Seismic Analysis and Design Principles for RC Buildings

1. Dynamic Analysis of Buildings per IS 1893:2016

Dynamic analysis considers the actual dynamic behavior of a building under earthquake ground motion, including its mass, stiffness, natural periods, and mode shapes.

• Methodology: It is primarily carried out by Modal Response Spectrum Analysis.
• Idealization: The building is idealized as a system with lumped masses at floor levels and structural elements represented by their appropriate stiffness.
• Eigenvalue Problem: Natural frequencies and mode shapes are determined by solving the structural system's eigenvalue problem.
• Modal Analysis: Each mode of vibration is analyzed separately using the design response spectrum specified in IS 1893:2016.
• Seismic Coefficient: The design horizontal seismic coefficient (A_h) is evaluated using the zone factor (Z), importance factor (I), response reduction factor (R), and spectral acceleration.
• Combination: Seismic responses from different modes are combined using methods like SRSS (Square Root of Sum of Squares) or CQC (Complete Quadratic Combination).
• Mass Participation: A sufficient number of modes must be considered so that the sum of modal masses is at least 90% of the total seismic mass.
• Base Shear: The total design base shear from dynamic analysis is compared with the equivalent static method; results are scaled if required.
• Output: Dynamic analysis provides storey forces, displacements, drifts, member forces, and reactions for safe, ductile design.

2. Mathematical Modeling of RC Buildings

Mathematical modeling represents the actual structure as an analytical model to evaluate behavior under gravity and earthquake loads.

• Purpose: Used to determine natural periods, mode shapes, storey displacement, drift, base shear, and member forces.
• Structural Elements: Beams and columns are modeled as frame elements; shear walls use shell or wall elements.
• Mass Modeling: Seismic mass includes dead load and the appropriate portion of imposed load per IS 1893:2016.
• Rigid Diaphragm: Assumes high in-plane stiffness; all joints at a floor level undergo the same translation and rotation.
• Flexible Diaphragm: Has low in-plane stiffness; force distribution depends on the diaphragm's flexibility and connections.
• Semi-Rigid Diaphragm: Represents actual in-plane stiffness using shell or plate elements for realistic force distribution.
• Diaphragm Action: Transfers inertial forces to vertical elements and maintains compatibility.
• Openings: Large openings and discontinuities reduce stiffness and must be properly represented.

3. Concept of Capacity-Based Design

Capacity-based design is a philosophy where the structure is designed so that desired members yield in a controlled manner, while critical members remain stronger to avoid premature failure.

• Objective: Ensure ductile behavior during severe earthquakes rather than sudden, brittle collapse.
• Strong Column–Weak Beam: Per IS 13920:2016, beams are intended to undergo plastic hinging before columns.
• Plastic Hinges: Allowed at selected locations (beam ends) where large inelastic rotations occur without significant strength loss.
• Component Strength: Columns and joints are designed to resist forces generated when ductile members reach their probable maximum capacity.
• Shear Prevention: Design shear force considers the probable flexural strength of adjoining members to prevent brittle shear failure.
• Joint Integrity: Beam-column joints are designed to remain stronger than connected beams.
• Mechanism Control: Prevents continuous mechanisms involving column hinges over several storeys.
• Detailing: Proper longitudinal and transverse reinforcement, confinement, and anchorage are essential.

4. Procedure for Equivalent Static Analysis (ESA)

1. Collect Data: Determine building height, storeys, dimensions, structural system, soil condition, and importance.
2. Calculate Seismic Weight: Determine total weight using dead loads and appropriate imposed loads.
3. Determine Natural Period: Calculate the fundamental period based on height and structural system.
4. Determine Spectral Acceleration: Obtain values from the design response spectrum based on the period and soil condition.
5. Calculate Seismic Coefficient: Determine the design horizontal seismic coefficient.
6. Calculate Base Shear: Compute the total design base shear.
7. Distribute Base Shear: Distribute shear to floor levels based on seismic weight and height.
8. Apply Lateral Forces: Apply forces horizontally at each floor level.
9. Perform Analysis: Determine storey shear, moments, axial forces, torsion, and drift.
10. Check Safety: Verify drift, stability, torsion, and strength; provide ductile detailing.

