Stiffness Coefficient for Deflection at Free End of Cantilever Beam

To determine the stiffness coefficient for deflection at the free end of a cantilever beam, several factors need to be considered. These include the span of the beam, the applied load, and the material properties of the beam.

Span of the Beam:
The span of the beam is given as 10m. This refers to the distance between the fixed support and the free end of the beam.

Applied Load:
A point load of 20kN is applied at the free end of the cantilever beam. This means that the entire load is concentrated at a single point.

Material Properties:
The stiffness coefficient for deflection at the free end depends on the material properties of the beam. The Young's modulus (E) of the material is a crucial factor in determining the stiffness of the beam. Young's modulus represents the ability of a material to withstand deformation under an applied load.

To calculate the stiffness coefficient for deflection at the free end, we can use the formula:

k = 3EI/L^3

Where:
k = Stiffness coefficient for deflection at the free end
E = Young's modulus of the material
I = Moment of inertia of the beam cross-section
L = Span of the beam

The moment of inertia (I) of the beam cross-section can be determined based on the shape and dimensions of the beam. For simplicity, let's assume a rectangular cross-section.

For a rectangular cross-section, the moment of inertia is given by the formula:

I = (b * h^3) / 12

Where:
b = Width of the rectangular cross-section
h = Height of the rectangular cross-section

Let's assume the width (b) of the beam is 0.3m and the height (h) is 0.5m.

Now we can calculate the moment of inertia (I):

I = (0.3 * 0.5^3) / 12
I = 0.005625 m^4

Using the given span (L) of 10m and the calculated moment of inertia (I), we can substitute these values into the formula to find the stiffness coefficient (k):

k = 3 * E * I / L^3

As we do not have the value of Young's modulus (E) for the material, we cannot calculate the exact stiffness coefficient. Young's modulus varies depending on the material used for the beam, such as steel or concrete. You can refer to material specifications or engineering handbooks to find the Young's modulus for the specific material you are working with.

Once you have the Young's modulus value, you can substitute it into the formula to find the stiffness coefficient for deflection at the free end of the cantilever beam.