Conceptual design of a building with columns and shear walls
Q1.The building shown, 20 × 35 m in plan, has columns on a 5 × 5 m grid and shear walls (with dimensions shown in m, 250 mm in thickness) in three alternative arrangements, (a), (b), (c), all with the same total cross-sectional area of the shear walls. Compare the three alternatives, taking into account the restraint of floor shrinkage, the lateral stiffness and the torsional one with respect to the vertical axis, the vertical reinforcement required for the same total flexural capacity at the base, the static eccentricity, the system’s redundancy, foundation systems, architectural constraints etc.
Restraint of Floor Shrinkage:
Alternative (a): Shrinkage restraint would be relatively higher due to the closely spaced shear walls.
Alternative (b): Shrinkage restraint may be moderate due to the intermediate spacing of shear walls.
Alternative (c): Shrinkage restraint would be relatively lower due to the widely spaced shear walls.
Lateral Stiffness:
Alternative (a): High lateral stiffness due to closely spaced shear walls.
Alternative (b): Moderate lateral stiffness due to intermediate spacing of shear walls.
Alternative (c): Lower lateral stiffness due to widely spaced shear walls.
Torsional Stiffness:
Alternative (a): Higher torsional stiffness due to closely spaced shear walls.
Alternative (b): Moderate torsional stiffness due to intermediate spacing of shear walls.
Alternative (c): Lower torsional stiffness due to widely spaced shear walls.
Vertical Reinforcement:
To achieve the same total flexural capacity at the base, alternative (c) would likely require more vertical reinforcement in shear walls due to their greater span.
Alternative (a) might require moderate reinforcement, and alternative (b) would likely require the least.
Static Eccentricity:
Alternative (a): Lower static eccentricity due to closely spaced shear walls.
Alternative (b): Moderate static eccentricity due to intermediate spacing.
Alternative (c): Higher static eccentricity due to widely spaced shear walls.
System's Redundancy:
Alternative (a): Higher redundancy due to more shear walls.
Alternative (b): Moderate redundancy.
Alternative (c): Lower redundancy due to fewer shear walls.
Foundation Systems:
Alternative (a): May require more complex and costly foundation systems due to the closely spaced shear walls.
Alternative (b): Foundation systems may be less complex and more economical than (a) but more than (c).
Alternative (c): Likely to have the simplest and most economical foundation systems.
Architectural Constraints:
Architectural preferences and constraints can greatly impact the choice. Some arrangements may be more suitable for specific architectural designs.
2. Discuss the suitability for earthquake resistance of the moment resisting framing plan of a three-storey building depicted here(cross sectional dimensions in cm), the eccentricity of the center of the mass ( as centroid of floor ) to the center of stiffness ( from the moment of inertia of the column ) as shown. Suggest an alternative. Also, is there torsional flexibility? Are the two fundamental translational modes of vibration larger than the fundamental torsional mode of vibration. Discuss qualitatively.
The structural frame under consideration exhibits a two-way eccentricity between the center of mass and the center of stiffness, with the eccentricity being more pronounced in the x-direction compared to the y-direction. This eccentricity can have implications for the structure's response to lateral forces, particularly during seismic events.
The design of this structure appears to follow a "Weak Column Strong Beam" philosophy, wherein beams are engineered to be stronger than the columns. Consequently, the structure relies on robust beams to resist significant loads, especially lateral forces, which can be detrimental to column stability.
To enhance the earthquake resistance of this structure, the incorporation of shear walls is deemed necessary. Shear walls, when combined with columns, play a pivotal role in mitigating column failure when subjected to lateral forces, as observed in seismic events.
Analyzing the frame plan, it is evident that beams B1 and B2 in the x-direction, and B11 & B12, B9 & B10 in the y-direction exhibit a uniform and continuous alignment. However, all other beams in the structure are discontinuous. This discontinuity can pose challenges in uniformly distributing loads throughout the structure when subjected to lateral forces.
Additionally, beams with longer spans may experience their top reinforcement primarily influenced by factored gravity loads rather than seismic design considerations. As a result, it is advisable to explore alternatives that offer better structural symmetry and balance.
