Piping Fundamental as The Important Pipe Elements

Starting today, Piping & Fabrication will start the new chapter of this pipe handbook, and now we go to PIPING FUNDAMENTAL as the important pipe elements.

FORCES, MOMENTS, AND EQUILIBRIUM
Simple Forces. When two or more forces act upon a body at one point, they may be single or combined into a resultant force. Conversely, any force may be resolved into component forces. In the figure, let the vectors F1 and F2 represent two forces acting on a point O. The resultant force F is represented in direction and magnitude by the diagonal of the parallelogram of which F1 and F2 are the sides. Conversely, any force F may be resolved into component forces by a reverse of the above operation.

vector and moments

Moments.
The moment of a force with respect to a given point is the tendency of that force to produce rotation around it. The magnitude of the moment is represented by the product of the force and the perpendicular distance from its line of action to the point or center of moment. In the English system of weights and measures, moments are expressed as the product of the force in pounds and the length of the moment arm in feet or inches, the unit of the moment being termed the pound-foot or the pound-inch. Moments acting in a clockwise direction are designated as positive, and those acting in a counterclockwise direction are negative. They may be added and subtracted algebraically, as moments, regardless of the direction of the forces themselves.

 

With respect of that figures, moments about an arbitrary point x are calculated as follows: Extend the line of action of F1 until its extension intersects the perpendicular ax drawn from point x. Draw bx from x perpendicular to F2. The sum of moments about point x due to the two forces is then Alternatively, since F1 and F2 have been shown to be the vector equivalent of the resultant F, the moments about x can be calculated as

Couples.
Two parallel forces of equal magnitude acting in opposite directions constitute a couple. The moment of the couple is the product of one of the forces and the perpendicular distance between the two. A couple has no single resultant and can be balanced only by another couple of equal moment of opposite sign.

Law of Equilibrium.
When a body is at rest, the external forces acting upon it must be in equilibrium and there must be a zero net moment on the body. This means that (1) the algebraic sums of the components of all forces with reference to any three axes of reference at right angles with one another must each be zero and (2) the algebraic sum of all moments with reference to any three such axes must be zero. When the forces all lie in the same plane, the algebraic sums of their components with respect to any two axes must be equal to zero and the algebraic sum of all moments with respect to any point in the plane must be zero.

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