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Pull-Request [TWP-1-15-2025] from Obsidian #241

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319 changes: 160 additions & 159 deletions content/Courses/2025/ARC2046H/ARC2046H.md
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Expand Up @@ -434,165 +434,166 @@ Ultimate Limit States Calculator
```

> [!abstract]- Assignment 02

**Question 1**
What live load would be required for the design of living room floor members in a residential unit?
Group of answer choices

7.2 kPa
1.9 kPa
✔️4.8 kPa
2.4 kPa
1.4 kPa

**Question 2**
What is the total dead load (kPa) for a roof with asphalt strip shingles, 19mm plywood sheathing, 2x8 joists at 16" c/c, 100mm of blown glass fibre insulation, 20mm of gypsum wallboard, and assuming an allowance of 0.05 kPa for mechanical/electrical?
Group of answer choices

0.55 kPa
✔️0.60 kPa
0.72 kPa
0.69 kPa
0.52 kPa

Refer to `DEAD LOADS.pdf`
asphalt strip shingles => 0.15
19mm plywood sheathing => 0.11
2x8 joists at 16" c/c => 0.09 ($8in = \lfloor203mm\rfloor=184mm$)
100mm of blown glass fibre insulation => 0.04
20mm of gypsum wallboard => 0.16
mechanical/electrical => 0.05
$\sum = 0.60 kPa$

**Question 3**
For the following loads acting on a roof, what would the worst case Factored Load Combination be? All loads are acting downward. Dead=1.25kPa, Live=2.40kPa, Snow=1.12kPa and Wind=1.00kPa
Group of answer choices

5.77 kPa
✔️6.28 kPa
6.68 kPa
5.16 kPa
5.64 kPa

Refer to `LOAD COMBINATIONS.pdf`
Use the Ultimate Limit States Calculator above

**Question 4**
The following is a part plan from a project under construction. What is the Length of 2WB04?
Provide your answers in meters.
![[./Attachments/ARC2046H/Part Plan NFX.jpg|400]]

12

**Question 5**
From the same partial plan as the previous question, what is the Tributary Width of 2WB04?
Provide your answers in meters.

4

**Question 6**
From the same partial plan as the previous questions, what is the Tributary Area of 2WB04?
Provide your answers in m2.

48

**Image for question 7-11**
![[./Attachments/ARC2046H/Pasted image 20250115172052.png|Pasted image 20250115172052]]
*Dumbest answers are provided for when you can't trust your instincts.*

**Question 7**
For the following question, what are the Reactions (kN)?
Write your answer to 1 decimal place (XX.X)

wf = 9.3 kN/m
L = 13.4 m

$\lfloor\frac{9.3\times13.4}{2}\rfloor=62.3$

**Question 8**
For the following question, what the maximum Vf (kN)?
Write your answer to 1 decimal place (XX.X). The Numbers differ from the previous question.

wf = 7.9 kN/m
L = 11.2 m

$R1=\lfloor\frac{7.9\times11.2}{2}\rfloor=44.24$
$R1-7.9X-V=0$
$V = 44.24 - 7.9x$
```chart
type: line
labels: [0, 2.8, 5.6, 8.4, 11.2]
series:
- title: V = 44.24 - 7.9X
data: [44.24, 22.12, 0, -22.12, -44.24]
tension: 1
width: 77%
labelColors: false
fill: true
beginAtZero: false
bestFit: false
bestFitTitle: undefined
bestFitNumber: 0
```
<canvas id="myChart" width="0" height="0" style="display: block; box-sizing: border-box; height: 0px; width: 0px;"><span></span></canvas>

**Question 9**
For the following, where is Vf=0 kN?
Write your answer to 1 decimal place (XX.X). The Numbers differ from the previous question.

wf = 6.2 kN/m
L = 11.2 m

$R1=\lfloor\frac{6.2\times11.2}{2}\rfloor=34.72$
$R1-6.2X-V=0$
$V = 34.72 - 6.2x$
$x=34.72\div6.2=5.6$

**Question 10**
For the following question, what the maximum Mf (kN)?
