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Beam Buckling Load

Calculate beam buckling load for general beams (user defined stiffness EI).

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 plot the buckling load versus end type. Refer to the figures and help pages for more details. Refer to the links below for other beam options.

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

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Links : ±
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
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