The beam is supported by a roller at $\backslash ($ B $\backslash )$ and a pin at $\backslash ($ C $\backslash )$ and is subjected to the distributed load shown with intensity $\backslash ($ w$=120\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$m$\}\backslash ).$ The maximum positive and negative internal bending moments are critical factors in the design of the beam material and geometry. Determine the largest positive and negative internal bending moments that occur in the beam and the points along the length where each occurs. Take $\backslash ($ x$=0\backslash )$ to be at point $\backslash ($ A $\backslash )$ at the left edge of the beam.

Values for dimensions on the figure are given in the following table. Note the figure may not be to scale.

The maximum negative internal bending moment is $\backslash (\backslash$mathrm$\{$N$\}-\backslash$mathrm$\{$m$\}\backslash )$ and occurs at $\backslash ($ x$=\backslash )$ m to the right of $\backslash ($ A $\backslash ).$

The maximum positive internal bending moment is $\backslash (\backslash$mathrm$\{$N$\}-\backslash$mathrm$\{$m$\}\backslash )$ and occurs at $\backslash ($ x$=\backslash )$ m to the right of $\backslash ($ A $\backslash ).$