in practical problems is the computation of moments of force. Let be a force vector acting at a point A in a body. The moment of this force about a reference point (O) is defined as where is the moment vector and is the position vector from the reference point (O) to the point of application of the force (A). The symbol indicates the vector cross product. For many problems, it is more convenient to compute the moment of force about an axis that passes through the reference point O. If the unit vector along the axis is , the moment of force about the axis is defined as where indicates the vector dot product. Example The adjacent figure shows a beam that is acted upon by a force . If the coordinate system is defined by the three unit vectors , we have the following Therefore, The moment about the axis is then Sign conventions The negative value suggests that a moment that tends to rotate a body clockwise around an axis should have a negative sign. However, the actual sign depends on the choice of the three axes . For instance, if we choose another right handed coordinate system with , we have Then, For this new choice of axes, a positive moment tends to rotate body clockwise around an axis. Computing the bending moment In a rigid body or in an unconstrained deformable body, the application of a moment of force causes a pure rotation. But if a deformable body is constrained, it develops internal forces in response to the external force so that equilibrium is maintained. An example is shown in the figure below. These internal forces will cause local deformations in the body. For equilibrium, the sum of the internal force vectors is equal to the negative of the sum of the applied external forces, and the sum of the moment vectors created by the internal forces is equal to the negative of the moment of the external force. The internal force and moment vectors are oriented in such a way that the total force (internal + external) and moment (external + internal) of the system is zero. The internal moment vector is called the bending moment. Though bending moments have been used to determine the stress states in arbitrary shaped structures, the physical interpretation of the computed stresses is problematic. However, physical interpretations of