# Forces in beams and cables
## Shear
$$V-(W\Delta x)-(V+\Delta V) = 0$$

$$\Delta V = -W\Delta x$$

$$\lim_{\Delta \to 0}$$

$$dV/dx = -W$$

$$dV = -W\ dx$$

$$\int_{x_i}^{x_f} dV = \int_{x_i}^{x_f} W(x)\ dx$$
:::success
$$\Delta V = \int_{x_i}^{x_f} W(x)\ dx$$
:::
## Bending moment
$$\sum M = 0$$

$$(M+\Delta M)-M-V\Delta x+W\Delta x(\Delta x/2) = 0$$

$$\Delta M/\Delta x = V-W\Delta x/2$$

$$\lim_{\Delta \to 0}$$

$$dM/dx = V$$

$$\int_{x_i}^{x_f} dM = \int_{x_i}^{x_f} V(x)\ dx$$

$$\Delta M = \int_{x_i}^{x_f} V(x)\ dx$$
:::success
$$M = \int \int W(x)\ dx$$
:::