Concrete column and ultimate compressive stength

[emma louise]

Homework Statement

a concrete column, 4.5m long, is reinforced with steel bars and carries a compressive load of 58 tonnes. The overall cross-sectional area of the column is 0.1m squared and the steel reinforcement accounts for 5 percent of this area. take young's modulus for steel as 200 GN/m squared, young's modulus for concrete as 20 GN/m squared and ultimate compressive strength
for concrete 50 MPa. calculate,

the stress taken by the steel?

change in length of the column?

the factor of safety based upon the UCS for concrete?

 

[tiny-tim]

welcome to pf!

hi emma louise! welcome to pf!

show us what you've tried, and where you're stuck, and then we'll know how to help!

 

[emma louise]

hiii:) i haven't tried anything yet, I am just wondering how to start it?

 

[berkeman]

hiii:) i haven't tried anything yet, I am just wondering how to start it?

You start by posting the Relevant Equations. Does Young's Modulus have anything to do with stress and strain?

 

[DeeNos]

I would first like to clarify that the ultimate compressive strength (UCS) for concrete is typically measured in megapascals (MPa), not newtons per square meter (N/m^2). Therefore, the UCS for concrete in this scenario would be 50 MPa, not 50 N/m^2.

To calculate the stress taken by the steel, we can use the formula for stress, which is force divided by cross-sectional area. In this case, the force acting on the steel bars can be calculated by multiplying the compressive load of 58 tonnes by the percentage of steel reinforcement, which is 5%. This gives us a force of 2.9 tonnes (or 29 kN). The cross-sectional area of the steel bars can be calculated by subtracting the area of the concrete from the overall cross-sectional area of the column. This gives us a steel cross-sectional area of 0.095m^2. Plugging these values into the formula for stress, we get a stress of approximately 305 kPa.

To calculate the change in length of the column, we can use the formula for strain, which is change in length divided by original length. The original length of the column is 4.5m, and the change in length can be calculated by multiplying the stress of 50 MPa (ultimate compressive strength for concrete) by the cross-sectional area of the column (0.1m^2) and dividing by the young's modulus for concrete (20 GN/m^2). This gives us a change in length of approximately 1.25 mm.

Finally, to calculate the factor of safety based on the UCS for concrete, we can divide the ultimate compressive strength of 50 MPa by the stress taken by the steel, which is 305 kPa. This gives us a factor of safety of approximately 164, meaning that the column can withstand 164 times the applied load before reaching its ultimate compressive strength. This is a relatively high factor of safety, indicating that the column is designed to be very strong and stable.