MSASect2

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<div align="center"><img src='./image/logo.png' style="height:auto; width: 15%; min-width: 15%; max-width: 200px;"/>
<h1>MSASect2</h1>
<strong>Advanced Cross-section Analysis Software (Available on Windows and MacOS)</strong>  
  <br><br>
</div>

[![Official Website](http://img.shields.io/badge/Website-msasect.com-green?style=flat&logo=world&logoColor=white)](http://www.MSASect.com)
<a href="https://github.com/zsulsw/MSASect2/releases" target="_blank">
<img alt="macOS" src="https://img.shields.io/badge/-macOS-red?style=flat-square&logo=apple&logoColor=white" />
</a>
<a href="https://github.com/zsulsw/MSASect2/releases" target="_blank">
<img alt="Windows" src="https://img.shields.io/badge/-Windows-blue?style=flat-square&logo=windows&logoColor=white" />
</a>

![Screen Shot Gif](https://raw.githubusercontent.com/zsulsw/MSASect2/main/image/v2.5.0-Main-Page.gif)

## 🌟 About the Software

**MSASect2** is a cross-platform software developed for comprehensive analysis of arbitrary cross-sections with nonsymmetric shapes. This includes examining their cross-sectional properties, yield strengths, global and local buckling capacities,stress analysis, heat transfer analysis, etc. The software is developed to address design challenges associated with complex and irregular cross-sections, which are increasingly popular in modern structures due to their superior structural efficiency. The software is free for both research and educational use.

</div>

### 📥 Download Latest Version

**Latest release stats (auto-updated):**  
[![Latest release](https://img.shields.io/github/v/release/zsulsw/MSASect2?label=latest%20release&style=flat-square)](https://github.com/zsulsw/MSASect2/releases/latest)
[![Downloads (latest release)](https://img.shields.io/github/downloads/zsulsw/MSASect2/latest/total?label=downloads%20(latest%20release)&style=flat-square)](https://github.com/zsulsw/MSASect2/releases/latest)
[![Downloads (all releases)](https://img.shields.io/github/downloads/zsulsw/MSASect2/total?label=downloads%20(all%20releases)&style=flat-square)](https://github.com/zsulsw/MSASect2/releases)

<table>
  <tr>
    <th>Platform</th>
    <th>Download</th>
    <th>File Size</th>
    <th>Downloads</th>
  </tr>
  <tr>
    <td><img src='./image/windows.png' style="height:auto; width: 18px" alt="Windows" /> <b>Windows</b></td>
    <td><a href='https://github.com/zsulsw/MSASect2/releases/tag/%23stable-v2.5.1/20260602-MSASect2-v2.5.1-Windows.zip'><b>20260602-MSASect2-v2.5.1-Windows.zip</b></a></td>
    <td>263 MB</td>
    <td align="center"><a href="https://github.com/zsulsw/MSASect2/releases/latest"><img alt="Downloads" src="https://img.shields.io/badge/dynamic/json?style=flat&label=&color=3fb950&query=%24.assets%5B2%5D.download_count&url=https%3A%2F%2Fapi.github.com%2Frepos%2Fzsulsw%2FMSASect2%2Freleases%2Flatest" /></a></td>
  </tr>
  <tr>
    <td><img src='./image/mac.png' style="height:auto; width: 19px" alt="Mac" /> <b>macOS (Apple Silicon)</b></td>
    <td><a href='https://github.com/zsulsw/MSASect2/releases/tag/%23stable-v2.5.1/20260602-MSASect2-v2.5.1-MacOS-ARM.zip'><b>20260602-MSASect2-v2.5.1-MacOS-ARM.zip</b></a></td>
    <td>287 MB</td>
    <td align="center"><a href="https://github.com/zsulsw/MSASect2/releases/latest"><img alt="Downloads" src="https://img.shields.io/badge/dynamic/json?style=flat&label=&color=3fb950&query=%24.assets%5B0%5D.download_count&url=https%3A%2F%2Fapi.github.com%2Frepos%2Fzsulsw%2FMSASect2%2Freleases%2Flatest" /></a></td>
  </tr>
  <tr>
    <td><img src='./image/mac.png' style="height:auto; width: 19px" alt="Mac" /> <b>macOS (Intel)</b></td>
    <td><a href='https://github.com/zsulsw/MSASect2/releases/tag/%23stable-v2.5.1/20260602-MSASect2-v2.5.1-MacOS-x86.zip'><b>20260602-MSASect2-v2.5.1-MacOS-x86.zip</b></a></td>
    <td>337 MB</td>
    <td align="center"><a href="https://github.com/zsulsw/MSASect2/releases/latest"><img alt="Downloads" src="https://img.shields.io/badge/dynamic/json?style=flat&label=&color=3fb950&query=%24.assets%5B1%5D.download_count&url=https%3A%2F%2Fapi.github.com%2Frepos%2Fzsulsw%2FMSASect2%2Freleases%2Flatest" /></a></td>
  </tr>
</table>

* <sub> Windows: Windows 10 or later (64-bit, x86-64). </sub>
* <sub> macOS (Apple Silicon): Apple silicon (M-series: M1/M2/M3/M4 and later, ARM64) build. </sub>
* <sub> macOS (Intel): Intel-based Macs (x86-64) build. </sub>

If you find the software helpful for your research or have thoughts on collaborative research, we would be delighted to hear from you.

