Analyzing a supported beam under unsymmetrical loadings requires a reference tangent with a known slope to identify the level point.

The slope of the reference tangent is calculated by determining the tangential shift between the ends.

The slope of the beam at any point can be determined by using the first moment area theorem and then writing an equation for that slope.

The vertical distance from a point to the reference tangent, also known as the tangential deviation of that point regarding the support, can be determined using the second moment area theorem.

This deviation equals a certain segment and signifies the vertical distance from the point to the reference tangent. The deflection at a point indicates its vertical distance from a horizontal line.

Since this deflection equals a specific segment in size, it can be defined as the difference between two segments.

By studying similar triangles, one of these segments can be determined. Considering the sign conventions for deflections and tangential deviations, the deflection at a point is noted.