How to Properly Consider a New Segment in Shear Force and Bending Moment Diagrams

What is the essential consideration when adding a new segment in shear force and bending moment diagrams?

a) Ignore the new segment

b) Continue with the previous segment's calculations

c) Start a new set of calculations for the new segment

d) Skip the diagram for the new segment

Answer:

When adding a new segment in shear force and bending moment diagrams, continue with the previous segment's calculations and incorporate any new forces or changes that occur at the new segment boundary.

When considering a new segment while doing shear force and bending moment diagrams, it is essential to continue with the previous segment's calculations (option b). This is because the effect of the forces and moments are cumulative and need to be considered throughout the entire structure. Consequently, as you move to a new segment, you need to carry the effects from the previous segment forward and incorporate any new forces or changes that occur at the new segment boundary.

To illustrate this concept, if we consider an object's ability to withstand force without accelerating - as represented by the force F applied perpendicular to a reference length Lo and parallel to the cross-sectional area A - the shear modulus S plays a significant role in its resistance to deformation. A long thin pencil with a small A is easier to bend than a short thick one, and both are more easily bent than similar steel rods with a larger shear modulus S.

Drawing a free body diagram and correctly labeling all forces, directions, and points of application are crucial steps in solving problems related to shear force and bending moments. The conditions for equilibrium, net F = 0 and net t = 0, are essential to determine the system's stability. Judging the reasonableness of your calculations by examining the magnitude, direction, and units of the answer continues to be an important step, which becomes easier with experience.