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5.1 FIGUUR 5.1 op ANTWOORDBLAD B toon die ruimtediagram van 'n afdak - NSC Civil Technology Civil Services - Question 5 - 2017 - Paper 1
Question 5
5.1 FIGUUR 5.1 op ANTWOORDBLAD B toon die ruimtediagram van 'n afdak. Bepaal grafies op skaal 1 mm = 1 N op ANTWOORDBLAD B die grootte en aard van die kragte in die ... show full transcript
Worked Solution & Example Answer:5.1 FIGUUR 5.1 op ANTWOORDBLAD B toon die ruimtediagram van 'n afdak - NSC Civil Technology Civil Services - Question 5 - 2017 - Paper 1
Step 1
5.1 FIGUUR 5.1 op ANTWOORDBLAD B toon die ruimtediagram van 'n afdak. Bepaal grafies op skaal 1 mm = 1 N op ANTWOORDBLAD B die grootte en aard van die kragte in die onderdelen van die kap deur die kragdiagram te teken en die tabel te voltooi.
Answer
To determine the forces acting on the structure, start by identifying all the forces indicated in FIGUUR 5.1 at points A, B, C, D, and E. For accuracy, draw the force diagram using the specified scale of 1 mm = 1 N.
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Draw Force Vectors:
- For the 40 N force at A, draw a vector downward.
- For the 60 N force at B at an angle of 30°, calculate its horizontal and vertical components.
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Calculate Components:
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Horizontal Component of B:
F_{Bx} = F_B imes ext{cos}(30°) = 60 imes rac{ ext{√3}}{2} ext{ N}
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Vertical Component of B:
F_{By} = F_B imes ext{sin}(30°) = 60 imes rac{1}{2} = 30 ext{ N}
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Complete the Diagram:
- Draw the resultant vector based on the established forces and angles.
- Fill the values into the table accordingly.
Step 2
5.2.1 Die buigmomentwaardes
Answer
To calculate the bending moment values:
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Identify Point Loads: Recognize the point loads acting on the beam from FIGUUR 5.2: 10 N, 20 N, 40 N, and 60 N.
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Apply Moment Equilibrium Equations: For each section of the beam, consider the moments created by these forces about a fixed point.
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Calculate Moments:
For each section:
- At point A:
- Continue calculating until point D, adjusting for direction (clockwise or counter-clockwise).
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Fill in Calculated Values: Write the calculated moment values in the appropriate table column.
Step 3
5.2.2 Voltooi die buigmomentdiagram op skaal 1 mm = 1 N volgens die buigmomentwaardes
Answer
To complete the bending moment diagram:
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Draw Axis: Define the axes for the bending moment diagram where the horizontal axis represents the length of the beam, and the vertical axis represents the bending moments.
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Plot Values: For each moment calculated in section 5.2.1, plot the corresponding values on the graph at their respective positions along the beam.
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Connect Points: Connect the plotted points smoothly to illustrate the bending moment distribution along the beam.
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Label Diagram: Clearly label the maximum and minimum moment values on the diagram, ensuring clarity in interpretation.
Step 4
5.3 Bereken die sentroïed van die liggaam in FIGUUR 5.3 vanaf punt P.
Answer
To calculate the centroid of the body:
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Identify Dimensions: Observe and list all dimensions of the shape in FIGUUR 5.3, which are provided as 6, 4, and 6.
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Area Calculation: Calculate the area of each section of the shape.
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Use Centroid Formula: Apply the centroid formulas:
ar{x} = rac{ ext{Sum of } (x_i imes A_i)}{ ext{Total Area}} ar{y} = rac{ ext{Sum of } (y_i imes A_i)}{ ext{Total Area}}
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Perform Calculations: Substitute the areas and distances from point P into the formulas to find the coordinates of the centroid.