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FIGURE 7.4 below shows a steel framework - NSC Mechanical Technology Welding and Metalwork - Question 7 - 2021 - Paper 1
Question 7
FIGURE 7.4 below shows a steel framework. Answer the questions that follow. Construct the vector/force diagram using scale 1 mm = 1 kN. Determine graphically the m... show full transcript
Worked Solution & Example Answer:FIGURE 7.4 below shows a steel framework - NSC Mechanical Technology Welding and Metalwork - Question 7 - 2021 - Paper 1
Step 1
Construct the vector/force diagram using scale 1 mm = 1 kN.
Answer
To construct the vector/force diagram, we begin by determining the directions and magnitudes of the forces at joint B. The vertical force at B is 500 kN, and the horizontal forces are 125 kN to the left and 375 kN to the right.
- Start by drawing the vertical force originating from joint B, 500 kN upwards.
- From point B, draw the horizontal force of 375 kN to the right and mark point C.
- Draw the force of 125 kN to the left from point B, marking point D.
- Using the scale, accurately measure and label each force vector. Ensure that the angles (30° for CD, 60° for BD) are maintained correctly based on the geometry.
- Finally, close the triangle formed by these vectors to determine the resultant forces.
Step 2
Determine graphically the magnitude and nature of the force in AD, BD and CD.
Answer
To determine the forces graphically:
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Use the drawn force diagram to measure the lengths of the force vectors for AD, BD, and CD based on the constructed scale.
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For member AD:
- Measure from point A to point D.
- Using the scale, if AD measures 250 mm, then force in AD = 250 kN (compression).
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For member BD:
- Measure from point B to D.
- If BD measures 433 mm, then force in BD = 433 kN (tension).
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For member CD:
- Measure from point C to D.
- If CD measures 216 mm, then force in CD = 216 kN (tension).
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The final forces will indicate if they are in tension or compression based on their vectors in the framework.