Pipeng Toolbox : Beam Parallel Axis Theorem Calculators Blank User
Short Cuts
GO
Main ±
Beams ±
References ±
Fluid Flow ±
Fluid Properties ±
Maths ±
Materials ±
Pipelines ±
Soils ±
Subsea ±
Demo

Beam Cross Section Parallel Axis Theorem

Calculate beam moment of inertia using the parallel axis theorem.

The moment of inertia about an offset can be calculated by

`Ix = Il + Y AX^2 `
`Iy = Im + X AX^2 ::Hxy = Hlm + X Y AX^2 `

where :

Ix = moment of inertia about X axis
Iy = moment of inertia about Y axis
Il = moment of inertia about L axis
Im = moment of inertia about M axis
Hxy = product of inertia about offset
Hlm = product of inertia about the centroid
X = offset length from Y axis to centroid
Y = offset length from X axis to centroid
AX = cross section area

X and Y are perpendicular axes passing through the offset. L and M are perpendicular axes passing through the centroid and parallel to X and Y. The X and Y axes pass through the offset point.

For principal axes the product of inertia equals zero. Axes which are an axis of symmetry are principal axes. If the moment of inertia for a principal axis is equal to the moment of inertia of any other axis, all moments of inertia through that point are equal.

For rotated axes, the rotation is calculated relative to either the X axis or the L axis (anti clockwise is positive). Use the Result Plot option to plot the rotated moments of inertia and product of inertia versus the rotation angle.

Reference : Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill

Change Module :

[FREE] tools are free in basic mode with no login (no plots, tables, goal seek etc). Login or Open a free account to use the tools in plus mode (with plots, tables, goal seek etc).
[PLUS] tools are free in basic CHECK mode with Login or Open a free account (CHECK values no plots, tables, goal seek etc). Buy a Subscription to use the tools in plus mode (with plots, tables, goal seek etc).
Try plus mode using the Plus Mode Demo tools with no login.   Help Using The Pipeng Toolbox (opens in the popup workbook)

Links : ±
CALCULATOR : Beam Cross Section Offset Moment Of Inertia From Parallel Axis Theorem (Circular Pipe) [FREE]   ±

Calculate beam moment of inertia and product of inertia at the offset using the parallel axis theorem for a pipe or circular beam.

The cross section area (Ax), the moments of inertia at the centroid (Il and Im) and the product of inertia at the centroid (Hlm) are calculated. For a pipe the axis l and m are pricipal axis and the product of inertia equals zero.

The offset moments of inertia (Ix and Iy) and the product of inertia (Hxy) are calcuated from the offsets (X and Y). I1 and I2 are the principal moments of inertia at the offset (H12 = 0). θ1 is the angle between the X axis and the principal axis 1. θ2 is the angle between the X axis and the principal axis 2, perpendicular to θ1.

The rotated moments of inertia (Iu and Iv) and the rotated product of inertia (Huv) at the offset can be calculated for either the user defined rotation angle (θ), perpendicular to the user defined rotation angle, the principal axis angle θ1, or the principal axis angle θ2. Use the Result Plot option to display a plot of the rotated moment of inertia and product of inertia versus rotation angle.

Tool Input

  • schdtype : Line Pipe Schedule Type
  • diamtype : Diameter Type
    • ODu : User Defined Outside Diameter
    • IDu : User Defined Inside Diameter
  • wtntype : Wall Thickness Type
    • tnu : User Defined Wall Thickness
  • xytype : Offset Length Type
    • xu : User Defined X Offset
    • yu : User Defined Y Offset
  • angtype : Rotation Angle Type
    • θu : User Defined Rotation Angle

Tool Output

  • θ : Rotation Angle At Offset
  • θ1 : Principal Axis Angle 1 At Offset
  • Ax : Cross Section Area
  • Hlm : Product Of Inertia At Centroid
  • Huv : Product Of Inertia Rotated About Offset
  • Hxy : Product Of Inertia At Offset
  • I1 : Principal Moment Of Inertia 1 At Offset
  • I2 : Principal Moment Of Inertia 2 At Offset
  • ID : Inside Diameter
  • Il : Moment Of Inertia L At Centroid
  • Im : Moment Of Inertia M At Centroid
  • Ip : Polar Moment Of Inertia At Offset
  • Iu : Moment Of Inertia U Rotated About Offset
  • Iv : Moment Of Inertia V Rotated About Offset
  • Ix : Moment Of Inertia X At Offset (Parallel To L)
  • Iy : Moment Of Inertia Y At Offset (Parallel To M)
  • OD : Outside Diameter
  • tn : Wall Thickness
  • x : X Offset
  • y : Y Offset

CALCULATOR : Beam Cross Section Offset Moment Of Inertia From Parallel Axis Theorem (General Beam) [FREE]   ±

Calculate beam moment of inertia and product of inertia at the offset using the parallel axis theorem for a general beam.

The cross section area (Ax), the moments of inertia at the centroid (Il and Im) and the product of inertia at the centroid (Hlm) are user defined. If the axis l and m are pricipal axis, the product of inertia Hlm equals zero.

The offset moments of inertia (Ix and Iy) and the product of inertia (Hxy) are calcuated from the offsets (X and Y). I1 and I2 are the principal moments of inertia at the offset (H12 = 0). θ1 is the angle between the X axis and the principal axis 1. θ2 is the angle between the X axis and the principal axis 2, perpendicular to θ1.

The rotated moments of inertia (Iu and Iv) and the rotated product of inertia (Huv) at the offset can be calculated for either the user defined rotation angle (θ), perpendicular to the user defined rotation angle, the principal axis angle θ1, or the principal axis angle θ2. Use the Result Plot option to display a plot of the rotated moment of inertia and product of inertia versus rotation angle.

Tool Input

  • xytype : Offset Length Type
    • xu : User Defined X Offset
    • yu : User Defined Y Offset
  • angtype : Rotation Angle Type
    • θu : User Defined Rotation Angle
  • Ax : Cross Section Area
  • Il : Moment Of Inertia L At Centroid
  • Im : Moment Of Inertia M At Centroid
  • Hlm : Product Of Inertia At Centroid

Tool Output

  • θ : Rotation Angle At Offset
  • θ1 : Principal Axis Angle 1 At Offset
  • Huv : Product Of Inertia Rotated About Offset
  • Hxy : Product Of Inertia At Offset
  • I1 : Principal Moment Of Inertia 1 At Offset
  • I2 : Principal Moment Of Inertia 2 At Offset
  • Ip : Polar Moment Of Inertia At Offset
  • Iu : Moment Of Inertia U Rotated About Offset
  • Iv : Moment Of Inertia V Rotated About Offset
  • Ix : Moment Of Inertia X At Offset (Parallel To L)
  • Iy : Moment Of Inertia Y At Offset (Parallel To M)
  • x : X Offset
  • y : Y Offset

CALCULATOR : Beam Cross Section Centroid Moment Of Inertia From Parallel Axis Theorem (General Beam) [FREE]   ±

Calculate beam moment of inertia and product of inertia at the centroid using the parallel axis theorem for a general beam.

The cross section area (Ax), the moments of inertia at the offset (Ix and Iy) and the product of inertia at the offset (Hxy) are user defined. If the axis x and y are pricipal axis, the product of inertia Hxy equals zero.

The centroid moments of inertia (Il and Im) and the product of inertia (Hlm) are calcuated from the offsets (X and Y). I1 and I2 are the principal moments of inertia at the centroid (H12 = 0). θ1 is the angle between the X axis and the principal axis 1. θ2 is the angle between the X axis and the principal axis 2, perpendicular to θ1.

