Engr Help

Forces and Moments (Vectors)

Key Concepts: Forces and moments are vectors having magnitude, direction

(line of action), and point of application. The moment of a force can be calculated

about a designated point or about a designated line.

In a Nut Shell: Engineers design structures, such as supports, bridges, buildings,

cell towers, pavement, submerged plates, and so forth to support loads including

forces and moments. It will be important for you to manipulate vectors including vector

addition, vector subtraction, and vector multiplication and to calculate components of

applied forces, moments of applied forces, and concentrated moments on structures.

Recall in elementary calculus there are two forms of vector multiplication. They are the

scalar product (also called the dot product) and the vector product (also called the cross

product).

Forces acting on structures may be two or three dimensional. The figure below shows

a force in a rectangular coordinate system with its three components – F_x, F_y, and F_z.

In general the component of a force in a given direction is just the dot product of the

force with a unit vector in the given direction. i.e. F_x, can be calculated using the

dot product F ● i .