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7.1.1 Calculate the reactions at RL and RR - NSC Mechanical Technology Welding and Metalwork - Question 6 - 2021 - Paper 1
Question 6
7.1.1 Calculate the reactions at RL and RR. 7.1.2 Calculate the bending moments at points B, C and D. 7.1.3 Construct the bending moment diagram for points B, C an... show full transcript
Worked Solution & Example Answer:7.1.1 Calculate the reactions at RL and RR - NSC Mechanical Technology Welding and Metalwork - Question 6 - 2021 - Paper 1
Step 1
Calculate the reactions at RL and RR.
Answer
To find the reactions at supports RL and RR, we can use the equilibrium equations. The sum of vertical forces must equal zero.
Let R_L and R_R be the reactions at supports.
The total downward load is
.
Setting up the equilibrium equations:
.
Taking moments about point R_L:
.
Calculating:
\Rightarrow 680 = R_R imes 8\ \Rightarrow R_R = 85 ext{ N}$$. Substituting for R_R: $$R_L = 240 - 85 = 155 ext{ N}$$. Thus, the reactions are: - R_L = 155 N - R_R = 85 NStep 2
Calculate the bending moments at points B, C and D.
Answer
The bending moments at points B, C, and D can be calculated using the moments established from the reactions and loads applied.
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At Point B:
- Moment due to R_L:
.
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At Point C:
- Moment due to R_L and downward force at B:
.
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At Point D:
- Consider moments from R_L, B and C:
\Rightarrow 1085 - 400 - 120 = 565 ext{ Nm}$$.
Step 3
Construct the bending moment diagram for points B, C and D by using scale 1 m = 1 cm and 10 Nm = 1 cm.
Answer
To construct the bending moment diagram:
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Establish a scale suitable for the values obtained; for instance, use 1 cm for 1 m and 0.1 Nm for 1 cm.
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Mark the calculated moments on the horizontal line representing the length of the bar from A to E.
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Plot points:
- For Point B at 3 m, mark 46.5 cm upwards.
- Draw a line to Point C, marking 61.5 cm upwards.
- From point C to D, mark 56.5 cm downwards.
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Connect these points with straight lines, ensuring to reflect any changes in moment due to loads.
The diagram should visually represent the variation of bending moments along the structure.
Step 4
Calculate the diameter of the bar.
Answer
Using the tensile stress formula:
A = rac{40,000}{20 imes 10^6} = 0.002 m^2$$. The area of a circle is $A = rac{ ext{π}}{4} d^2$, so: $$ rac{ ext{π}}{4} d^2 = 0.002\ \Rightarrow d^2 = rac{0.002 imes 4}{ ext{π}}\ \Rightarrow d = rac{4 imes 0.002}{ ext{π}}^{0.5}\ \Rightarrow d = 0.0503 ext{ m} ext{ or } 50.3 ext{ mm}$$.Step 5
Calculate the strain.
Answer
Strain is calculated as:
\Rightarrow ext{Change in Length} = ext{Stress} imes rac{ ext{Length}}{E}$$, where E (Young's modulus) = 90 GPa = 90 imes 10^9 Pa: $$ ext{Change in Length} = rac{20 imes 10^6 imes 2}{90 imes 10^9} = 0.00044444 ext{ m} = 0.44444 ext{ mm}$$. Substituting: $$ ext{Strain} = rac{0.4444 imes 10^{-3}}{2} ightarrow 0.00022222$$.Step 6