This section will explore how we apply loads to an analytical model. The following are typical applications one may encounter:

Moment (or Torsion) Load

A moment \(M\) or torsional load \(T\) is a force that causes something to rotate. The former causes the structure to bend, while torsion loads cause it to twist.

The load is a product of force \(F\) and its lever arm \(d\). The resulting rotation may be clockwise or counterclockwise.

We can represent these loads as a couple - two parallel forces equal in magnitude but opposite in their directional sense. In addition, these two forces must not share a line of action.

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Concentrated loads (or point loads) act at a specific point in the structure. It may represent a reaction load from an adjacent building, or a heavy piece of machinery or furniture, to name a few.

We represent a concentrated load using any force \(F\) or \(P\). Depending on its applied orientation, it may act upward or downward or to the left or right.

Distributed Load

Distributed loads act over a specified length. It may represent live loads, water pressure, or earth pressure.

Distributed loads \(w\) are force per unit length. It may act upward or downward or to the left or right, like concentrated loads.

Typically, we express distributed loads as polynomial functions. Depending on the degree, there are other variations of distributed loads:

Uniform Loads

The distributed load is uniform if we have a polynomial function of 0th degree (meaning it's a horizontal line); so if we have a \(5kN/m\) uniform distributed load, it means that for every \(1m\), we have a force of \(5kN\). We equally distribute the said force throughout its length.

Uniform Varying

Uniform varying means the function of the distributed load is in the first degree (a line). The force either linearly gets larger or smaller depending on the orientation. For example, if we represent water pressure as a uniform varying load, the load at the surface is zero, but as we go deeper, it becomes larger and larger.

Since the function is linear, the change in load among points can be solved using ratio and proportion or slopes.

Non-Uniform

Any distributed load higher than the first degree is non-uniform. Examples of non-uniform loads may range from dynamic loads such as wind or earthquakes.

Typically, when representing these loads, we must know their mathematical function.

Planar Loads

Planar loads act over an area. It may represent all sorts of loads (dead loads, live loads, water/earth pressure, and the like).

We represent these as force per unit area, similar to stress/pressure; Like concentrated and distributed loads, it may act upward or downward or to the left or right.

Similar to distributed loads, we can represent these loads using plane curves. A uniform planar load would mean a flat horizontal plane acting on an area - the pressure is equal at any point along the affected area.

Summary

A moment or torsional load is a force that causes something to rotate.

Moment (or torsional) load is a product of force \(F\) and its lever arm \(d\). The resulting rotation may be clockwise or counterclockwise.

Concentrated loads (or point loads) act at a specific point in the structure.

We represent a concentrated load using any force \(F\). Depending on its applied orientation, it may act upward or downward or to the left or right.

Distributed loads work over a specified length.

Distributed loads \(w\) are force per unit length. It may act upward or downward or to the left or right, like concentrated loads.

Typically, we express distributed loads as polynomial functions.

The distributed load is uniform if we have a polynomial function of 0th degree.

Uniform varying means the function of the distributed load is in the first degree.

Any distributed load higher than the first degree is non-uniform.

Planar loads act over an area.

We represent these as force per unit area; Like concentrated and distributed loads, it may act upward or downward or to the left or right.

Similar to distributed loads, we can represent these loads using plane curves.