Structural Beams Diagrams Python Application Script

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Structural Beams Diagrams Python Application Script

Beam Deflection and Stress Calculators Formulas & Structural Analysis

Beams diagrams for shear, moments, angle, and deflection Python Application Script

This applications is python-based to perform engineering analysis on beams with diagrams for shear, moments, angle, and deflection

Perform engineering analysis on beams with diagrams for shear, moments, angle, and deflection including 3D plots.

Python code - This application requires knowledge of Python installation and code execution.

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Download: Beams Diagrams for Shear, Moments, Angle, and Deflection

Sample Code

E = 207 * 10 ** 6
L = 1.0
CS = CrossSection ( CrossSectionTypes . CIRC , [ .01 ])
B = Beam ( L , E , crossSection = CS )
B . addPointLoad ( 0 , 11 , 45 )
B . addPointLoad ( L / 2 , - 20 , 45 )
B . addPointLoad ( L , 11 , 45 ) B . addDistributedLoad ( 0 , L , - 2 , 45 ) B . addBoundaryCondition ( L / 2 , BoundaryConditionTypes . ANGLE , 0 )
B . addBoundaryCondition ( L , BoundaryConditionTypes . DEFLECTION , 0 )
B . runAnalysis ( outputToFile = True )

Requirements

Currently reactions are not solved for...
- All loads and reactions must be inputted
Boundary conditions currently required
- one angle AND one deflection value
- OR two deflection parameters
Beam weight is not accounted for by default
- represent it with a distributed load

Python Module Requirements

numpy
matplotlib

# Testing
pytest

Application demos

Simple Cantilever Beam

Cantilever Graphs

Cantilever Analysis Console Output

[BEAM ANALYSIS] - Running analysis with beam parameters:
[BEAM ANALYSIS] - length: 1.0
[BEAM ANALYSIS] - Young's modulus of material: 2070000
[BEAM ANALYSIS] - Moment of inertia: 4.9087385212340526e-06
# =============================================================================== #
[BEAM ANALYSIS] - [SOLVING] - Solved for xy angle constant C1 = 0.0
[BEAM ANALYSIS] - [SOLVING] - Solved for xy deflection constant C2 = 0.0
# =============================================================================== #
[BEAM ANALYSIS] - Singularity functions in XY:
10.0 - 20.0<x - 0.5>^0 + 10.0<x - 1.0>^0
10.0<x - 0>^1 - 20.0<x - 0.5>^1 + 10.0<x - 1.0>^1
(10.0 / 2)<x - 0>^2 - (20.0 / 2)<x - 0.5>^2 + (10.0 / 2)<x - 1.0>^2 + 0.0
(10.0 / 6)<x - 0>^3 - (20.0 / 6)<x - 0.5>^3 + (10.0 / 6)<x - 1.0>^3 + 0.0 + 0.0
# =============================================================================== #
[BEAM ANALYSIS] - Report in XY:
Max Shear: 10.0 [N]
Max Moment: 4.995 [N-m]
Max Angle: 0.24604 [rad]
Max Deflection: 0.12302 [m]
# =============================================================================== #

Cantilever Input Parameters and Loads

# =================================== #
# 1. Define Beam Parameters #
# =================================== #
# E - Youngs Modulus #
# I - Moment of Inertia I #
# L - Beam Length #
# =================================== #
E = 207 * 10**4
L = 1.0
CS = CrossSection(CrossSectionTypes.CIRC, [.05])
B = Beam(L, E, crossSection=CS)

# =================================== #
# 2. Add Loads #
# =================================== #
# Use theta = 0 to indicate XY plane #
# Use theta = 90 to indicate XZ plane #
# #
# | (90 - XZ plane) #
# \ | #
# \ | #
# \|________ (0 - XY plane) #
# =================================== #
B.addPointLoad(0, 10, 0)

B.addPointLoad(L/2, -20, 0)

B.addPointLoad(L, 10, 0)

