Section 8.5 Conclusion
You have likely realized that in engineering (and life) that there are multiple ways to solve a problem. The four different techniques in this chapter to compute internal loadings are a demonstration of this.
The table below may help you consider the advantages and disadvantages of each method. In the end, the decision of which method to useis yours, and the better you know each method the easier it will be to choose the one which is both applicable and efficient.
| Method | Description | Advantages | Disadvantages |
Section Cut to find Internal Loadings at a Single Point |
Cut a rigid body at a specific location to expose and then solve for the internal loadings at that location |
is computationally efficient works for any shape rigid body (not just beams) takes advantage of tools you have already learned in previous chapters |
requires knowledge of specialized sign conventions for internal loadings only reveals internal loading values at a single point does not reveal all values of shear and moment for a body |
Section Cut Equations for Shear and Moment Diagrams |
Break a beam into loading segments and develop equations for shear and moment using a cut through each section |
allows computation without calculus computations or knowledge |
requires knowledge of specialized sign conventions for internal loadings is computationally time-intensive computational steps lack conceptual cross-checks |
Graphical Method for Shear and Moment Diagrams |
Use mathematical relationship among loading, shear, and moment to graphically create shear and moment diagrams |
requires only simple computations to support conceptual relationships conceptual nature allows many cross-checks for accuracy handles point loads, uniform distributed loads, and couple moments |
requires solid calculus knowledge of slopes and areas related to derivatives and integrals requires you learn a few simple graphical rules and that you work from left to right |
Calculus-Based Equations for Shear and Moment Diagrams |
Use mathematical relationship among loading, shear, and moment to develop equations for shear and moment diagrams |
allows shear and moment diagram computation of complicated loading distributions (e.g. non-uniform distributed loads) |
requires accurate computation of derivatives and integrals requires you learn a few simple graphical rules for concentrated forces and couple moments |