A 3.0 m tall, 42 cm diameter concrete column supports a 230,000 kg load. By how much is the column compressed? Assume Young's modulus for concrete to be 3.0 1010 N/m2.
in mm
strain = delta L /L = sigma/modulus
sigma = Force/area
= 2.3*10^5/(pi * .24^2)
delta L = 3 * 2.3*10^5 / (pi * .24^2 *3*10^10) in meters
To find how much the column is compressed, you need to use Hooke's Law, which states that the compression or elongation of a material is directly proportional to the force applied, given a constant called the Young's modulus (E).
The formula to calculate the compression in a column is:
ΔL = (F × L) / (E × A)
Where:
ΔL is the change in length (compression),
F is the force applied (load),
L is the original length of the column,
E is the Young's modulus, and
A is the cross-sectional area of the column.
To calculate the compression in mm, follow these steps:
1. Convert the given dimensions to meters:
Column height: 3.0 m
Column diameter: 42 cm = 0.42 m
2. Calculate the original length (L) of the column:
Original length (L) = Column height = 3.0 m
3. Calculate the cross-sectional area (A) of the column:
Cross-sectional area (A) = π × (diameter/2)²
= π × (0.42 m / 2)²
4. Convert the given load to Newtons (N):
Load = 230,000 kg
Force (F) = Load × gravitational acceleration (g)
= 230,000 kg × 9.8 m/s² (gravitational acceleration)
5. Plug the values into the formula mentioned earlier to find the compression (ΔL):
ΔL = (F × L) / (E × A)
6. Convert the compression from meters to millimeters:
Compression in mm = ΔL × 1000
By following these steps, you can find the amount of compression in millimeters that the concrete column experiences under the given load.