Area Moments
Subject
The term 'area moment'defines the 2D structural properties of a 3D body's crosssection and thereby its ability to resist deformation.
You can improve a body's resistance to a particular loading condition with little or no weight penalty simply by altering the shape of its crosssection.
For example, an IBeam of a given crosssectional area (or weight) will provide greater bending resistance than an equivalent HBeam with similar crosssectional area but less torsional resistance, and large thinwall sections will provide considerably greater bending and torsional resistance than a smaller thickwalled section of similar weight.
You simply select the lightest, strongest sectional shape for your purposes.
Calculator
Area Moments includes five calculation options for solid and/or hollow; polygons, triangles, quadrilaterals, ellipses and parts of a circle about their natural and strongweak axes and for each of which it calculates the area, second moment of area, polar moment of inertia, centre of area and radius of gyration.
The output data from Area Moments may be used as input to other calculators such as Beams, Engineering Principles, Beams+ and Mode Shapes.
For help using this calculator, including its internal selfchecking facility, see Technical Help
Area Moments Calculator  Options
Hollow Triangle
Hollow Triangle provides solutions for hollow and solid triangles with both obtuse and acute triangles and a constant wall thickness.
You enter: 
and the second moment of area calculator will provide: 


Crosssectional area

Second moment of area (with respect to horizontal, vertical, strong and weak axes)

Radii of gyration (with respect to horizontal, vertical, strong and weak axes)

Polar moment of inertia

Hollow Quadrangle
Hollow Quadrangle provides solutions for hollow and solid quadrilaterals with both obtuse and acute and a constant wall thickness. The only constraint with respect to shape variation is that the base and cap must be parallel.
You enter: 
and the second moment of area calculator will provide: 


Crosssectional area

Second moment of area (with respect to horizontal, vertical, strong and weak axes)

Radii of gyration (with respect to horizontal, vertical, strong and weak axes)

Polar moment of inertia

Polygon
Polygon calculates the properties of a solid regular polygon with up to and including 1E+307 sides.
You enter: 
and the second moment of area calculator will provide: 


Circumscribed radius (to a corner)

Crosssectional area

Second moment of area

Radii of gyration (with respect to horizontal, vertical, strong and weak axes)

Polar moment of inertia

Ellipse
Ellipse calculates the properties of a solid regular ellipse.
You enter: 
and the second moment of area calculator will provide: 


Crosssectional area

Second moment of area

Radii of gyration (with respect to horizontal, vertical, strong and weak axes)

Polar moment of inertia

Sector
Sector calculates the properties of part of a circle (up to and including a full circle) with a constant wall thickness.
You enter: 
and the second moment of area calculator will provide: 


Crosssectional area

Second moment of area

Radii of gyration (with respect to horizontal, vertical, strong and weak axes)

Polar moment of inertia

Important Note: Area Moments calculates the structural properties of individual shapes, both solid and hollow. You can combine these shapes to calculate the structural properties of complex shapes using Area Moments+.
Check minimum system requirements