Checklist for Solving Statics Problems
Solving statics problems can be complicated; each problem requires a list of items to account for and equations to create and solve. Solve statics problems with ease by using this checklist:
Draw a free-body diagram of the entire system.
In addition to dimensions and angles, you must include four major categories of items on a properly constructed free-body diagram:
Applied external loads
Revealed internal loads
Write equilibrium equations to compute as many unknown support reactions as possible.
To solve for internal forces, identify the type of structure and write your equilibrium equations.
After you identify the type of structure, you then know which technique to use to help you write your equilibrium equations:
Trusses/axial members: Members are loaded with internal axial forces only. To solve, you can use the method of joints or the method of sections.
Beams (bending members): Members are loaded with internal axial forces, shear forces, and moments. To solve, cut the member at the desired location, draw a new free-body diagram of the cut section, and write equilibrium equations.
Frames/machines: Members are loaded with internal axial forces, shear forces, and moments. To solve, use the blow-it-all-apart approach to break the structure into smaller pieces. Look for internal hinges as common places to separate your structure and draw free-body diagrams to solve for the connecting pin forces.
Cable structures: Members are constructed from axially loaded cables. Identify the type of cable loading (concentrated, parabolic/uniform, or catenary). Compute the cable tension at the location of known maximum sag (or vice versa).
Submerged surfaces: Members are subjected to fluid pressure. To solve, draw a free-body diagram of the hydrostatic pressure diagram which is zero at the fluid surface and linearly increases with depth. Include the weight of the fluid on objects with non-vertical faces.