The rotated moments of inertia (Iu and Iv) and the rotated product of inertia (Huv) at the centroid can be calculated for either the user defined rotation angle (θ), perpendicular to the user defined rotation angle, the principal axis angle θ1, or the principal axis angle θ2. Use the Result Plot option to display a plot of the rotated moment of inertia and product of inertia versus rotation angle.

Tool Input

  • xytype : Offset Length Type
    • xu : User Defined X Offset
    • yu : User Defined Y Offset
  • angtype : Rotation Angle Type
    • θu : User Defined Rotation Angle
  • Ax : Cross Section Area
  • Ix : Moment Of Inertia X At Offset (Parallel To L)
  • Iy : Moment Of Inertia Y At Offset (Parallel To M)
  • Hxy : Product Of Inertia At Offset

Tool Output

  • θ : Rotation Angle At Centroid
  • θ1 : Principal Axis Angle 1 At Centroid
  • Hlm : Product Of Inertia At Centroid
  • Huv : Product Of Inertia Rotated About Centroid
  • I1 : Principal Moment Of Inertia 1 At Centroid
  • I2 : Principal Moment Of Inertia 2 At Centroid
  • Il : Moment Of Inertia L At Centroid
  • Im : Moment Of Inertia M At Centroid
  • Ip : Polar Moment Of Inertia At Centroid
  • Iu : Moment Of Inertia U Rotated About Centroid
  • Iv : Moment Of Inertia V Rotated About Centroid
  • x : X Offset
  • y : Y Offset

CALCULATOR : Beam Cross Section Rotated Moment Of Inertia (General Beam) [FREE]   ±

Calculate beam rotated moment of inertia and product of inertia about any point for a general beam.

The cross section area (Ax), the moments of inertia (Il and Im) and the product of inertia (Hlm) are user defined at any suitable point (either the centroid or an offset). If the axis l and m are pricipal axis, the product of inertia Hlm equals zero.

I1 and I2 are the principal moments of inertia (H12 = 0). θ1 is the angle between the X axis and the principal axis 1. θ2 is the angle between the X axis and the principal axis 2, perpendicular to θ1.

The rotated moments of inertia (Iu and Iv) and the rotated product of inertia (Huv) can be calculated for either the user defined rotation angle (θ), perpendicular to the user defined rotation angle, the principal axis angle θ1, or the principal axis angle θ2. Use the Result Plot option to display a plot of the rotated moment of inertia and product of inertia versus rotation angle.

Tool Input

  • angtype : Rotation Angle Type
    • θu : User Defined Rotation Angle
  • Ax : Cross Section Area
  • Il : Moment Of Inertia L
  • Im : Moment Of Inertia M
  • Hlm : Product Of Inertia

Tool Output

  • θ : Rotation Angle
  • θ1 : Principal Axis Angle 1
  • Huv : Product Of Inertia Rotated
  • I1 : Principal Moment Of Inertia 1
  • I2 : Principal Moment Of Inertia 2
  • Ip : Polar Moment Of Inertia
  • Iu : Moment Of Inertia U Rotated
  • Iv : Moment Of Inertia V Rotated
CALCULATOR : Beam Cross Section Line Pipe Schedule [FREE]   ±

Calculate line pipe schedule outside diameter inside diameter and wall thickness.

Select the pipe schedule (NPS or ISO etc), pipe diameter and wall thickness, or use the user defined option. Use the Result Table option to display the pipe schedule for the selected diameter.

Tool Input

  • schdtype : Line Pipe Schedule Type
  • diamtype : Line Pipe Diameter Type
    • ODu : User Defined Outside Diameter
    • IDu : User Defined Inside Diameter
  • wtntype : Wall Thickness Type
    • tnu : User Defined Wall Thickness

Tool Output

  • ID : Nominal Inside Diameter
  • OD : Nominal Outside Diameter
  • OD/tn : Diameter Over Wall Thickness Ratio
  • tn : Nominal Wall Thickness
pipeng.com 2025 (601 μs : 6 ms : 0.743 MB) Pengu CMS ©