pymas
Model and analyze framed structures with Python.
Table of Contents
Background
pymas is a Python package that implements the direct stiffness method to help you model and analyze linear elastic framed structures under static loads.
Install
You can install pymas using pip:
pip install git+https://github.com/rvcristiand/pymas.git
Manual Installation
You can obtain a copy of pymas from its repository by downloading a ZIP archive, or by cloning it using Git:
git clone https://github.com/rvcristiand/pymas.gitTo install pymas, navigate to the project directory in your terminal and run:
pip install .This will install pymas and any required dependencies.
Usage
You can model and analyze linear elastic framed structures using the Structure class.
Examples
Simple beam
The following code models a simple concrete beam subjected to its self weight and outputs key results:
from pymas import Structure
# model simple beam
# model and analyze a simple concrete beam subjected to its self weight
# dimensions of the rectangular cross section
b = 0.5 # width, m
h = 1 # heigh, m
# length and stiffness modulus
L = 10 # length, m
E = 4700*28**0.5*1000 # stiffness module, kN/m2
# cross-sectional area and self weight
A = b*h # cross-sectional area, m2
w = 24*A # self weight per length, kN/m
# create the model
model = Structure(type='beam')
# add materials
model.add_material('concrete 28 MPa', E)
# add sections
model.add_rectangular_section('0.5x1.0', base=b, height=h)
# add joints
model.add_joint('a', x=0)
model.add_joint('b', x=L)
# add frame
model.add_frame('beam', 'a', 'b', 'concrete 28 MPa', '0.5x1.0', bending_z=True)
# add supports
model.add_support('a', r_uy=True)
model.add_support('b', r_uy=True)
# add load patterns
model.add_load_pattern('self weight')
# add distributed loads
model.add_distributed_load('self weight', 'beam', fy=-w)
# analyze the model
model.run_analysis()
model.export('simple_beam.json')
print(f'Θa: {model.displacements['self weight']['a'].rz:+.3e} rad')
print(f'Θb: {model.displacements['self weight']['b'].rz:+.3e} rad')
print(f'Ra: {model.reactions['self weight']['a'].fy:+.1f} kN')
print(f'Rb: {model.reactions['self weight']['b'].fy:+.1f} kN')
print(f'Mmax: {max(model.internal_forces['self weight']['beam'].mz):.1f} kN m')
print(f'νmax: {min(model.internal_displacements['self weight']['beam'].uy):.3e} m')
Output
Θa: -4.825e-04 rad
Θb: +4.825e-04 rad
Ra: +60.0 kN
Rb: +60.0 kN
Mmax: 150.0 kN m
νmax: -1.508e-03 m
Space truss
The following code models a space truss subject to points loads at their joints and outputs key results:
from pymas import Structure
"""
Solution to problem 7.2 from 'Microcomputadores en Ingeniería Estructural'
"""
# create the model
model = Structure(type='space_truss')
# add material
model.add_material("2100 t/cm2", 2100e4)
# add sections
model.add_section("10 cm2", 10e-4)
model.add_section("20 cm2", 20e-4)
model.add_section("40 cm2", 40e-4)
model.add_section("50 cm2", 50e-4)
# add joints
model.add_joint('1', 2.25, 6, 4.8)
model.add_joint('2', 3.75, 6, 2.4)
model.add_joint('3', 5.25, 6, 4.8)
model.add_joint('4', 0.00, 0, 6.0)
model.add_joint('5', 3.75, 0, 0.0)
model.add_joint('6', 7.50, 0, 6.0)
# add frames
model.add_frame('1-2', '1', '2', "2100 t/cm2", '20 cm2', axial=True)
model.add_frame('1-3', '1', '3', "2100 t/cm2", '20 cm2', axial=True)
