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Refer to the figure - NSC Civil Technology Civil Services - Question 5 - 2017 - Paper 1
Question 5
Refer to the figure. Given a structure with various members subjected to forces, determine the nature and magnitude of the forces in the members as indicated in the... show full transcript
Worked Solution & Example Answer:Refer to the figure - NSC Civil Technology Civil Services - Question 5 - 2017 - Paper 1
Step 1
5.2(a) - Calculate the forces in the structure
Answer
To determine the forces in each member, we will analyze the structure using equilibrium equations. We start by assuming the forces in the structure members AC, BC, CD, and DA.
- Draw a Free Body Diagram (FBD): Label all the forces acting on the structure including the external loads and reactions.
- Set Up Equilibrium Equations: Use the equations of equilibrium:
- Sum of vertical forces:
- Sum of horizontal forces:
- Sum of moments about a point:
- Solve the system of equations to find the unknown forces in the members AC, BC, CD, and DA. This will yield the magnitudes and nature (tension/compression) of each member.
Step 2
5.2(b) - Draw the vector diagram
Answer
To draw the vector diagram, follow these steps:
- Identify Magnitudes: From the previous calculations, note down the force magnitudes from each member (e.g., 54.5 N for AC, etc.).
- Choose a Scale: Select a suitable scale where 1 mm represents 1 N or any convenient scale to make drawing feasible.
- Draw Vectors: Starting from a common point, draw each force vector to scale and in the correct direction. Ensure to maintain the angle measurements as per the earlier analysis (e.g., 45°, 60°).
- Label Each Vector with its respective member name and magnitude for clarity.
Step 3
5.2(c) - Construct the space diagram
Answer
For the space diagram:
- Reproduce the Structure: Draw the original structure layout, accurately reflecting the member connections and lengths as shown in the figure.
- Label Each Member: Clearly label each member (AC, BC, CD, DA) on the diagram to indicate where the forces were calculated.
- Indicate Forces: Add the force arrows on each member (drawn to scale) based on the values computed earlier. Ensure arrows point in the correct direction indicating tension or compression.