# =================================== #
# 3. Input Boundary Conditions #
# =================================== #
# Use the loading angle convention #
# =================================== #
# B.addBoundaryCondition(L/2, BoundaryConditionTypes.ANGLE, 0)
B.addBoundaryCondition(0, BoundaryConditionTypes.DEFLECTION, 0)
B.addBoundaryCondition(0, BoundaryConditionTypes.ANGLE, 0.0)

# =================================== #
# 4. Run Analysis #
# =================================== #
B.runAnalysis()

Fixed-Support Beam

Fixed-Support Graphs

Fixed-Support Analysis Console Output

[BEAM ANALYSIS] - Running analysis with beam parameters:
[BEAM ANALYSIS] - length: 1.0
[BEAM ANALYSIS] - Young's modulus of material: 207000000
[BEAM ANALYSIS] - Moment of inertia: 7.853981633974483e-09
# ================================================================================ #
[BEAM ANALYSIS] - [SOLVING] - Solved for xy angle constant C1 = -1.25
[BEAM ANALYSIS] - [SOLVING] - Solved for xy deflection constant C2 = 0.0
# ================================================================================ #
[BEAM ANALYSIS] - [SOLVING] - Solved for xz angle constant C1 = -1.25
[BEAM ANALYSIS] - [SOLVING] - Solved for xz deflection constant C2 = 0.0
# ================================================================================ #
[BEAM ANALYSIS] - Singularity functions in XY:
10.0 - 20.0<x - 0.5>^0 + 10.0<x - 1.0>^0
10.0<x - 0>^1 - 20.0<x - 0.5>^1 + 10.0<x - 1.0>^1
(10.0 / 2)<x - 0>^2 - (20.0 / 2)<x - 0.5>^2 + (10.0 / 2)<x - 1.0>^2 - 1.25
(10.0 / 6)<x - 0>^3 - (20.0 / 6)<x - 0.5>^3 + (10.0 / 6)<x - 1.0>^3 - 1.25 + 0.0
# ================================================================================ #
[BEAM ANALYSIS] - Singularity functions in XZ:
10.0 - 20.0<x - 0.5>^0 + 10.0<x - 1.0>^0
10.0<x - 0>^1 - 20.0<x - 0.5>^1 + 10.0<x - 1.0>^1
(10.0 / 2)<x - 0>^2 - (20.0 / 2)<x - 0.5>^2 + (10.0 / 2)<x - 1.0>^2 - 1.25
(10.0 / 6)<x - 0>^3 - (20.0 / 6)<x - 0.5>^3 + (10.0 / 6)<x - 1.0>^3 - 1.25 + 0.0
# ================================================================================ #
[BEAM ANALYSIS] - Report in XY:
Max Shear: 10.0 [N]
Max Moment: 4.995 [N-m]
Max Angle: 0.76886 [rad]
Max Deflection: 0.25629 [m]
# ================================================================================ #
[BEAM ANALYSIS] - Report in XZ:
Max Shear: 10.0 [N]
Max Moment: 4.995 [N-m]
Max Angle: 0.76886 [rad]
Max Deflection: 0.25629 [m]
# ================================================================================ #
Fixed-Support Input Parameters and Loads
# =================================== #
# 1. Define Beam Parameters #
# =================================== #
# E - Youngs Modulus #
# I - Moment of Inertia I #
# L - Beam Length #
# =================================== #
E = 207 * 10**6
L = 1.0
CS = CrossSection(CrossSectionTypes.CIRC, [.01])
B = Beam(L, E, crossSection=CS)

B.addPointLoad(L/2, -20, 0)
B.addPointLoad(L/2, -20, 90)

B.addPointLoad(L, 10, 0)
B.addPointLoad(L, 10, 90)

# =================================== #
# 4. Run Analysis #
# =================================== #
B.runAnalysis()

Source

Python code - This application requires knowledge of Python installation and code execution.

Support:

Engineers Edge has tested the basic functions and operation of this application using Python 3.11.9 and supporting modules.
Supporting Windows application "Visual Studio Code".
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

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