Webshop

Contact Sales Team

Industries

Reinforced Concrete Structures

Prestressed Concrete Structures

Steel Structures

Timber and Wood Structures

Masonry Structures

Aluminum and Lightweight Structures

Buildings

Industrial Structures and Plants

Pipelines

Bridge Structures

Cranes and Craneways

Towers and Masts

Glass Structures

Tensile Membrane Structures

Cable and Tensile Structures

Laminate and Sandwich Structures

Temporary Structures

Scaffolding and Rack Structures

Offshore Structures

Silos and Storage Tanks

Renewable Energy Plants

Solar Structures & Mounting Systems

Shipbuilding and Floating Bodies

Conveyor Structures

Drilling Structures

Swimming Pools and Water Parks

Container Structures

Drilled Pile Foundations

Staircase Structures

Power Plants

Hydraulic Steel Engineering

Mechanical Engineering

Pneumatic Structures
Application Areas

Structural Engineering

Finite Element Analysis (FEA)

Wind Simulation and Wind Load Generation

Stress Analysis

Nonlinear Analysis

Stability Analysis

Nonlinear Buckling Analysis

Warping Torsion Analysis

Dynamic and Seismic Analysis

Nonlinear Dynamic Analysis

Pushover Analysis

Form-Finding and Cutting Patterns

Steel Joints

BIM Planning

Cold-Formed Sections

Soil-Structure Interaction

Facade Analysis

Foundations and Foundation Engineering

Construction Stages

Fire Resistance
Standards

Eurocodes (EC)

German Standards (DIN)

British Standards (BS EN, BS)

Italian Standards (NTC)

US Standards

Canadian Standards (CSA)

Australian Standards (AS)

Swiss Standards (SIA)

Chinese Standards (GB, HK)

Indian Standards (IS)

Mexican Standards (RCDF, CFE Sismo 15)

Russian Standards (SP)

South African Standards (SANS)

Brazilian Standards (NBR)
Online Services

Snow Load, Wind Speed, and Seismic Load Maps

Cloud Calculations

Structural Analysis Wiki

Cross-Section Properties of Steel Cross-Sections
Structural Design for Solar Systems

Dlubal Software helps you create and verify any solar mounting system. Work efficiently with steel, aluminum, and concrete structures in a single environment.

Explore Tools

Dlubal API

The new Dlubal API service (gRPC) provides you with a flexible interface to the structural analysis software based on Python and C#, with direct access to the entire Dlubal product range.

Start With API
RFEM 6 Only Structural Analysis and Design Software You Need for Your Projects

RFEM 6 serves as the basis of the modular program family and is used to define structures, materials, and actions for plate, wall, shell, and beam structures, as well as for solids and contact elements.
More Information

Add-ons

Additional Analyses

Dynamic Analysis

Special Solutions

Design

Connections
RSTAB 9 Iconic Frame and Truss Analysis Software

RSTAB 9 is a powerful analysis and design software for 3D beam, frame, or truss structure calculations, reflecting the current state of the art and helping structural engineers meet requirements in modern civil engineering.
More Information

Add-ons

Additional Analysis

Dynamic Analysis

Special Solutions

Design
RSECTION 1 User-Defined Cross-Section Properties

RSECTION supports structural engineers by determining cross-section properties for a wide variety of cross-sections and allowing for subsequent stress analysis.
More Information

RWIND 3 CFD Software for Digital Wind Tunnels

RWIND 3 is a digital wind tunnel for simulating wind flows around any building geometry and for the calculation of the wind loads on their surfaces.
More Information
Dlubal API Your Gateway to Parametric Modeling and Automation

The new Dlubal API service (gRPC) provides you with a flexible interface to the structural analysis software based on Python and C#, with direct access to the entire Dlubal product range. Benefit from seamless and powerful integration into your Dlubal software—ideal for parametric modeling and complex optimization tasks.
Discover API

API Documentation

Index

Getting Started

Applications

Model Objects

Subscriptions & Pricing

Examples
FEA for Steel Connections

Design and analyze steel connections using CBFEM, compliant with EN 1993‑1‑8 and AISC 360, fully integrated in RFEM 6 for faster, more accurate structural workflows.

Learn More

Dlubal Community

This platform offers a space for technical inquiries, engaging discussions on structural analysis and design, feature suggestion, and direct interaction with the Dlubal team and fellow users.

Join Now

Outdated Products
Support

Frequently Asked Questions (FAQ)

Knowledge Base

Product Features

Licensing

Ask Individual Question

Our Support Team

Submit Program Feature or Idea

FAQ for Licensing & Authorization

Report Problem or Program Issue

Program Updates

Program Issues

Formulas | Math is fun!
Training

First Steps with RFEM

First Steps with RSTAB

Online Training

Training at Dlubal

Individual Training

Videos

E-Learning Videos

Webinars – Learn Online

Online Courses
Service

Free Support / Service

Extranet | My Account

Project Support

Service Contract

Geo-Zone Tool for Load Determination

Updates & Upgrades

Previous Program Versions
Sales

Webshop

Our Sales Team

Contact Our Sales Team

Schedule an online product demo

Why Dlubal Software
AI Support Assistant

Mia – Your 24/7 AI Assistant

Discover Your Personal AI Assistant
Free Support & Service

Need help? Access free support options including 24/7 AI assistance, email support, and webinars.

