Fixed Beam with Uniformly Distributed Load

A fixed beam is a type of beam that is supported at both ends and prevented from rotating. A uniformly distributed load is a load that is spread evenly along the length of the beam. The deflection at the center of the beam is the amount of vertical displacement at the midpoint of the beam.

Formula for Deflection at Center of Fixed Beam with Uniformly Distributed Load

The deflection at the center of a fixed beam with a uniformly distributed load can be calculated using the following formula:

δ = (5wL^4) / (384EI)

where:

δ = deflection at the center of the beam
w = uniformly distributed load per unit length
L = span of the beam
E = modulus of elasticity of the beam material
I = moment of inertia of the beam cross-section

Explanation of the Formula

The deflection at the center of the beam is directly proportional to the load and the span of the beam. It is also inversely proportional to the modulus of elasticity of the beam material and the moment of inertia of the beam cross-section.

The moment of inertia of the beam cross-section is a measure of its resistance to bending. A higher moment of inertia indicates a stiffer beam that is less likely to deflect under load.

The modulus of elasticity of the beam material is a measure of its stiffness. A higher modulus of elasticity indicates a stiffer material that is less likely to deflect under load.

Conclusion

In conclusion, the deflection at the center of a fixed beam with a uniformly distributed load can be calculated using the formula δ = (5wL^4) / (384EI). This formula takes into account the load, span, modulus of elasticity, and moment of inertia of the beam cross-section. By understanding this formula, civil engineers can design fixed beams that are strong enough to resist deflection under load.