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Distributed force Dimensional Analysis

Distributed force represents a force that is spread out over a length. On the other hand, when the force is spread out over a surface it's called a pressure.

The dimensional analysis stems from the interrelation of two other quantities: force and length.

Distributed force = force / length
                  = M¹ L¹ / T² / L¹
                  = M¹ L⁰ T⁻²
                  = M¹ T⁻²

Distributed Force Examples

Distributed forces are a common concept in structural engineering, as they allow engineers to model the behavior of various structures and materials under different loading conditions. Here are some examples of distributed forces in structural engineering:

  • The self-weight of a beam: When a beam is loaded, it exerts a force on its own weight in addition to any external loads. This force is distributed uniformly along the length of the beam and can be represented as a distributed force along its axis. The magnitude of the force is proportional to the weight of the beam per unit length.
Simple supported beam under uniform distributed force
  • The weight of the railing of a bridge: The railing of a bridge is a safety feature that provides protection for pedestrians and vehicles. However, the weight of the railing will also exert a distributed force on the bridge structure. This force can be modeled as a distributed load per unit length, and its intensity depends on the design and materials used.

  • The hydrostatic pressure of the water on a dam: Damns are designed to withstand the pressure of the water that they hold back. This pressure is distributed hydrostatically, meaning that it varies with the depth of the water. The pressure can be modeled as a distributed force per unit length, and is typically highest at the base of the dam.

  • The wind pressure on a wall: Buildings and structures are subject to various types of wind loads, including gusts, turbulence, and steady winds. These loads can cause the structure to bend or sway, which can result in damage or failure. Wind pressure can be modeled as a distributed load per unit length, and varies depending on the wind speed, direction, and shape of the structure.

Damn under hydrostatic pressure and building wall under wind pressure as distributed forces
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