10) Horizontal beam supported on both ends - square profil 100 × 100 × 5, length is 800 mm.It is bent by the force in the middle of the beam by 0.2 mm. To achieve approximately half of the value of deflection,you will use the beam:
To calculate the required beam profile to achieve approximately half of the given deflection value, we need to use the equation for deflection in a simply supported beam.
The equation for deflection in a simply supported beam under a concentrated load at the center can be expressed as:
δ = (F * L^3) / (48 * E * I)
Where:
δ = deflection
F = applied force
L = length of the beam
E = modulus of elasticity
I = moment of inertia
Given:
δ = 0.2 mm (deflection)
L = 800 mm (length of the beam)
F = unknown
E = constant (material property)
I = unknown
We can rearrange the equation to solve for the applied force (F):
F = (δ * 48 * E * I) / L^3
Since we want to achieve approximately half the given deflection value, we use:
Desired deflection = δ / 2 = 0.2 mm / 2 = 0.1 mm
Now, we can substitute the known values into the equation:
F = (0.1 * 48 * E * I) / L^3
To determine the required beam profile, we need to calculate the moment of inertia (I).
For a square beam profile, the moment of inertia (I) can be calculated as:
I = (width * height^3) / 12
Given:
width = height = 100 mm
Substituting these values, we get:
I = (100 * 100^3) / 12
Now, we can substitute the calculated values into the equation for the applied force:
F = (0.1 * 48 * E * [(100 * 100^3) / 12]) / 800^3
Note: The modulus of elasticity (E) is a material property that depends on the specific material used for the beam. You need to know the material of the beam to substitute the appropriate value for E. The value of E is typically provided in material property tables for different materials, such as steel or aluminum.
With the provided information, you can now substitute the given values and the appropriate value for E to calculate the required applied force (F) using the equation above.