## 💻 Install
<table>
  <tr>
    <td><a href='https://github.com/zsulsw/MSASect2/releases'><img src='./image/windows.png' style="height:auto; width: 18px" /> <b>Windows:</b></a></td>
    <td><b>1. Download "MSASect2-(version number)-Windows.zip"<br>2. Unzip and Run "MSASect2.exe"</b></td>
  <tr>
    <td><a href='https://github.com/zsulsw/MSASect2/releases'><img src='./image/mac.png' style="height:auto; width: 19px" /> <b>MacOS - ARM:</b></a></td>
    <td><b>1. Download "MSASect2-(version number)-MacOS-ARM.dmg"<br>2. Open DMG file and copy "MSASect2" to Application</b></td>
  <tr>
    <td><a href='https://github.com/zsulsw/MSASect2/releases'><img src='./image/mac.png' style="height:auto; width: 19px" /> <b>MacOS - x86:</b></a></td>
    <td><b>1. Download "MSASect2-(version number)-MacOS-x86.dmg"<br>2. Open DMG file and copy "MSASect2" to Application</b></td>

</table>

## 📌 What's New in MSASect2-v2.5.1 ?

+ **Cross-section Properties**  
  - **Finite Element Method (FEM):** Added calculation of **Torsional plastic section modulus**, **nominal torsional strength**, and **torsional shape factor**.

+ **Section Buckling Analysis**  
  - **Shell Finite Strip Method:**  
  - Added elastic buckling evaluation for **anisotropic material properties** (e.g., WAAM).  
  - Added elastic buckling evaluation for **cross-sections with tapered thickness**.  
  - Enhanced **modal decomposition and participation** analysis for cross-sections with tapered thickness.

+ **General Improvements**  
  - Fixed several potential bugs and addressed user-reported issues.

## 📕 Functions and Features

### Advanced Analysis Algorithms
+ **Cross-section Properties:**
  - **Coordinate Method (CM):** Specifically designed for thin-walled sections modeled via **centerlines**.
  - **Finite Element Method (FEM):** Suitable for general cross-sections modeled by **outlines**.
  - Geometric and sectorial properties, elastic and plastic modulus, Wagner coefficients, etc.
  - Support for isotropic and anisotropic material properties analysis.
+ **Section Buckling Analysis:**
  - **Shell Finite Strip Method:** Efficient computational method for thin-walled sections (import and export to CUFSM5 supported). 
  - **Solid Finite Strip Method:** Advanced computational method that extends the classic Finite Strip Method by enabling the analysis of arbitrary three-dimensional geometries, eliminating the reliance on thin-wall assumptions or centerline modeling.
  - **Inelastic Finite Strip Method:** Material nonlinearity is supported in the buckling analysis of members with arbitrary sections using FSM.
  - **Shell Finite Element Method (SFEM):** Advanced computational method for the sections modeled via centerlines.
  - **Modal Participation:** Quantifies the contribution of different structural modes (like global, distortional, and local) to a component's overall deformation.
  - Elastic eigen-buckling analysis to evaluate the local, distortional and global buckling behaviors.  
+ **Member Buckling Analysis:**
  - **Twisting Effects:** As the requirements in American Steel Design Specification (ANSI/AISC 360-22),the buckling behaviors of members with nonsymmetric or monosymmetric sections should be studied for the twisting effects.
  - **Analytical Solutions:** Flexural buckling, lateral torsional buckling, axial-torsional buckling.  
  - **Eigen-buckling Analysis:** Buckling analysis using advanced line finite-element, derived based on the nonsymmetric cross-section assumption, for general buckling conditions.
  - **Semi-Rigid Connections:** Semi-rigid connections in any DOFs can be considered.
+ **Yield-surface Analysis:**
  - **Quasi-Newton Divergence-Free Algorithms:**  Robust numerical algorithms for generation of yield surfaces.
  - **Fiber Section Solution:** Stress integration method using fibers is adopted with less computational efficiency but versatile. 
  - **Gaussian Line-Segment Solution:** New stress integration method using gaussian line segments for centerline models and very efficient computationally.
  - Initial yield surface, failure surface, strength interaction surfaces at a specific strain status.  
+ **Stress Analysis:**
  - **Stress Analysis over the Cross-section:** A stress analysis determines the stresses in a section resulting from various forces and moments. These include axial force, shear force, bending moment, torque, and bi-moment.
  - The algorithms consider different **warping restraints**. These include free-free, fixed-fixed, and fixed-free conditions at both ends of the support.
  - Various types of stress contours can be generated for output including normal stress, shear stress, von Mises stress, and major and minor principal stresses.
+ **Heat Transfer Analysis:**
  - **Finite Element Method (FEM):** Robust numerical algorithms for general cross-sections modeled by outlines.
  - **Refined cross-section analysis:** This method uses Nonhomogeneous planar triangular elements to obtain cross-sectional properties with thermal gradients and is computationally efficient.
  - **Steady-state and transient analysis** for heat transfer considering different boundary conditions, e.g., temperature, heat flux, convection, and emissivity.
  - **Fireproof coatings and localized fires** are considered in the analysis.
+ **Moment Curvature Analysis:**
  - **Divergence-Free Algorithms:** Stable numerical procedure.
  - **Under Applied Axial Load:** Automatically find the netural axis.  
  - Moment Curvature, moment vs. strain, moment vs. stress, tangent slops, sceant slopts and m vs. tau.
### User-Friendly UI and Visualization
- Multiplatform application
- Support arbitrary geometry modeled by either centerlines or outlines
- Support dxf, excel, text files
- Opengl module for visualization
- Import and export to CUFSM5
- Export to MASTAN2

