stableX

A Python library for stability analysis of structures

Installation

>> pip install stablex

Usage

# pinned_column.py

import stablex as stx

# column length
l = 3000

# create nodes at quarter lengths
n1 = stx.Node(0, 0)
n2 = stx.Node(0, 0.25*l)
n3 = stx.Node(0, 0.5*l)
n4 = stx.Node(0, 0.75*l)
n5 = stx.Node(0, l)

# create section
section = stx.Rectangle(100, 100)

# create Frame elements and specify node connectivity and geometric non-linearity (Modulus of elasticity = 200000 MPa by default)
e1 = stx.FrameElement(n1, n2, section, True)
e2 = stx.FrameElement(n2, n3, section, True)
e3 = stx.FrameElement(n3, n4, section, True)
e4 = stx.FrameElement(n4, n5, section, True)

# assign boundary conditions (pinned at base, roller at top)
n1.x_dof.restrained = True
n1.y_dof.restrained = True
n5.x_dof.restrained = True

# assign load
p = -1
n5.y_dof.force = p

# create structure assembly of elements
structure = stx.Structure([e1, e2, e3, e4])

# create an Eigenvalue solver
solver = stx.EigenSolver(structure)

# solve for the required mode shape
eigenvalue, eigenvector = solver.solve(mode_shape=1)

# visualize the buckling mode shape
stx.plot_structure(structure, 1000)

Executing this script will open a window displaying the buckling mode and print the associated critical buckling load value.

print(f"Critical Buckling Load: {eigenvalue/1000:.3f} N")

 Output: Critical Buckling Load: 1828.640 kN 

Verification with Euler's formula

$$ P_{cr} = \frac{\pi^2 EI}{l^2} = \frac{\pi^2 \times 200 \times 10^3 \times (100)^4/12}{3000^2 \times 1000} = 1827.705 kN $$

With an error = 0.05%

For the second mode:

eigenvalue, eigenvector = solver.solve(mode_shape=2)

stx.plot_structure(structure, 1000)

print(f"Critical Buckling Load: {eigenvalue/1000:.3f} N")

 Output: Critical Buckling Load: 7365.812 kN 

Verification with Euler's formula

$$ P_{cr} = n^2 \frac{\pi^2 EI}{l^2} = 2^2 \frac{\pi^2 \times 200 \times 10^3 \times (100)^4/12}{3000^2 \times 1000} = 7310.818 kN $$

With an error = 0.75%

Other Examples:

Rigid Bars with Intermediate Spring

 Output: Critical Buckling Load: 666.667 N 

$$ P_{cr} = 2 \frac{k}{l} = 2 \frac{1 \times 10^6}{3000} = 666.667 N $$

Trapezoidal Frame

Triangulated Frame

Trussed Column

Arch

1st mode

2nd mode

Mult-storey Frame

1st mode

4th mode

2nd mode (Braced)

Portal Frame

Overhang

Truss Cantilever

Contributing

Interested in contributing? Check out the contributing guidelines. Please note that this project is released with a Code of Conduct. By contributing to this project, you agree to abide by its terms.

License

stablex was created by Hazem Kassab. It is licensed under the terms of the MIT license.

Credits

stablex was created with cookiecutter and the py-pkgs-cookiecutter template.