Updated Module 1 - Introduction to Theory of Structures PDF

Theory of Structures (ATSTRUCT) Module 1: Introduction to Theory of Structures Engr. Vuangh Erick B. Barrantes, MSc Instructor  Introduction The Theory of Structures is a fundamental aspect of structural engineering that focuses on analyz...

Theory of Structures (ATSTRUCT) Module 1: Introduction to Theory of Structures Engr. Vuangh Erick B. Barrantes, MSc Instructor  Introduction The Theory of Structures is a fundamental aspect of structural engineering that focuses on analyzing how structures respond to various loads and forces. It encompasses principles and methods essential for designing safe and efficient structures. Engr. Vuangh Erick B. Barrantes, MSc  Introduction Key Concepts in Structural Engineering: Structural Analysis: Evaluates internal forces and stresses in components (e.g., beams, trusses) to ensure they can bear applied loads safely. Load Analysis: Identifies and categorizes loads (dead, live, environmental) for precise structural design. Material Behavior: Examines material responses (elastic/plastic) to stress for appropriate selection in structural applications. Engr. Vuangh Erick B. Barrantes, MSc  Introduction Key Concepts in Structural Engineering: Equilibrium and Stability: Ensures force balance and structural stability under various conditions to prevent collapse. Compatibility: Verifies consistent deformations within the structure to maintain integrity. Engr. Vuangh Erick B. Barrantes, MSc  Structural Design Process 1. Planning Phase: Often part of Conceptual Design, it involves defining the structure's purpose, scope, and constraints, along with site analysis and preliminary feasibility studies. 2. Preliminary Structural Design: Sometimes called Schematic Design, this phase involves creating initial layouts and selecting potential structural systems based on functionality, aesthetics, and feasibility. 3. Estimation of Loads: This is part of Load Analysis and involves determining the forces acting on the structure, including dead loads, live loads, wind loads, seismic forces, and other environmental impacts. Engr. Vuangh Erick B. Barrantes, MSc  Structural Design Process 4. Structural Analysis: This involves the application of principles and methods to calculate internal forces, stresses, and displacements in the structure to ensure it can withstand the estimated loads. 5. Safety and Serviceability Checks: Known as Structural Design Validation, these checks ensure that the structure is safe under ultimate loads and performs well under service loads without excessive deflection or vibration. 6. Revised Structural Design: This phase involves Iterative Design Refinement, where modifications are made based on analysis and checks to meet safety, functionality, and economic criteria. Engr. Vuangh Erick B. Barrantes, MSc  Classification of Structures Based on how structure resists loads and transfer forces to supports 1. Tension Structures: These structures primarily resist forces through tension, where the material is pulled or stretched under load. Examples: Suspension Bridges: Cables support the deck by transferring loads to towers. Cable Systems: Used in lightweight roofs or bridges. Engr. Vuangh Erick B. Barrantes, MSc  Classification of Structures Based on how structure resists loads and transfer forces to supports 2. Compression Structures Structures that resist loads primarily through compression, where the material is squeezed or shortened under load. Examples: Columns: Vertical members in buildings. Arches: Curved elements transferring loads to supports through compression. Domes: Spherical shells distributing loads evenly in all directions. Engr. Vuangh Erick B. Barrantes, MSc  Classification of Structures Based on how structure resists loads and transfer forces to supports 3. Bending Structures Structures that resist loads through bending, where one side experiences tension and the opposite side experiences compression. Examples: Beams: Horizontal elements in floors or bridges. Cantilevers: Projections supported at one end only. Frames: Systems of beams and columns in modern buildings. Engr. Vuangh Erick B. Barrantes, MSc  Classification of Structures Based on how structure resists loads and transfer forces to supports 4. Combined Force Structures (TRUSS) Truss are composed of straight members connected at their ends by hinged connections to form a stable configuration Engr. Vuangh Erick B. Barrantes, MSc  Classification of Structures Based on how structure resists loads and transfer forces to supports 5. Shear Structures Structures that resist lateral loads through shear forces. Examples: Shear Walls: Vertical walls in buildings resisting wind or seismic forces. Braced Frames: Frames with diagonal members resisting lateral forces. Engr. Vuangh Erick B. Barrantes, MSc  Types of Structural Connections 1. Pinned (Hinged) Connections: Allow rotation but resist translation in any