Lesson Notes By Weeks and Term v5 - Grade 9

Lesson Video

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Performance objectives

• Explain the principle of triangulation.
• Identify different types of forces acting on structures.
• Analyze how structural systems distribute forces.
• Apply concepts to design a simple, stable structure.
• Describe properties and uses of different building materials.

Lesson summary

This week, we delve into advanced structural systems and forces, building upon the foundational knowledge you gained in previous weeks. Understanding these concepts is crucial because structures are all around us, from the houses we live in to the bridges we cross. In South Africa, with its diverse landscape and growing infrastructure needs, knowledge of structural systems and forces is particularly important for safe and sustainable development. Knowing how structures behave under different loads allows engineers to design buildings that can withstand earthquakes (common in some areas), heavy rainfall, strong winds, and even soil erosion.

Lesson notes

a)

Triangulation: Triangulation is a fundamental principle used to create strong and stable structures. A triangle is inherently rigid because its angles are fixed. This means that its shape cannot be changed without changing the length of its sides. In contrast, a rectangle or square can easily be deformed into a parallelogram because its angles can change. Imagine a square frame. If you push on one corner, it easily collapses. Now, add a diagonal brace across the square, dividing it into two triangles. The frame is now much more resistant to deformation because the triangles prevent the shape from changing. This is the essence of triangulation. Many structures, such as bridges, roof trusses, and cell phone towers, utilize triangulation extensively to distribute loads and maintain stability. The triangles spread the forces evenly, preventing any single point from bearing too much stress. b)

Types of Forces: Understanding the different types of forces acting on a structure is essential for designing it to withstand these forces.

The primary forces are: Tension: A pulling force that tends to stretch or elongate a material. Imagine pulling on a rope – the rope is under tension. Cables in suspension bridges are under tension.

Compression: A pushing force that tends to shorten or compress a material. A column supporting a roof is under compression.

Shear: A force that acts parallel to a surface, causing one part of the material to slide or deform relative to another. Imagine cutting paper with scissors – the paper is subjected to shear force. Bolts connecting two pieces of wood are subjected to shear force.

Torsion: A twisting force that causes rotation around an axis. Twisting a screwdriver applies torsion. The axles of a car are under torsion.

Bending: A combination of tension and compression, where one side of a structural member is stretched (tension) and the other side is compressed. A beam supporting a load is subjected to bending. The top of the beam is under compression, while the bottom is under tension. c)

Structural Systems: Different structural systems are designed to handle forces in different ways: Trusses: Trusses are frameworks of interconnected members (usually triangles) designed to distribute loads efficiently. They are commonly used in bridges, roofs, and towers. The members of a truss primarily experience tension or compression.

Arches: Arches are curved structures that transfer loads down to their supports (abutments) through compression. They are very strong and can span large distances without the need for intermediate supports. Ancient Roman aqueducts are excellent examples of arch structures.

Suspension Bridges: Suspension bridges use cables suspended between towers to support the bridge deck. The cables are under tension, and the towers are under compression. These bridges are suitable for spanning very long distances. The Nelson Mandela Bridge in Johannesburg is an example of a cable-stayed bridge, which is related to suspension bridges. d)

Material Properties: The choice of building materials is crucial for structural integrity. Different materials have different strengths and weaknesses when subjected to various forces.

Steel: Steel is strong in both tension and compression, making it suitable for beams, columns, and cables.

Concrete: Concrete is strong in compression but weak in tension. It is often reinforced with steel to improve its tensile strength. Reinforced concrete is used extensively in buildings, bridges, and dams.

Wood: Wood is strong in tension and compression along the grain but weaker perpendicular to the grain. It is commonly used in timber-frame houses and roofs. The type of wood affects its strength; for instance, hardwoods like oak are generally stronger than softwoods like pine. e) Worked

Examples: Example 1: Analyzing Forces on a Bridge Support Consider a bridge support column made of concrete. A truck weighing 100,000 N is passing over the bridge, and half of its weight is supported by one column. Calculate the compressive force on the column. Force = 100,000 N / 2 = 50,000 N The compressive force on the column is 50,000

N. Example 2: Calculating Tension in a Cable A cable is used to lift a container weighing 5,000 N. Calculate the tension in the cable. Tension = Weight of the container = 5,000 N The tension in the cable is 5,000

N. Example 3: Triangulation in a Roof Truss A simple roof truss is constructed using wooden beams. Explain how triangulation contributes to the stability of the truss. The roof truss is made of interconnected triangles. When a load is applied to the roof (e.g., from rain or snow), the forces are distributed along the members of the triangles. The rigid triangular shapes prevent the truss from collapsing or deforming under the load. The wooden beams primarily experience compression or tension, which they are well-suited to handle.