Theorem of three moments
![Figure 02-Mohr's First Theorem](/Images/godic/202502/16/Mohr's_First_Theorem0613.png")
![Figure03-Mohr's Second Theorem](/Images/godic/202502/16/Mohr's_Second_Theorem0613.png")
![Figure 04-Deflection Curve of a Continuous Beam Under Settlement](/Images/godic/202502/16/Deflection_Curve_of_a_Continuous_Beam0613.png")
![Figure 05 - M / EI Diagram](/Images/godic/202502/16/Moment_Diagram0613.png")
In civil engineering and structural analysis Clapeyron's theorem of three moments is a relationship among the bending moments at three consecutive supports of a horizontal beam.
Let A,B,C be the three consecutive points of support, and denote by l the length of AB by ![l'](/Images/godic/202502/16/c07717f29a52139c97273a1897112f8e0613.png")
the length of BC, by w and ![w'](/Images/godic/202502/16/8624c3694bf8d786aba4c979661866b20613.png")
the weight per unit of length in these segments. Then the bending moments ![M_A,\, M_B,\, M_C](/Images/godic/202502/16/df8de887c46056af233dffbcee0941e20613.png")
at the three points are related by: