Shear Force Example (Intermediate - Hard)

This example for Shear Force and Bending Moments is going to be a lot more complex than the previous with the addition of calculating the Maximum Bending Moment. This is all fitted on a single piece of paper so the working out can be a lot less than shown.

The first step is to calculate the Forces in the Y direction and the Moment, and from this you can work out the reaction forces. (This is shown in the top right of the figure)

The second step is to work out the shear Force which isn't that complex, you simply take an area between two points working from left to right until you reach the final force. The forces are added or subtracted depending on the rotation of your global axis. For me forces acting upwards are positive and forces acting downwards are negative.
When you have a UDL you have to remember to multiply the force giving by the distance you are using at that particular time. 

The final result should add up to zero, if it doesn't go back you must have made a mistake.

The third step is to calculate the hardest part which is bending moment. This is only difficult due to all forces acting at a distance from a point and the can get complicated especially with the UDL.
Start at point A and take the force and multiply the by the distance it acts from force A, which is zero. Therefore Force A will always be zero.
You follow the same principle throughout the entire beam. This changes slightly when measuring the UDL. This time you need to multiply it from the distance and then multiply it again by half the distance. Don't worry this is all shown in the figure and Calculations.
Once you have calculated across the entire beam the value should be equal to zero, if it isn't you've made a mistake.

Finally you need to plot the Shear Force diagram, and where it crosses the X axis into negative is called the "Point of Inflection" and this is where the maximum bending moment occurs. You can then see at which points the bending moment occurs, for this example it happens between point B and C. So you take the shear Force equation for point B and C and solve it for UDL at X distance. For this example we get 7m.
This 7m is then put into the bending moment equation as the distance between points B and C and then the maximum bending moment is found. This all sounds complicated and it is but follow the calculations on the figure and it all should make sense.