Lagrange-d’Alembert principle is generally known as D’Alembert’s principle, stated by French physicist and mathematician polymath Jean le Rond d’Alembert. According to d’Alembert’s principle, the external forces acting on a body and the resultant inertia forces on a…

Selecting the factor of safety to be used for various applications is one of the most critical engineering tasks. On the one hand, if a factor of safety is chosen too small, the possibility of failure becomes unacceptably large; on the other hand, if a factor of safety…

A key is a machine element fitted in an axial direction into the mating member, such as pulleys, gears. The key's primary function is to prevent the relative rotation between the shaft and mating member. In most applications, the keys' secondary function is to…

In statics, Lami’s theorem is an equation that relates the magnitudes of three coplanar, concurrent, and non-collinear forces that keep a body in static equilibrium. Lami’s theorem states that if three forces acting at a point are in equilibrium, each force is propo…

Beams are generally horizontal structural members that transfer loads horizontally along their length to the supports, where the loads are usually resolved into vertical forces. Beams are used to resist vertical loads, shear forces, and bending moments. Different typ…

Often, materials are subject to an external force when they are used. Mechanical engineers calculate those forces, and material scientists determine how materials deform or break as a function of force, time, temperature, and other conditions. Materials scientists lear…