General
The purpose of the app is to perform moment - curvature analysis of rectangular reinforced concrete sections with or without axial load. The app is still under development. A Beta version can be downloaded from Google Play Store:
Disclaimer
Beta version of the app.
NOT FOR DESIGN! NOT FOR ASSESSMENT OF REAL STRUCTURES!
App is currently in testing phase.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
Source code
The source code of the main function dealing with the moment - curvature analysis is available on GitHub: https://github.com/brisidi/moment-curvature (source code does not include the Graphical User Interface - GUI).
How to contribute:
directly contact the author for suggestions, recommendations, errors, bug fixes etc., or
directly contribute on GitHub.
Privacy Policy
The app does not collect any data from users.
Instructions
Geometry and axial load:
The following data should be provided:
h (mm) - depth of the cross section, in millimeters. The moment acts about an axis perpendicular to h;
b (mm) - width of cross section, in millimeters.
Cover (mm) - this is the minimum distance from the confined core to the edge of the section, assumed to be uniform for all edges.
Reinforcement bars are defined by their coordinates x and y and the diameter Φ (all in millimeters). Press "+" to add a bar and "-" to remove a bar with the given x, y and Φ.
N, in kN, in the axial load, compression positive, tension negative.
Materials:
In the current version of the app, tensile strength of concrete is neglected. The stress-strain curve follows a parabolic law up the compressive strength fc (fc,c for the confined core), corresponding to strain εc0 (εc0,c for the confined core). For larger strains, a linear relationship is assumed until the ultimate point with strain εcu (εcu,c for the confined core) and stress fcu (fcu,c for the confined core).
In the current version of the app, a bilinear law of steel is assumed. The modulus of elasticity of steel is assumed to be 200 GPa. Steel yielding stress fy should be provided in MPa. The strain hardening ratio is the ratio between post-yield tangent and the modulus of elasticity. The ultimate strain (unitless) should also be provided.
After the ultimate point, the stress drops to zero for both concrete and steel.
All material properties should be provided as positive numbers.
Stress-strain curves for concrete (confined and unconfined) are displayed in the following screen.
Advanced controls:
IMPORTANT: Use the "advanced controls" only when the analysis fails to converge. This feature is still experimental. It includes:
No. of points - number of points in the moment - curvature curve. In the current version the points are evenly distributed in the curvature axis.
Tolerance (mm) - neutral axis depth tolerance while checking equilibrium.
Max. iterations - maximum number of iterations;
No. fibres core - number of fibres through the confined core;
No. fibres cover - number of fibres through the unconfined cover.
Results:
Strain and stress profiles are provided if the analysis converges for more than 1 value of the curvature. Move the slider to update the analysis step.
The next screen shows the moment - curvature curve, including characteristic points, which are currently defined as follows:
cover spalling - when the strain in the top fiber of the section exceeds εcu;
steel yielding - when first yielding of bars is detected;
core crushing - when the strain in the top fiber of the confined core exceeds εcu,c;
steel rupture - when strain in one bar exceeds ultimate strain.
Export results:
The moment - curvature pairs can be copied to clipboard and pasted into other apps. The results are formatted as text in two columns separated by spaces.
This is how the app looks like:
Future developments
The following is a non-exhaustive list of known deficiencies and future plans:
improve convergence for tensile loading;
check buckling of compression reinforcement;
improve convergence for high axial loads;
further test the app;
improve the accuracy of determining the characteristic points (yield, spalling etc.). Currently the accuracy depends on the number of points in the moment - curvature curve.
add US customary units;
use same scale for x and y axes at the cross section plot;
improve GUI for large screens (center text), improve reinforcement input (consider showing a list of bars);
add unit tests.
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