7.1 Graphically determine the magnitude and type of member in the framework shown in FIGURE 7.1 below. Members: AE, BF, CF, DE and EF. SCALE: Space diagram: 1 : 100 Force diagram: 1 mm = 5 N 7.2 FIGURE 7.2 below shows a uniform beam. The beam is supported at points RL and RR. Three point loads of 4 N, 5 N and 3 N are exerted onto the beam. 7.2.1 Calculate the reactions at supports RL and RR. 7.2.2 Calculate the bending moments at point B, C and D. 7.2.3 Draw a bending-moment diagram. SCALES: Space diagram: 10 mm = 1 m Bending-moment diagram: 5 mm = 1 N.m

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7.1 Graphically determine the magnitude and type of member in the framework shown in FIGURE 7.1 below - NSC Mechanical Technology Welding and Metalwork - Question 7 - 2019 - Paper 1

Question 7

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7.1 Graphically determine the magnitude and type of member in the framework shown in FIGURE 7.1 below. Members: AE, BF, CF, DE and EF. SCALE: Space diagram: 1 : 10... show full transcript

Worked Solution & Example Answer:7.1 Graphically determine the magnitude and type of member in the framework shown in FIGURE 7.1 below - NSC Mechanical Technology Welding and Metalwork - Question 7 - 2019 - Paper 1

Step 1

7.2.1 Calculate the reactions at supports RL and RR.

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Answer

To calculate the reactions at supports RL and RR, we apply the principles of static equilibrium. We can sum the vertical forces and moments around one of the supports.

Given the total loads acting on the beam: 4 N, 5 N, and 3 N, locate their positions relative to RL or RR. Then, apply the following equations:

Sum of vertical forces:

$R_L + R_R - (4 + 5 + 3) = 0$
Sum of moments about RL (select RL to eliminate $R_L$ ):

$- R_R imes 6 + 4 imes 1.5 + 5 imes 3 + 3 imes 4.5 = 0$

Solving these equations yields:

$R_L = 6.25$ N
$R_R = 5.75$ N

Step 2

7.2.2 Calculate the bending moments at point B, C and D.

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To find the bending moments at points B, C, and D, we consider the equilibrium of sections of the beam:

At Point B:

$M_B = R_L imes 3 - 4 imes 1.5$

$= 6.25 imes 3 - 4 imes 1.5 = 18.75 ext{ N.m}$
At Point C:

$M_C = R_L imes 6 - 5 imes 3 - 4 imes 1.5$

$= 6.25 imes 6 - 5 imes 3 - 4 imes 1.5 = 25.5 ext{ N.m}$
At Point D:

$M_D = R_L imes 9 - 5 imes 6 - 4 imes 1.5 - 3 imes 6.5$

$= 6.25 imes 9 - 5 imes 6 - 4 imes 1.5 - 3 imes 6.5 = 17.25 ext{ N.m}$

Step 3

7.2.3 Draw a bending-moment diagram.

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Answer

The bending moment diagram can be represented graphically by plotting the bending moments calculated at points A, B, C, D, and E.

At A (0): $M_A = 0$ N.m
At B: $M_B = 18.75$ N.m
At C: $M_C = 25.5$ N.m
At D: $M_D = 17.25$ N.m
At E (support): $M_E = 0$ N.m

The diagram will have lines connecting these points, showing the bending moment distribution, with negative moments between supports and positive peaks near the applied loads.

7.1 Graphically determine the magnitude and type of member in the framework shown in FIGURE 7.1 below - NSC Mechanical Technology Welding and Metalwork - Question 7 - 2019 - Paper 1

Worked Solution & Example Answer:7.1 Graphically determine the magnitude and type of member in the framework shown in FIGURE 7.1 below - NSC Mechanical Technology Welding and Metalwork - Question 7 - 2019 - Paper 1

7.2.1 Calculate the reactions at supports RL and RR.

7.2.2 Calculate the bending moments at point B, C and D.

7.2.3 Draw a bending-moment diagram.

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