model.add_frame('1-4', '1', '4', "2100 t/cm2", '40 cm2', axial=True)
model.add_frame('1-6', '1', '6', "2100 t/cm2", '50 cm2', axial=True)
model.add_frame('2-3', '2', '3', "2100 t/cm2", '20 cm2', axial=True)
model.add_frame('2-4', '2', '4', "2100 t/cm2", '50 cm2', axial=True)
model.add_frame('2-5', '2', '5', "2100 t/cm2", '40 cm2', axial=True)
model.add_frame('3-5', '3', '5', "2100 t/cm2", '50 cm2', axial=True)
model.add_frame('3-6', '3', '6', "2100 t/cm2", '40 cm2', axial=True)
model.add_frame('4-5', '4', '5', "2100 t/cm2", '10 cm2', axial=True)
model.add_frame('4-6', '4', '6', "2100 t/cm2", '10 cm2', axial=True)
model.add_frame('5-6', '5', '6', "2100 t/cm2", '10 cm2', axial=True)
# add supports
model.add_support('4', True, True, True)
model.add_support('5', True, True, True)
model.add_support('6', True, True, True)
# add load pattern
model.add_load_pattern("point loads")
# add point loads
model.add_joint_point_load("point loads", '1', 10, 15, -12)
model.add_joint_point_load("point loads", '2', 5, -3, -10)
model.add_joint_point_load("point loads", '3', -4, -2, -6)
# analyze the model
model.run_analysis()
model.export('space_truss.json')
for joint in ['1', '2', '3']:
print(f'joint: {joint}')
print(f'\tux: {model.displacements["point loads"][joint].ux:.3e} m')
print(f'\tux: {model.displacements["point loads"][joint].uy:.3e} m')
print(f'\tux: {model.displacements["point loads"][joint].uz:.3e} m')
Output
joint: 1
ux: 8.048e-04 m
ux: 3.326e-05 m
ux: -4.464e-03 m
joint: 2
ux: 2.226e-03 m
ux: -7.277e-04 m
ux: -2.732e-03 m
joint: 3
ux: 7.512e-04 m
ux: 3.670e-04 m
ux: -1.773e-03 m
Space frame
The following code models a space frame subject to distributed loads and outputs key results:
from pymas import Structure
"""
Solution to problem 7.6 from 'Microcomputadores en Ingeniería Estructural'
"""
# structure
model = Structure('space_frame')
# add material
model.add_material('material1', 220e4, 85e4)
# add sections
model.add_section('section1', 0.12, 1.944e-3, 9e-4, 1.6e-3)
model.add_section('section2', 0.10, 1.2734e-3, 1.333e-3, 5.208e-4)
# add joints
model.add_joint('1', 0, 3, 3)
model.add_joint('2', 5, 3, 3)
model.add_joint('3', 0, 0, 3)
model.add_joint('4', 0, 3, 0)
# add frames
deformations = {
'axial': True,
'torsional': True,
'bending_y': True,
'bending_z': True
}
model.add_frame('1-2', '1', '2', 'material1', 'section1', **deformations)
model.add_frame('4-1', '4', '1', 'material1', 'section2', **deformations)
model.add_frame('3-1', '3', '1', 'material1', 'section1', **deformations)
# add supports
model.add_support('2', *6 * (True,))
model.add_support('3', *6 * (True,))
model.add_support('4', *6 * (True,))
# add load pattern
model.add_load_pattern("distributed loads")
# add distributed loads
model.add_distributed_load('distributed loads', '1-2', fy=-2.4)
model.add_distributed_load('distributed loads', '4-1', fy=-3.5)
# solve
model.run_analysis()
# export
model.export('space_frame.json')
print(model.displacements['distributed loads']['1'])
Output
{'load_pattern': 'distributed loads', 'joint': '1', 'ux': 2.687315391431904e-05, 'uy': -0.00011574968996290452, 'uz': -1.000611510850756e-05, 'rx': -0.0005668526305782732, 'ry': 7.904785530558646e-06, 'rz': -0.0006309015221398215}
Contributing
You can contribute to this project creating a new issue or creating pull requests.