structural walls, which significantly impacts stress redistributions in both the transfer beam and the shear walls in the interactive zone (Kuang and Zhang, 2003) However, current design practices for transfer beam-shear wall systems in tall buildings typically overlook this interaction effect, failing to account for its influence on the overall structural behavior of the system.
Modeling the behavior of transfer beams using standard beam or deep beam theories is inadequate due to the significant beam-wall interaction Additionally, lateral loads, such as wind forces acting on the shear wall, generate extra stresses on the transfer beam as the shear wall directly transfers vertical stress and moments to it.
Objective 3
The primary aim of this project is to analyze the stress distribution in a shear wall-transfer beam structure, focusing on the interaction effects between the wall and beam, utilizing LUSAS 13.5 finite element software A standard finite element model of the shear wall-transfer beam is developed for the analysis The study derives key stress parameters, including vertical stress, horizontal stress, shear stress, and bending moment, to elucidate the behavior of the transfer beam and shear wall under the influence of their interaction.
The shear wall-transfer beam structure will be analyzed in two scenarios, starting with vertical loads only This analysis aims to compare the stress distribution of the structure with findings from J.S Kuang and Shubin LI (2001), who utilized the finite element software SAP 2000 in their earlier research.
The structure is analyzed under vertical and wind loads to assess its stress behavior from the added lateral wind force This analysis helps determine the shear force and bending moment in the beam, which will be essential for designing the reinforcement of the transfer beam.
Research Scopes 4
The scopes of research that needs to be carried out are as follows:
1 Select a case study comprising in plane shear wall supported by a transfer beam to study the stress behaviour of the shear wall-transfer beam structure
Develop a 2D linear elastic finite element model featuring an in-plane shear wall supported by a transfer beam The entire structure will be analyzed under the influence of wind loads, as well as vertical dead and live loads.
Using the finite element method and Lusas 13.5 software, this analysis focuses on the shear wall-transfer beam structure model to investigate the interaction effects between the transfer beam and shear wall The study aims to elucidate key structural behaviors, including vertical stress, horizontal stress, shear stress in the wall, and the bending moment in the beam.
This study compares the structural behaviors of shear wall-transfer beam systems analyzed through the finite element method, utilizing Lusas 13.5 software, with results obtained from J.S Kuang and Shubin Li's (2001) analysis using SAP 2000 finite element code.
5 Design for the reinforcement of the transfer beam as per Ciria Guide 2: 1977 and BS8110 based on the results of analysis in case 2
2.1 Finite Element Modelling of Transfer Beam – Shear Wall System Using Finite Element Code SAP 2000
In a study conducted by J.S Kuang and Shubin Li (2001), a finite element model was developed to analyze the interaction effects between transfer beams and shear walls, utilizing four-node square plane-stress elements for the transfer beam, support columns, and walls The analysis was performed using the finite element software SAP2000, which facilitated the computation of structural stresses.
To analyze the interaction effects between the transfer beam and shear wall on structural behavior, the shear wall height (H) is set to exceed twice the total span (L) of the transfer beam Additionally, the beam's breadth is defined as twice the thickness of the shear wall The finite element model of this system is illustrated in Figure 2.1.
2.1.1 Structural Behaviour - Vertical Stress in Wall
The investigation carried out by J.S Kuang and Shubin LI (2001) shows that vertical loads are generally transferred to the beam system through the compression arch as shown in Figure 2.3
Figure 2.2 Typical transfer beam–shear wall system
Elements for transfer beam Elements for column
H, height of shear wall hc, width of column h b , height of beam shear wall
Figure 2.3 illustrates the vertical stress distribution along the height of a shear wall under a uniformly distributed vertical load (w) per unit length Despite the uniform loading, the vertical stress becomes non-uniform in the lower section of the wall This variation occurs as the vertical load is transmitted to the support columns via a compression arch, which is influenced by the interaction between the transfer beam and the shear wall.
Beyond a height approximately equal to the total span of the transfer beam (L) from the wall-beam surface, the interaction between the transfer beam and the shear wall minimally affects the vertical stress distribution, leading to a uniform stress pattern Within the height L, the vertical stresses of the wall experience redistribution, with the most significant changes occurring at the wall-beam interface.
