## 10.3.1 How to compute torque and bending moments on beams

Figure 10.3 of the textbook is reproduced below: Figure 10.2: Forces and moments on the (x,y,z) user c.s. Panels numbered 1 through 5. Nodes numbered 1 through 6. Panel c.s. denoted by (x,s,r) on each panel. Reproduced from the textbook. Click the Back button on your browser to return to your previous page.

Torque , and bending moments , are positive following the conventional right-hand rule.

In CADEC, three moments can be input, which are free vectors (i.e., invariants w.r.t. translations). Also, a number of forces can be input. Each force is a vector described by its three components and the point of application x, y, z, of each force.

The horizontal (y) and vertical (z) components of the forces produce shear bending w.r.t. the c.g., and torque w.r.t the shear center, calculated in Equation 10.1.

The axial component of the forces add up to a total axial force applied at the mechanical neutral axis of bending (c.g.),1 plus bending moments calculated in (Equation 10.2 10.4).

In summary, (10.1)

and   (10.2)   (10.3)   (10.4)

Footnotes

1. For inhomogeneous materials, the mechanical neutral axis of bending is not necessarily the center of gravity but it is abbreviated c.g. to follow tradition.