Lesson Notes By Weeks and Term v5 - Grade 11

Lesson Video

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Performance objectives

• Identify and classify structural members.
• Define and differentiate between types of forces.
• Analyze forces in simple structures like trusses.
• Calculate the magnitude of forces in simple members.
• Draw Free Body Diagrams of simple trusses.

Lesson summary

This week, we delve into the fascinating world of structural members and the forces acting within simple structures. Understanding these principles is crucial for any aspiring civil technologist. From the bridges we drive over to the houses we live in, and the shopping malls we visit, every structure relies on the ability of its members to withstand various forces. Consider the challenges South Africa faces in providing affordable and safe housing and infrastructure. A solid understanding of structural principles is vital for building sustainable and reliable structures that can withstand the test of time and provide safe living environments for all South Africans.

Lesson notes

2. 1.

Structural Members: Structural members are the individual components of a structure that work together to support loads and resist external forces. The type of member is defined by the primary load it carries: Tension Members: These members are designed to resist pulling forces, known as tension. Imagine pulling on a rope; the rope is under tension. Common examples include cables in suspension bridges, and tie rods. In South Africa, tension members are used in securing the frames of houses, supporting roofs, and various other structures.

Compression Members: These members resist pushing or crushing forces, known as compression. Think of a column holding up a roof. The column is under compression. Examples include columns in buildings, struts in trusses, and foundation piles. The foundations of buildings in South Africa use these principles and materials due to the climate and conditions.

Beams: Beams are horizontal structural members designed to primarily resist bending forces. They support loads applied perpendicular to their longitudinal axis. Examples include floor joists, lintels above windows and doors, and bridge decks. In South Africa, concrete beams are used to provide support to roads when crossing over a bridge.

Columns: Vertical structural members that primarily support axial compressive loads.

Struts: Similar to columns, but often shorter and used in trusses to resist compression at an angle. 2.

2. Types of Forces: Forces are actions that tend to change the state of rest or motion of a body. In structural analysis, we primarily deal with the following types of forces: Tension: A pulling force that tends to elongate or stretch a member. It is measured in Newtons (N). The internal resistance in a tension member balances the applied tensile force.

Compression: A pushing or crushing force that tends to shorten a member. It is also measured in Newtons (N). The internal resistance in a compression member balances the applied compressive force.

Shear: A force that acts parallel to a surface, causing one part of the member to slide relative to the adjacent part. Think of cutting paper with scissors – the blades apply a shear force. Measured in Newtons (N). Shear is present in beams, especially near supports.

Bending: A combination of tension and compression forces acting on a structural member that is subjected to a load perpendicular to its length. The top fibers of a bending beam are in compression, while the bottom fibers are in tension.

Torsion: A twisting force that tends to rotate a member about its longitudinal axis. Think of twisting a screwdriver. Measured in Newton-meters (Nm). Torsion is important in the design of axles and shafts. 2.

3. Statics and Equilibrium: Statics is the branch of mechanics that deals with bodies at rest or in equilibrium (constant velocity). For a structure to be stable, it must be in equilibrium, meaning the sum of all forces acting on it must be zero. Mathematically, this is expressed as: ΣFx = 0 (Sum of horizontal forces = 0) ΣFy = 0 (Sum of vertical forces = 0) ΣM = 0 (Sum of moments = 0) 2.

4. Free Body Diagrams (FBDs): A Free Body Diagram (FBD) is a simplified representation of a structure or a part of a structure, showing all the forces acting on it. FBDs are essential for analyzing forces and determining reactions in structural members.

Steps to draw a FBD: Isolate the member or joint you want to analyze. Draw the member or joint as a simple shape. Represent all external forces acting on the member or joint with arrows.

Include: Applied loads (e.g., weight, external forces). Reactions at supports (e.g., vertical and horizontal reactions). Forces exerted by other members connected to the joint. Label each force with its magnitude and direction. Include any relevant dimensions or angles. 2.

5. Worked

Examples: Example 1: Tension Member A steel cable is used to support a sign weighing 5000

N. Calculate the tension force in the cable.

Solution: Since the sign is in equilibrium, the tension in the cable must be equal to the weight of the sign. Tension (T) = Weight (W) = 5000 N Example 2: Compression Member A concrete column supports a load of 200 k

N. Calculate the compressive force in the column.

Solution: The compressive force in the column is equal to the load it supports. Compression (C) = Load (P) = 200 kN = 200,000 N Example 3: Simple Truss Analysis (Method of Joints) Consider a simple truss with two members, AB and BC, supporting a vertical load of 1000 N at joint B. Angle ABC is 90 degrees and the angle between member AB and the horizontal is 45 degrees. Determine the forces in members AB and BC.