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7.1 Define the following terms: 7.1.1 Stress 7.1.2 Hooke's law 7.2 FIGURE 7.2 is a diagram of a steel frame structure - NSC Mechanical Technology Welding and Metalwork - Question 7 - 2021 - Paper 1
Question 7
7.1 Define the following terms: 7.1.1 Stress 7.1.2 Hooke's law 7.2 FIGURE 7.2 is a diagram of a steel frame structure. Answer the questions that follow. 7.2.1 Con... show full transcript
Worked Solution & Example Answer:7.1 Define the following terms: 7.1.1 Stress 7.1.2 Hooke's law 7.2 FIGURE 7.2 is a diagram of a steel frame structure - NSC Mechanical Technology Welding and Metalwork - Question 7 - 2021 - Paper 1
Step 1
Define Stress
Answer
Stress is defined as the internal resistance of a body to an external force or load. It is measured as the force applied per unit area within materials, typically expressed in Pascals (Pa). Mathematically, it can be represented as:
where F is the force applied, and A is the cross-sectional area.
Step 2
Define Hooke's Law
Answer
Hooke's Law states that the strain in a solid material is proportional to the applied stress, provided the elastic limit is not exceeded. This relationship can be expressed mathematically as:
where k is the constant of proportionality, known as the stiffness of the material.
Step 3
Construct the space diagram according to the given scale of 10 mm = 1 m
Answer
To construct the space diagram, proceed as follows:
- Identify the dimensions provided in the problem:
- Force of 200 N acting vertically at point B.
- Horizontal length of 150 mm between points A and C.
- Inclined lengths corresponding to the angles given in the diagram.
- Use the scale of 10 mm = 1 m to create a scaled diagram showing the forces and points correctly marked.
Step 4
Construct the vector diagram using scale 1 mm = 1 N
Answer
For the vector diagram:
- Start by representing the forces acting on the structure. The 200 N vertical force acts downwards at point B.
- Next, represent the horizontal and diagonal forces at points A, C, and D using the correct proportions; for instance, 50 N is to be shown horizontally at point C.
- Ensure that all vectors are drawn to scale based on the 1 mm = 1 N configuration to accurately reflect the sizes of the forces.
Step 5
Determine the magnitude and nature of the forces in members AD, BD and CD from the vector diagram
Answer
- Analyze the vector diagram to find the forces in the members:
- Member AD: The force determined is approximately 172 N to 176 N, categorized as a strut.
- Member BD: The force computed is around 100 N to 104 N, also classified as a strut.
- Member CD: For this member, the force is approximately 87 N to 91 N, classified as a tie.
- The nature of these forces indicates how they react under load – struts being in compression and ties in tension.