Write your answer to 1 decimal place (XX.X). The Numbers differ from the previous question.

wf = 7.8 kN/m
L = 9.6 m

$R1=\lfloor\frac{7.8\times9.6}{2}\rfloor=37.44$
$\sum_M=0=7.8\times x\times \frac{1}{2}x-37.44x+M_f$
$M_f=-3.9x^2+37.44x$
$\arg\max_{x \in (0,9.6)} M_f(x)=-\frac{b}{2a}=4.8$
$\max_{x \in (0,9.6)} M_f(x)=M_f(4.8)=89.856$
<canvas id="myChart" width="0" height="0" style="display: block; box-sizing: border-box; height: 0px; width: 0px;"><span></span></canvas>

**Question 11**
For the following question, where does the maximum Mf occur?
Write your answer to 1 decimal place (XX.X). The Numbers differ from the previous question.

wf = 9.7 kN/m
L = 13 m

$R1=\lfloor\frac{9.7\times13}{2}\rfloor=63.05$
$\sum_M=0=9.7\times x\times \frac{1}{2}x-63.05x+M_f$
$M_f=-4.85x^2+63.05x$
$\arg\max_{x \in (0,9.6)} M_f(x)=-\frac{b}{2a}=6.5$
<canvas id="myChart" width="0" height="0" style="display: block; box-sizing: border-box; height: 0px; width: 0px;"><span></span></canvas>

**Question 12**
What is the worst Cf (kN) on the following column?
![[./Attachments/ARC2046H/Pasted image 20250115172353.png|300]]
296 kN
182 kN
✔️263 kN
322 kN
346 kN

**Question 13**
In the previous question, where does the maximum Cf occur on the column?
Group of answer choices

At L3
✔️L1 to L2
Below L1
L3 to Roof
L2 to L3
>
> **Question 1**
> What live load would be required for the design of living room floor members in a residential unit?
> Group of answer choices
>
> 7.2 kPa
> 1.9 kPa
> ✔️4.8 kPa
> 2.4 kPa
> 1.4 kPa
>
> **Question 2**
> What is the total dead load (kPa) for a roof with asphalt strip shingles, 19mm plywood sheathing, 2x8 joists at 16" c/c, 100mm of blown glass fibre insulation, 20mm of gypsum wallboard, and assuming an allowance of 0.05 kPa for mechanical/electrical?
> Group of answer choices
>
> 0.55 kPa
> ✔️0.60 kPa
> 0.72 kPa
> 0.69 kPa
> 0.52 kPa
>
> Refer to `DEAD LOADS.pdf`
> asphalt strip shingles => 0.15
> 19mm plywood sheathing => 0.11
> 2x8 joists at 16" c/c => 0.09 ($8in = \lfloor203mm\rfloor=184mm$)
> 100mm of blown glass fibre insulation => 0.04
> 20mm of gypsum wallboard => 0.16
> mechanical/electrical => 0.05
> $\sum = 0.60 kPa$
>
> **Question 3**
> For the following loads acting on a roof, what would the worst case Factored Load Combination be? All loads are acting downward. Dead=1.25kPa, Live=2.40kPa, Snow=1.12kPa and Wind=1.00kPa
> Group of answer choices
>
> 5.77 kPa
> ✔️6.28 kPa
> 6.68 kPa
> 5.16 kPa
> 5.64 kPa
>
> Refer to `LOAD COMBINATIONS.pdf`
> Use the Ultimate Limit States Calculator above
>
> **Question 4**
> The following is a part plan from a project under construction. What is the Length of 2WB04?
> Provide your answers in meters.
> ![[./Attachments/ARC2046H/Part Plan NFX.jpg|400]]
>
> 12
>
> **Question 5**
> From the same partial plan as the previous question, what is the Tributary Width of 2WB04?
> Provide your answers in meters.
>
> 4
>
> **Question 6**
> From the same partial plan as the previous questions, what is the Tributary Area of 2WB04?