For effective seismic resistance, the connections between columns and beams should be meticulously designed to ensure proper cross-sectional area, thereby enhancing lateral stiffness, mass distribution regularity, and moment-resisting capability.
Considering the "beam-sway" mechanism within the context of strong column/weak beam design frames appears to be a favorable approach. This design philosophy promotes the achievement of a uniformly spread, global inelastic displacement demand at the roof level across all storeys, contributing to the structure's overall seismic resilience and stability.
The modifications made to the structural design by changing columns C5 and C8 to a combined footing and introducing a new column C10 to maintain the center of mass and center of stiffness are notable improvements in response to seismic considerations.
Combined Footing for C5 and C8: Converting columns C5 and C8 into a combined footing is a strategic move. It helps distribute the loads from these columns more effectively to the foundation, reducing the risk of differential settlement and maintaining the integrity of the center of stiffness. This alteration enhances the structural stability under lateral forces.
Addition of Column C10: The inclusion of a new column, C10, at the boundary of the plan is a prudent decision. This new column serves multiple purposes. Firstly, it helps maintain the center of mass, which is critical for the overall balance and stability of the structure during lateral horizontal force actions. Secondly, it contributes to restoring the center of stiffness, which is crucial for uniform load distribution and effective resistance to seismic forces.
These modifications demonstrate a thoughtful approach to address the structural irregularities and vulnerabilities that were initially present in the design. By maintaining balance in the distribution of mass and stiffness and ensuring that the lateral forces are effectively transmitted through the structural system, the structure is better prepared to withstand seismic events and minimize potential damage or failure. This approach aligns with best practices in earthquake-resistant structural design. However, it is essential to conduct thorough structural analysis and engineering calculations to confirm the effectiveness of these modifications and ensure compliance with local building codes and regulations.
3. A multi-storey building with basement, with a quadrilateral ( non symmetric floor plan) plan as, has interior columns in an irregular(not in a grid) pattern in plan that serves architectural and functional considerations. Partition wall and interior beams supporting the slab have different layout in different stories. However there is no constraint to the type, location and size of the lateral force resisting components and sub-system in the perimeter. Proposals are to be made and justified for the choice of the lateral-load-resisting system and its foundation.
The proposed structural plan appears to be unsuitable for heavy seismic zone areas due to several notable irregularities and design choices. To evaluate these concerns in a professional engineering context:
Column Asymmetry: One significant issue is the lack of symmetry in the placement of interior columns within the building's plan. In seismic design, symmetrical distribution of mass and stiffness is crucial for balanced load distribution during an earthquake.
Partition Walls at Base of Beams: Partition walls located at the base of beams are expected to provide lateral support for structural deformations. However, their effectiveness in resisting lateral seismic forces is questionable, as they may not possess the necessary strength and ductility required for seismic resistance.
Interior Beam-Slab Arrangement: The structural system involves interior beams supporting the slab. This arrangement may not be sufficient to resist lateral loads effectively, especially in a seismic event, as beams are not designed primarily for lateral load resistance.
Use of Flat Slabs: The use of flat slabs instead of traditional beam-column junctions appears to be driven by the irregular column layout. Flat slabs can provide direct support to columns' centroidal axes, but they may not offer the required lateral load resistance. Additionally, flat slabs may reduce the overall building weight, contributing to some level of ductility but might not be adequate for seismic design on their own.
Shear Wall Solution: To address the structural irregularities and enhance seismic performance, the incorporation of shear walls extending from the foundation vertically is recommended. Shear walls are designed to withstand lateral forces and help distribute seismic loads efficiently, minimizing the risk of sudden structural failure during an earthquake.
In conclusion, for structures located in heavy seismic zones, it is essential to prioritize seismic design principles. This includes ensuring symmetrical distribution of mass and stiffness, using structural elements designed for lateral load resistance, and incorporating shear walls to enhance overall seismic performance. These measures are crucial for minimizing the risk of structural failure and ensuring the safety and integrity of the building during seismic events.