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5.1 FIGURE 5.1 on ANSWER SHEET B shows the space diagram of a lean-to roof - NSC Civil Technology Woodworking - Question 5 - 2017 - Paper 1
Question 5
5.1 FIGURE 5.1 on ANSWER SHEET B shows the space diagram of a lean-to roof. Determine graphically on scale 1 mm = 1 N on ANSWER SHEET B the size and nature of the fo... show full transcript
Worked Solution & Example Answer:5.1 FIGURE 5.1 on ANSWER SHEET B shows the space diagram of a lean-to roof - NSC Civil Technology Woodworking - Question 5 - 2017 - Paper 1
Step 1
5.1 Determine graphically on scale 1 mm = 1 N
Answer
To determine the size and nature of the forces in the truss:
- Construct a force diagram by analyzing the angles and forces given in the lean-to roof diagram.
- Use the provided measurements and scale where 1 mm represents 1 N to plot the forces for 40 N and 60 N.
- Calculate the resultant force at joint D by using vector addition, considering the 30° angle and the two forces acting on it.
- Identify the forces in the members of the truss (AB, BC, and CD) by resolving them into vertical and horizontal components.
- Complete the table with the calculated magnitudes and nature (tension/compression) of each member.
Step 2
5.2.1 The bending moment values
Answer
To compute the bending moment values:
- Analyze the beam under the applied loads to determine the shear force at each section, using static equilibrium equations:
- Sum of vertical forces = 0
- Sum of moments about any point = 0.
- Calculate the moments at points A, B, C, and D considering their respective distances from the loads.
- Document the bending moments at each critical point taking into account positive and negative moments.
Step 3
5.2.2 Complete the bending moment diagram
Answer
To complete the bending moment diagram:
- Using the bending moment values computed in the previous step, plot these values along the beam.
- Mark the positive and negative moments appropriately on the diagram based on your calculations.
- Draw a smooth curve connecting these points to illustrate the variation of bending moments along the beam.
Step 4
5.3 Determine the centroid of the body
Answer
To determine the centroid from point P:
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Identify the shape and dimensions of the body illustrated in FIGURE 5.3.
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Use the formula for the centroid based on the defined geometric shapes:
ar{x} = \frac{\sum (x_i A_i)}{\sum A_i} \quad ext{and} \quad \bar{y} = \frac{\sum (y_i A_i)}{\sum A_i}
where ( (x_i, y_i) ) are the coordinate points of areas ( A_i ) of shapes.
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Calculate the centroid coordinates systematically for all segments in the figure.