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	~~Hi there. Allow me begin psychic solutions by lynne~~ (~~[http://www~~.~~octionx~~.~~sinfauganda~~.co.ug/~~node~~/~~22469 relevant internet page]~~) ~~introducing~~ the ~~author~~, ~~her title is Sophia Boon but she never truly liked that title~~. The ~~preferred pastime~~ for ~~him~~ and ~~his kids~~ is ~~to play lacross and he would never give it up~~. ~~Ohio~~ is ~~where her home~~ is. ~~He is~~ an ~~info officer~~.		The '''first moment of area''', sometimes misnamed as the '''first moment of inertia''', is based in the mathematical construct [[Moment %28mathematics%29#Moments in metric spaces\|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 relation to an axis.

			'''First moment of area''' is commonly used to determine the [[centroid]] of an area.

			==Definition==
			Given an area, ''A'', of any shape, and division of that area into ''n'' number of very small, elemental areas (''dA<sub>i</sub>''). Let ''x<sub>i</sub>'' and ''y<sub>i</sub>'' 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:
			:<math>
			S_x = A \bar y = \sum_{i=1}^n {y_i \,dA_i} = \int_A y dA
			</math>
			and
			:<math>
			S_y = A \bar x = \sum_{i=1}^n {x_i \,dA_i} = \int_A x dA
			</math>.

			The [[International System of Units\|SI]] unit for '''first moment of area''' is a cubic [[metre]] (''m''<sup>3</sup>). In the American Engineering and Gravitational systems the unit is a cubic [[foot (length)\|foot]] (''ft''<sup>3</sup>) or more commonly [[inch]]<sup>3</sup>.

			==Applications==
			===Statical 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:

			<math>Q_{j,x} = \int y_i dA</math>, where

			* ''Q''<sub>''j,x''</sub> - 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''.

			===Shear 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:

			:<math> q = \frac{V_y S_x}{I_x}</math>

			*''q'' - the shear flow through a particular web section of the cross-section
			*''V''<sub>''y''</sub> - the shear force perpendicular to the neutral axis ''x'' through the entire cross-section
			*''S''<sub>''x''</sub> - the first moment of area about the neutral axis ''x'' for a particular web section of the cross-section
			*''I''<sub>''x''</sub> - 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:

			:<math> {\tau} = \frac{q}{t}</math>

			* <math> {\tau} </math> - 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

			==See also==
			* [[Second moment of area]]
			* [[Polar moment of inertia]]
			* [[Section modulus]]

			[[Category:Solid mechanics]]

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2012-01-04T21:26:20Z

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Hi there. Allow me begin psychic solutions by lynne ([http://www.octionx.sinfauganda.co.ug/node/22469 relevant internet page]) introducing the author, her title is Sophia Boon but she never truly liked that title. The preferred pastime for him and his kids is to play lacross and he would never give it up. Ohio is where her home is. He is an info officer.

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