 The reactions can be computed using balances of forces and moments about point A, i.e.,
If formula_27 is the length of the beam, we have
If we solve for the reactions we have
Looking at the free body diagram of the part of the beam to the left of point X, the total moment of the external forces about the point X is
If we compute the cross products, we have
For this situation, the only non-zero component of the bending moment is
For the sum of the moments at X about the axis formula_13 to be zero, we require
At formula_35, we have formula_36.In the above discussion, it is implicitly assumed that the bending moment is positive when the top of the beam is compressed.That can be seen if we consider a linear distribution of stress in the beam and find the resulting bending moment.