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:

Comparison of Shear Wall Arrangements in the 20 × 35 m Building

1. Restraint of Floor Shrinkage

• (a) Distributed Shear Walls: Better shrinkage control due to uniform restraint.
• (b) Concentrated at Core: Minimal restraint for peripheral floors, higher chances of shrinkage-induced cracking.
• (c) One Side Concentration: Highest differential restraint, increasing crack risks on the opposite side.

2. Lateral Stiffness

• (a) Distributed Walls: Most effective in resisting lateral loads in both directions.
• (b) Core Walls: High stiffness in torsion but may be less effective for lateral loads unless heavily reinforced.
• (c) Single-Side Walls: Least lateral stiffness and highest deflections in the weak direction.

3. Torsional Stiffness (With Respect to Vertical Axis)

• (a) Distributed Walls: Balanced response with low torsional effects.
• (b) Core Walls: Good torsional resistance but sensitive to eccentric loading.
• (c) Single-Side Walls: High torsional effects, leading to undesirable rotation under lateral loads.

4. Vertical Reinforcement for Same Flexural Capacity at the Base

• (a) Distributed Walls: More evenly spread reinforcement, reducing localized reinforcement congestion.
• (b) Core Walls: Requires concentrated vertical reinforcement, leading to potential congestion.
• (c) Single-Side Walls: Heaviest reinforcement demand due to high moment demand on the limited shear walls.

5. Static Eccentricity

• (a) Symmetrical Walls: Least static eccentricity, well-balanced response.
• (b) Core Walls: Small eccentricity unless the core is off-center.
• (c) Single-Side Walls: High eccentricity, leading to excessive torsion.

6. System Redundancy

• (a) Most Redundant: Multiple walls ensure alternate load paths.
• (b) Medium Redundancy: If core fails, significant loss of lateral load resistance.
• (c) Least Redundant: Failure of the wall significantly impacts lateral stability.

7. Foundation System

• (a) Distributed Walls: More balanced foundation loads, leading to uniform settlements.
• (b) Core Walls: Requires a strong central foundation, possibly a large mat.
• (c) Single-Side Walls: Generates unbalanced foundation reactions, leading to differential settlements.

8. Architectural Constraints

• (a) Distributed Walls: May interfere with openings but provides flexible planning.
• (b) Core Walls: Efficient use of space for vertical circulation.
• (c) Single-Side Walls: Limits design flexibility, restricting usable space.

Conclusion

• Best for Structural Performance: (a) Distributed shear walls.
• Best for Architectural & Functionality: (b) Core walls (if well-placed).
• Least Favorable: (c) Single-side shear walls due to high eccentricity and instability.

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:

Suitability of Moment-Resisting Frame for Earthquake Resistance

1. Eccentricity Between Center of Mass (CM) and Center of Stiffness (CS)

• If the eccentricity between CM and CS is significant, torsional effects will arise during an earthquake.
• Large eccentricities cause coupled lateral-torsional motion, leading to uneven lateral displacements and higher demands on certain columns.

2. Torsional Flexibility

• Torsional flexibility is high if:
• The stiffness distribution is uneven.
• The torsional mode frequency is lower than the translational modes.
• The building plan is irregular (e.g., L-, T-, or U-shaped).
• If CS is far from CM, the torsional response will be significant, worsening seismic performance.

3. Fundamental Translational vs. Torsional Modes

• If the first two translational modes dominate (i.e., they have lower frequencies than the torsional mode), the building will primarily undergo lateral displacements rather than rotation.
• However, if the fundamental torsional mode is lower than or comparable to the translational modes, torsional motion will be significant, making the structure highly susceptible to seismic effects.
• The stiffness and mass distribution of the structure determine whether torsional effects will dominate.

Alternative for Improved Seismic Performance

• Reduce Eccentricity: Align CS closer to CM by redistributing column stiffness.
• Add Shear Walls or Braced Frames: Improve lateral stiffness, reducing torsional flexibility.
• Strengthen Torsional Resistance: Increase the torsional stiffness by using a dual system (moment frames + shear walls).
• Ensure Symmetry: A more uniform stiffness and mass distribution will improve dynamic behavior.

Conclusion

• If the given frame has large eccentricity and torsional flexibility, its earthquake resistance is poor.
• A better alternative is a dual system with strategically placed shear walls or bracing, ensuring that translational modes remain dominant over torsional modes.

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:

Proposal for Lateral-Load-Resisting System & Foundation

1. Challenges Due to Irregularities

• Plan Irregularity (Non-Symmetric Layout): Leads to eccentricity between mass and stiffness centers, causing torsional effects under seismic and wind loads.
• Vertical Irregularity (Changing Interior Beams & Partitions): Causes stiffness discontinuities between floors, leading to weak or soft-story effects.
• Irregular Column Layout: Uneven force distribution, making it harder to ensure uniform lateral load resistance.

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Proposed Lateral-Load-Resisting System

A. Dual System (Moment Frames + Shear Walls or Bracing) – Recommended

• Perimeter Shear Walls or Braced Frames: Provide strong lateral stiffness and minimize torsional response.
• Interior Moment Frames: Maintain flexibility for architectural needs while contributing to lateral resistance.
• Key Justifications:
• Reduces the impact of irregular interior columns.
• Enhances overall stiffness while allowing some flexibility.
• Controls both translational and torsional displacements.

B. Other Possible Configurations (Less Ideal)

1. Moment-Resisting Frames Only:
• Works for moderate seismic zones but struggles with torsion and drift.
• Requires large, heavily reinforced columns and beams.
2. Shear Walls Only (Perimeter & Strategic Interiors):
• More stiffness, but may limit architectural freedom.
• Less redundancy compared to a dual system.
3. Braced Frames (Concentrically or Eccentrically Braced):
• More efficient than shear walls in steel structures.
• Works well when combined with moment frames.

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Foundation Proposal

• Basement Walls as Part of the Lateral-Load System: Utilize reinforced concrete basement walls as shear walls to contribute to stiffness.
• Deep Foundations (Piles or Rafts) if Needed:
• If soil conditions are poor, deep foundations can mitigate differential settlement.
• A raft foundation may be preferable if high column loads are present.
• Balanced Load Transfer:
• Shear walls and braced frames should be supported by strong foundations to prevent excessive settlements or tilting.

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Conclusion

• Best Choice: Dual System (Perimeter Shear Walls/Bracing + Interior Moment Frames) for seismic efficiency, redundancy, and architectural flexibility.
• Foundation: Utilize basement shear walls + raft or deep foundation based on soil conditions.
• This ensures torsional control, stiffness balance, and efficient lateral load transfer while accommodating the irregular plan.