.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/frames/plot_frame05.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_frames_plot_frame05.py: ====================================================== Buckling of a building frame ====================================================== modeled using a 2D frame element .. list-table:: setting given parameters * - N = 2 - number of elements * - L = 100.0 - column length * - EA = 2000000.0 - axial stiffness * - EI = 21000.0 - flexural stiffness * - w = 0.1 - applied lateral load Author: Peter Mackenzie-Helnwein .. GENERATED FROM PYTHON SOURCE LINES 23-297 .. code-block:: Python from femedu.examples.Example import * from femedu.domain import * from femedu.solver.NewtonRaphsonSolver import * from femedu.elements.finite.Frame2D import * from femedu.materials.ElasticSection import * class ExampleFrame05(Example): def problem(self): # initialize a system model N = 8 # number of elements B = 720. H = 720. E = 29000.0 A = 150.0 I = 250.0 w = 0.10 load_at_nodes_only = False # set to True to apply equivalent nodal forces and moments Ph = 0.01 # additional horizontal load per floor Ph = 0.10 # additional horizontal load per floor Ph = 1.00 # additional horizontal load per floor Ph = 0.00 # additional horizontal load per floor # ========== setting global parameters ============== target_load_level = 33. max_steps = 10 load_levels = np.linspace(0, target_load_level, max_steps) # ========= build your structural model ============= model = System() model.setSolver(NewtonRaphsonSolver()) x0 = 0.0 x1 = B / 3 x2 = 2 * B / 3 x3 = B y0 = 0.0 y1 = H / 4 y2 = 2 * H / 4 y3 = 3 * H / 4 y4 = H X10 = Node(x0, y0) X11 = Node(x0, y1) X12 = Node(x0, y2) X13 = Node(x0, y3) X14 = Node(x0, y4) X20 = Node(x1, y0) X21 = Node(x1, y1) X22 = Node(x1, y2) X23 = Node(x1, y3) X24 = Node(x1, y4) X30 = Node(x2, y0) X31 = Node(x2, y1) X32 = Node(x2, y2) X33 = Node(x2, y3) X34 = Node(x2, y4) X40 = Node(x3, y0) X41 = Node(x3, y1) X42 = Node(x3, y2) X43 = Node(x3, y3) X44 = Node(x3, y4) model.addNode(X10, X11, X12, X13, X14) model.addNode(X20, X21, X22, X23, X24) model.addNode(X30, X31, X32, X33, X34) model.addNode(X40, X41, X42, X43, X44) # columns params = {'E': E, 'A': A, 'I': I} C11 = Frame2D(X10, X11, ElasticSection(params)) C12 = Frame2D(X11, X12, ElasticSection(params)) C13 = Frame2D(X12, X13, ElasticSection(params)) C14 = Frame2D(X13, X14, ElasticSection(params)) model.addElement(C11, C12, C13, C14) params = {'E': E, 'A': 2 * A, 'I': 1.5 * I} C21 = Frame2D(X20, X21, ElasticSection(params)) C22 = Frame2D(X21, X22, ElasticSection(params)) C23 = Frame2D(X22, X23, ElasticSection(params)) C24 = Frame2D(X23, X24, ElasticSection(params)) model.addElement(C21, C22, C23, C24) C31 = Frame2D(X30, X31, ElasticSection(params)) C32 = Frame2D(X31, X32, ElasticSection(params)) C33 = Frame2D(X32, X33, ElasticSection(params)) C34 = Frame2D(X33, X34, ElasticSection(params)) model.addElement(C31, C32, C33, C34) params = {'E': E, 'A': A, 'I': I} C41 = Frame2D(X40, X41, ElasticSection(params)) C42 = Frame2D(X41, X42, ElasticSection(params)) C43 = Frame2D(X42, X43, ElasticSection(params)) C44 = Frame2D(X43, X44, ElasticSection(params)) model.addElement(C41, C42, C43, C44) # floors params = {'E': E, 'A': A, 'I': 3 * I} F11 = Frame2D(X11, X21, ElasticSection(params)) F12 = Frame2D(X21, X31, ElasticSection(params)) F13 = Frame2D(X31, X41, ElasticSection(params)) model.addElement(F11, F12, F13) F21 = Frame2D(X12, X22, ElasticSection(params)) F22 = Frame2D(X22, X32, ElasticSection(params)) F23 = Frame2D(X32, X42, ElasticSection(params)) model.addElement(F21, F22, F23) F31 = Frame2D(X13, X23, ElasticSection(params)) F32 = Frame2D(X23, X33, ElasticSection(params)) F33 = Frame2D(X33, X43, ElasticSection(params)) model.addElement(F31, F32, F33) F41 = Frame2D(X14, X24, ElasticSection(params)) F42 = Frame2D(X24, X34, ElasticSection(params)) F43 = Frame2D(X34, X44, ElasticSection(params)) model.addElement(F41, F42, F43) # fixities X10.fixDOF('ux', 'uy', 'rz') # fixed X20.fixDOF('ux', 'uy', 'rz') # fixed X30.fixDOF('ux', 'uy', 'rz') # fixed X40.fixDOF('ux', 'uy', 'rz') # fixed # reference load # Pcr = np.pi**2 * EI / L**2 model.resetLoad() # size load vector and initialize # model.addLoad(Xn, -Pcr, dof=0) # add a horizontal force (first dof only) ; remember C-style indexing: 0,1,...,(n-1) if load_at_nodes_only: # floor loading as nodal loads ... Pe = w * B / 3 Mi = w * (B / 3) ** 2 / 12 X11.addLoad([-Pe / 2., -Mi], ['uy', 'rz']) X21.addLoad([-Pe / 2., 0.], ['uy', 'rz']) X31.addLoad([-Pe / 2., 0.], ['uy', 'rz']) X41.addLoad([-Pe / 2., Mi], ['uy', 'rz']) X12.addLoad([-Pe / 2., -Mi], ['uy', 'rz']) X22.addLoad([-Pe / 2., 0.], ['uy', 'rz']) X32.addLoad([-Pe / 2., 0.], ['uy', 'rz']) X42.addLoad([-Pe / 2., Mi], ['uy', 'rz']) X13.addLoad([-Pe / 2., -Mi], ['uy', 'rz']) X23.addLoad([-Pe / 2., 0.], ['uy', 'rz']) X33.addLoad([-Pe / 2., 0.], ['uy', 'rz']) X43.addLoad([-Pe / 2., Mi], ['uy', 'rz']) X14.addLoad([-Pe / 2., -Mi], ['uy', 'rz']) X24.addLoad([-Pe / 2., 0.], ['uy', 'rz']) X34.addLoad([-Pe / 2., 0.], ['uy', 'rz']) X44.addLoad([-Pe / 2., Mi], ['uy', 'rz']) else: # floor loading as distributed loads ... F11.setDistLoad(-w) F12.setDistLoad(-w) F13.setDistLoad(-w) F21.setDistLoad(-w) F22.setDistLoad(-w) F23.setDistLoad(-w) F31.setDistLoad(-w) F32.setDistLoad(-w) F33.setDistLoad(-w) F41.setDistLoad(-w) F42.setDistLoad(-w) F43.setDistLoad(-w) # wind load ... X11.addLoad([Ph], ['ux']) # horizontal load X12.addLoad([Ph], ['ux']) # horizontal load X13.addLoad([Ph], ['ux']) # horizontal load X14.addLoad([Ph / 2], ['ux']) # horizontal load # show model information print(model) print("\n==== perform the analysis ===\n") # * apply the load in multiple smaller load steps # set up data recorder model.initRecorder() model.trackStability(True) # initialize the analysis: model.resetDisplacements() # set