Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

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Performance objectives

• Define forces like tension, compression, shear, and torsion.
• Explain how shapes like triangles and arches add strength.
• Identify different types of loads on structures.
• Describe how materials affect a structure's strength.
• Design and build a simple structure to withstand a load.

Lesson summary

This week, we delve into the fascinating world of structures and how forces affect them. Understanding forces and strength in structures is crucial, not just for building bridges and skyscrapers, but also for understanding the everyday objects around us. Think about the chair you're sitting on, the roof over your head, or even the cell phone in your hand – all of these are structures that rely on specific designs to withstand various forces. In South Africa, this knowledge is particularly relevant as we strive to improve infrastructure and create sustainable and safe buildings for our communities.

Lesson notes

What is a Structure? A structure is something that supports a load. This could be anything from a small table to a massive dam. Structures are designed to withstand forces. What is Force? A force is a push or a pull that can cause an object to change its shape, speed, or direction. Forces are measured in Newtons (N). In the context of structures, forces act on them, and the structures must be strong enough to resist these forces without collapsing.

Types of Forces Acting on Structures: Tension: A force that pulls or stretches an object. Imagine pulling on a rope; the rope is under tension. In structures, tension often occurs in cables or ropes supporting loads. Think of the suspension cables on a bridge.

Example: The cables of the Bloukrans Bridge, one of the world's highest bungee jumping bridges in South Africa, are under significant tension.

Compression: A force that pushes or squeezes an object. Think of stacking books on top of each other; the books at the bottom are under compression. In structures, columns and walls are often under compression.

Example: The pillars of a traditional rondavel (African round house) are under compression supporting the weight of the roof.

Shear: A force that acts parallel to a surface, causing layers of the material to slide past each other. Imagine cutting paper with scissors; the blades apply shear force. In structures, shear force can occur in beams where they connect to columns.

Example: Think of the rivets or bolts connecting two pieces of metal in a bridge. Shear force is acting on these fasteners.

Torsion: A force that twists an object. Imagine wringing out a wet cloth; you're applying torsion. In structures, torsion can occur in shafts or axles that are rotating.

Example: Consider a winding road on a steep hill. The road surface experiences torsional forces from the turning wheels of vehicles.

Types of Loads on Structures: Dead Load: The weight of the structure itself and any permanently attached items.

Example: The weight of the concrete, steel, and fixtures in a school building is the dead load.

Live Load: The weight of movable objects and people that the structure supports.

Example: The weight of students, desks, and books in a classroom is the live load.

Environmental Load: Forces from the environment, such as wind, rain, snow, or earthquakes.

Example: The wind pressure on a building during a storm or the force of floodwaters against a bridge are environmental loads.

Structural Shapes and Strength: The shape of a structure significantly affects its strength. Certain shapes are better at distributing forces than others.

Triangles: Triangles are incredibly strong because their rigid shape evenly distributes forces. They are commonly used in trusses and bridges. Think of the Warren truss bridge design frequently used in railway bridges in South Africa.

Arches: Arches distribute compressive forces along their curve, making them very strong for supporting heavy loads. They are often used in bridges and tunnels. Consider the many arched bridges found throughout South Africa.

Cylinders: Cylinders are strong under compression and are often used for columns and pipes.

Materials and Strength: The material used to build a structure also affects its strength. Different materials have different properties.

Steel: Strong in both tension and compression. Used in bridges, buildings, and other large structures.

Concrete: Strong in compression but weak in tension. Often used with steel to create reinforced concrete, which is strong in both tension and compression.

Wood: Relatively strong in both tension and compression, but less so than steel or concrete. Used in houses, furniture, and other smaller structures.

Worked example

Example 1: Tension in a Suspension Bridge Cable

A suspension bridge cable with a diameter of 0.2m is supporting a section of the bridge with a weight of 5,000,000 N. Calculate the tensile stress (force per unit area) in the cable.

Step 1: Calculate the cross-sectional area of the cable.

Area (A) = πr² = π (0.1m)² ≈ 0.0314 m²

Step 2: Calculate the tensile stress.

Tensile Stress = Force / Area = 5,000,000 N / 0.0314 m² ≈ 159,235,669 Pa (Pascals)

This high stress indicates why suspension bridge cables need to be made of very strong materials like high-strength steel.

Example 2: Compression on a Building Column