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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 Construction - 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 Construction - Question 5 - 2017 - Paper 1
Step 1
The bending moment values
Answer
To determine the bending moment values, we must apply the principles of statics. First, we will analyze the reactions at supports and calculate the shear forces along the beam. Using the given point loads and their distances from the supports, we can apply the formula for bending moments:
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Calculate Reactions:
- Let the reactions at supports A and D be R_A and R_D respectively. By summing up vertical forces and moments, we find the values of R_A and R_D.
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Shear Force Calculations:
- Starting from the left, calculate the shear forces between the loads and at the supports.
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Bending Moment Calculations:
- Calculate the bending moment at points along the beam using the formula: where M is the bending moment, R is the reaction force, d is the distance to the point of interest, V is the shear force, and x is the distance from the last load or support.
Step 2
Complete the bending moment diagram on scale 1 mm = 1 N according to the bending moment values.
Answer
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Choose Scale:
- Utilize the given scale of 1 mm = 1 N for accuracy.
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Plot Bending Moments:
- Mark the values obtained from step 1 (bending moments) along the lengths of the beam (between points a, b, c, and d) on the diagram.
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Connect Points:
- Draw a smooth curve connecting the plotted points to form the bending moment diagram.
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Label Diagram:
- Ensure all points, values, and scales are clearly labeled for easy interpretation.
Step 3
Determine the centroid of the body in FIGURE 5.3 from point P.
Answer
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Identify the Area Shapes:
- Break down the figure into recognizable geometric shapes (rectangles, triangles, etc.) for easier calculations.
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Calculate Area of Each Shape:
- Use the respective formulas:
- For rectangles: Area = width × height
- For triangles: Area = 1/2 × base × height
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Locate Centroids of Each Shape:
- For each shape, find the centroid coordinates.
- Rectangles: Centroid lies at its mid-point.
- Triangles: Centroid located at (1/3 from base along height).
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Use the Composite Centroid Formula:
- The X-coordinate of the centroid can be calculated by:
- Similarly, calculate the Y-coordinate of the centroid using: where A_i is the area of each shape, and (x_i, y_i) are the coordinates of their respective centroids.