## 📌 Citation

If you use MSASect2 for academic research, please cite the software using the following:

<details>
<summary><strong>APA Format:</strong> 📋</summary>

Liu, S. W., & Ziemian, R. D. (2023). MSASect2 - Matrix Structural Analysis Software for Arbitrary Cross-sections. Retrieved from http://www.msasect.com

</details>

<details>
<summary><strong>MLA Format:</strong> 📋</summary>

Liu, Si-Wei, and Ziemian, Ronald D. "MSASect2 - Matrix Structural Analysis Software for Arbitrary Cross-sections." 2023. Web. <http://www.msasect.com>
</details>

<!-- If you use MSASect2 for academic research, please cite the software using the following:

**APA:**
```
Liu, S. W., & Ziemian, R. D. (2023). MSASect2 - Matrix Structural Analysis Software for Arbitrary Cross-sections. Retrieved from http://www.msasect.com
```
**MLA:**
```
Liu, Si-Wei, and Ziemian, Ronald D. "MSASect2 - Matrix Structural Analysis Software for Arbitrary Cross-sections." 2023. Web. <http://www.msasect.com>.```
```
-->

## 🎁 Contributing

**Your contributions** are greatly appreciated! If you have any questions or suggestions that could further enhance the software, please don't hesitate to open a [**github issue**](https://github.com/zsulsw/MSASect2/issues). Your input will help make the software even better.

We welcome contributions from the community to help improve and enhance MSASect2. Whether it's code improvements, bug fixes, or new features, your contributions are valuable. If you are interested in research collaborations related to the software's capabilities, please contact [**Dr.Siwei Liu**](https://zsulsw.github.io/)  at Email: [**si-wei.liu@polyu.edu.hk**](mailto:si-wei.liu@polyu.edu.hk).

</div>

## ✔️ Disclaimer

**Considerable care** has been taken to ensure the accuracy of this software. However, the user assumes full responsibility for its use, and the developers or distributors will not be liable for any damage caused by the use or misuse of this software. The user should have a thorough understanding of the software's modeling, analysis, and design algorithms, and should compensate for any aspects that are not addressed.

</div>

## 📜 Useful References

<details>
<summary><strong>Click to expand/collapse references</strong> 📚</summary>

- Liu, S.W., Liu, Y.P. & Chan, S.L.:
*"Advanced analysis of hybrid steel and concrete frames: part 1: cross-section analysis technique and second-order analysis"*,
Journal of Constructional Steel Research, 2012. 70, 326-336.
[DOI](https://doi.org/10.1016/j.jcsr.2011.09.003)

- Chen, L., Liu, S.W. & Chan, S.L.:
*"Divergence-free algorithms for moment-thrust-curvature analysis of arbitrary sections"*,
Steel and Composite Structures, An International Journal, 2017, 25 (5), 557-569
[DOI](https://doi.org/10.12989/scs.2017.25.5.557)