2.1.2 Structural Behaviour - Horizontal Stress in Wall
The distribution of the horizontal stress σ x is shown in Figure 2.4 J.S Kuang and Shubin LI (2001) prove that the shear wall is almost in compression in the
The distribution of vertical stress in a shear wall under vertical loading reveals that horizontal stress intensity varies with height Specifically, the horizontal stress (σ x) is minimal at the wall-beam interface and approaches zero beyond a height equal to the total span of the transfer beam (L) from this interface.
When the depth of a transfer beam is small, it experiences full tension along its span due to the interaction with the wall, as illustrated in Figure 2.4(a) In contrast, a deeper beam may exhibit some compression stress in its upper section, although this compression zone remains limited Figure 2.4 clearly indicates that a transfer beam does not function like a conventional beam in bending or a deep beam; instead, it operates in full tension or flexural tension along its span because of the wall-beam interaction Consequently, a transfer beam that supports in-plane loaded shear walls should be regarded as a flexural-tensile member, distinguishing it from typical beams or deep beams.
Figure 2.4 Distribution of horizontal stress in the wall–beam system
2.1.3 Structural Behaviour - Shear Stress in Wall
The distribution of shear stress in the wall-beam system reveals that shear stress is primarily concentrated in the lower section of the shear wall, with its maximum intensity occurring at the wall-beam interface, as identified by J.S Kuang and Shubin Li (2001) Additionally, the shear stress intensity is zero at heights above L from the wall-beam interface, indicating that the interaction effect does not influence shear stress distribution in the upper portions of the shear wall.
2.1.4 Structural Behaviour – Bending Moment in Beam
The distribution of bending moments in a transfer beam reveals that the maximum bending moment is located at the mid-span, decreasing towards the support columns, as illustrated in Figure 2.6 Research by J.S Kuang and Shubin Li (2001) identifies two contraflexural points near the beam's ends, indicating the presence of negative moments in these areas.
Figure 2.5 Distribution of shear stress in the system
Figure 2.7 illustrates the relationship between bending moments at mid-span and varying depth-span ratios for different support stiffness values (hc/L) The data indicates that an increase in the depth of the transfer beam leads to a corresponding rise in the bending moment, assuming the support stiffness remains constant.
As depicted in Figure 2.7, an increase in the stiffness of support columns results in a decrease in the bending moment of the beam When the support columns possess sufficient stiffness, they effectively restrain the beam's displacement, causing the transfer beam to function like a fixed beam, with contraflexural points of the bending moment typically located between 0.1L and 0.2L from the beam's supports Conversely, if the support columns exhibit lower stiffness, the beam behaves as a simply supported beam.
Figure 2.7 Variation of bending moment at mid-span against different depth– span ratios for different support stiffness
Figure 2.6 Variation of bending moment in the beam along the span
J.S Kuang and Shubin Li (2001) conducted a finite element analysis on the interaction behavior of the transfer beam-shear wall system, leading to the creation of interaction-based design tables for assessing internal forces in transfer beams that support in-plane loaded shear walls These design tables utilize an equivalent portal frame model, as illustrated in Figure 2.8 Notably, the model introduces an axial force (T) in the transfer beam, a result of the interaction with the shear wall, and reveals that the bending moments (M2 and M3) are unequal due to the shear wall absorbing a portion of the bending moment from the transfer beam.
Interaction-based design tables are presented in Tables A1 to A6 in Appendix
The design of a transfer beam-shear wall system under uniformly distributed loading involves widths of the transfer beam that are typically double or triple the thickness of the shear wall, represented as b = 2t and b = 3t Key design parameters include the span-to-depth ratio (L/hb) of the transfer beam and the relative flexural stiffness of support columns (hc/L) Utilizing provided tables, engineers can easily calculate critical values such as the maximum vertical stress in the shear wall (σy) and the bending moments in the beam and support columns (M1, M2, M3, and M4).
Figure 2.8 Equivalent portal frame model
2.1.6 Interaction-Based Design Formulas for Transfer Beams Based on Box Foundation Analogy