Theorem of three moments

Let A,B,C-D be the three consecutive points of support, and denote by- l the length of AB and

at the three points are related by: This equation can also be written as [2] where a1 is the area on the bending moment diagram due to vertical loads on AB, a2 is the area due to loads on BC, x1 is the distance from A to the centroid of the bending moment diagram of beam AB, x2 is the distance from C to the centroid of the area of the bending moment diagram of beam BC.

The deflection of k1 and k2 relative to the point of intersection between tangent at k1 and k2 and vertical through k1 is equal to the moment of M/EI diagram between k1 and k2 about k1.

(Figure 03) The three moment equation expresses the relation between bending moments at three successive supports of a continuous beam, subject to a loading on a two adjacent span with or without settlement of the supports.

According to the Figure 04, PB'Q is a tangent drawn at B' for final Elastic Curve A'B'C' of the beam ABC.

Figure 01-Sample continuous beam section
Figure 02-Mohr's First Theorem
Figure03-Mohr's Second Theorem
Figure 04-Deflection Curve of a Continuous Beam Under Settlement
Figure 05 - M / EI Diagram