Lecture 20: Resolving Distributed Loads

Lecture 20:

Resolving Distributed Loads

Many structural members are subjected to distributed loads rather than concentrated loads. However, when solving for their reactions, it is often convenient to replace the distributed loads with an equivilent concentrated load(s) .

The most common type of distributed load is the uniform load, in which a load of constant magnitude is applied along a length of a beam or an area of a surface. The resultant of these distributed loads has the same magnitude as the area of the distributed load and acts through the center of gravity, or the centroid, of the load area. This point is located at the intersection of the diagonals of a rectangular, or uniform, load area.

Distributed Loads

Not all distributed loads are of a constant value. Some examples of loading conditions that may cause triangular loads are:

the load on a lintel in a masonry wall due to the arching of the masonry;
the load on a vertical surface below grade due to soil or water pressure;
the load on the vertical surface of a structure due to wind loading.

These triangular loads can be replaced by a single concentrated load which acts through the centroid of the distributed load and acting in the same direction. The centroid of a triangular load area is found at the intersection of its medians which always equals 1/3 of the height above any of its bases.

Triangular Loads

Triangular loads can be caused by either soil or water pressure. Note that it constantly increases with depth! The magnitude of the greatest load that is applied is simply the unit weight of the material multiplied by the deepest point in question.

There are cases where a uniformly distributed load combines with a triangularly distributed load to create a trapezoidal load. This loading condition is most easily solved by separating the triangular and uniform loads and calculating separate resultants for each. These resultants can then be treated as a series of concentrated loads or transformed into a single resultant for the system.

Trapezoidal Loads