- Liu, S.W., Ziemian, R.D., Chen, L., and Chan S.L.:
*"Bifurcation and large-deflection analyses of thin-walled beam-columns with non-symmetric open-sections"*,
Thin-Walled Structures, 2018. 132: p. 287-301,
[DOI](https://doi.org/10.1016/j.tws.2018.07.044)

- Liu, S.W., Gao, W.L., & Ziemian, R.D.:
*"Improved line-element formulations for the stability analysis of arbitrarily- shaped open-section beam-columns"*,
Thin-Walled Structures, 2019. 144, 106290,
[DOI](https://doi.org/10.1016/j.tws.2019.106290)

- Gao, W.L., Abdelrahman, A.H.A., Liu, S.W., & Ziemian, R.D.:
*"Second-order dynamic time-history analysis of beam-columns with nonsymmetrical thin-walled steel sections"*,
Thin-Walled Structures, 2021. 160(3), 107367,
[DOI](https://doi.org/10.1016/j.tws.2020.107367)

- Liu, S.W., Pekoz, T., Gao, W.L., Ziemian, R.D., & Crews, J:
*"Frame analysis and design of industrial rack structures with perforated cold-formed steel columns"*,
Thin-Walled Structures, 2021. 163, 107755,
[DOI](https://doi.org/10.1016/j.tws.2021.107755)

- Chen, L., Gao, W.L., Liu, S.W., Ziemian, R.D., & Chan, S.L.:
*"Geometric and material nonlinear analysis of steel members with nonsymmetric sections"*,
Journal of Constructional Steel Research, 2022. 198, 107537,
[DOI](https://doi.org/10.1016/j.jcsr.2022.107537)

- Chen, L., Zhang, H. Y., Liu, S.W., & Ziemian, R.D.: 
*"Efficient Line-Element Method for the Second-Order Analysis of Steel Members with Nonsymmetric Thick-Walled Cross Sections"*,
Journal of Structural Engineering, 2024. 150(2), 04023226,
[DOI](https://doi.org/10.1061/JSENDH.STENG-12543)

- Li, G. H., Gu, Z. Z., Zhang, H. Y., Ouyang W. H,. & Liu, S.W.:
*"Line finite element method for geometrically nonlinear analysis of functionally graded members accounting for twisting effects"*,
Composite Structures, 2024. 343, 118268.
[DOI](https://doi.org/10.1016/j.compstruct.2024.118268)

- Li, G. H., Gu, Z. Z., Ouyang W. H., Liu, S.W., & Abdelrahman, A.H.A.:
*"Finite-element-based cross-section analysis method for functionally graded sandwich members with arbitrary shapes and gradients"*,
Journal of Sandwich Structures & Materials, 2024. 150(2), 04023226.
[DOI](https://doi.org/10.1177/10996362241275557)

- Zhang, H. Y., Ho, G. W., Liu, S.W., Chen, L., & Chan S. L.:
*"Advanced line-finite-element for lateral-torsional buckling of beams with torsion and warping restraints"*,
Journal of Constructional Steel Research, 2025. 224, 109103.
[DOI](https://doi.org/10.1016/j.jcsr.2024.109103)

- Li, G. H., Gu, Z. Z., Du, E. F., Liu, S.W. Liu Y. P., & Chan S. L.:
*"Global buckling analysis of IFC-protected steel members with irregular sections under fire"*,
Journal of Constructional Steel Research, 2025. 224, 109158.
[DOI](https://doi.org/10.1016/j.jcsr.2024.109158)

- Li, G. H., Gu, Z. Z., Chen, L., & Liu, S. W.:
*"Geometrically nonlinear analysis of steel members under non-uniform fire considering twisting effects"*,
Journal of Constructional Steel Research, 2025. 231, 109596.
[DOI](https://doi.org/10.1016/j.jcsr.2025.109596)

- Gao, W. L., Chen, L., Ziemian, R.D., & Liu, S. W.: 
*"Improved shell-finite strip method for inelastic buckling analysis of thin-walled steel members with residual stresses"*,
Thin-Walled Structures, 2025. 211, 113064.
[DOI](https://doi.org/10.1016/j.tws.2025.113064)

- Xue, H. E., Li, Y. L., Zhao, X. L., Chen L., & Liu, S. W.:
*"Improved finite-element-based stress analysis method for cylindrical orthotropic members with arbitrary cross-sections considering ring orientation"*,
Structures, 2025. 80, 110109.
[DOI](https://doi.org/10.1016/j.istruc.2025.110109)

- Zhang, H. Y., Liang, A. R., Liu, S. W., Liu Y. P., & Chan S. L.:
*"Refined FE-based cross-section analysis for line element simulation of WAAM steel members considering anisotropy"*,
Structures, 2025. 81, 110236.
[DOI](https://doi.org/10.1016/j.istruc.2025.110236)

</details>

MSASect2

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