Lesson Notes By Weeks and Term v5 - Grade 9

Lesson Video

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Performance objectives

• Define and differentiate between arches, trusses, and suspension bridges.
• Explain load distribution and stability in these systems.
• Identify forces like tension, compression, shear, torsion, and bending.
• Analyse forces in a simple truss structure.
• Describe the pros and cons of each system for use in South Africa.

Lesson summary

This week, we delve deeper into the fascinating world of structures, moving beyond basic shapes to explore advanced structural systems and the forces that act upon them. Understanding these concepts is crucial because structures are all around us, from the houses we live in to the bridges we cross and the buildings where we work and learn. In South Africa, with our diverse landscape and growing infrastructure, a solid understanding of structural principles is essential for safe and sustainable development.

Lesson notes

Advanced Structural Systems: We’ve previously explored basic structural forms. This week, we look at more complex systems that allow us to build larger and stronger structures.

Arches: An arch is a curved structural member spanning an opening and supporting a load. The key principle is that the load is primarily carried in compression along the curve of the arch. This allows arches to span greater distances than simple beams. The stability of an arch depends on its shape and the support at its ends (abutments). Roman arches, like those found in historical sites, are testament to their durability. A modern South African example is the use of arch-shaped roof structures in large warehouses or sports stadiums.

Trusses: A truss is a structure composed of interconnected members, typically arranged in triangles, which are inherently stable shapes. Truss members are primarily subjected to either tension (pulling force) or compression (pushing force). Trusses are exceptionally strong for their weight, making them ideal for bridges, roof supports, and other applications where long spans are required. Think of the large steel structures supporting the roofs of shopping malls or the framework for electrical pylons - these are often trusses. In South Africa, you will find trusses supporting roofs of houses, schools and other buildings.

Suspension Bridges: A suspension bridge uses cables suspended between towers to support the bridge deck. The main cables carry the load in tension, while the towers resist compression. Suspension bridges can span exceptionally long distances, making them suitable for crossing wide rivers or valleys. The Bloukrans Bridge in South Africa, famous for bungee jumping, is technically an arch bridge, but large suspension bridges, while less common in SA, are vital infrastructure in other parts of the world and understanding their principles is important.

Forces Acting on Structures: Understanding the different types of forces acting on structures is critical for designing stable and safe structures.

Tension: A pulling force that tends to stretch or elongate a structural member. Imagine pulling on a rope – the rope is in tension.

Compression: A pushing force that tends to compress or shorten a structural member. Imagine pushing down on a table leg – the leg is in compression.

Shear: A force that acts parallel to a surface, causing one part of the material to slide past the other. Imagine using scissors to cut paper – the paper experiences shear force.

Torsion: A twisting force that causes a structural member to rotate. Imagine twisting a screwdriver – the screwdriver is subjected to torsion.

Bending: A combination of tension and compression caused by a force applied perpendicular to a structural member. Imagine placing a heavy book in the middle of a ruler supported at both ends – the ruler bends, with the top surface in compression and the bottom surface in tension.

Load Distribution and Stability: Load Distribution: The way in which a load is spread across a structure. In a well-designed structure, the load is distributed evenly to prevent any single point from being overloaded. For example, in a truss, the load applied to the top chord is distributed through the triangular members to the supports.

Stability: The ability of a structure to resist deformation or collapse under load. A stable structure maintains its shape and position even when subjected to external forces. Stability is achieved through careful design, material selection, and construction techniques.

Worked example

Arch Load Distribution: Consider a small stone arch bridge spanning a dry riverbed (donga) in a rural community. The weight of the stones above and any traffic passing over the bridge creates a load. The arch shape ensures that this load is primarily converted into compressive forces within the stones. The abutments (supports at the ends of the arch) resist the outward thrust of the arch, preventing it from collapsing. If one abutment is weakened by erosion, the arch becomes unstable and can collapse.

Truss Force Analysis: Let's analyze a simple A-frame truss, commonly used for roof supports. Assume a weight of 500N is applied at the apex (top point) of the truss. The vertical load of 500N is divided equally between the two members of the truss. Each member now experiences a compressive force. The magnitude of the force in each member depends on the angle of the truss. Let's assume the angle between each member and the horizontal support is 45 degrees. Then, the compressive force in each member can be calculated as follows:

Vertical component of force in each member = 500N/2 = 250N

Compressive Force = Vertical Component / sin(angle) = 250N / sin(45°) = 250N / 0.707 ≈ 353.55N.

Each member experiences approximately 353.55N of compression. The horizontal support at the base will experience outward tension forces.

Suspension Bridge Cable Tension: Imagine a small pedestrian suspension bridge crossing a stream in a park. The weight of the bridge deck and any pedestrians walking on it is the load. This load is transferred to the main cables, which are in tension. The towers support the cables and resist the compressive force from the cables pulling inwards. The longer the span, the greater the tension in the cables.

Guided Practice (With Solutions)

Question: Identify the type of structural system used in a cell phone tower and explain why that system is appropriate.

Solution: Cell phone towers typically use a truss structure. This is appropriate because trusses are lightweight and strong, allowing the tower to be tall and stable while minimizing the amount of material used. The open framework of a truss also reduces wind resistance.

Question: A wooden beam is supporting a heavy load in the center. What type of force is primarily acting on the top surface of the beam? What type of force is primarily acting on the bottom surface?

Solution: The top surface of the beam is primarily experiencing compression. The bottom surface is primarily experiencing tension. The bending of the beam causes these forces.

Question: Explain how an arch bridge distributes the load it carries. Why is the shape of the arch important for this load distribution?

Solution: An arch bridge distributes the load primarily through compression along the curve of the arch to the abutments. The arch shape is crucial because it efficiently converts the vertical load into compressive forces, minimizing bending and shear forces. If the arch were a straight beam, it would be much weaker and prone to bending.

Question: A bridge is designed to withstand tension, compression and shear forces. Explain how each force is present in the bridge's design.