Learn More

Find Answers Fast

Find quick answers to common questions about Dlubal Software. Search or filter hundreds of FAQ to solve issues in no time.

View FAQ
News

Current News

New Product Features

Subscribe to Newsletter

New Programs

Dlubal Blog
Training

Online Training

Individual Training
Events

Event Overview

Trade Fairs and Conferences

Webinars
Master Engineering with Webinars

Join industry leaders and explore solutions in structural engineering and software. Enhance your skills with our live sessions!

See Next Webinars

Unlock the Power of Innovation

Discover cutting-edge tools and enhancements designed to boost your engineering workflow.

Explore New Features
Download Full Version

Would you like to try out the capabilities of the Dlubal Software programs? You have the opportunity to do so! With the free 90-day full version you can thoroughly test all our programs.
Start Trial Version Now

Dlubal Free Zone

In the Dlubal free zone, you can access webinars, articles, and software trial versions—all free of charge and conveniently located in one place.
More Information
Examples

Structural Analysis Models to Download

Submit Structural Analysis Model

Introductory Examples and Tutorials

Verification Examples

Image Overview
Documents

Online Manuals

Manuals
References

Customer Projects

Why Submit Your Customer Project?

How to Submit Customer Project?

Submit Customer Project
Free Models to Download

Explore thousands of ready-to-use structural models. Download, adapt, and use them as templates to accelerate your design process.

Discover Models

Dlubal Free Zone

Get expert help whenever you need it. Enjoy free AI assistance, email support, live webinars, and premium services for Service Contract Pro users.

Get Support
E-Learning

RFEM 6 for Beginners

RFEM 6 for Students

Programming with RFEM 6 and Python

RFEM 6 with Rhino & Grasshopper

RFEM 5 for Beginners

Modeling with RFEM 5

Structural Analysis Learning Videos for Students

Quick Tutorials for Dlubal Programs

Best Tips and Tricks in RFEM

Dlubal Online Training Recordings

Recorded Dlubal Webinars
Students and Schools

Free Structural Analysis Software for Students

Request or Renew Free Student License

Request for Free Instructor License

Submit Thesis

Why Submit Your Thesis?

Graduation Theses with Dlubal Structural Analysis Software

Free Structural Analysis Software for Educational Institutions

Request School Package

Free Introductory Training at Your University

Request Training Date
Knowledge Platform

First Steps with RFEM

Videos

Online Manuals

Structural Analysis Wiki

Knowledge Base

Frequently Asked Questions (FAQ)
Infotainment

Podcast

Dlubal Blog

Introduction to Structural Analysis and Design
First Steps with RFEM 6

Take your first steps with RFEM 6 and discover how quickly you can model and calculate. Customize with add-ons for even more possibilities.

Get Started

Free Structural Analysis Software for Students

Thousands of students worldwide already benefit from Dlubal Software. Enjoy free access, training, and expert support throughout your studies.

Get Free License
About Us

History and Facts

Company Philosophy

Why Dlubal Software?

Product Comparison

Quality Policy

Our Team
Contact

Dlubal Locations Worldwide

Authorized Dlubal Resellers
References

Customer Reviews

Customer Projects

Why submit your customer project?

Verification Examples

Your Review

Participation in Research Projects
Our Customers

We present our customers who realize their projects with Dlubal Software. Learn how our customers worldwide implement innovative solutions in construction and engineering using advanced tools for structural analysis and dynamic analysis.
View Our Customers
Building Success Together

Discover how leading engineers around the world trust our solutions to elevate their projects with us.

See Our Customers

Meet the Experts

Our dedicated engineers are here to assist you with modeling, design, and technical challenges—anytime, anywhere.

Connect with Support
Career

Jobs

Teams

Colleague Blog

Insights
Jobs

All Open Positions

Product Development

Customer Support

Sales

Marketing

Software Development

Administration

Interns

Others
Teams

Product Development

Customer Service

Sales

Marketing

Software Development

Administration
Why Dlubal?

Employee Benefits
Build Your Future with Us

Reveal how our team shapes the future of engineering. Experience innovation, growth, and exciting challenges.

Your Career Opportunities

Find Your Dream Job

Join a global leader in engineering software and take your career to new heights.

Explore Open Positions
Webshop

90-Day Free Trial

Back to Formulas

15x

002223

2026-02-03

Volumetric Strain Invariant, ε_v

Volumetric strain invariant ε_v

ε_{v} = ε_{11} + ε_{22} + ε_{33}

Strain invariant

;