the two balance equations Summing the forces, we have and summing the moments around the free end (A) we have We can solve these equations for Rb and Rc in terms of Ra and Mc : and If we sum moments about the first support from the left of the beam we have If we plug in the expressions for Rb and Rc we get the trivial identity 0 = 0 which indicates that this equation is not independent of the previous two. Similarly, if we take moments around the second support, we have Once again we find that this equation is not independent of the first two equations. We could also try to compute moments around the clamped end of the beam to get This equation also turns out not to be linearly independent from the other two equations. Therefore, the beam is statically indeterminate and we will have to find the bending moments in segments of the beam as functions of Ra and Mc. Step 2: Break beam into segments After the reaction forces are found, you then break the beam into pieces. The location and number of external forces on the member determine the number and location of these pieces. The first piece always starts from one end and ends anywhere before the first external force. Step 3: Compute shear forces and moments - first piece Let V1 and M1 be the shear force and bending moment respectively in a cross-section of the first beam segment. As the section of the beam moves towards the point of application of the external force the magnitudes of the shear force and moment may change. This makes the shear force and bending moment a function of the position of cross-section (in this example x). By summing the forces along this segment and summing the moments, the equations for the shear force and bending moment are obtained. These equations are: and Therefore, Step 4: Compute shear forces and moments - second piece Taking the second segment, ending anywhere before the second internal force, we have and Therefore, Notice that because the shear force is in terms of x, the moment equation is squared. This is due to the fact that the moment is the integral of the shear force. The tricky part of this moment is the distributed force. Since the force changes with the length of the segment, the force