Course

Module 1

Mathematical Applications in Architecture

• Basic geometry in architecture design.
• Trigonometry in structural analysis.
• The Golden Ratio in architecture.
• Introduction to fractal theory and its relevance in architecture.

Module 2

Structural Design Principles

• Introduction to basic structural design.
• Understanding various structural forms and elements in architecture.
• Principles governing the behavior of external loads (Statics).
• Role of mathematics in predicting structural behavior and performance.

Module 3

Introduction to Structural Systems and Theory of Structures

• Aims, objectives, and scope of the theory of structures for architects.
• Technical names and functions of structural components (foundation to roof).
• Relevance of structural design in architecture.
• Introduction to SI system and units.
• Understanding structural integrity – Why things don’t fall down?

Module 4

Structural Components and Load Analysis

• Structural systems – Ways to create inner space.
• Types and functions of structural components: beams, columns, trusses, slabs, etc.
• Types of loads: Dead, live, wind, earthquake, and other loads.
•  Analysis of structural loads and their distribution.

Module 5

Forces and Moments

• Definition, cause, effect, and units of forces and moments.
• Types of forces (compressive, tensile, shear).
• Conditions of equilibrium.
• Beam reactions and load-bearing behavior.

Module 6

Trusses and Structural Forms

• Types of trusses and their applications.
• Truss analysis – Joint and section method.
• Structural forms in architecture: arches, domes, vaults, shells.
• Importance of cross-sections in structural resistance.

Module 7

Fundamental Mechanics and Principles of Statics

• Statics of particles and rigid bodies.
• Basic concepts: force, moment, equilibrium.
• Principle of resistance – Stress, strain, and deformation in materials.
• Load transfer mechanisms in buildings.

Module 8

Advanced Structural Analysis and Mathematical Integration

• Detailed study of moment and shear force diagrams.
• Importance of structural cross-sections in resisting external forces.
• Complex geometrical and mathematical applications in architectural design.
• Case studies on innovative structural designs integrating mathematical principles.

• Students will gain a foundational understanding of how structural systems function and their role in architectural design.
•  Students will develop the ability to analyze the effects of forces and loads on various structural elements.
• Students will apply mathematical concepts like geometry and trigonometry to design problems, integrating them into their architectural solutions.
• Students will be able to recognize the relevance of different structural forms and elements in architectural design, including trusses, beams, and cross-sections.

• To introduce fundamental principles of structural systems and their relevance to architectural design.
• To understand the mechanics of forces, moments, and equilibrium in structures.
• To explore the relationship between geometry, trigonometry, and architecture design, emphasizing mathematical principles like the golden ratio and fractal theory.
• To develop an appreciation for the importance of structural components and their behavior under various loads, fostering informed decision-making in architectural design.

Course Outcomes:

• Students will gain a foundational understanding of how structural systems function and their role in architectural design.
• Students will develop the ability to analyze the effects of forces and loads on various structural elements.
• Students will apply mathematical concepts like geometry and trigonometry to design problems, integrating them into their architectural solutions.
• Students will be able to recognize the relevance of different structural forms and elements in architectural design, including trusses, beams, and cross-sections.

References:

1. Why Buildings Stand Up – Mario Salvadori

· Covers fundamental structural principles and their architectural implications.

2. Structures: Or Why Things Don’t Fall Down – J. E. Gordon

· Introduces the understanding of structural systems and materials in everyday life.

3. Engineering Mechanics: Statics – J. L. Meriam and L. G. Kraige

· Explains the fundamental principles of forces, moments, and equilibrium.

4. Introduction to Structural Mechanics – T.H.G. Megson

· Discusses structural components, load analysis, and fundamental mechanics.

5. Structural Design in Architecture – Salvadori and Heller

· Provides insights into structural forms, design principles, and their application in architecture.

6. Mathematics for the Environment – Martin Walter

· Introduces mathematical principles, including geometry and trigonometry, in environmental and structural contexts.

7. The Golden Ratio: The Story of Phi, the World’s Most Astonishing Number – Mario Livio

· Explores the golden ratio and its significance in architectural design.

8. Fractals: Form, Chance, and Dimension – Benoit Mandelbrot

· Discusses fractal theory and its relevance in architectural forms and structures.

9. The Geometry of Art and Life – Matila Ghyka

· Highlights the role of geometry in the artistic and architectural design process.

10. Structural Analysis – Russell C. Hibbeler

· A comprehensive guide to truss analysis, moment calculations, and shear force diagrams.