2025-03-18_Assignment 10

Assignment 10

This is for determining the answers to Questions 1 to 14

We have a column supporting Pf=800kN and an Mf=11.2kNm and we need to determine the longitudinal reinforcing required if the column is 200x200. We are using concrete with f’c=30MPa, there is 25mm cover, and 10M ties. Assume 20M bars with an equal number of bars on each face.

Question 1

What is b (mm)?

200

Question 2

What is h (mm)?

200

Question 3

What is the value of f’c (MPa)?

30

Question 4

What is the cover (mm)?

25

Question 5

What is the diameter of the ties (mm)?

10

Question 6

What is the diameter of the main reinforcing (mm)?

20

Question 7

What is the dimension $\gamma$h (mm)?

---

• $\gamma h=h-2\times (Cover+\text{unicode}x2300Ties+\frac{1}{2}\text{unicode}x2300Bars)$---

Interaction Diagram

---

---

$\gamma h=200-2\times (25+10+\frac{1}{2}20)=110$

Question 8

What is the ratio of bar distance to h?

Write your answer to 2 decimal places (X.XX)

$\gamma =\gamma h÷h$
$\gamma =110/200=0.55$

Question 9

What is Ag of the column?

Write the answer in mm²

$A_g(m{m}^2)=b\times h=40,000$

Question 10

Remembering we need a column with Pr of at least Pf, what is Pr/Ag (N/mm² or MPa)? (Pay attention to units)

$P_r/A_g(MPa)=P_F(N)÷A_g(m{m}^2)=800,000N÷40,000m{m}^2=20MPa$

Question 11

Remembering we need a column with Mr of at least Mf, what is Mr/Agh (N/mm² or MPa)? (Pay attention to units)

Write your answer to 1 decimal place (X.X)

$M_r/A_{gh}(MPa)=M_F(Nmm)÷(A_g\times h)=11,200,000Nmm÷(40,000\times 200)=1.4MPa$

Question 12

Using the Concrete Column Interaction Diagrams for the appropriate f’c and for a column with equal reinforcement on all sides, what is the required reinforcement ratio for the column?

Write your answer to 2 decimal places (X.XX)

$P_r/A_g(MPa)=20$
$M_r/A_{gh}(MPa)=1.4$

Interaction Diagram

---

---

$P_g=0.03$

Question 13

Using the answer from the previous question, what is the required reinforcement area (mm²)?

Write your answer with no decimal places.

$A_{s}req=e\times A_g=P_g\times A_g=0.03\times 40,000=1,200m{m}^2$

Question 14

What reinforcement do we need to meet our strength requirements for the reinforced concrete column?

• ✔️4-20M
• 4-10M
• 6-20M
• 8-20M
• 6-15M

$N_{Bars}=A_{s}req÷A_{Bars}=1200/300=4$

Question 15

Which of the following is an appropriate stress block (stress profile) of an idealized under-reinforced concrete beam?

• ✔️Orange
• Pink
• Green
• Blue
• Yellow

For Questions 16 to 24, use the following diagram

Question 16

What is the Area (mm²) of the tension steel?

Write your answer to zero decimal places.

$3\times 200=600$

Question 17

What is the Tension capacity (kN) of the tension steel?

Write your answer to zero decimal places.

$T(N)={\varphi }_S\times A_S\times f_y=0.85\times 600\times 400=204,000$

Question 18

This question depends on previous answers. Pay attention to units.

What is $\beta 1c$ (mm) for the beam?

Write your answer to 2 decimal places.

${\beta }_{1}c(mm)=T/({\alpha }_1\times {\varphi }_c\times f{’}_c\times b)=204,000/(0.8\times 0.65\times 30\times 300)=43.59$

Question 19

What is the effective depth, d (mm), of the concrete beam above?

Write your answer to 1 decimal place.

$d=500-30-10-15/2=452.5$

Question 20

This question depends on previous answers.

What is the Moment Capacity, Mr (kNm), of the concrete beam?

Write your answers in kNm to 1 decimal place. Pay attention to units.

$M_r(Nmm)=T\times (d-({\beta }_{1}c)/2)=204,000\times (452.5-(43.59)/2)=87,863,820Nmm=87.9kNm$

Question 21

What is the area of shear steel, Av (mm²)?

Write your answer to zero decimal places.

$A_v=2\times 100=200$

Question 22

What is the shear resistance, Vc (kN), of the concrete?

Write your answer to 1 decimal place.

$V_c(N)=0.2\times \lambda \times {\varphi }_c\times \sqrt{f{’}_c}\times b_w\times d=0.2\times 1.0\times 0.65\times \sqrt{30}\times 300\times 452.5=96659N=96.7kN$

Question 23

What is the shear resistance, Vs (kN), of the steel?

Write your answer to 1 decimal place.

$V_s(N)={\varphi }_s\times A_v\times f_y\times d÷s=0.85\times 200\times 400\times 452.5÷300=102,566.66N=102.6kN$

Question 24

What is the total shear resistance, Vr (kN), of the reinforced concrete beam?

Write your answer to 1 decimal place.

$V_r(N)=V_c+V_s=199.3$

---

Excalidraw Data

Text Elements