Find the distance by which a 42cm diameter, 9.4m tall concrete column is compressed when it supports a 12900kg load

Young’s Modulus E=17•10⁹ N/m²

σ=Eε
mg/A=E(ΔL/L)
ΔL= mgL/AE= 4mgL/ πD²E=
=4•12900•9.8•9.4/π•0.42²•17•10⁹=
=5•10⁻⁴ m=0.5 mm.

To find the distance by which the concrete column is compressed, we need to consider the weight of the load and the properties of the column.

First, let's calculate the cross-sectional area of the concrete column. The diameter of the column is given as 42cm, which means the radius is half of that, or 21cm (0.21m).

The cross-sectional area (A) of a circular column is calculated using the formula: A = π * r^2, where r is the radius.
Plugging in the values, we get: A = 3.14 * (0.21)^2 = 0.138 m^2.

Next, we need to calculate the weight of the load supported by the column. The weight (W) is given as 12900 kg.

Since weight (W) is equal to mass (m) multiplied by acceleration due to gravity (g), we can find the mass of the load using the formula: W = m * g.

Note that acceleration due to gravity is approximately 9.8 m/s^2.

Rearranging the formula, we get: m = W / g = 12900 kg / 9.8 m/s^2 = 1316.33 kg.

Now, let's consider the compression or shortening of the column. We can use Hooke's law, which states that the change in length (∆L) of an object is directly proportional to the applied force (F) and the material's stiffness (k).

In this case, the applied force is the weight of the load (W), and the stiffness is the Young's modulus (E) of concrete.

The Young's modulus of concrete can vary, but a typical value is around 30 gigaPascals (GPa). However, to simplify calculations, let's assume E = 30 × 10^9 Pascal (Pa).

The formula for Hooke's law is: ∆L = (F * L) / (A * E).

Plugging in the values, we get: ∆L = (W * L) / (A * E) = (1316.33 kg * 9.8 m/s^2 * 9.4 m) / (0.138 m^2 * 30 × 10^9 Pa).

Evaluating the expression, we find: ∆L ≈ 0.0001296 m.

Therefore, the concrete column is compressed by approximately 0.0001296 meters (or 0.1296 millimeters) when it supports a 12900kg load.