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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 Civil Services - 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 Civil Services - Question 5 - 2017 - Paper 1
Step 1
Determine bending moment values
Answer
To calculate the bending moment values for the beam shown in FIGURE 5.2, we must begin by applying the equilibrium equations for moments about a point. We will calculate the moments at different sections of the beam (a, b, c, d) based on given point loads. The positive moment convention assumes counterclockwise moments as positive.
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Calculate moments at point A (left end):
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Calculate moments at point B:
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Calculate moments at point C:
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Calculate moments at point D:
Finally, compile the bending moments into a table for presentation.
Step 2
Complete the bending moment diagram on scale 1 mm = 1 N
Answer
Once the moment values are calculated, plot them on the bending moment diagram. Use a scale of 1 mm representing 1 N. Start from the left side of the beam and move toward the right side, marking the values at points a, b, c, and d on the X-axis. Draw a smooth curve to connect these points, indicating the change in the bending moment along the beam.
Step 3
Determine the centroid from point P
Answer
To find the centroid of the body in FIGURE 5.3, utilize the formula for the centroid located at point P:
the coordinates of the centroid (ar{x}, ar{y}) can be calculated using the following approach:
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Divide the body into simple shapes (e.g., rectangles).
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Calculate the area and centroid of each shape.
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Use the formula:
ar{x} = \frac{\sum (x_i A_i)}{\sum A_i}, \, \bar{y} = \frac{\sum (y_i A_i)}{\sum A_i}
- Combine the results to find the overall centroid of the composite shape.