Assignment 09

Periodic Notes/Atomic/2025/2025-03-12_Assignment 09/2025-03-12_Assignment 09.svg

Question 1

Load tends to go to the ______________ element.

strongest
elastic
weakest
✔️stiffest

Question 2

What is the increase in Area when two square elements on top of each other are analyzed as Composite instead of Load Sharing?

Triple (3x)
Double (2x)
✔️The same (1x)
Quadruple (4x)

Question 3

What is the increase in Bending Moment when two square elements on top of each other are analyzed as Composite instead of Load Sharing?

Quadruple (4x)
The same (1x)
Triple (3x)
✔️Double (2x)

Question 4

What is the increase in Bending Stiffness when two square elements on top of each other are analyzed as Composite instead of Load Sharing?

The same (1x)
✔️Quadruple (4x)
Double (2x)
Triple (3x)

Question 5

What is critical for two elements to be composite?

Transformed Section
✔️Longitudinal Shear Transfer
Load Sharing
Stiffness

Questions 6 to 14 refer to the following information:

A W150x37 has been cast in a 305 mm Diameter sonotube. This is below grade, so we don’t have any buckling issue. The concrete has an E=30,000 MPa

NOTE: The Steel code has been updated for W150x37. The area is 4730mm2

Question 6

What is EAsteel?

✔️946x10^6 N
2050x10^6 N
13,666x10^6 N
2996x10^6 N
2192x10^6 N
141.9x10^6 N

$E A_{s} = 200, 000 \times 4730 = 946, 000, 000 N$

Question 7

What is EAconcrete?

2192x10^6 N
13,666x10^6 N
✔️2050x10^6 N
141.9x10^6 N
2996x10^6 N
946x10^6 N

$A_{c} = ((305/2)^{2} \times π) - 4730 = 68, 331 m m^{2}$
$E A_{c} = 30, 000 \times A_{c} = 2, 049, 949, 924 N$

Question 8

What is EAtotal?

13,666x10^6 N
✔️2996x10^6 N
946x10^6 N
2050x10^6 N
141.9x10^6 N
2192x10^6 N

$E A_{t o t a l} = \sum E A = 2, 995, 949, 924 N$

Question 9

What percentage of the load goes to the Steel?

Write the answer as a % to one decimal place (XX.X)

$E A_{s} \div E A_{t o t a l} = 0.3157 = 31.6%$

Question 10

What percentage of the load goes to the Concrete?

Write the answer as a % to one decimal place (XX.X)

$E A_{s} \div E A_{t o t a l} = 0.6842 = 68.4%$

Question 11

Remembering that buckling isn’t an issue, so the capacity of a steel column would be Cr = fyA, what is the compressive capacity of the Steel portion in kN?

Write the answer in kN to no decimal places (XXXX)

Compression Squashing (Strength)
- $P_{y} = f_{y} A$
  - Derived from $σ = \frac{P}{A}$ ---

$C_{r} = 350 MP a \times 4730 m m^{2} = 1, 655, 500 N = 1, 656 k N$

Question 12

If the reduction factor for concrete is 0.65 and the maximum stress this concrete can see in compression is f’c = 20MPa, what is the compressive resistance of the concrete portion?

Write the answer in kN to no decimal places (XXX)

$C_{r} = 0.65 \times 20 MP a \times 68, 331 = 888, 303 N = 888 k N$

Question 13

If the load on the load-sharing column is Pf=1500kN, knowing the percentage of load that goes to each material and the capacity of each of those members, does the STEEL work (is Cf<Cr)?

✔️Yes
No

$C_{f} = 1500 k N \times 31.6% = 474 k N < C_{r} = 1, 656 k N$

Question 14

If the load on the load-sharing column is Pf=1500kN, knowing the percentage of load that goes to each material and the capacity of each of those members, does the CONCRETE work (is Cf<Cr)?

✔️No
Yes

$C_{f} = 1500 k N \times 68.4% = 1, 026 k N > C_{r} = 888 k N$

Question 15

Did you complete this question?

✔️Yes
No

Questions 16 to 23 refer to the following:

Question 16

What is the area of the steel?

Write your answer in mm² to zero decimal places. Do not write the units.

$A_{s} = 5 \times 500 = 2500 m m^{2}$

Question 17

What is the area of the concrete? You do not need to subtract the area of the steel.

Write your answer in mm² to zero decimal places. Do not write the units.

$A_{c} = 300 mm * 600 mm = 180, 000 m m^{2}$

Question 18

What is the E (MPa) of the steel?

Write your answer to zero decimal places. Do not write the units.

$E_{s} = 200, 000 MP a$

Question 19

What is the E (MPa) of the concrete?

Write your answer to zero decimal places. Do not write the units.

$E_{c} = 27, 500 MP a$

Question 20

What is the area of the steel if we transform it to concrete?

Write your answer in mm² to zero decimal places. Do not write the units.

$A_{s t c} = A_{s} \times (E_{s} / E_{c}) = 18, 182 m m^{2}$

Question 21

What is the Total Equivalent Area of the section if we transformed the steel to concrete?

Write your answer in mm² to zero decimal places. Do not write the units.

$A_{Tt c} = 18, 182 + 180, 000 = 198, 182 m m^{2}$

Question 22

What is the area of the concrete if we transformed it to steel instead?

Write your answer in mm² to zero decimal places. Do not write the units.

$A_{c t s} = A_{c} \times (E_{c} / E_{s}) = 24, 750 m m^{2}$

Question 23

What is the Total Equivalent Area of the section if we transformed the concrete to steel?

Write your answer in mm² to zero decimal places. Do not write the units.

$A_{Tt s} = 2500 + 24, 750 = 27, 250 m m^{2}$

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2025-03-12_Assignment 09

Assignment 09

Question 1

Question 2

Question 3

Question 4

Question 5

Questions 6 to 14 refer to the following information:

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Questions 16 to 23 refer to the following:

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22

Question 23

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