Laboratorios virtuales:

Cada laboratorio virtual tiene introducción, objetivos, instrucciones, conclusiones y ayuda.

1-Sections open & closed Class 1 to 4 (local buckling {effective width}) (different materials) N Vy Vz B My Mz Tt Tw (Class 4 works with 1 layer):

https://labmatlab-was.upv.es/webapps/home/thinwallsectionmaterials_class4.html

https://labmatlab-was.upv.es/webapps/home/thinwallsectionmaterials_class4_es.html

2-Sections open & closed Class 1 to 3 (different materials E, G, fc & ft) N Vy Vz B My Mz Tt Tw. Figure below node & element definition in example by default:

https://laboratoriosvirtuales.upv.es/webapps/thinwallsectionmaterials.html

https://labmatlab-was.upv.es/webapps/home/thinwallsectionmaterials_es.html

3.1-Sections open & closed Class 1 to 3 N Vy Vz B My Mz Tt Tw. Figure below node & element definition in example by default::

https://laboratoriosvirtuales.upv.es/webapps/thinwallsectiongeneral.html

https://labmatlab-was.upv.es/webapps/home/thinwallsectiongeneral_es.html

3.2 Thin wall section elastic & plastic:

https://labmatlab-was.upv.es/webapps/home/thinwallsectionelasticplastic.html

4-Sections open Class 1 to 3 N Vy Vz B My Mz Tw (Figure below The plastic stresses [blue & yellow tension or compression] are for My, table on the right section properties):

https://laboratoriosvirtuales.upv.es/webapps/thinwallsectionopen.html

https://labmatlab-was.upv.es/webapps/home/thinwallsectionopen_es.html

5-Sections open & closed Class 1 to 3 N Vy Vz My Mz Tt (Suggested if Iw=0):

https://labmatlab-was.upv.es/webapps/home/thinwallsectionopenclosed.html

https://labmatlab-was.upv.es/webapps/home/thinwallsectionopenclosed_es.html

6-Sections open & closed Class 1 to 3 N Vy Vz B My Mz Tt Tw. 4 section Shapes {I;U;Z;Box}:

https://labmatlab-was.upv.es/webapps/home/thinwallresopenclosed.html

https://labmatlab-was.upv.es/webapps/home/thinwallresopenclosed_es.html

7-Sections open Class 1 to 3 N My Mz B:

https://laboratoriosvirtuales.upv.es/webapps/ThinWallResNMyMzB.html

https://labmatlab-was.upv.es/webapps/home/ThinWallResNMyMzB_es.html

8-Sections open & closed Class 1 to 3 N My Mz:

https://laboratoriosvirtuales.upv.es/webapps/ThinWallResNMyMz.html

https://labmatlab-was.upv.es/webapps/home/ThinWallResNMyMz_es.html

9-Sections open Class 1 to 3 N Vy Vz B My Mz Tt Tw. 3 section Shapes {I;U;Z} Further information in help:

https://labmatlab-was.upv.es/webapps/home/thinwallres.html

10- Composites sections (for instance reinforced concrete or steel-concrete)

https://laboratoriosvirtuales.upv.es/webapps/sectionfibersNMyMz.html

11- Strain stress analysis. 3 Strain gages (Rosette)

https://laboratoriosvirtuales.upv.es/webapps/Strain_Gages.html

Codigo fuente en:

https://es.mathworks.com/matlabcentral/profile/authors/3792691

In mathworks different software of cross section optimization can be found using different algorithm.

https://es.mathworks.com/matlabcentral/fileexchange/122447-cross-section-optimization-general?s_tid=prof_contriblnk

articulos:

New interaction formula for the plastic resistance of I- and H-sections under combinations of bending moments M_y,Ed, M_z,Ed and bimoment B_Ed.

https://doi.org/10.1016/j.istruc.2020.11.059

New interaction formula for plastic resistance of channel sections under combinations of bending moments M_y,Ed, M_z,Ed and bimoment B_Ed.

https://doi.org/10.1016/j.istruc.2022.08.038

New Interaction Formulae for Plastic Resistances of Z-Sections under Combinations of Bending Moments M_y,Ed, M_z,Ed and Bimoment B_Ed

https://doi.org/10.3390/buildings13071778

Improved Interaction Formula for the Plastic Resistance of I- and H-Sections under a Combination of Bending Moments M_y,Ed, M_z,Ed, and Bimoment B_Ed

https://doi.org/10.3390/app12157888

Elastic and Plastic Resistance of Thin Walled HVH Sections

https://doi.org/10.1063/5.0170340

Plastic design of metal thin walled cross sections of any shape under any combination of internal forces

https://www.preprints.org/manuscript/202409.0512/v1

Results laboratorios viruales (examples)

Plastic Interaction diagram for U section:

Plastic Interaction diagram for I section, different profiles:

Plastic Interaction diagram for Z section, different profiles:

Normal stresses for example due to My software Thinwallsection open:

Shear stresses for example due to Vz software Thinwallsection open:

Von Mises stresses for example due to Vz + My software Thinwallsection open:

Plastic interaction diagram {N,My,Mz other internal forces in this case=0} software Thinwallsection open:

Class 4 section example under My. The sections properties are obtained for the gross & effective section. In the figure below you can see the section, the stresses in gross section and in the effective section. If several materials are used the sections properties are obtained taking as reference material of element 1.

Example closed section:

Plot Shear stresses due to shear force Vz in 3D below, the plot can be rotated to improve the view:

Plot normal stresses due to Bimoment (B):

Plot shear stresses due to warping torsion (Tw):

Plot of plastic stresses due to a Bimoment (B) (blue & yellow, tension or compresssion):

Section properties closed section:

Iy = 1848945.156 Iz = 13236887.149 Iyz = 0.000 Imax = 13236887.149 Imin = 1848945.156 angle = 0.000 Iw = 1041230410.240 J = 145712.334 ySC = 50.000 zSC = 52.756 yG = 50.000 zG = 63.658

Another example of open section:

Plot shear stresses due to warping torsion (Tw):

PLot normal stresses due to Bimoment (B):

Plot of plastic stresses due to a Bimoment (B) (blue & yellow, tension or compresssion):

Section properfties open section:

Iy = 164131.579 Iz = 177934.211 Iyz = -67855.263 Imax = 239238.209 Imin = 102827.580 angle = -0.735 Iw = 92582163.465 J = 228.750 ySC = 50.565 zSC = 48.632 yG = 38.947 zG = 6.316

Examples asymmetrical open section & symmetrical closed section. Normal & shear stresses due to N, Vy,Vz,My,Mz,B,Tt,Tw.

Examples of Class 4 sections stresses effective & gross section. Different materials elastic section properties{E,G} & strength {fc,ft}.