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 calculate the reactions at supports RL and RR:

1. Select a Point: Choose point RR for moment calculation.

2. Apply Moments about RR: $RL \times 10 = (8 \times 8) + (4 \times 5) + (6 \times 2)$

   • Calculate RL: RL = 9.6 kN.

3. Apply Moments about RL: $RR \times 10 = (6 \times 8) + (4 \times 5) + (8 \times 2)$

   • Calculate RR: RR = 8.4 kN.

To find the bending moments:

1. Using the Reaction Forces: Use the previously calculated reactions (RL and RR) to calculate moments around points A, B, C, D, and E.

2. Calculate Each Moment:

   • At A: Moment = 0 kN.m.
   • At B: $M_B = RL \times 2 - 19.2 \\ 2 \text{ kN.m}$
   • At C: $M_C = RL \times 5 - 24 \\ kN.m$
   • At D: $M_D = (RL \times 8) - (4 \times 6) - (16.8) \\ kN.m$
   • At E: $M_E = RL \times 10 - (4 \times 8) - (6 \times 2) \\ 0 kN.m$

To draw a bending moment diagram:

1. Plot Points: Using the calculated bending moments for A, B, C, D, and E.
2. Connect Points: Connect the points with straight lines, indicating regions of curvature where necessary (where the loading changes direction).
3. Label the Diagram: Clearly label the diagrams with respective values and scales.

To calculate the load:

1. Calculate the Area: The cross-sectional area of the bar is given by: $A = \frac{\pi d^2}{4} = \frac{\pi (0.02)^2}{4} \approx 3.14 \times 10^{-4} \,m^2$

2. Using Stress Formula: The tensile stress formula is: $\text{Stress} = \frac{\text{Load}}{\text{Area}}$ Rearranging for load gives: $\text{Load} = \text{Stress} \times \text{Area}$ $\text{Load} = 80 \times 10^6 \times 3.14 \times 10^{-4} \approx 25,133 \text{ N}$