5. Column Design Clauses (IS 13920:2016)

• Minimum Size: Generally 300 mm to resist axial load, bending, and earthquake forces.
• Longitudinal Reinforcement: Uniformly distributed, typically 0.8% to 6% of the gross area.
• Bar Arrangement: Minimum four bars for rectangular columns; six for circular.
• Lateral Ties: Closely spaced closed hoops to confine concrete and prevent buckling.
• Special Confinement: Required near beam-column joints and column ends.
• Lap Splicing: Avoided near joints and plastic hinge regions; must be properly confined.
• Strong-Column Weak-Beam: Columns must be stronger than beams to ensure beam-hinging.
• Shear and Ductility: Adequate shear strength is required to withstand repeated loading.

6. Seismic Retrofitting and Sources of Weakness

Seismic Retrofitting

• Techniques: Column/beam jacketing, adding shear walls, strengthening joints, FRP wrapping, and steel bracing.
• Objective: Increase strength, stiffness, and ductility to prevent collapse.

Sources of Weakness

• Soft Storey: Open ground floor attracting excessive forces.
• Irregularity: Plan/vertical irregularities causing torsion.
• Weak Joints: Poor detailing leading to brittle failure.
• Weak Columns: Inadequate strength leading to storey collapse.
• Poor Detailing: Insufficient confinement or anchorage.
• Short-Column Effect: Partial-height walls creating vulnerable short columns.

7. Masonry Retrofitting and Failure Modes

Code Provisions

• Assessment: Inspect for cracks and seismic vulnerability.
• Repair: Use grout or mortar for cracks.
• Strengthening: Use reinforced concrete layers or wire mesh.
• Integrity: Provide seismic bands at lintel/roof levels and improve wall-floor connections.
• Vertical Reinforcement: Add at corners and junctions.

Failure Modes

• Out-of-Plane: Bending or overturning.
• In-Plane Shear: Diagonal cracking.
• Sliding: Movement along mortar joints.
• Corner Failure: Separation at junctions.
• Opening Failure: Cracks around doors/windows.
• Wall-Floor Separation: Loss of connection leading to collapse.

8. Shear Walls in Earthquake-Resistant Structures

A shear wall is a vertical reinforced concrete member designed to resist lateral loads and transfer them to the foundation.

• Lateral Resistance: Resists horizontal earthquake forces.
• Stiffness: Increases structural stiffness and reduces deformation.
• Drift Control: Limits inter-storey drift and damage.
• Stability: Increases resistance to overturning.
• Torsion Control: Helps manage torsional effects.
• Load Reduction: Carries lateral forces, reducing demand on frames.

9. Global vs. Local Retrofitting

• Global Retrofitting: Strengthens the entire system (e.g., adding shear walls). Used for major deficiencies; redistributes forces throughout the building.
• Local Retrofitting: Strengthens specific members (e.g., jacketing). Used for localized damage or weak components; more economical.

10. Elastomeric Base Isolation

Elastomeric base isolation uses flexible rubber-like bearings between the superstructure and foundation to reduce vibration transmission.

• Construction: Alternate layers of rubber and steel plates.
• Flexibility: Rubber allows horizontal movement.
• Vertical Strength: Steel plates provide vertical load capacity.
• Energy Dissipation: Lead cores (in LRB) dissipate energy.
• Performance: Increases natural period and reduces seismic acceleration.

11. Types of Base Isolators

• Laminated Rubber Bearing: Standard rubber/steel layers.
• Lead-Rubber Bearing (LRB): Includes a lead core for damping.
• High-Damping Rubber Bearing (HDRB): Uses high-damping rubber.
• Friction Pendulum System (FPS): Uses a curved sliding surface.
• Sliding Bearing: Low-friction surface for horizontal movement.
• Elastomeric with Sliding: Combines flexibility and sliding.
• Roller Bearing: Uses rollers for movement.
• Combined System: Integrates multiple isolator types.

12. Requirements for Base Isolation Installation

• Foundation: Must have sufficient strength and stiffness.
• Load Path: Clear, continuous path from superstructure to soil.
• Configuration: Regular and symmetrical plan preferred.
• Rigid Level: Isolation level must have adequate horizontal stiffness.
• Clearance: Space for horizontal movement to prevent pounding.
• Connections: Securely anchored to foundation and superstructure.
• Utility Flexibility: Services must accommodate seismic movement.
• Stability: Stable under vertical and lateral loads.
• Maintenance: System must be accessible for inspection.

13. RCC Beam Reinforcement Calculation

Calculation of reinforcement for a 350 mm x 650 mm beam (4.5 m span, M20/Fe415) based on ductile detailing requirements.

[Note: Detailed calculation and sketch to be provided based on specific design parameters.]