direction. Example: Truss joints where members are connected using pins or bolts, permitting rotation without moment transfer. Engr. Vuangh Erick B. Barrantes, MSc  Types of Structural Connections 2. Rigid (Moment) Connections: Resist both rotation and translation, allowing moment transfer between members. Characteristics: Provide stability against lateral loads. Example: Concrete and Welded beam-to-column connections Engr. Vuangh Erick B. Barrantes, MSc  Types of Structural Connections 3. Semi-Rigid Connections: Exhibit partial rigidity, allowing limited moment transfer while permitting some rotation. Example: Bolted end plate connections that offer flexibility between pinned and rigid connections. Engr. Vuangh Erick B. Barrantes, MSc Types of Structural Supports Engr. Vuangh Erick B. Barrantes, MSc  Structural Members and Other Forms of Structures Structural elements are the fundamental building blocks of any structure, designed to transfer and resist forces: Beams Columns Slabs Footings Engr. Vuangh Erick B. Barrantes, MSc  Types of Beams Simply Supported Beams Engr. Vuangh Erick B. Barrantes, MSc  Types of Beams Simply Supported Beams (Statically Determinate Beam): A statically determinate beam is a structure where all the reactions and internal forces can be determined using only the equations of static equilibrium: ΣV=0: The sum of vertical forces must be zero. ΣH=0: The sum of horizontal forces must be zero. ΣMs=0: The sum of moments about any point must be zero. One end has a roller support: This allows vertical movement but resists horizontal forces. The other end has a pin support: This restricts both vertical and horizontal movements but allows rotation. Engr. Vuangh Erick B. Barrantes, MSc  Types of Beams Overhanging Beam: An overhanging beam is a beam that extends beyond its support(s) on one ends. Engr. Vuangh Erick B. Barrantes, MSc  Types of Beams A double overhanging beam has extensions beyond the supports on both ends, creating two overhangs. These sections are unsupported at their outer edges, while the central part of the beam is supported at two points. Engr. Vuangh Erick B. Barrantes, MSc  Types of Beams Fixed Beam A fixed beam is a type of beam where both ends are rigidly fixed to supports. This means that the beam cannot rotate or translate at the supports, and moments are induced at these points. Engr. Vuangh Erick B. Barrantes, MSc  Types of Beams Fixed Beam Both ends of the beam have fixed supports. These supports provide: Vertical Reaction to resist vertical loads. Horizontal Reaction to resist axial loads. Restraining Moments to resist rotation at the supports. Load Application: The yellow downward arrows represent a uniformly distributed load (UDL) applied across the entire length of the beam. This load creates bending and shear stresses throughout the beam. The beam curves downward under the UDL, with the deflection being minimal at the fixed supports due to the restraining moments. The deflection is more pronounced near the midspan but remains less than that of a simply supported beam due to the additional restraint provided by the fixed ends. Engr. Vuangh Erick B. Barrantes, MSc  Types of Beams Cantilever Beam A cantilever beam is a beam that is fixed at one end and free at the other. This simple yet powerful structural element is commonly used in a variety of engineering applications, from bridges to building frameworks. Engr. Vuangh Erick B. Barrantes, MSc  Types of Beams Cantilever Beam The fixed support at the left end of the cantilever beam restricts both translation (vertical and horizontal) and rotation. The free end of the beam is unsupported, meaning it cannot resist any vertical or horizontal forces, and the beam may experience deflection or rotation at this point when subjected to loads. Loads can be applied in various ways, but typically the beam may carry: Point loads at any position along its span. Uniformly distributed loads (UDL) across all or part of the beam’s length. Moment loads applied at specific points. Engr. Vuangh Erick B. Barrantes, MSc  Types of Beams Continuous Beam A continuous beam is a beam that extends over more than two supports. Unlike simply supported beams, which have only two supports, continuous beams are supported at multiple points, often creating a more efficient distribution of forces. Engr. Vuangh Erick B. Barrantes, MSc  Types of Beams Continuous Beam A continuous beam is statically indeterminate, meaning the number of unknown reactions exceeds the number of static equilibrium equations. To solve for the reactions and internal forces, additional methods, such as the equilibrium method, moment distribution method, or slope-deflection method, are required. Continuous beams have less deflection than simply supported beams under the same loading conditions. This is because the additional supports reduce the amount of bending and help distribute the load more efficiently. Engr. Vuangh Erick B. Barrantes, MSc