<< Back to Axial, Shear, & Moment Diagrams 
Step 1: Find the support reaction forces/moments.
We should always begin by drawing the free body diagram (FBD). Knowing all the externally applied forces and moments, we can determine the reactions at the supports by summing the forces and moments. 
From the FBD, we know that there are only externally applied vertical forces. Therefore, there are only vertical, opposite reactions at the supports. To find these reactions, we sum the forces and moments. For consistency, the up forces and counterclockwise moments are positive. 
Note that RA and RB are positive values, meaning that they are pointing upwards, according to our sign convention. They also match the direction of the arrows in our current FBD. However, if we selected the reaction forces to point downwards in the FBD, both values would be negative, meaning that the actual reaction forces are pointing upwards. Either way gives us the same results. Therefore, the main takeaway is that the positive and negative signs have to be consistent with the FBD and chosen sign convention.
Step 2: Determine axial/shear forces.
Right off the bat, we know that there are no external axial forces, so there are no internal axial forces. Therefore, there is no need to draw an axial force diagram (AFD).
To determine the internal shear forces (V), we are going to look at four segments. The first segment represents the part of the beam with distributed load. The second segment includes the part of the beam between the distributed load and point load. The third segment includes the part of the beam to the right of the point load. The fourth segment includes the cantilevered end. Generally, we can find the shear force along each segment of the beam by summing all forces.
Mathematically, we can say the shear force at distance x from the left is: 
Step 3: Draw axial/shear force diagrams.
Once we have the shear equation for each segment, we can plot the shear force diagram (SFD). Note that the shear force at the supports is equal to the reaction. Also, as stated in the list of basic rules, the SFD does not have to be continuous. 
Step 4: Determine bending moment.
Similarly, to determine the bending moments (Mz), we are going to look at the same four segments. Generally, we can find Mz along each segment of the beam by summing all the moments.
Mathematically, we can say the bending moment at distance x from the left is: 
Step 5: Draw bending moment diagram.
Once we have the bending moment equation for each segment, we can plot the bending moment diagram (BMD). Note that the bending moment is zero at the ends. Also, as stated in the list of basic rules, the BMD is continuous. 
Recall that shear is the rate of change or derivative or slope of moment. From calculus, we know that there is a local maximum or minimum value when the slope of a function is zero. Therefore, when there is a zero shear value (zero slope), there has to be a corresponding local maximum or minimum moment value. Because shear is the derivative of moment, or inversely, moment is the anti-derivative of shear, we can determine this critical point in the BMD by finding the area under the SFD up to that point. The maximum moment is at support B, and it is equal to the area of the rightmost rectangle in the SFD, or (8k)(4ft) = 32k-ft.
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