U to all zeros model.setLoadFactor(0.0) # define a known equilibrium solution model.startRecorder() detKt = [] lambdas = [] # solve for all load_levels for loadfactor in load_levels: # define node X2 as the controled node; downward direction is prescribed: model.setLoadFactor(loadfactor) model.solve(verbose=True) # stability check lambdas.append(model.loadfactor) detKt.append(model.solver.checkStability()) # report results print('+') # model.report() print("\n=== next load level ===\n") # # ==== create some nice plots === # model.report() model.plot(factor=10.0, filename="frame5_deformed.png", show_bc=1) fig, ax = plt.subplots() ax.plot(lambdas, detKt, '--*r') ax.grid(True) ax.set_xlabel('Load factor, $ \\lambda $') ax.set_ylabel("Stability index, $ {det}\\: {\\bf K}_t $") fig.savefig("frame5_stability.png") fig.show() model.beamValuePlot("F", filename="frame5_force.png") model.beamValuePlot("V", filename="frame5_shear.png") model.beamValuePlot("M", filename="frame5_moment.png") model.plotBucklingMode(factor=100., mode=0, filename="frame5_buckling_mode0.png") model.plotBucklingMode(factor=100., mode=1, filename="frame5_buckling_mode1.png") model.plotBucklingMode(factor=100., mode=2, filename="frame5_buckling_mode2.png") model.plotBucklingMode(factor=100., mode=3, filename="frame5_buckling_mode3.png") .. GENERATED FROM PYTHON SOURCE LINES 313-315 Run the example by creating an instance of the problem and executing it by calling :py:meth:`Example.run()` .. GENERATED FROM PYTHON SOURCE LINES 315-321 .. code-block:: Python if __name__ == "__main__": ex = ExampleFrame05() ex.run() .. rst-class:: sphx-glr-horizontal * .. image-sg:: /auto_examples/frames/images/sphx_glr_plot_frame05_001.png :alt: Deformed System (magnification=10.00) :srcset: /auto_examples/frames/images/sphx_glr_plot_frame05_001.png :class: sphx-glr-multi-img * .. image-sg:: /auto_examples/frames/images/sphx_glr_plot_frame05_002.png :alt: plot frame05 :srcset: /auto_examples/frames/images/sphx_glr_plot_frame05_002.png :class: sphx-glr-multi-img * .. image-sg:: /auto_examples/frames/images/sphx_glr_plot_frame05_003.png :alt: Axial Forces :srcset: /auto_examples/frames/images/sphx_glr_plot_frame05_003.png :class: sphx-glr-multi-img * .. image-sg:: /auto_examples/frames/images/sphx_glr_plot_frame05_004.png :alt: Shear Forces :srcset: /auto_examples/frames/images/sphx_glr_plot_frame05_004.png :class: sphx-glr-multi-img * .. image-sg:: /auto_examples/frames/images/sphx_glr_plot_frame05_005.png :alt: Bending Moment :srcset: /auto_examples/frames/images/sphx_glr_plot_frame05_005.png :class: sphx-glr-multi-img * .. image-sg:: /auto_examples/frames/images/sphx_glr_plot_frame05_006.png :alt: Mode Shape for $ \lambda = -0.05 $ :srcset: /auto_examples/frames/images/sphx_glr_plot_frame05_006.png :class: sphx-glr-multi-img * .. image-sg:: /auto_examples/frames/images/sphx_glr_plot_frame05_007.png :alt: Mode Shape for $ \lambda = 3.53 $ :srcset: /auto_examples/frames/images/sphx_glr_plot_frame05_007.png :class: sphx-glr-multi-img * .. image-sg:: /auto_examples/frames/images/sphx_glr_plot_frame05_008.png :alt: Mode Shape for $ \lambda = 13.51 $ :srcset: /auto_examples/frames/images/sphx_glr_plot_frame05_008.png :class: sphx-glr-multi-img * .. image-sg:: /auto_examples/frames/images/sphx_glr_plot_frame05_009.png :alt: Mode Shape for $ \lambda = 34.10 $ :srcset: /auto_examples/frames/images/sphx_glr_plot_frame05_009.png :class: sphx-glr-multi-img .. rst-class:: sphx-glr-script-out .. code-block:: none System object Node_204(x=[0 0], u=None) Node_205(x=[0 180], u=None) Node_206(x=[0 360], u=None) Node_207(x=[0 540], u=None) Node_208(x=[0 720], u=None) Node_209(x=[240 0], u=None) Node_210(x=[240 180], u=None) Node_211(x=[240 360], u=None) Node_212(x=[240 540], u=None) Node_213(x=[240 720], u=None) Node_214(x=[480 0], u=None) Node_215(x=[480 180], u=None) Node_216(x=[480 360], u=None) Node_217(x=[480 540], u=None) Node_218(x=[480 720], u=None) Node_219(x=[720 0], u=None) Node_220(x=[720 180], u=None) Node_221(x=[720 360], u=None) Node_222(x=[720 540], u=None) Node_223(x=[720 720], u=None) Frame2D(Node_204, Node_205, ElasticSection(Material)({'E': 29000.0, 'A': 150.0, 'I': 250.0, 'nu': 0.0, 'fy': 1e+30})) Frame2D(Node_205, Node_206, ElasticSection(Material)({'E': 29000.0, 'A': 150.0, 'I': 250.0, 'nu': 0.0, 'fy': 1e+30})) Frame2D(Node_206, Node_207, ElasticSection(Material)({'E': 29000.0, 'A': 150.0, 'I': 250.0, 'nu': 0.0, 'fy': 1e+30})) Frame2D(Node_207, Node_208, ElasticSection(Material)({'E': 29000.0, 'A': 150.0, 'I': 250.0, 'nu': 0.0, 'fy': 1e+30})) Frame2D(Node_209, Node_210, ElasticSection(Material)({'E': 29000.0, 'A': 300.0, 'I': 375.0, 'nu': 0.0, 'fy': 1e+30})) Frame2D(Node_210, Node_211, ElasticSection(Material)({'E': 29000.0, 'A': 300.0, 'I': 375.0, 'nu': 0.0, 'fy': 1e+30})) Frame2D(Node_211, Node_212, ElasticSection(Material)({'E': 29000.0, 'A': 300.0, 'I': 375.0, 'nu': 0.0, 'fy': 1e+30})) Frame2D(Node_212, Node_213, ElasticSection(Material)({'E': 29000.0, 'A': 300.0, 'I': 375.0, 'nu': 0.0, 'fy': 1e+30})) Frame2D(Node_214, Node_215, ElasticSection(Material)({'E': 29000.0, 'A': 300.0, 'I': 375.0, 'nu': 0.0, 'fy': 1e+30})) Frame2D(Node_215, Node_216, ElasticSection(Material)({'E': 29000.0, 'A': 300.0, 'I': 375.0, 'nu': 0.0, 'fy': 1e+30})) Frame2D(Node_216, Node_217, ElasticSection(Material)({'E': 29000.0, 'A': 300.0, 'I': 375.0, 'nu': 0.0, 'fy': 1e+30})) Frame2D(Node_217, Node_218, ElasticSection(Material)({'E': 29000.0, 'A': 300.0, 'I': 375.0, 'nu': 0.0, 'fy': 1e+30})) Frame2D(Node_219, Node_220, ElasticSection(Material)({'E': 29000.0, 'A': 150.0, 'I': 250.0, 'nu': 0.0, 'fy': 1e+30})) Frame2D(Node_220, Node_221, ElasticSection(Material)({'E': 29000.0, 'A': 150.0, 'I': 250.0, 'nu': 0.0, 'fy': 1e+30})) Frame2D(Node_221, Node_222, ElasticSection(Material)({'E': 29000.0, 'A': 150.0, 'I': 250.0, 