aerosandbox.structures.buckling#

Module Contents#

Functions#

column_buckling_critical_load(elastic_modulus, ...[, ...])

Computes the critical load (in N) for a column or tube in compression to buckle via primary buckling. Uses Euler's classical critical

thin_walled_tube_crippling_buckling_critical_load(...)

Computes the critical load for a thin-walled tube in compression to fail in the crippling mode. (Note: you should also check for

plate_buckling_critical_load(length, width, ...[, ...])

Computes the critical compressive load (in N) for a plate to buckle via plate buckling.
aerosandbox.structures.buckling.column_buckling_critical_load(elastic_modulus, moment_of_inertia, length, boundary_condition_type='pin-pin', use_recommended_design_values=True)[source]#

Computes the critical load (in N) for a column or tube in compression to buckle via primary buckling. Uses Euler’s classical critical load formula.

Parameters:

  • elastic_modulus (float) – The elastic modulus of the material, in Pa.

  • moment_of_inertia (float) – The moment of inertia of the cross-section, in m^4.

  • length (float) – The length of the column, in m.

  • boundary_condition_type (str) – The boundary condition type. Options are: - “pin-pin” - “pin-clamp” - “clamp-clamp” - “clamp-pin” - “clamp-free” - “free-clamp”

  • use_recommended_design_values (bool) – Whether to use the recommended design value of K for a given boundary condition (True)

  • value (or to use the less-conservative theoretical) –

    • Recommended values are from Table C.1.8.1 in Steel Construction Manual, 8th edition, 2nd revised

    printing, American Institute of Steel Construction, 1987 via WikiMedia: https://commons.wikimedia.org/wiki/File:ColumnEffectiveLength.png

Returns:

The critical compressive load (in N) for the column or tube to buckle via primary buckling.

aerosandbox.structures.buckling.thin_walled_tube_crippling_buckling_critical_load(elastic_modulus, wall_thickness, radius, use_recommended_design_values=True)[source]#

Computes the critical load for a thin-walled tube in compression to fail in the crippling mode. (Note: you should also check for failure by primary buckling using the column_buckling_critical_load() function.)

The crippling mode is a specific instability mode for tubes with thin walls when loaded in compression. It can be seen when you step on a soda can and it buckles inwards. The critical load for this mode is given by the following formula:

stress_crippling = crippling_constant * (E * t / r)

where:

A recommended value of crippling_constant = 0.3 is given in Raymer: Aircraft Design: A Conceptual Approach, 5th Edition, Eq. 14.33, pg. 554.

A theoretically more accurate value of crippling_constant = 0.605 is given in the Air Force Stress Manual, Section 2.3.2.1, Eq. 2-20. This value assumes mu = 0.3, which is a good assumption for most metals.

and E is the elastic modulus, t is the wall thickness, and r is the radius.

For more info, see the Air Force Stress Manual, Section 2.3.2.1: https://engineeringlibrary.org/reference/column-crippling-air-force-stress-manual

And see Raymer: Aircraft Design: A Conceptual Approach, 5th Edition, pg. 554.

Parameters:

  • elastic_modulus (float) – The elastic modulus of the material, in Pa.

  • wall_thickness (float) – The wall thickness of the tube, in m.

  • radius (float) – The radius of the tube, in m.

  • use_recommended_design_values (bool) – Whether to use the recommended design value of crippling_constant (True)

  • value (or to use the less-conservative theoretical) –

Returns:

The critical compressive load (in N) for the tube to buckle in the crippling mode.

aerosandbox.structures.buckling.plate_buckling_critical_load(length, width, wall_thickness, elastic_modulus, poissons_ratio=0.33, side_boundary_condition_type='clamp-clamp')[source]#

Computes the critical compressive load (in N) for a plate to buckle via plate buckling.

Assumes a rectangular plate with dimensions: - length - width - wall_thickness

A compressive force is applied such that it is aligned with the length dimension of the plate.

Uses constants from NACA TN3781.

Methdology taken from “Stress Analysis Manual,” Air Force Flight Dynamic Laboratory, Oct. 1986. Section 6.3: Axial Compression of Flat Plates Reproduced at “Engineering Library”: https://engineeringlibrary.org/reference/analysis-of-plates-axial-compression-air-force-stress-manual

Parameters:

  • length (float) – The length of the plate, in m.

  • width (float) – The width of the plate, in m.

  • wall_thickness (float) – The wall thickness of the plate, in m.

  • elastic_modulus (float) – The elastic modulus of the material, in Pa.

  • side_boundary_condition_type (str) – The boundary condition type at the sides of the plate. Options are: - “clamp-clamp” - “pin-pin” - “free-free”

  • poissons_ratio (float) –

Returns:

The critical compressive load (in N) for the plate to buckle via plate buckling.