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Rotated Beam Buckling Load

Calculate beam buckling load for rotated beams.

Enter the beam moments of inertia and product of inertia at the centroid. For the principal axes the product of inertia is zero.

Beam end types include: free fixed (cantilever), guided fixed, pinned fixed, fixed fixed (built in or fixed), pinned pinned (simply supported), and guided pinned beam ends. The beam end conditions are of the form left end - right end (for example Pin-Fix is left end pinned and right end fixed).

The buckling load can be calculated using either the Euler equation (suitable for long beams), the Johnson equation (suitable for short beams), or the buckling load equation can be determined from the transition length. The buckling load is positive. The axial load is negative in compression. Buckling will generally occur about the axis with the lowest EI, depending on constraints.

The effective length factor should be used for beams on a soft foundation such as soil, where the beam ends are poorly defined. For defined beam ends, such as structures, the effective length factor should be set to one (fe = 1).

Use the Result Plot option to plot the buckling load versus nominal length. Use the Result Table option to display the buckling load versus end type. Refer to the figures and help pages for more details.

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

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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 Buckling Load (General Beam) [FREE]   ±

Calculate beam buckling load from beam effective length for general beams (user defined properties).

Beam end types include: free fixed (cantilever), guided fixed, pinned fixed, fixed fixed (built in or fixed), pinned pinned (simply supported), and guided pinned beam ends. The beam end conditions are of the form left end - right end (for example Pin-Fix is left end pinned and right end fixed). All distances are measured from the left end of the beam.

The buckling load can be calculated using either the Euler equation (suitable for long beams), the Johnson equation (suitable for short beams), or the buckling load equation can be determined from the transition length. The buckling load is positive. The axial load is negative in compression.

The effective length factor should be used for beams on a soft foundation such as soil, where the beam ends are poorly defined. For defined beam ends, such as structures, the effective length factor should be set to one (fe = 1).

Use the Result Plot option to plot the buckling load versus nominal length. Use the Result Table option to display the buckling load versus end type. Refer to the figures and help pages for more details.

Tool Input

  • modptype : Material Property Type
    • αu : User Defined Thermal Expansion Coefficient
    • Eu : User Defined Elastic Modulus
  • eitype : E x I Type
    • Iu : User Defined Section Modulus
    • ru : User Defined Radius Of Gyration
    • EIu : User Defined E x I
  • eaatype : E x A x alpha Type
    • EAαu : User Defined E x A x alpha
  • loadtype : Axial Load Type
    • Td : User Defined Operating Temperature
    • Tin : User Defined Installation Temperature
    • Fin : User Defined Preload
    • Fau : User Defined Axial Load
  • fbtype : Buckling Load Type
    • Fbu : User Defined Buckling Load
  • endtype : End Type
  • leftype : Effective Length Type
    • feu : User Defined Effective Length Factor
  • AX : Cross Section Area
  • Lo : Nominal Length
  • Sy : Yield Stress

Tool Output

  • α : Thermal Expansion Coefficient
  • E : Elastic Modulus
  • EAα : E x A x alpha (E x AX x α)
  • EI : E x I
  • Fa : Axial Load
  • Fa/Fb : Axial Load Over Buckling Load Ratio (< 1)
  • Fb : Buckling Load
  • I : Moment Of Inertia
  • Le : Effective Length
  • Le/r : Slenderness Ratio
  • Lt : Transition Length (Short to Long Beam)
  • r : Radius Of Gyration

CALCULATOR : Beam Buckling Yield Stress [FREE]   ±

Calculate beam buckling yield stress (SMYS) and tensile stress (SMTS).

Select one of the API, ASME or DNV stress table options. Use the Result Table option to display the stress values for the selected stress table.

Tool Input

  • syutype : Stress Table Type
  • mattype : Material Type
    • SMYSu : User Defined Specified Minimum Yield Stress
    • SMTSu : User Defined Specified Minimum Tensile Stress

Tool Output

  • SMTS : Specified Minimum Tensile Stress
  • SMTS/SMYS : Tensile Stress Over Yield Stress Ratio
  • SMYS : Specified Minimum Yield Stress
  • SMYS/SMTS : Yield Stress Over Tensile Stress Ratio
CALCULATOR : Beam Buckling Material Property [FREE]   ±

Calculate beam buckling elastic modulus, shear modulus, bulk modulus, density, and thermal expansion coefficient.

The table values of Poisson ratio and bulk modulus are calculated from the elastic modulus and shear modulus. Use the Result Table option to display a table of properties versus material type.

Tool Input

  • modptype : Material Type
    • Eu : User Defined Elastic Modulus
    • Gu : User Defined Shear Modulus
    • Ku : User Defined Bulk Modulus
    • νu : User Defined Poisson Ratio
    • ρu : User Defined Density
    • αu : User Defined Thermal Expansion Coefficient

Tool Output

  • α : Thermal Expansion Coefficient
  • ν : Poisson Ratio
  • ρ : Density
  • E : Elastic Modulus
  • G : Shear Modulus
  • K : Bulk Modulus
CALCULATOR : Beam Buckling Load (Rotated General Beam) [PLUS]   ±

Calculate beam buckling load for rotated beams.

The beams are assumed to be rotated about the centroid. Enter the beam moments of inertia, product of inertia, and the rotation angle. The product of inertia is zero for the principal axes.

Beam end types include: free fixed (cantilever), guided fixed, pinned fixed, fixed fixed (built in or fixed), pinned pinned (simply supported), and guided pinned beam ends. The beam end conditions are of the form left end - right end (for example Pin-Fix is left end pinned and right end fixed). All distances are measured from the left end of the beam.

The buckling load can be calculated using either the Euler equation (suitable for long beams), the Johnson equation (suitable for short beams), or the buckling load equation can be determined from the transition length. The buckling load is positive. The axial load is negative in compression.

The effective length factor should be used for beams on a soft foundation such as soil, where the beam ends are poorly defined. For defined beam ends, such as structures, the effective length factor should be set to one (fe = 1).

Use the Result Plot option to plot the buckling load versus nominal length. Use the Result Table option to display the buckling load versus end type. Refer to the figures and help pages for more details.

Tool Input

  • modptype : Material Property Type
    • αu : User Defined Thermal Expansion Coefficient
    • Eu : User Defined Elastic Modulus
  • loadtype : Axial Load Type
    • Td : User Defined Operating Temperature
    • Tin : User Defined Installation Temperature
    • Fin : User Defined Preload
    • Fau : User Defined Axial Load
  • fbtype : Buckling Load Type
    • Fbu : User Defined Buckling Load
  • endtype : End Type
  • leftype : Effective Length Type
    • feu : User Defined Effective Length Factor
  • 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
  • Lo : Nominal Length
  • Sy : Yield Stress

Tool Output

  • α : Thermal Expansion Coefficient
  • θ : Rotation Angle
  • E : Elastic Modulus
  • EAα : E x A x alpha (E x AX x α)
  • EI : E x I
  • Fa : Axial Load
  • Fa/Fb : Axial Load Over Buckling Load Ratio (< 1)
  • Fb : Buckling Load
  • Huv : Product Of Inertia Rotated
  • I : Moment Of Inertia Rotated
  • Le : Effective Length
  • Le/r : Slenderness Ratio
  • Lt : Transition Length (Short to Long Beam)
  • r : Radius Of Gyration

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