'nu': 0.0, 'fy': 1e+30})) Frame2D(Node_222, Node_223, ElasticSection(Material)({'E': 29000.0, 'A': 150.0, 'I': 250.0, 'nu': 0.0, 'fy': 1e+30})) Frame2D(Node_205, Node_210, ElasticSection(Material)({'E': 29000.0, 'A': 150.0, 'I': 750.0, 'nu': 0.0, 'fy': 1e+30})) Frame2D(Node_210, Node_215, ElasticSection(Material)({'E': 29000.0, 'A': 150.0, 'I': 750.0, 'nu': 0.0, 'fy': 1e+30})) Frame2D(Node_215, Node_220, ElasticSection(Material)({'E': 29000.0, 'A': 150.0, 'I': 750.0, 'nu': 0.0, 'fy': 1e+30})) Frame2D(Node_206, Node_211, ElasticSection(Material)({'E': 29000.0, 'A': 150.0, 'I': 750.0, 'nu': 0.0, 'fy': 1e+30})) Frame2D(Node_211, Node_216, ElasticSection(Material)({'E': 29000.0, 'A': 150.0, 'I': 750.0, 'nu': 0.0, 'fy': 1e+30})) Frame2D(Node_216, Node_221, ElasticSection(Material)({'E': 29000.0, 'A': 150.0, 'I': 750.0, 'nu': 0.0, 'fy': 1e+30})) Frame2D(Node_207, Node_212, ElasticSection(Material)({'E': 29000.0, 'A': 150.0, 'I': 750.0, 'nu': 0.0, 'fy': 1e+30})) Frame2D(Node_212, Node_217, ElasticSection(Material)({'E': 29000.0, 'A': 150.0, 'I': 750.0, 'nu': 0.0, 'fy': 1e+30})) Frame2D(Node_217, Node_222, ElasticSection(Material)({'E': 29000.0, 'A': 150.0, 'I': 750.0, 'nu': 0.0, 'fy': 1e+30})) Frame2D(Node_208, Node_213, ElasticSection(Material)({'E': 29000.0, 'A': 150.0, 'I': 750.0, 'nu': 0.0, 'fy': 1e+30})) Frame2D(Node_213, Node_218, ElasticSection(Material)({'E': 29000.0, 'A': 150.0, 'I': 750.0, 'nu': 0.0, 'fy': 1e+30})) Frame2D(Node_218, Node_223, ElasticSection(Material)({'E': 29000.0, 'A': 150.0, 'I': 750.0, 'nu': 0.0, 'fy': 1e+30})) ==== perform the analysis === norm of the out-of-balance force: 0.0000e+00 ** Stability check: (smallest 1 eigenvalues of Kt) mode 0: 1.45 + ** Stability check: (smallest eigenvalue of Kt) = 1.4498657937285275 + === next load level === norm of the out-of-balance force: 4.9858e+03 norm of the out-of-balance force: 2.5683e+01 norm of the out-of-balance force: 6.8710e-03 norm of the out-of-balance force: 2.4430e-06 norm of the out-of-balance force: 1.6512e-07 ** Stability check: (smallest 1 eigenvalues of Kt) mode 0: 1.30 + ** Stability check: (smallest eigenvalue of Kt) = 1.3039606866245097 + === next load level === norm of the out-of-balance force: 4.9858e+03 norm of the out-of-balance force: 5.2545e+01 norm of the out-of-balance force: 2.8485e-02 norm of the out-of-balance force: 2.0784e-05 norm of the out-of-balance force: 7.0993e-08 ** Stability check: (smallest 1 eigenvalues of Kt) mode 0: 1.16 + ** Stability check: (smallest eigenvalue of Kt) = 1.1558244386254235 + === next load level === norm of the out-of-balance force: 4.9858e+03 norm of the out-of-balance force: 8.0699e+01 norm of the out-of-balance force: 6.6491e-02 norm of the out-of-balance force: 7.4326e-05 norm of the out-of-balance force: 7.1854e-08 ** Stability check: (smallest 1 eigenvalues of Kt) mode 0: 1.00 + ** Stability check: (smallest eigenvalue of Kt) = 1.0049715576213192 + === next load level === norm of the out-of-balance force: 4.9858e+03 norm of the out-of-balance force: 1.1028e+02 norm of the out-of-balance force: 1.2275e-01 norm of the out-of-balance force: 1.8726e-04 norm of the out-of-balance force: 2.5030e-07 ** Stability check: (smallest 1 eigenvalues of Kt) mode 0: 0.85 + ** Stability check: (smallest eigenvalue of Kt) = 0.8507250234763356 + === next load level === norm of the out-of-balance force: 4.9858e+03 norm of the out-of-balance force: 1.4143e+02 norm of the out-of-balance force: 1.9938e-01 norm of the out-of-balance force: 3.8921e-04 norm of the out-of-balance force: 6.6359e-07 ** Stability check: (smallest 1 eigenvalues of Kt) mode 0: 0.69 + ** Stability check: (smallest eigenvalue of Kt) = 0.6920949784275 + === next load level === norm of the out-of-balance force: 4.9858e+03 norm of the out-of-balance force: 1.7435e+02 norm of the out-of-balance force: 2.9877e-01 norm of the out-of-balance force: 7.1689e-04 norm of the out-of-balance force: 1.5020e-06 norm of the out-of-balance force: 1.3625e-08 ** Stability check: (smallest 1 eigenvalues of Kt) mode 0: 0.53 + ** Stability check: (smallest eigenvalue of Kt) = 0.5275391348656064 + === next load level === norm of the out-of-balance force: 4.9858e+03 norm of the out-of-balance force: 2.0925e+02 norm of the out-of-balance force: 4.2361e-01 norm of the out-of-balance force: 1.2154e-03 norm of the out-of-balance force: 3.0769e-06 norm of the out-of-balance force: 2.8825e-08 ** Stability check: (smallest 1 eigenvalues of Kt) mode 0: 0.35 + ** Stability check: (smallest eigenvalue of Kt) = 0.35442857202021694 + === next load level === norm of the out-of-balance force: 4.9858e+03 norm of the out-of-balance force: 2.4638e+02 norm of the out-of-balance force: 5.7696e-01 norm of the out-of-balance force: 1.9401e-03 norm of the out-of-balance force: 5.8237e-06 norm of the out-of-balance force: 2.2737e-08 ** Stability check: (smallest 1 eigenvalues of Kt) mode 0: 0.17 + ** Stability check: (smallest eigenvalue of Kt) = 0.1676343891118212 + === next load level === norm of the out-of-balance force: 4.9858e+03 norm of the out-of-balance force: 2.8607e+02 norm of the out-of-balance force: 7.6225e-01 norm of the out-of-balance force: 2.9585e-03 norm of the out-of-balance force: 1.0392e-05 norm of the out-of-balance force: 3.3931e-08 ** Stability check: (smallest 1 eigenvalues of Kt) mode 0: -0.05 + ** Stability check: (smallest eigenvalue of Kt) = -0.04529626517253338 + === next load level === System Analysis Report ======================= Nodes: --------------------- Node_204: x: [0.000 0.000] fix: ['ux', 'uy', 'rz'] u: [0.000 0.000 0.000] Node_205: x: [0.000 180.000] u: [-0.002 -0.058 -0.024] Node_206: x: [0.000 360.000] u: [0.000 -0.102 -0.020] Node_207: x: [0.000 540.000] u: [-0.001 -0.131 -0.018] Node_208: x: [0.000 720.000] u: [0.005 -0.146 -0.030] Node_209: x: [240.000 0.000] fix: ['ux', 