- 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 thecentroid 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 ("dA

_{i}"). Let "x_{i}" and "y_{i}" 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: :$M\_x\; =\; A\; ar\; y\; =\; sum\_\{i=1\}^n\; \{y\_i\; ,dA\_i\}\; =\; int\_A\; y\; dA$ and :$M\_y\; =\; A\; ar\; x\; =\; sum\_\{i=1\}^n\; \{x\_i\; ,dA\_i\}\; =\; int\_A\; x\; dA$.The SI unit for

**first moment of area**ismetre 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 commonlyinch ^{3}.**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 toshear stress . By definition:$Q\_\{j,x\}\; =\; int\; y\_i\; dA$, 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 asemi-monocoque structure is::$q\; =\; frac\{V\_y\; Q\_x\}\{I\_x\}$

*"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"}- thefirst moment of area about the neutral axis "x" for a particular web section of the cross-section

*"I"_{"x"}- thesecond moment of area about the neutral axis "x" for the entire cross-sectionShear stress may now be calculated using the following equation::$\{\; au\}\; =\; frac\{q\}\{t\}$

* $\{\; au\}$ - 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 **External links*** http://www.iaengr.org/forum/messages//468.html

* http://mywebsite.bigpond.com/npajkic/solid_mechanics/first_moment_of_area/index.html

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