Lesson Notes By Weeks and Term v5 - Grade 9

Lesson Video

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Performance objectives

• Define and differentiate between key forces: tension, compression, shear, torsion, and bending.
• Explain how structural systems like arches, trusses, and cantilevers distribute forces.
• Identify forces acting on specific structural elements.
• Calculate simple stress and strain in structural members.

Lesson summary

This week, we're diving deeper into the world of structures, moving beyond simple frames and exploring more advanced structural systems and the forces that act upon them. Understanding how structures are designed to withstand forces is crucial for building safe and efficient buildings, bridges, and other infrastructure. This knowledge is incredibly relevant to South Africa, where we constantly need to develop and maintain infrastructure to support our growing population and economy. From the houses we live in to the roads we travel on, structural integrity is paramount. This lesson will explore how engineers use their understanding of forces to create stable and durable structures.

Lesson notes

2.1 Types of Forces: Tension: Tension is a pulling force that tends to elongate or stretch a material. Imagine pulling on a rope – that's tension. In structures, tension is often found in cables, ropes, or the bottom chord of a truss. Examples in South Africa include the cables of suspension bridges and the guy wires supporting cell phone towers.

Compression: Compression is a pushing or squeezing force that tends to shorten a material. Think of pushing down on a spring or stacking bricks. Columns and walls in buildings are primarily designed to withstand compressive forces. A concrete pillar supporting a bridge deck is a prime example of compression.

Shear: Shear is a force that causes layers of a material to slide past each other. Imagine cutting paper with scissors – that's shear. Shear forces are common in bolts and rivets that connect structural members, as well as in beams close to their supports. Consider the force exerted on a bolt connecting two steel plates.

Torsion: Torsion is a twisting force that tends to rotate a material. Think of twisting a screwdriver or wringing out a wet cloth. Drive shafts in vehicles and axles are designed to withstand torsion. The forces generated by wind on a tall building can induce torsional stress in its supporting structure.

Bending: Bending is a combination of tension and compression. When a beam is bent, one side is stretched (tension), while the other side is compressed. The top of a beam sagging under its own weight experiences compression while the bottom experiences tension. Bridges and roof beams are subjected to bending forces. 2.2 Structural Systems: Arches: Arches are curved structures that distribute compressive forces along their curve. This allows them to span large distances without requiring support in the middle. The Romans perfected the arch, and it's still used today, especially in bridge construction. Although not as prevalent as in Europe, you can find arch bridges in South Africa and arched roofs in some historical buildings.

Trusses: Trusses are frameworks of interconnected members (usually triangles) that are designed to efficiently distribute forces. They are typically made of steel or wood and are used in bridges, roofs, and towers. Trusses are very common in South Africa for roof support in factories, warehouses, and even some residential buildings, due to their strength and relatively low material cost.

Cantilevers: Cantilevers are beams or structures that are supported at only one end. The other end projects out freely. Examples include balconies, overhanging roofs, and some types of bridges. Cantilever bridges are sometimes used in challenging terrain where intermediate supports are difficult to build. Imagine a balcony extending out from a building; it's held up only on one end. 2.3 Stress and Strain: Stress: Stress is the force acting per unit area within a material. It's a measure of the internal forces that molecules within a continuous material exert on each other. Stress is usually measured in Pascals (Pa) or pounds per square inch (psi).

Formula: Stress (σ) = Force (F) / Area (A)

Strain: Strain is the deformation of a material caused by stress. It's a measure of how much the material has stretched or compressed relative to its original size. Strain is a dimensionless quantity.

Formula: Strain (ε) = Change in Length (ΔL) / Original Length (L) 2.4 Worked Examples (Stress and Strain): Example 1 (Tension): A steel cable with a cross-sectional area of 0.001 m² is used to lift a concrete block weighing 5000

N. Calculate the stress in the cable.

Solution: Force (F) = 5000 N Area (A) = 0.001 m² Stress (σ) = F / A = 5000 N / 0.001 m² = 5,000,000 Pa (5 MPa) Therefore, the stress in the cable is 5 million Pascals or 5 Mega Pascals.

Example 2 (Compression): A concrete column with a cross-sectional area of 0.25 m² supports a load of 200,000

N. Calculate the stress in the column.

Solution: Force (F) = 200,000 N Area (A) = 0.25 m² Stress (σ) = F / A = 200,000 N / 0.25 m² = 800,000 Pa (0.8 MPa) Therefore, the stress in the column is 800,000 Pascals or 0.8 Mega Pascals.

Example 3 (Strain): A steel rod with an original length of 2 meters is subjected to a tensile force, causing it to elongate by 0.002 meters. Calculate the strain in the rod.

Solution: Change in Length (ΔL) = 0.002 m Original Length (L) = 2 m Strain (ε) = ΔL / L = 0.002 m / 2 m = 0.001 Therefore, the strain in the rod is 0.001 (dimensionless). Guided Practice (With Solutions)

Question 1: A wooden beam is supported at both ends and has a load applied in the middle. What type of force is most prominent at the top of the beam directly under the load?

Solution: Compression. The load applied to the middle of the beam causes the top portion of the beam to compress as the beam bends.

Question 2: A bridge cable is holding up a section of the bridge deck. What type of force is acting on the cable?

Solution: Tension. Cables are designed to resist pulling forces, which is tension.