🏗️ civil engineering

A Unified Dynamic Framework for Buildings with Architecturally-Induced Mass and Stiffness Asymmetry

This paper proposes a unified framework for Architecturally-Induced Dynamic Irregularity (AIDI) that identifies four fundamental asymmetry types and introduces Dynamic Form Factors (DFFs) to systematically quantify how unconventional architectural geometries alter the dynamic behavior of mid-to-high-rise buildings, thereby enabling early-stage integration of these effects into design processes.

Original authors: Vijay Kumar Khanna

Published 2026-06-26✓ Author reviewed ⓘ

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Vijay Kumar Khanna

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are building a tower of blocks. If the tower is a perfect, straight rectangle with weight evenly distributed, it sways gently in the wind like a calm tree. But what happens if you start twisting the blocks, leaning the tower to one side, or stacking a heavy, oversized room on top of a skinny floor?

That is exactly what this paper is about. The author, Vijay Kumar Khanna, is saying that modern architects are designing buildings that look amazing—twisted, tilted, and stepped—but these cool shapes create hidden "dynamic problems" that current building rules don't fully understand.

Here is a simple breakdown of the paper's main ideas:

1. The Problem: Cool Shapes, Hidden Wobbles

Current building codes (the rulebooks for safety) are great at checking for structural mistakes, like a floor that is too soft or a wall that is too weak. However, they treat weird shapes mostly as "accidents" or simple errors.

The paper argues that architecture itself is the driver of the problem. When an architect decides to twist a tower or put a heavy garden on the 40th floor, they are changing how the building moves in an earthquake or high wind. The building might start to spin (torsion) or wobble in a way a normal building wouldn't, even if the steel and concrete inside are perfectly strong.

2. The Solution: The "AIDI" Framework

To fix this confusion, the author created a new system called AIDI (Architecturally-Induced Dynamic Irregularity). Think of this as a "menu" of four specific ways a building's shape can make it wobble dangerously:

Type A: The Off-Center Weight (Plan Eccentricity)
- The Metaphor: Imagine a spinning top where the weight is glued to one side instead of the center. It doesn't just spin; it wobbles violently.
- The Reality: If the building's floor plan isn't symmetrical (like an L-shape or an offset core), the center of mass moves away from the center of stiffness. This makes the building twist more than expected.
Type B: The Leaning Tower (Vertical Offset)
- The Metaphor: Think of a stack of books where every few books, you slide the stack slightly to the left, or you lean the whole stack like the Tower of Pisa.
- The Reality: This includes setbacks (where the building gets smaller as it goes up) or leaning facades. These create "kinks" where the building bends sharply, concentrating stress in specific spots.
Type C: The Spiral (Rotational Asymmetry)
- The Metaphor: Imagine a corkscrew or a twisted candy cane. As you go up, the building rotates.
- The Reality: When floors are rotated relative to each other, the building's movement becomes a mix of swaying and twisting. It's like trying to run while your legs are moving in a spiral pattern; it's inefficient and stressful.
Type D: The Heavy Hat (Mass Concentration)
- The Metaphor: Imagine a tall, thin pole with a giant, heavy bowling ball balanced on the very tip.
- The Reality: This happens when a heavy feature (like a sky garden, a mechanical room, or a heavy glass observation deck) is stuck on a specific floor. That heavy spot creates a local "whiplash" effect, making the floors right below it shake harder.

3. The Tool: "Dynamic Form Factors" (DFFs)

The author didn't just list the problems; he developed a quantitative framework using Dynamic Form Factors that allows architects and engineers to estimate the influence of architectural geometry during conceptual design.

How it works: Imagine you are sketching a building. You have a "baseline" number for how much a normal, straight building would sway.
The Magic: If you add a twist, the DFF tells you, "Okay, your sway will be 1.5 times worse." If you add a heavy roof, it might say, "Your stress will be 2 times worse."
The Goal: It allows an architect to say, "If I twist this tower by 10 degrees, the building will need to be much stronger," before they even hire a structural engineer to do the complex math. It turns "cool shape" into "quantifiable risk."

4. How They Tested It

The author didn't build real buildings or shake them in a lab (that would be too expensive and dangerous!). Instead, he used computer simulations.

He created digital models of standard 20, 30, and 40-story buildings.
He kept the materials (concrete, steel) exactly the same for every model.
He only changed the shape (twisting it, leaning it, adding a heavy top).
He watched how the computer models reacted to simulated earthquakes and winds.

5. The Big Takeaway

The paper concludes that shape is destiny when it comes to how a building moves.

You can have a perfectly strong structure, but if the shape is weird, the building will still behave unpredictably.
Current codes primarily evaluate irregularities after geometry has already been defined, whereas AIDI introduces a systematic method to identify architecturally induced dynamic irregularities during the conceptual design stage.
This new framework helps architects and engineers talk the same language, ensuring that the most beautiful, expressive buildings are also safe and stable from day one.

In short: This paper gives architects a "warning label" system for their wildest designs, helping them understand that a twisted tower isn't just a visual statement—it's a physics challenge that needs to be solved early.

