# Calculating the Dimensions of a Reinforced Concrete Column Under Stress

• anthonyk2013
In summary, the following conversation discusses how to calculate the dimensions of a square section strut if the stress in the concrete is not to exceed 7MN/m2 and the load is to be 400KN. The strut will have a cross sectional area of 982*10-3m2 and a compressive force of 400KN.
anthonyk2013
A concrete column having a modulus of elasticity of 20GN/m2 is reinforced by two steel bars of 25mm diameter having modulus of 200GN/m2.
Calculate the dimensions of a square section strut if the stress in the concrete is not to exceed 7MN/m2 and the load is to be 400KN.

σ in conctete not to exceed 7*106
E of steel=200GN/m2
E of concrete=20GN/m2

Area of steel=3.14*252/4*2=982*10-3m2
Area of concrete=?

σc/Ecs/Es

σcs*Ec/Es

σcs*20/200

σcs*.1

7*106s*.1

7/.1*106s

σs=70*106MN/M2

Wondering if I m on the right track?

Last edited:
You could indicate the units of your calculations.

SteamKing said:
You could indicate the units of your calculations.

Any help would be appreciated

anthonyk2013 said:
Any help would be appreciated
Let S be the side of the square cross section column. What is the total area of the cross section. What is the cross sectional area of the steel rods (this time calculate it correctly, taking into account that 1 mm = 0.001 m)? In terms of S, what is the cross sectional area of the concrete?

Chestermiller said:
Let S be the side of the square cross section column. What is the total area of the cross section. What is the cross sectional area of the steel rods (this time calculate it correctly, taking into account that 1 mm = 0.001 m)? In terms of S, what is the cross sectional area of the concrete?

Area of the steel is 3.14*.0252/4=.0004908
Because there is two rods I multiply .0004908*2=.000981747m2

S=L*B

anthonyk2013 said:
Area of the steel is 3.14*.0252/4=.0004908
Because there is two rods I multiply .0004908*2=.000981747m2

S=L*B

What are L and B?

For the cross sectional area of the concrete, I get (S - 0.000981747) m2.

Chestermiller said:
What are L and B? Length x breath

For the cross sectional area of the concrete, I get (S - 0.000981747) m2.

Yes S-0.000981747

anthonyk2013 said:
Yes S-0.000981747
Actually, S2-0.000981747. What is your recommendation as to what to do next in this problem?

I need the get area using the values I have.

do I use σc/Ecs/Es

σcs=Ec/Es

σc=Fc/Ac and σs=Fs/As

THEN Fc/Ac*As/Fs=Ec/Es

Last edited:
anthonyk2013 said:
I need the get area using the values I have.

do I use σc/Ecs/Es

σcs=Ec/Es

σc=Fc/Ac and σs=Fs/As

THEN Fc/Ac*Fs/As=Ec/Es
Let ε be the compressive strain in the steel and concrete. What value of ε causes the stress in the concrete to equal 7MN/m2? What is the stress in the bars? In terms of S, what is the compressive force in the bars and in the concrete? What are the sum total of the compressive forces? What value of S causes this total compressive force to equal 400 kN.

ε of concrete=ε in steel?

σ=E*ε

ε=σ/E ε=7MN/m2/20N/m2

Would the correct way the write this be ε=7*106/20*109=.35*10-3

σ in steel=.35*200=70MN

Total force is 400KN so I need to find what load is on the steel.

Last edited:
anthonyk2013 said:
ε of concrete=ε in steel?

σ=E*ε

ε=σ/E ε=7MN/m2/20N/m2

Would the correct way the write this be ε=7*106/20*109=.35*10-3

σ in steel=.35*200=70MN

Total force is 400KN so I need to find what load is on the steel.
So far, so good. Now, you know the stress in the steel. What is the load carried by the two steel bars?

Chestermiller said:
So far, so good. Now, you know the stress in the steel. What is the load carried by the two steel bars?

σ=F/A→F=σ*A→F=70*106*0.000981747m2=.06872MN/m2

or 69KN/m2

Total force is 400KN, force in steel is 69KN so 400KN-69KN=331KN

Force in concrete=331KN
σ in concrete=7MN/m2

Area=f/σ A=331*103/7*106=47.285*103 or 47285

$\sqrt{}47285$=217.45mm2

Answer in my notes is 220mm2

anthonyk2013 said:
Total force is 400KN, force in steel is 69KN so 400KN-69KN=331KN

Force in concrete=331KN
σ in concrete=7MN/m2

Area=f/σ A=331*103/7*106=47.285*103 or 47285

$\sqrt{}47285$=217.45mm2

Answer in my notes is 220mm2
You're still not being careful about units. You made two errors that canceled each other out. Incidentally, the length of the side of the square cannot be in mm2. It has to be mm.

Chestermiller said:
You're still not being careful about units. You made two errors that canceled each other out. Incidentally, the length of the side of the square cannot be in mm2. It has to be mm.

217.45mm is what should have wrote?

anthonyk2013 said:
217.45mm is what should have wrote?
Not exactly. You had to add the area of the bars back to get the total area. Then take the square root. That's probably why you got 217 and the book had 220.

To get the dimensions I need to find the total area. Concrete +steel and square root that.

Thanks for your help Chester, big help again.

## What is stress in compound bar?

Stress in compound bar refers to the internal force that is exerted on the material of the bar due to external forces acting on it. It can be caused by various factors such as tension, compression, and bending.

## How is stress calculated in a compound bar?

Stress in a compound bar is calculated by dividing the applied force by the cross-sectional area of the bar. This gives the stress in units of force per unit area, such as pounds per square inch or megapascals.

## What is the difference between tensile and compressive stress in a compound bar?

Tensile stress refers to the internal force that is pulling the material of the bar apart, while compressive stress refers to the force that is pushing the material together. Both types of stress can occur in a compound bar depending on the external forces applied.

## What factors can affect the stress in a compound bar?

The stress in a compound bar can be affected by various factors such as the material properties of the bar, the magnitude and direction of the external forces applied, and the geometry of the bar. Additionally, changes in temperature and environmental conditions can also affect the stress in the bar.

## How is stress in a compound bar related to its strength?

The stress in a compound bar is directly related to its strength, as the maximum stress that a material can withstand without breaking is known as its ultimate strength. Therefore, understanding the stress in a compound bar is crucial in determining its overall strength and ability to withstand external forces.

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