Solving 2D Frames and Trusses using Python
In this post, I will show you how to analyse 2D frames and Trusses using the python library anaStruct.
anaStruct is a python library for the analysis of 2D Frames and trusses. For more information please visit the anaStruct’s documentation.
Before you run the examples below you need to install the library. For this, type in the terminal or in your Jupyter notebook the following::
pip install anastruct
Then, you can import the necessary libraries.
import math
import numpy as np
import matplotlib.pyplot as plt
from anastruct.fem.system import SystemElements
Standerd Elements
Standard elements have bending and axial stiffness and therefore will implement shear force, bending moment, axial force, extension, and deflection.
Example 1
ss = SystemElements()
# Add beams to the system.
ss.add_element(location=[[0, 0], [3, 4]])
ss.add_element(location=[[3, 4], [8, 4]])
# Add supports.
ss.add_support_hinged(node_id=1)
ss.add_support_fixed(node_id=3)
# Add loads.
ss.q_load(element_id=2, q=-10)
# Solve
ss.solve()
# Get visual results.
ss.show_structure()
ss.show_reaction_force()
ss.show_axial_force()
ss.show_shear_force()
ss.show_bending_moment()
ss.show_displacement()
ss = SystemElements(EA=15000, EI=5000)
# Add beams to the system.
ss.add_element(location=[0, 5])
ss.add_element(location=[[0, 5], [5, 5]])
ss.add_element(location=[[5, 5], [5, 0]])
# Add a fixed support at node 1.
ss.add_support_fixed(node_id=1)
# Add a rotational spring support at node 4.
ss.add_support_spring(node_id=4, translation=3, k=4000)
# Add loads.
ss.point_load(Fx=30, node_id=2)
ss.q_load(q=-10, element_id=2)
# Solve
ss.solve()
# Get visual results.
ss.show_structure()
ss.show_reaction_force()
ss.show_axial_force()
ss.show_shear_force()
ss.show_bending_moment()
ss.show_displacement()
Truss Elements
Truss elements don’t have bending stiffness and will therefore not implement shear force, bending moment and deflection. It does model axial force and extension.
Example 1
ss = SystemElements(EA=5000)
ss.add_truss_element(location=[[0, 0], [0, 5]])
ss.add_truss_element(location=[[0, 5], [5, 5]])
ss.add_truss_element(location=[[5, 5], [5, 0]])
ss.add_truss_element(location=[[0, 0], [5, 5]], EA=5000 * math.sqrt(2))
ss.add_support_hinged(node_id=1)
ss.add_support_hinged(node_id=4)
ss.point_load(Fx=10, node_id=2)
ss.show_structure()
ss.solve()
ss.show_reaction_force()
ss.show_axial_force()
ss.show_displacement(factor=10)
Example 2
ss = SystemElements()
element_type = 'truss'
# create triangles
x = np.arange(1, 10) * np.pi
y = np.cos(x)
y -= y.min()
ss.add_element_grid(x, y, element_type=element_type)
# add top girder
ss.add_element_grid(x[1:-1][::2], np.ones(x.shape) * y.max(), element_type=element_type)
# add bottom girder
ss.add_element_grid(x[::2], np.ones(x.shape) * y.min(), element_type=element_type)
# supports
ss.add_support_hinged(1)
ss.add_support_roll(-1, 2)
# loads
ss.point_load(node_id=np.arange(2, 9, 2), Fy=-100)
ss.solve()
ss.show_structure()
ss.show_reaction_force()
ss.show_axial_force()
ss.show_displacement(factor=1)