Technical Summary: A Unified Dynamic Framework for Buildings with Architecturally-Induced Mass and Stiffness Asymmetry

Problem Statement
Contemporary architecture increasingly employs expressive, unconventional forms—such as twists, tilts, setbacks, and perched volumes—that introduce geometric and mass asymmetries. While current seismic and wind design codes (e.g., IS 1893, Eurocode 8, ASCE 7) address structural irregularities like soft stories or abrupt stiffness changes, they do not explicitly recognize architectural geometry as an independent driver of dynamic behavior. In practice, these form-induced effects are often handled indirectly through accidental eccentricity factors or case-specific finite element (FE) studies conducted at advanced design stages. Consequently, there is a lack of a unified framework to systematically link architectural form parameters to key dynamic response characteristics (natural periods, mode shapes, torsional coupling, and drift) during the conceptual design phase.

Methodology
The study employs a purely numerical investigation to isolate the influence of architectural geometry from structural detailing. The methodology involves:

Baseline Models: A family of generic 20-, 30-, and 40-storey reinforced concrete buildings with a 40m × 40m plan and a central core/perimeter frame system.
Parameterization: Four fundamental Architecturally-Induced Dynamic Irregularity (AIDI) types were introduced into these baseline models by varying specific geometric parameters while keeping material properties and gravity loads constant:
- Type A (Plan Eccentricity): Varying the eccentricity ratio ( $e/B$ ) from 0.05 to 0.30.
- Type B (Vertical Offset): Introducing setbacks ( $s/H$ ) and lean angles ( $\theta$ ) up to 6°.
- Type C (Rotational/Torsional): Applying cumulative floor rotations ( $\alpha$ ) up to 2.0° per floor.
- Type D (Mass Concentration): Adding localized heavy masses (e.g., perched volumes) with mass factors ( $m_c$ ) up to 2.0.
Analysis: Linear elastic 3D FE analysis was conducted using modal and response spectrum methods (0.25g design spectrum, 5% damping) to extract natural periods, mode shapes, torsional participation factors, and drift patterns.
Derivation: Response quantities were normalized against the symmetric baseline to derive dimensionless amplification indicators.

Key Contributions
The paper proposes two primary conceptual tools:

The AIDI Classification Framework: A systematic vocabulary categorizing architectural asymmetry into four distinct types (Plan Eccentricity, Vertical Offset, Rotational Asymmetry, and Mass Concentration), each with specific dynamic signatures.
Dynamic Form Factors (DFFs): A set of dimensionless amplification indicators defined as $DFF = R_{asym} / R_{baseline}$ . These factors relate simple geometric parameters to normalized dynamic responses (e.g., drift, period, torsion). The paper provides illustrative quadratic or multi-parameter formulations for each AIDI type and suggests a multiplicative approach for combined irregularities.

Key Results
The numerical simulations revealed that architectural geometry alone significantly alters dynamic behavior even when structural systems remain regular:

Modal Characteristics: Asymmetry shifts natural periods and causes torsional modes to approach translational frequencies, increasing modal coupling. Type A and Type C geometries notably reduce torsional frequencies.
Mode Shape Distortion: Asymmetric forms generate helical or curved mode shapes. Type B (setbacks/leans) creates inflection points in mode shapes, while Type D (mass concentration) induces local curvature.
Drift and Torsion:
- Type A: Causes asymmetric drift distributions and high torsional participation.
- Type B: Leads to localized drift concentrations ("kinks") at setback levels and increased P- $\Delta$ sensitivity.
- Type C: Results in helical drift patterns and very high torsional response.
- Type D: Creates local drift peaks at massed levels.
Amplification: An illustrative example of a 30-storey building with moderate combined asymmetries (eccentricity, setback, and perched mass) demonstrated a Combined DFF of approximately 1.9, indicating a near-doubling of drift and torsional demands compared to a symmetric baseline.

Significance and Scope
The paper claims significance as a conceptual bridge between architectural creativity and structural rationality. It aims to provide architects and engineers with a systematic means to recognize, classify, and roughly quantify the "dynamic penalties" of unconventional geometry at the early design stage.

The authors explicitly state the following limitations and scope:

Conceptual Tool, Not Code: The AIDI-DFF framework is intended as a screening tool to guide design judgment and identify the need for advanced analysis, not as a prescriptive design rule or a replacement for detailed FE modeling.
Linear Elastic Limitations: The study is confined to linear elastic analysis; it does not address nonlinear time-history behavior, ultimate performance, or experimental validation.
Future Work: The authors note that the DFFs require calibration against broader numerical and experimental databases (including shake-table and wind tunnel testing) before potential incorporation into design guidelines.

In summary, the work establishes a foundation for understanding how architectural form independently drives dynamic irregularity, offering a structured approach to integrate these considerations earlier in the design process to avoid late-stage surprises and re-design.

1. The Problem: Cool Shapes, Hidden Wobbles

2. The Solution: The "AIDI" Framework

3. The Tool: "Dynamic Form Factors" (DFFs)

4. How They Tested It

5. The Big Takeaway

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