The analysis of a framed building with shear walls under both horizontal and vertical loads is a complex, three-dimensional problem. With the advent of advanced computer programs, conducting a three-dimensional analysis has become more manageable. These programs enable designers to model the structure accurately, reflecting the behavior of the building as it responds to the applied forces. Although time-consuming, this method is sometimes the only viable approach, especially in the case of dynamic analysis.
However, in many scenarios, a simplified approach can be applied, breaking down the problem into two-dimensional components. While this approach reduces the complexity, it requires the designer to fully understand the behavior of the structure to ensure the accuracy of the analysis. This article aims to explore the behavior of combined shear wall and framed structures, methods of apportioning loads, and the various failure modes of shear walls.
Behavior of Combined Shear Wall and Framed Structures
Framed buildings with shear walls are commonly used to resist lateral loads such as wind and earthquake forces. The combined behavior of these components is crucial to the overall performance of the building under load. Shear walls are typically designed to resist horizontal forces, while the frame handles vertical loads. The interaction between these two systems, however, is more complex than a straightforward separation of their functions.
The behavior of the structure depends largely on the relative stiffness of the shear walls and the frame. In some cases, the walls may attract most of the horizontal load, while the frame carries more of the vertical load. The load distribution is not fixed across the height of the structure; it varies depending on the height, stiffness of each component, and the position of the load. This complexity requires a comprehensive understanding of the behavior of both shear walls and framed structures to ensure proper load distribution.
Methods of Apportioning Loads
In a structure with combined shear walls and frames, the loads are distributed between these components based on their relative stiffness. The force acting on the shear wall is shared with the frame and the core, and this distribution depends on several factors, such as the position of the load and the stiffness of each component.
It is commonly assumed that the floors are rigid in-plane, meaning they do not deform significantly in the horizontal direction. Each component’s stiffness can be represented by a stiffness parameter, Kj, and the center of rotation of the building is determined statically. The force per component (Fj) resulting from the total force on the shear wall (Ft) can then be calculated based on this stiffness.
In many cases, the torsional stiffness of the structure can be ignored except for core walls, which may have substantial openings. This simplified approach is often valid when the center of rotation is close to the building’s center. Additionally, the torsional stiffness is assumed to be directly related to the in-plane inertia of the components, especially when horizontal deflections are primarily caused by flexure.
Frame and Shear Wall Behavior
The deformation behavior of shear walls and frames is a key factor in determining how they distribute loads. When subjected to horizontal loads, rigid frames and short shear walls typically deform in a pure shear mode. This results in a concave deflection profile in the upper part of the structure. On the other hand, cantilever shear walls primarily deform in a flexural manner, resulting in a convex curvature that persists throughout the height of the wall.
In cases of squat and coupled shear walls, the deformation is a combination of both shear and flexural actions, leading to a more complex deflection profile. Understanding these behaviors is essential for determining how the loads are shared between the frame and the shear wall.
In a symmetrical arrangement of shear walls and frames, the deflection of both components is identical due to the high in-plane stiffness of the floors. This forces the walls and frames to adopt the same deflection profile. However, frames and walls do not always attract a fixed percentage of the load throughout their height. In fact, rigid frames tend to attract a higher proportion of the load at the top of the structure, while attracting very little at the base due to their greater flexibility at lower levels.
In contrast, non-symmetrical arrangements of shear walls lead to a rotational effect about a vertical axis. The center of rotation will vary from floor to floor, and the rotation will not continuously increase in one direction. In such cases, a three-dimensional analysis is required to accurately predict the behavior of the structure.
Coupled Shear Walls
A coupled shear wall structure consists of two or more shear walls connected by beams or slabs at each floor level. This design can enhance the lateral stiffness of the building, improving its ability to resist horizontal loads. When the beam stiffness is small relative to the shear wall stiffness, or the beam-wall connection behaves like a hinge, the structure behaves like individual cantilever walls. In this case, the individual walls will have similar deflection profiles, although the tension in the ties increases with height, which introduces some restraining forces on the walls.
However, if the beam-wall connection is moment-resisting, the behavior of the structure changes. In this case, the structure behaves partly like individual cantilever walls and partly like a single wall bending about a common neutral axis. The degree of moment connection influences the extent to which the structure behaves as a single wall, with more rigid connections leading to a greater proportion of the structure bending as a single unit.
Failure Modes of Shear Walls
Shear walls are critical in resisting lateral forces, but they are susceptible to failure under certain conditions. The main failure modes of shear walls due to horizontal loads are:
- Flexural Failure: This occurs when the shear wall undergoes excessive bending, leading to cracking or failure of the material. Flexural failure is often observed in tall walls subjected to significant lateral loads.
- Horizontal Shear Failure: Horizontal shear failure occurs when the shear stress exceeds the shear capacity of the wall material. This type of failure is more common in shorter walls subjected to high horizontal loads.
- Vertical Shear Failure: This type of failure occurs when the shear stress along the height of the wall exceeds the material’s vertical shear capacity. Vertical shear failure is typically observed in shorter walls or those subjected to combined vertical and horizontal loads.
Each of these failure modes can compromise the integrity of the structure, and designers must account for them when designing shear walls to ensure the building performs safely under both vertical and horizontal loads.
Conclusion
The analysis of a framed building with shear walls under horizontal and vertical loads requires a thorough understanding of the behavior of both the shear walls and the frame. Load distribution, deflection profiles, and the interaction between these components are critical to ensuring the building’s structural integrity. Simplified two-dimensional models can be used in many cases, but a full three-dimensional analysis may be necessary, especially in non-symmetrical designs. Additionally, recognizing and mitigating potential failure modes, such as flexural, horizontal shear, and vertical shear failures, is essential for the safe design of shear walls. By understanding the interactions between the shear walls and frames, designers can optimize the building’s performance under load, ensuring both safety and efficiency.