Diseño Y Construcción De Un Puente a Escala.

Applying mechanics to a scale wooden bridge involves analyzing how forces act on its structure and how the material (in this case, wood) responds under different conditions. At the scale model level, the goal is to replicate the physical principles at work on a real bridge, albeit adapted to a smaller size. Here's a step-by-step explanation of how mechanics is applied in this context:

Wooden sticks (recycled)

Cardboard

Hot glue

Before any analysis, it is essential to define the scale of the model. If the model is, for example, 1:10, it means that each unit in the model represents 10 in reality.

⚠ Important: Forces and properties do not always scale linearly. Mass, for example, scales with the cube of the linear dimension, while area scales with the square of the square.

In a bridge (real or scale), the main forces to consider are:

• Vertical load (self-weight + applied load)

• Reactions at supports

• Internal forces: tension, compression, bending, shear.

This can be analyzed using statics, using the basic equations:

• ∑F = 0 (force equilibrium)

• ∑M = 0 (moment equilibrium)

Depending on the type of bridge (beam, arch, cable strut, truss), each structural component operates differently:

• Beams: support bending and shear.

• Columns: operate in compression.

• Tie rods (if present): operate in tension.

• Connections: must resist moments or shears depending on the design.

In scale models, this can be studied by applying small loads (e.g., weights) and measuring the deformation.

Wood's properties don't change just because it's scaled, but its response to stress does depend on the element's cross-section and length.

• The modulus of elasticity (E) remains the same.

• However, the stiffness (EI) does change, as it depends on the moment of inertia, which scales with the fourth power of the linear dimension.

A common way to apply mechanics to a scale model is to perform:

• Load tests: place weights and measure deflection.

• Strength tests: test the model until it collapses to study the point of failure.

• Structural simulation: using software (such as SAP2000 or ANSYS) to adapt the model's parameters to scale.

Stresses and strains can be calculated theoretically using classical mechanics formulas (such as the Euler-Bernoulli beam equations), and then compared with experimental data from the model.