Test problem 14

Test problem 14#

import micropip
await micropip.install('../../packages/sympy-1.15.0.dev0-py3-none-any.whl')
#takes a while

%pip install git+https://github.com/saiudayagiri/sympy.git@borek-27130

from sympy.physics.continuum_mechanics.structure2d import Structure2d
from sympy import symbols
s = Structure2d()
E, I, A = symbols('E I A')
s.add_member(0, 0, 3, 4, 10**2, 10**2, 10**2)
s.add_member(3, 4, 7, 1, E, I, A)
s.apply_load(3, 4, 18, 0, 0, 7, 1)
s.apply_support(0, 0,"fixed")
s.apply_support(7, 1,"roller")

s.draw(show_load_values=True);

../../_images/01fe73479bfdcc5854521e4155fe155c12821f31d346ad09da7ccbf4fc4cf0c4.png

s.solve_for_reaction_loads()

{R_v (x=0,y=0): 5427/1120,
 R_h (x=0,y=0): -90,
 T (x=0,y=0): 30573/160,
 R_v (x=7,y=1): -5427/1120}

s.plot_axial_force_on_structure();

../../_images/db7193a434b346fc61f1b86b9ee63f922c24b60da357817823501fcf28c1ad9a.png

s.plot_shear_force_on_structure();

../../_images/4c5b3fd93ba0f1ded6ac6a240b2fd3ba77745d9eeb64f26b93a15667f70eb4fc.png

s.plot_bending_moment_on_structure();

../../_images/a0a57a8ff0380063c2d5a0a41d2c36b71b25ee585cc0df9996e3d1d73e79130a.png

s.plot_deformation_on_structure(factor = 0.1)

(<Figure size 640x480 with 1 Axes>, <Axes: xlabel='x', ylabel='y'>)

../../_images/4cb86e7b422c66cdc6ab62bb06e7c3f4cbb369a0b77221d7df7f0b1d0eeddadf.png

s.summary();

===================== Structure Summary =====================

Reaction Loads:
R_v   (x=0.00,y=0.00)  (unwrapped x=0.00)          = 5427/1120
R_h   (x=0.00,y=0.00)  (unwrapped x=0.00)          = -90
T     (x=0.00,y=0.00)  (unwrapped x=0.00)          = 30573/160
R_v   (x=7.00,y=1.00)  (unwrapped x=10.00)         = -5427/1120

Points of Interest - Bending Moment:
bending_moment at (x=0.00,y=0.00)  (unwrapped x=0.00) = -30573/160
bending_moment at (x=1.50,y=2.00)  (unwrapped x=2.50) = -41103/2240
bending_moment at (x=3.00,y=4.00)  (unwrapped x=5.00) = 43227/280
bending_moment at (x=3.00,y=4.00)  (unwrapped x=5.00) = 43227/280
bending_moment at (x=5.00,y=2.50)  (unwrapped x=7.50) = 24327/560
bending_moment at (x=7.00,y=1.00)  (unwrapped x=10.00-) = 0.00000387643410704186

Points of Interest - Shear Force:
shear_force at (x=0.00,y=0.00)  (unwrapped x=0.00+) = -oo
shear_force at (x=3.00,y=4.00)  (unwrapped x=5.00-) = 386919/5600
shear_force at (x=3.00,y=4.00)  (unwrapped x=5.00+) = -81027/1400
shear_force at (x=7.00,y=1.00)  (unwrapped x=10.00-) = -3.87643937142856

Points of Interest - Axial Force:
axial_force at (x=0.00,y=0.00)  (unwrapped x=0.00+) = 81027/1400
axial_force at (x=3.00,y=4.00)  (unwrapped x=5.00-) = 81027/1400
axial_force at (x=3.00,y=4.00)  (unwrapped x=5.00+) = 386919/5600
axial_force at (x=7.00,y=1.00)  (unwrapped x=10.00-) = -2.90730702857145