7.1 Determine graphically (Bow's notation) the magnitude and nature of ALL the members of the framework in FIGURE 7.1 below - NSC Mechanical Technology Welding and Metalwork - Question 7 - 2018 - Paper 1

To find the reactions at the supports RL and RR:

1. Choose a point for calculating moments, often a support point. Here, we take moments about point RR.
2. Apply the equation for moment equilibrium: $RL \times 10 = (8 \times 8) + (4 \times 5) + (6 \times 2)$ Simplifying this gives: $RL = 9.6 kN$
3. To verify, take moments about RL this time and solve for RR:
   $RR \times 10 = (6 \times 8) + (4 \times 5) + (8 \times 2)$ Simplifying reveals: $RR = 8.4 kN$ Thus, the reactions calculated are:

• RL = 9.6 kN
• RR = 8.4 kN.

To compute the bending moments at each designated point:

1. Calculate the moment at point A:
   $M_A = 0 \, kN.m$(as there is no moment applied).

2. Calculate the moment at point B using the reaction at RL: $M_B = RL \times 2 - (8 \times 2) = 19.2 \, kN.m$

3. Calculate the moment at point C: $M_C = (RL \times 5) - (4 \times 3) = 24 \, kN.m$

4. Calculate the moment at point D: $M_D = (RL \times 8) - (4 \times 5) - (6 \times 3) = 16.8 \, kN.m$

5. Calculate the moment at point E: $M_E = RL \times 10 - (6 \times 8) = 0 \, kN.m$

Summarizing the bending moments:

• M_A = 0 kN.m
• M_B = 19.2 kN.m
• M_C = 24 kN.m
• M_D = 16.8 kN.m
• M_E = 0 kN.m.

To create a bending moment diagram based on the calculated moments:

1. Set up the axes with the horizontal axis representing the length of the beam and the vertical axis representing the bending moments.

2. Plot the calculated points from moments at A, B, C, D, and E on the diagram:

   • At A, plot at 0 kN.m
   • At B, plot at 19.2 kN.m
   • At C, plot at 24 kN.m
   • At D, plot at 16.8 kN.m
   • At E, plot at 0 kN.m.

3. Connect the plotted points smoothly to depict how the bending moments vary along the beam. Use straight lines to connect the points and ensure the correct representation of signs (positive/negative moments). This is essential for understanding how forces influence bending along the member.

Your diagram should show positive moments rising from A to C and descending to E, showing how forces act along the beam.

To calculate the load (P) required:

1. Understand the relationship between stress and load: $\text{Stress} = \frac{\text{Load}}{\text{Area}} \implies \text{Load} = \text{Stress} \times \text{Area}$

2. Calculate the cross-sectional area (A) of the round stainless steel bar: $A = \frac{\pi d^2}{4} \text{ where } d = 20 \text{ mm} = 0.02 \text{ m}$ $A = \frac{\pi (0.02)^2}{4} = 3.14 \times 10^{-4} \, m^2$

3. Substitute the values into the load equation: $P = 80 \times 10^6 \, Pa \times 3.14 \times 10^{-4} \, m^2 = 25.13 \, kN$

Thus, the load required to achieve a tensile stress of 80 MPa in the bar is approximately 25.13 kN.