AA SEZC method 6.1 section properties general

Abbott Aerospace – Analysis Method

XL-VIKINGDisplay Your Math in Excel

Taken from: Analysis and Design of Composite and Metallic Flight Vehicle Structures

Section Properties - General

http://www.abbottaerospace.com/

http://www.xl-viking.com/

http://www.abbottaerospace.com/wpdm-package/analysis-and-design-of-composite-and-metallic-flight-vehicle-structures





The centroid of a shape represents the point about which the area of the section is evenly distributed. The centroidal distance is the distance from the centroid of a cross section to the extreme fiber.

Centroid by Integration:

ҧ𝑥 = 𝑥𝑑𝐴

𝐴ത𝑦 =

𝑦𝑑𝐴

𝐴

Centroid by Area Moment Summation for aComposite Area:

ҧ𝑥 =𝑥1 ∙ 𝑎1 + 𝑥2 ∙ 𝑎2 + ∙∙∙∙ +𝑥𝑛 ∙ 𝑎𝑛

𝑎1 + 𝑎2 +∙∙∙∙ +𝑎𝑛=σ 𝑥 ∙ 𝑎

𝐴

ത𝑦 =𝑦1 ∙ 𝑎1 + 𝑦2 ∙ 𝑎2 + ∙∙∙∙ +𝑦𝑛 ∙ 𝑎𝑛

𝑎1 + 𝑎2 +∙∙∙∙ +𝑎𝑛=σ 𝑦 ∙ 𝑎

𝐴








The first moment of area or statical moment is a measure of the distribution of thearea of a shape in relation to the axis. The first moment of area is the summation ofarea multiplied by the distance of the centroid of that area to an axis.

𝑄𝑥 = න𝑦𝑑𝐴 𝑄𝑦 = න𝑥𝑑𝐴

The first moment of area is used to calculate the plastic bending shape factor. It is also used to calculate the shear stress distribution in a cross section








The area moment of inertia, also known as second moment of inertia, moment ofinertia of a plane area or second area moment.

The area moment of inertia of a plane area is referred to the second moment of areasince the first moment Q is multiplied by the differential area moment arm

𝐼𝑥 = න𝑦2𝑑𝐴 𝐼𝑦 = න𝑥2𝑑𝐴

Where the elements are integrated over the whole body.

The area moment of inertia about the Z axis (polar moment of inertia) is given by the following expression

𝐼𝑧 = 𝐼𝑥 + 𝐼𝑦




AA SEZC method 6.1 section properties general

Engineering

Transcript of AA SEZC method 6.1 section properties general