> Provide your answers in m2.
>
> 48
>
> **Image for question 7-11**
> ![[./Attachments/ARC2046H/Pasted image 20250115172052.png|Pasted image 20250115172052]]
> *Dumbest answers are provided for when you can't trust your instincts.*
>
> **Question 7**
> For the following question, what are the Reactions (kN)?
> Write your answer to 1 decimal place (XX.X)
>
> wf = 9.3 kN/m
> L = 13.4 m
>
> $\lfloor\frac{9.3\times13.4}{2}\rfloor=62.3$
>
> **Question 8**
> For the following question, what the maximum Vf (kN)?
> Write your answer to 1 decimal place (XX.X). The Numbers differ from the previous question.
>
> wf = 7.9 kN/m
> L = 11.2 m
>
> $R1=\lfloor\frac{7.9\times11.2}{2}\rfloor=44.24$
> $R1-7.9X-V=0$
> $V = 44.24 - 7.9x$
> ```chart
> type: line
> labels: [0, 2.8, 5.6, 8.4, 11.2]
> series:
> - title: V = 44.24 - 7.9X
> data: [44.24, 22.12, 0, -22.12, -44.24]
> tension: 1
> width: 77%
> labelColors: false
> fill: true
> beginAtZero: false
> bestFit: false
> bestFitTitle: undefined
> bestFitNumber: 0
> ```
> <canvas id="myChart" width="0" height="0" style="display: block; box-sizing: border-box; height: 0px; width: 0px;"><span></span></canvas>
>
> **Question 9**
> For the following, where is Vf=0 kN?
> Write your answer to 1 decimal place (XX.X). The Numbers differ from the previous question.
>
> wf = 6.2 kN/m
> L = 11.2 m
>
> $R1=\lfloor\frac{6.2\times11.2}{2}\rfloor=34.72$
> $R1-6.2X-V=0$
> $V = 34.72 - 6.2x$
> $x=34.72\div6.2=5.6$
>
> **Question 10**
> For the following question, what the maximum Mf (kN)?
> Write your answer to 1 decimal place (XX.X). The Numbers differ from the previous question.
>
> wf = 7.8 kN/m
> L = 9.6 m
>
> $R1=\lfloor\frac{7.8\times9.6}{2}\rfloor=37.44$
> $\sum_M=0=7.8\times x\times \frac{1}{2}x-37.44x+M_f$
> $M_f=-3.9x^2+37.44x$
> $\arg\max_{x \in (0,9.6)} M_f(x)=-\frac{b}{2a}=4.8$
> $\max_{x \in (0,9.6)} M_f(x)=M_f(4.8)=89.856$
> <canvas id="myChart" width="0" height="0" style="display: block; box-sizing: border-box; height: 0px; width: 0px;"><span></span></canvas>
>
> **Question 11**
> For the following question, where does the maximum Mf occur?
> Write your answer to 1 decimal place (XX.X). The Numbers differ from the previous question.
>
> wf = 9.7 kN/m
> L = 13 m
>
> $R1=\lfloor\frac{9.7\times13}{2}\rfloor=63.05$
> $\sum_M=0=9.7\times x\times \frac{1}{2}x-63.05x+M_f$
> $M_f=-4.85x^2+63.05x$
> $\arg\max_{x \in (0,9.6)} M_f(x)=-\frac{b}{2a}=6.5$
> <canvas id="myChart" width="0" height="0" style="display: block; box-sizing: border-box; height: 0px; width: 0px;"><span></span></canvas>
>
> **Question 12**
> What is the worst Cf (kN) on the following column?
> ![[./Attachments/ARC2046H/Pasted image 20250115172353.png|300]]
> 296 kN
> 182 kN
> ✔️263 kN
> 322 kN
> 346 kN
>
> **Question 13**
> In the previous question, where does the maximum Cf occur on the column?
> Group of answer choices
>
> At L3
> ✔️L1 to L2
> Below L1
> L3 to Roof
> L2 to L3
>

### Module 03 Stress and Strain - Part 01

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