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 determine the beam needed to achieve approximately half of the given deflection, we can use the formula for deflection in a simply supported beam. The formula for deflection in a simply supported beam under a mid-span load is:
δ = (F * L^3) / (48 * E * I)
where:
- δ is the deflection
- F is the force applied at the mid-span
- L is the length of the beam
- E is the modulus of elasticity of the material
- I is the moment of inertia of the beam section
In this case, we are given the deflection (0.2 mm), the length of the beam (800 mm), and the beam section (square profile 100 × 100 × 5). However, we need to find the force and the modulus of elasticity.
Since we want to achieve approximately half of the given deflection, we can rearrange the formula and solve for F:
F = (δ * 48 * E * I) / L^3 * 0.5
Now, let's calculate the moment of inertia (I) for the square profile beam:
For a square section, the moment of inertia can be calculated using the formula:
I = (b * h^3) / 12
where:
- b is the width of the beam (100 mm)
- h is the height of the beam (100 mm)
I = (100 * 100^3) / 12
I = 833,333.33 mm^4
Now, let's consider the modulus of elasticity (E) for the material. Assuming it is a common steel material, the modulus of elasticity for steel is around 200 GPa or 200,000 MPa.
E = 200,000 MPa
Now, we can substitute the values into the formula to calculate the force required to achieve half of the given deflection:
F = (0.2 * 48 * 200,000 * 833,333.33) / (800^3 * 0.5)
Calculating the above expression, we get:
F ≈ 20,833.33 N
Therefore, to achieve approximately half of the given deflection, you will need a beam that can withstand a force of around 20,833.33 N.