'uy', 'rz'] u: [0.000 0.000 0.000] Node_210: x: [240.000 180.000] u: [-0.001 -0.069 0.005] Node_211: x: [240.000 360.000] u: [0.000 -0.121 0.003] Node_212: x: [240.000 540.000] u: [-0.000 -0.156 0.002] Node_213: x: [240.000 720.000] u: [0.001 -0.173 0.007] Node_214: x: [480.000 0.000] fix: ['ux', 'uy', 'rz'] u: [0.000 0.000 0.000] Node_215: x: [480.000 180.000] u: [0.001 -0.069 -0.005] Node_216: x: [480.000 360.000] u: [-0.000 -0.121 -0.003] Node_217: x: [480.000 540.000] u: [0.000 -0.156 -0.002] Node_218: x: [480.000 720.000] u: [-0.001 -0.173 -0.007] Node_219: x: [720.000 0.000] fix: ['ux', 'uy', 'rz'] u: [0.000 0.000 0.000] Node_220: x: [720.000 180.000] u: [0.002 -0.058 0.024] Node_221: x: [720.000 360.000] u: [-0.000 -0.102 0.020] Node_222: x: [720.000 540.000] u: [0.001 -0.131 0.018] Node_223: x: [720.000 720.000] u: [-0.005 -0.146 0.030] Elements: --------------------- Frame2D_313: nodes ( Node_204 Node_205 ) material: ElasticSection internal forces: f0=-1412.58 V0=-28.72 M0=2190.63 fl=-1412.58 Vl=-28.72 Ml=-2981.99 Pw=0.00 Mw=0.00 Frame2D_314: nodes ( Node_205 Node_206 ) material: ElasticSection internal forces: f0=-1060.65 V0=-54.15 M0=4967.18 fl=-1060.65 Vl=-54.15 Ml=-4777.61 Pw=0.00 Mw=0.00 Frame2D_315: nodes ( Node_206 Node_207 ) material: ElasticSection internal forces: f0=-702.83 V0=-48.56 M0=4417.41 fl=-702.83 Vl=-48.56 Ml=-4323.51 Pw=0.00 Mw=0.00 Frame2D_316: nodes ( Node_207 Node_208 ) material: ElasticSection internal forces: f0=-343.13 V0=-63.72 M0=5307.41 fl=-343.13 Vl=-63.72 Ml=-6160.35 Pw=0.00 Mw=0.00 Frame2D_317: nodes ( Node_209 Node_210 ) material: ElasticSection internal forces: f0=-3339.42 V0=7.47 M0=-673.83 fl=-3339.42 Vl=7.47 Ml=668.39 Pw=0.00 Mw=0.00 Frame2D_318: nodes ( Node_210 Node_211 ) material: ElasticSection internal forces: f0=-2503.35 V0=12.97 M0=-1196.02 fl=-2503.35 Vl=12.97 Ml=1140.41 Pw=0.00 Mw=0.00 Frame2D_319: nodes ( Node_211 Node_212 ) material: ElasticSection internal forces: f0=-1673.17 V0=9.16 M0=-851.26 fl=-1673.17 Vl=9.16 Ml=797.45 Pw=0.00 Mw=0.00 Frame2D_320: nodes ( Node_212 Node_213 ) material: ElasticSection internal forces: f0=-844.87 V0=17.25 M0=-1328.12 fl=-844.87 Vl=17.25 Ml=1778.43 Pw=0.00 Mw=0.00 Frame2D_321: nodes ( Node_214 Node_215 ) material: ElasticSection internal forces: f0=-3339.42 V0=-7.47 M0=673.83 fl=-3339.42 Vl=-7.47 Ml=-668.39 Pw=0.00 Mw=0.00 Frame2D_322: nodes ( Node_215 Node_216 ) material: ElasticSection internal forces: f0=-2503.35 V0=-12.97 M0=1196.02 fl=-2503.35 Vl=-12.97 Ml=-1140.41 Pw=0.00 Mw=0.00 Frame2D_323: nodes ( Node_216 Node_217 ) material: ElasticSection internal forces: f0=-1673.17 V0=-9.16 M0=851.26 fl=-1673.17 Vl=-9.16 Ml=-797.45 Pw=0.00 Mw=0.00 Frame2D_324: nodes ( Node_217 Node_218 ) material: ElasticSection internal forces: f0=-844.87 V0=-17.25 M0=1328.12 fl=-844.87 Vl=-17.25 Ml=-1778.43 Pw=0.00 Mw=0.00 Frame2D_325: nodes ( Node_219 Node_220 ) material: ElasticSection internal forces: f0=-1412.58 V0=28.72 M0=-2190.63 fl=-1412.58 Vl=28.72 Ml=2981.99 Pw=0.00 Mw=0.00 Frame2D_326: nodes ( Node_220 Node_221 ) material: ElasticSection internal forces: f0=-1060.65 V0=54.15 M0=-4967.18 fl=-1060.65 Vl=54.15 Ml=4777.61 Pw=0.00 Mw=0.00 Frame2D_327: nodes ( Node_221 Node_222 ) material: ElasticSection internal forces: f0=-702.83 V0=48.56 M0=-4417.41 fl=-702.83 Vl=48.56 Ml=4323.51 Pw=0.00 Mw=0.00 Frame2D_328: nodes ( Node_222 Node_223 ) material: ElasticSection internal forces: f0=-343.13 V0=63.72 M0=-5307.41 fl=-343.13 Vl=63.72 Ml=6160.35 Pw=0.00 Mw=0.00 Frame2D_329: nodes ( Node_205 Node_210 ) material: ElasticSection internal forces: f0=25.43 V0=-44.07 M0=7890.83 fl=25.43 Vl=-44.07 Ml=-2686.63 Pw=-396.00 Mw=-15840.00 Frame2D_330: nodes ( Node_210 Node_215 ) material: ElasticSection internal forces: f0=19.93 V0=0.00 M0=-822.22 fl=19.93 Vl=0.00 Ml=-822.22 Pw=-396.00 Mw=-15840.00 Frame2D_331: nodes ( Node_215 Node_220 ) material: ElasticSection internal forces: f0=25.43 V0=44.07 M0=-2686.63 fl=25.43 Vl=44.07 Ml=7890.83 Pw=-396.00 Mw=-15840.00 Frame2D_332: nodes ( Node_206 Node_211 ) material: ElasticSection internal forces: f0=-5.60 V0=-38.17 M0=6644.98 fl=-5.60 Vl=-38.17 Ml=-2516.78 Pw=-396.00 Mw=-15840.00 Frame2D_333: nodes ( Node_211 Node_216 ) material: ElasticSection internal forces: f0=-1.79 V0=0.00 M0=-525.10 fl=-1.79 Vl=0.00 Ml=-525.10 Pw=-396.00 Mw=-15840.00 Frame2D_334: nodes ( Node_216 Node_221 ) material: ElasticSection internal forces: f0=-5.60 V0=38.17 M0=-2516.78 fl=-5.60 Vl=38.17 Ml=6644.98 Pw=-396.00 Mw=-15840.00 Frame2D_335: nodes ( Node_207 Node_212 ) material: ElasticSection internal forces: f0=15.17 V0=-36.30 M0=6209.08 fl=15.17 Vl=-36.30 Ml=-2503.48 Pw=-396.00 Mw=-15840.00 Frame2D_336: nodes ( Node_212 Node_217 ) material: ElasticSection internal forces: f0=7.08 V0=0.00 M0=-377.91 fl=7.08 Vl=0.00 Ml=-377.91 Pw=-396.00 Mw=-15840.00 Frame2D_337: nodes ( Node_217 Node_222 ) material: ElasticSection internal forces: f0=15.17 V0=36.30 M0=-2503.48 fl=15.17 Vl=36.30 Ml=6209.08 Pw=-396.00 Mw=-15840.00 Frame2D_338: nodes ( Node_208 Node_213 ) material: ElasticSection internal forces: f0=-63.72 V0=-52.87 M0=9679.65 fl=-63.72 Vl=-52.87 Ml=-3007.97 Pw=-396.00 Mw=-15840.00 Frame2D_339: nodes ( Node_213 Node_218 ) material: ElasticSection internal forces: f0=-46.47 V0=0.00 M0=-1229.55 fl=-46.47 Vl=0.00 Ml=-1229.55 Pw=-396.00 Mw=-15840.00 Frame2D_340: nodes ( Node_218 Node_223 ) material: ElasticSection internal forces: f0=-63.72 V0=52.87 M0=-3007.97 fl=-63.72 Vl=52.87 Ml=9679.65 Pw=-396.00 Mw=-15840.00 .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.690 seconds) .. _sphx_glr_download_auto_examples_frames_plot_frame05.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_frame05.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_frame05.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_frame05.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_