Custom

Shape

Universal

Beams

Universal

Columns

European

Beams

European

Columns

American

Beams

SHS

(Square)

RHS

(Rectangle)

CHS

(Circle)

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Center (x)
mm

Center (y)
mm

H
mm

W
mm

Section selected:

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Area
cm^{2}

Moment of intertia x-x
cm^{4}

Moment of intertia y-y
cm^{4}

Radius of Gyration x-x:
mm

Radius of Gyration y-y:
mm

Elastic Section Modulus x-x:
cm^{3}

Elastic Section Modulus y-y:
cm^{3}

Shape Complexity:

Area Percent Error:
%

Section depth
mm

Section width
mm

Root radius
mm

Web thickness
mm

Flange thickness
mm

Mass per m
kg/m

- The second moment of area (otherwise known as the moment of inertia), is a measure of the 'efficiency' of a cross-section to resist bending, caused by applied forces.

- The moment of inertia (otherwise known as the second moment of area), is a measure of the 'efficiency' of a cross-section to resist bending, caused by applied forces.

- There is no difference between the second moment of area and the moment of intertia, the terms can be used interchangeably.

- The centroid of a shape (otherwise known as the centre of gravity) is the geometric centre of the object and if the shape possesses an axis of symmetry this is where the axis will be located.

- The centroid of a complex shape can be calculated using hand calculation methods, by using the Method of Geometric Decomposition. To find the centroid, the individual centroids of each component shape are determined, the idividual centroid are then multiplied by the area of the correponding shape and summed. This summed value is then divided by the total area of all combined component shapes to give the centroid.

- There is no difference between the centroid of a shape and the centre of gravity, the terms can be used interchangeably.

- The radius of gyration of a shape is the distance between the shapes axis of rotation and the shapes centre of gravity.

- The radius of gyration is calculated using the formula
- k = sqrt ( I / A)
- Where I is the second moment of area of a shape and A is the area.

- The section modulus (otherwise known as the first moment of area) is a parameter which measures a section strength in bending. This can either be the elastic section modulus which considers the strength of the beam up to elastic yielding or the plastic section modulus which considers strength up to plastic yielding.

- The moment of inertia (otherwise known as second moment of area) is a a measure of a shapes resistance to angular acceleration.

- The second moment of area (otherwise known as moment of inertia) is a a measure of a shapes resistance to angular acceleration.

The moment of inertia can be calculated by hand for the most common shapes:

- Rectangle: (bh^3)/12
- >Circle: (pi * r^4)/4
- Triangle: (bh^3)/12
- If the shape is more complex then the moment of inertia can be calculated using the parallel axis thereom. The parallel axis thereom is used to seperate the shape into a number of simpler shapes. An axis is fixed and then the second moment of area of each shape is calculated and summed to the area multiplied by the distance between the fixed axis and the shape centroid squared.

What's this calculator used for?

This a free tool for Civil Engineers to calculate the geometrical properties of different shapes needed for structural analysis calculations. Calculate the section properties of custom beam and column section. Generate results to calculate the moment of inertia, elastic section modulus and radius of gyration for a profile. This tool use the parallel axis thereom to determine the neutral axis for the combined shape and then detemine section properties for a composite section.