Photo AI
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 graphically on scale 1 mm = 1 N on ANSWER SHEET B the size and nature of the forces in the parts of the truss.
Answer
To start determining the forces in the truss, we will use a graphical method. First, draw the force vectors based on the given forces at points A, B, C, and D in FIGURE 5.1:
- Draw force vectors: Begin by drawing force vectors for the known forces, starting with the 40 N downward force at point A.
- Add the 60 N force: Next, draw the 60 N force at angle 30° relative to the horizontal at point C.
- Calculate the resultant force: Using the triangle law of forces, complete the triangle of forces to find the reaction at point D. This will allow you to calculate and draw the vectors representing the forces in members AB, BC, and CD.
- Label the forces: Indicate the sizes and directions of each of the forces graphically.
Step 2
5.2.1 The bending moment values
Answer
To calculate the bending moment values, it is important to note the distances from the point of interest. The moments can be calculated using the formula:
where:
- M = moment
- F = force applied
- d = distance from the point to where the force acts.
- Calculate moments at points a, b, c, and d:
- At point a: Calculate the moment caused by the 10 N downward force:
- Moment = 10 N * 2 m = 20 N·m
- At point b: For the 40 N force (considering distances 2m and 4m):
- Moment = (60 N * 2 m) - (40 N * 4 m) = 120 N·m - 160 N·m = -40 N·m
- At point c: The moment generated due to the 20 N and 30 N forces must be considered:
- Moment = (20 N * 4 m) + (30 N * 6 m) = 80 N·m + 180 N·m = 260 N·m
- At point d: Analyze the forces to find the resulting moment.
- At point a: Calculate the moment caused by the 10 N downward force:
Step 3
5.2.2 Complete the bending moment diagram on scale 1 mm = 1 N according to the bending moment values.
Answer
To complete the bending moment diagram:
- Set up the axes: Draw the x-axis representing positions along the beam from point a to point d and a y-axis for the bending moment values.
- Plot the calculated values: Mark the calculated bending moment values for points a, b, c, and d on the graph.
- Connect the points: Draw smooth curves to represent the bending moments between the calculated points, keeping in mind the nature of the moments: positive moments results in bottom fibers in tension and negative moments results in compression.
- Label the diagram appropriately: Ensure that all plotted moments have corresponding labels to clearly show values on the bending moment diagram.
Step 4
5.3 Determine, from point P, the centroid of the body in FIGURE 5.3.
Answer
To determine the centroid of the body:
- Identify the shape: Look at FIGURE 5.3 to understand that it is a rectangular shape having specified dimensions.
- Use the formula: The centroid (C) for a rectangle can be calculated using:
Where:
- b = width of the rectangle (horizontal dimension)
- h = height of the rectangle (vertical dimension)
- Substitute measurements: Using the measurements given in the figure, substitute into the formulas to get the coordinates of the centroid.
- For example, if width = 60 and height = 40, then:
- The centroid will be located at point (30, 20).
- Conclude the position: State that the centroid of the body lies at coordinates (30, 20) from point P.