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FIGURE 7.1 below shows a steel framework - NSC Mechanical Technology Welding and Metalwork - Question 7 - 2020 - Paper 1
Question 7
FIGURE 7.1 below shows a steel framework. Answer the questions that follows. SCALE: Space diagram: 1 : 100 FORCE/VECTOR diagram: 1 mm = 10 kN Tolerance: ± 3 mm 7.1... show full transcript
Worked Solution & Example Answer:FIGURE 7.1 below shows a steel framework - NSC Mechanical Technology Welding and Metalwork - Question 7 - 2020 - Paper 1
Step 1
Determine the magnitude and nature of the members, as shown in FIGURE 7.1.
Answer
Calculate the magnitude of each member using equilibrium equations:
- Member AF:
- Magnitude: 1050 kN, Nature: Strut
- Member BG:
- Magnitude: 760 kN, Nature: Strut
- Member CH:
- Magnitude: 760 kN, Nature: Strut
- Member DI:
- Magnitude: 960 kN, Nature: Strut
- Member FG:
- Magnitude: 200 kN, Nature: Strut
- Member HI:
- Magnitude: 200 kN, Nature: Strut
- Member FE:
- Magnitude: 930 kN, Nature: Tie
- Member GH:
- Magnitude: 250 kN, Nature: Tie
- Member IE:
- Magnitude: 830 kN, Nature: Tie
Conversions should remain consistent with the scale used.
Step 2
Calculate the bending moments at points B, C and D.
Answer
To calculate the bending moments at points B, C, and D:
- At point B:
- Moment calculation:
- At point C:
- Use the same approach, considering loads on either side of point C.
- At point D:
- Since there’s no moment due to point loads after point D:
Use the appropriate moments according to equilibrium conditions.
Step 3
Draw a shear force diagram.
Answer
To draw the shear force diagram:
- Calculate shear forces at each major point (A, B, C, D) by taking into account the applied point loads:
- Start at A with the upward reaction force and subtract downwards loads progressively.
- Plot these values on a simple graph, with force magnitude on the vertical y-axis and beam length on the horizontal x-axis:
- Show positive values above the baseline and negative values below.
- Connect the points with straight lines according to calculated values, ensuring to account for any increases or decreases at point loads.
Step 4
Draw a bending moment diagram.
Answer
To create the bending moment diagram:
- Start from zero at point A.
- Calculate values at points B and C:
- Integrate the shear force to find the bending moment values,
- At each critical point, either max or min bending moments are plotted from previous calculations.
- Draw curves between points, indicating the nature of moments—positive (sagging) above the baseline and negative (hogging) below the line. Ensure that the bending moment diagram reflects correct scales as per the specifications.
Step 5
Calculate the maximum stress in the bar material.
Answer
The maximum stress is calculated by the formula: ext{Max Stress} = rac{ ext{Load}}{ ext{Area}} Substituting the given values: ext{Max Stress} = rac{6 ext{ kN}}{80 ext{ mm}^2} = rac{6000 ext{ N}}{80 imes 10^{-6} ext{ m}^2} = 75 imes 10^{6} ext{ Pa} = 75 ext{ MPa}
Step 6
Calculate the safe working stress of the bar.
Answer
Using the safety factor, the safe working stress is calculated by: ext{Safe Working Stress} = rac{ ext{Max Stress}}{ ext{Safety Factor}} Substituting the values: ext{Safe Working Stress} = rac{100 imes 10^{6} ext{ Pa}}{4} = 25 imes 10^{6} ext{ Pa} = 25 ext{ MPa}