(Bug?) HP48 Equation Library

[Brad Barton]

(02-12-2017 03:36 PM)Han Wrote:  There are a few other systems like this. As another example, Cantilever Moment has the equation
\[ Mx = P \cdot (x-a) + M - \frac{W}{2}\cdot (L^2-2\cdot L \cdot x + x^2) \]
This system defines a variable \( c \) that is never used in this formula. Are there any engineers and/or physicists here who can shed some light on these formulas?

This equation might be better understood if the AUR authors had used a subscript for Mx, and had also called it "bending moment" rather than "internal moment". It looks like they mean M*x, but they do not. Mx is the bending moment at any point along the beam. It is the sum of the external forces and moments acting on the beam on one side of the section. The variable "c" is not needed for this equation because wherever the applied moment "M" acts, the effect on the internal bending moment on that side of the beam is the same.

The rest of the terms are just summing the moments resulting from external point loads \[ P \cdot (x-a) \] and the internal weight distribution \[ \frac{W}{2}\cdot (L-x)^2 \]