Conceptual design of a building with columns and shear walls

Question 1:
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.

Ans:

1. Restraint of Floor Shrinkage:

• Arrangement (a): This arrangement provides the highest shrinkage restraint due to the fully enclosed perimeter walls. This can minimize differential movement but might increase internal stresses in the enclosed space.
• Arrangement (b): This arrangement offers moderate restraint with shear walls on two opposite sides. Some shrinkage-related cracking might occur in the unsupported directions.
• Arrangement (c): This arrangement offers the least shrinkage restraint due to open sides on two sides. Careful consideration of expansion joints and potential cracking is necessary.

2. Lateral Stiffness:

• Arrangement (a): The closed wall layout provides the highest lateral stiffness in both directions due to continuous load paths along all sides.
• Arrangement (b): This arrangement offers moderate stiffness with walls on two sides. It might require additional bracing for specific wind or seismic loads depending on the design requirements.
• Arrangement (c): This arrangement offers the lowest lateral stiffness due to open sides. It requires significant additional bracing or stiffer columns to meet design requirements, especially for wind loads perpendicular to the open sides.

3. Torsional Stiffness:

• Arrangement (a): The symmetrical layout minimizes torsional irregularity, resulting in the highest torsional stiffness.
• Arrangement (b): This arrangement has moderate torsional stiffness due to the presence of two shear walls on opposite sides. However, it's less symmetrical than (a) and might require an analysis for potential eccentricity depending on the specific wall placement.
• Arrangement (c): The L-shaped layout creates significant torsional irregularity, requiring substantial additional measures like strategically placed shear walls or bracing to achieve adequate torsional stiffness.

4. Vertical Reinforcement:

• All arrangements have the same total wall area, so the amount of vertical reinforcement should be approximately equal for the same flexural capacity at the base. However, the specific distribution of reinforcement might vary depending on the individual wall configurations.

5. Static Eccentricity:

• Arrangement (a): The symmetrical layout minimizes static eccentricity, leading to balanced loading on foundations.
• Arrangement (b): Analyze for potential eccentricity based on the specific wall placement. If significant eccentricity is present, it might require special foundation design.
• Arrangement (c): The L-shape creates significant static eccentricity due to the unbalanced mass distribution. This necessitates careful foundation design to account for eccentric loading.

6. System Redundancy:

• Arrangement (a): Enclosed walls provide redundancy in case of localized damage as there are multiple load paths for lateral forces.
• Arrangement (b): This arrangement offers moderate redundancy with two shear walls. However, it's less redundant than (a) and might be more susceptible to localized damage.
• Arrangement (c): This arrangement has the least redundancy due to open sides and concentrated load paths. It requires a robust design and detailing to ensure adequate performance in case of damage.

7. Foundation Systems:

• Arrangement (a): The continuous wall layout might allow for a continuous footing or mat foundation, which can be more economical and efficient.
• Arrangement (b): This arrangement may require individual footings or combined footings based on the locations and sizes of the shear walls.
• Arrangement (c): The significant eccentricity due to the L-shape might necessitate a complex foundation design with eccentric loading considerations. This could involve heavier reinforcement, deeper footings, or even piled foundations depending on the soil conditions and design loads.

8. Architectural Constraints:

• Consider how each arrangement fits the desired architectural layout and functionality.
• Analyze factors like openings, view corridors, desired floor plan flexibility, and potential future modifications.
• Arrangement (b) might offer more flexibility for future modifications to the enclosed space compared to (a).
• Arrangement (c) might be challenging to integrate into the architectural layout due to the open sides and the need for additional bracing or shear walls.

Question 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 centre of mass (as centroid of floor plan) to the centre of stiffness (from the moments of inertia of the columns) are 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.

Ans:

Locations of columns and shear walls:

• The image lacks clear markings for the columns and shear walls. Please indicate their positions on the plan.

Material properties:

• Knowing the materials used for the columns, beams, and slabs is crucial for assessing their earthquake resistance. Please specify the materials if possible.

Seismic zone:

• The building's earthquake resistance also depends on the seismic zone it's located in. Please provide the seismic zone information (if available).

I can provide a more detailed analysis based on the following aspects:

Center of mass (CM) and center of stiffness (CR):

• I'll calculate the eccentricities between the CM and CR in both directions (along the length and width of the building).
• Larger eccentricities will cause torsional effects during earthquakes, potentially increasing stress on structural elements.

Torsional flexibility:

• I'll assess the building's torsional flexibility based on the distribution of stiffness elements (columns, shear walls) and the openings in the plan.
• Higher torsional flexibility can lead to significant twisting during earthquakes, which can be detrimental.

Fundamental modes of vibration:

• I'll qualitatively compare the frequencies of the two fundamental translational modes (along the length and width) to the fundamental torsional mode.
• Ideally, the translational modes should have lower frequencies than the torsional mode, indicating better control over torsional response during earthquakes.

Alternative framing plan:

• Based on the identified vulnerabilities, I can suggest alternative framing plans or modifications to improve the building's earthquake resistance. This might involve adding shear walls, modifying column layouts, or using different materials.

Question 3:

A multi-storey building with basement, with a quadrilateral (non symmetrical floor plan) plan as, has interior columns in an irregular (not in a grid) pattern in plan that serves architectural and functional considerations. Partition walls 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-systems on the perimeter. Proposals are to be made and justified for the choice of the lateral-load-resisting system and its foundation.

Ans:

Seismic zone:

• Knowing the seismic zone where the building will be located is crucial, as it determines the design earthquake forces and governs the required level of earthquake resistance.

Number of stories:

• The number of stories above ground and the presence of the basement will influence the overall stiffness and strength requirements of the lateral load resisting system.

Height of each story:

• Different story heights can create irregularities and affect the distribution of seismic forces.

Architectural and functional considerations:

• Understanding the specific architectural and functional requirements of the building will help in proposing a system that integrates well with the design intent.

Soil conditions:

• The type of soil at the foundation level will influence the design and selection of the foundation system.

Irregularities:

• The non-symmetrical floor plan, irregular column layout, and varying beam layouts present challenges for lateral load resistance. I can help you assess the severity of these irregularities and their impact on system selection.

Perimeter freedom:

• The ability to freely place lateral load resisting elements on the perimeter offers flexibility in addressing the irregularities. I can suggest systems that leverage this advantage.

System proposals:

• Based on the information provided, I can propose suitable lateral load resisting systems such as:
  • Shear walls: These are vertical walls designed to resist lateral forces. They can be strategically placed around the perimeter to address irregularities and provide overall stiffness.
  • Moment-resisting frames (MRFs): These are frames with beams and columns designed to resist bending moments caused by lateral forces. They can be used in conjunction with shear walls or as a primary system in certain cases.
  • Braced frames: These use diagonal braces to resist lateral forces and are efficient for specific applications.
  • Core-wall systems: These are centralized structural cores made of shear walls or other elements that provide lateral resistance and stiffness.

Foundation system:

• The foundation system should be designed to transfer the loads from the lateral load resisting system to the soil safely. I can suggest appropriate foundation types such as spread footings, mat foundations, or pile foundations based on the soil conditions and design loads.

Justification:

• For each proposed system, I will explain its advantages and disadvantages in the context of your specific building, considering factors like effectiveness, cost, constructability, and architectural integration.

Remember, this analysis is for informational purposes only and should not be considered a substitute for professional engineering advice. A qualified structural engineer can conduct a detailed seismic analysis and design the lateral load resisting system and foundation based on your specific requirements and local building codes.