# First moment of area

First moment of area

The first moment of area, sometimes misnamed as the first moment of inertia, is based in the mathematical construct moments in metric spaces, stating that the moment of area equals the summation of area times distance to an axis [Σ("a" x "d")] . It is a measure of the distribution of the area of a shape in relationship to an axis.

First moment of area is commonly used in engineering applications to determine the centroid of an object or the statical moment of area.

Definition

Given an area, "A", of any shape, and division of that area into "n" number of very small, elemental areas ("dAi"). Let "xi" and "yi" be the distances (coordinates) to each elemental area measured from a given "x-y" axis. Now, the first moment of area in the "x" and "y" directions are respectively given by: : and :.

The SI unit for first moment of area is metre to the third power ("m"3). In the American Engineering and Gravitational systems the unit is foot to the third power ("ft"3) or more commonly inch3.

tatical moment of area

The static or statical moment of area, usually denoted by the symbol "Q", is a property of a shape that is used to predict its resistance to shear stress. By definition:

$Q_\left\{j,x\right\} = int y_i dA$, where

* "Q""j,x" - the first moment of area "j" about the neutral "x" axis of the entire body (not the neutral axis of the area "j");
* "dA" - an elemental area of area "j";
* "y" - the perpendicular distance to the element "dA" from the neutral axis "x".

hear Stress in a Semi-monocoque Structure

The equation for shear flow in a particular web section of the cross-section of a semi-monocoque structure is:

:$q = frac\left\{V_y Q_x\right\}\left\{I_x\right\}$

*"q" - the shear flow through a particular web section of the cross-section
*"V""y" - the shear force perpendicular to the neutral axis "x" through the entire cross-section
*"Q""x" - the first moment of area about the neutral axis "x" for a particular web section of the cross-section
*"I""x" - the second moment of area about the neutral axis "x" for the entire cross-section

Shear stress may now be calculated using the following equation:

:$\left\{ au\right\} = frac\left\{q\right\}\left\{t\right\}$

* $\left\{ au\right\}$ - the shear stress through a particular web section of the cross-section
*"q" - the shear flow through a particular web section of the cross-section
*"t" - the (average) thickness of a particular web section of the cross-section

ee also

* Second moment of area
* Polar moment of inertia

* http://www.iaengr.org/forum/messages//468.html
* http://mywebsite.bigpond.com/npajkic/solid_mechanics/first_moment_of_area/index.html

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• Second moment of area — The second moment of area, also known as the area moment of inertia or second moment of inertia, is a property of a shape that is used to predict its resistance to bending and deflection which are directly proportional. This is why beams with… …   Wikipedia

• Moment — Moment(s) may refer to: Moment (time) Contents 1 Science, engineering, and mathematics 2 Art and entertainment …   Wikipedia

• Moment of inertia — This article is about the moment of inertia of a rotating object, also termed the mass moment of inertia. For the moment of inertia dealing with the bending of a beam, also termed the area moment of inertia, see second moment of area. In… …   Wikipedia

• Moment (mathematics) — Second moment redirects here. For the technique in probability theory, see Second moment method. See also: Moment (physics) Increasing each of the first four moments in turn while keeping the others constant, for a discrete uniform distribution… …   Wikipedia

• First Battle of Bull Run — (First Manassas) Part of the American Civil War Fi …   Wikipedia

• First-order logic — is a formal logical system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic (a less… …   Wikipedia

• First Battle of El Alamein — Part of Western Desert Campaign …   Wikipedia

• First English Civil War — The First English Civil War (1642–1646) was the first of three wars known as the English Civil War (or Wars ). The English Civil War was a series of armed conflicts and political machinations which took place between Parliamentarians and… …   Wikipedia

• First Vision — The First Vision (also called the grove experience) is a religious belief held by many members of the Latter Day Saint movement (commonly called Mormonism) that God the Father and Jesus Christ appeared to the fourteen year old Joseph Smith, Jr.… …   Wikipedia

• First Stadtholderless Period — The First Stadtholderless Period or Era (1650 1672) (Dutch Eerste Stadhouderloze Tijdperk ) is the period in the history of the Dutch Republic in which it reached the zenith of its economic, military and political Golden Age. The term has… …   Wikipedia