James H. Allen III

As with any branch of physics, solving statics problems requires you to remember all sorts of calculations, diagrams, and formulas. The key to statics success, then, is keeping your shear and moment diagrams straight from your free-body diagrams and knowing the differences among the calculations for moments, centroids, vectors, and pressures.

Students and professional engineers in the mechanical sciences know that mechanics of materials deals extensively with stress on objects — from determining stress at a particular point to finding stresses in columns. Knowing how to apply some important laws and graphic representations can help you tackle stressful mechanics of materials problems with ease.

Deformations measure a structure's response under a load, and calculating that deformation is an important part of mechanics of materials. Deformation calculations come in a wide variety, depending on the type of load that causes the deformation. Axial deformations are caused by axial loads and angles of twist are causes by torsion loads.

When working submerged surface problems in statics, remember that all submerged surfaces have a fluid acting upon them, causing pressure. You must compute two pressures: the hydrostatic pressure resultant and the fluid self weight. Hydrostatic pressure resultant: The hydrostatic pressure resultant acts horizontally at 0.

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 Support reactions Self weight Write equilibrium equations to compute as many unknown support reactions as possible.

In many statics problems, you must be able to quickly and efficiently create vectors in the Cartesian plane. Luckily, you can accomplish your Cartesian vector creations easily with the handy vector formulas in this list: Force vectors and distance vectors are the most basic vectors that you deal with.

In statics, moments are effects (of a force) that cause rotation. When computing equilibrium, you must be able to calculate a moment for every force on your free-body diagram. To determine a force's moment, you use one of two different calculations, as you can see in the following list. Scalar calculation (for two dimensions): To calculate the moment about a Point O in scalar calculations, you need the magnitude of the force and the perpendicular distance from Point O to the line of action of the Force F.

Shear and moment diagrams are a statics tool that engineers create to determine the internal shear force and moments at all locations within an object. Start by locating the critical points and then sketching the shear diagram. Critical point locations: Start and stop of structure (extreme ends) Concentrated forces Concentrated moments Start and stop of distributed loads Internal hinges Support locations Points of zero shear (V = 0) — for moment diagrams only.

The centroid or center of area of a geometric region is the geometric center of an object's shape. Centroid calculations are very common in statics, whether you're calculating the location of a distributed load's resultant or determining an object's center of mass. To compute the center of area of a region (or distributed load), you can compute the x-coordinate (and the other coordinates similarly) from the following equations: For discrete regions: You can break discrete regions into simple shapes such as triangles, rectangles, circles, and so on.