three-moment equation

Problem 818
In Problem 817, determine the changed value of the applied couple that will cause M₂ to become zero.
 

Problem 817
Find the moment under the support R₂ of the continuous beam shown in Fig. P-817.
 

Problem 816
Determine the lengths of the overhangs in Fig. P-816 so that the moments over the supports will be equal
 

Problem 815
Find the moment at R₂ and R₃ of the continuous beam shown in Fig. P-815.
 

Problem 814
Find the moment at R₂ of the continuous beam shown in Fig. P-814.
 

Problem 813
Determine the moment over the support R₂ of the beam shown in Fig. P-813.
 

The three-moment equation gives us the relation between the moments between any three points in a beam and their relative vertical distances or deviations. This method is widely used in finding the reactions in a continuous beam.
 

Consider three points on the beam loaded as shown.