Architecture Design Guide

Classical framework (Vitruvius, 1st century BCE):

FIRMITAS (Structural Integrity)
- Structural systems: load paths, material behavior, safety factors
- Building physics: thermal, acoustic, moisture performance
- Durability: service life, maintenance, resilience to hazards
- Modern addition: seismic, wind, and climate resilience

UTILITAS (Function)
- Program: spatial organization, adjacency requirements
- Circulation: movement patterns, wayfinding, accessibility
- Flexibility: adaptability to changing uses over time
- Modern addition: Universal design, inclusive environments

VENUSTAS (Delight)
- Proportion, rhythm, scale, materiality
- Light: natural and artificial, atmosphere, perception
- Cultural meaning: symbolism, context, identity
- Modern addition: Biophilic design, multisensory experience

Contemporary additions:
SUSTAINABILITY (since 1990s)
- Energy performance, carbon footprint, resource efficiency
- Lifecycle assessment, circular economy principles
- Passive strategies, renewable energy integration

SOCIAL RESPONSIBILITY (since 2000s)
- Equity, community engagement, participatory design
- Affordable housing, public space, social infrastructure
- Post-occupancy evaluation, evidence-based design

Primary structural systems and their research applications:

FRAME STRUCTURES
- Material: Steel, reinforced concrete, timber
- Behavior: Moment-resisting frames, braced frames
- Research topics: Connection design, progressive collapse,
  fire resistance, seismic performance

SHELL STRUCTURES
- Types: Vaults, domes, hyperbolic paraboloids
- Behavior: Membrane forces (compression/tension), minimal bending
- Research topics: Form-finding, buckling, computational geometry
- Key method: Thrust network analysis (Block, 2009)

TENSILE STRUCTURES
- Types: Cable-stayed, membrane, tensegrity
- Behavior: Pure tension, anticlastic curvature
- Research topics: Form-finding, wind loading, material durability
- Key method: Dynamic relaxation, force density method

MASS TIMBER
- Types: CLT (cross-laminated timber), glulam, mass plywood
- Behavior: Orthotropic, fire charring provides structural reserve
- Research topics: Tall timber buildings, connections, moisture
- Growing field: embodied carbon advantages over concrete/steel

# Simple structural analysis for research
# Finite element analysis using Python (for educational purposes)

import numpy as np

def analyze_simply_supported_beam(
    length: float,       # meters
    load: float,         # kN/m (uniform distributed load)
    E: float,            # Young's modulus (GPa)
    I: float,            # Moment of inertia (mm^4)
    n_elements: int = 20,
) -> dict:
    """
    Analyze a simply supported beam under uniform load.
    Returns deflection, moment, and shear diagrams.
    """
    x = np.linspace(0, length, n_elements + 1)
    dx = length / n_elements

    # Analytical solutions
    # Maximum moment: wL^2/8
    max_moment = load * length**2 / 8  # kN-m

    # Moment diagram: M(x) = (w*x/2)*(L-x)
    moment = (load * x / 2) * (length - x)

    # Shear diagram: V(x) = w*(L/2 - x)
    shear = load * (length / 2 - x)

    # Deflection: delta(x) = (w*x)/(24*E*I) * (L^3 - 2*L*x^2 + x^3)
    E_pa = E * 1e9  # Convert GPa to Pa
    I_m4 = I * 1e-12  # Convert mm^4 to m^4
    w_nm = load * 1e3  # Convert kN/m to N/m
    deflection = (w_nm * x) / (24 * E_pa * I_m4) * (
        length**3 - 2 * length * x**2 + x**3
    )
    max_deflection = 5 * w_nm * length**4 / (384 * E_pa * I_m4)

    return {
        "x": x,
        "moment_kNm": moment,
        "shear_kN": shear,
        "deflection_mm": deflection * 1000,
        "max_moment_kNm": max_moment,
        "max_deflection_mm": max_deflection * 1000,
        "span_to_deflection_ratio": length / max_deflection if max_deflection > 0 else float("inf"),
    }