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Projected Loads

When the load on a beam is distributed the total load can be based on the actual length of the element or on the projected length of the element. Thus a load normal to the x axis of the element would have a projected length equal to the beam length while a load parallel to the x axis of the beam would have a projected length of zero. In the general case of a load in the a direction defined by a unit vector w\mathbf{w} and where the beam load x axis is denoted x\mathbf{x} the factor that has to be applied to the load intensity, defined in terms of the angle between the two vectors, is

ffsinθ=f1(xw)2f \rightarrow f\sin\theta = f\sqrt{1 - \left( \mathbf{x} \cdot \mathbf{w} \right)^{2}}