Shear formula calibration

Reliability-based calibration of Eurocode-2 and fib Model Code shear resistance formulas.

• Supporting code to the paper: Slobbe A., Rozsas A., Yuguang Y. () A reliability-based calibration of shear resistance formulas for reinforced concrete members without shear reinforcement (under review).
• Mixing Matlab, Python, and R due to time constraints.
• If you have a question related to the code please open an issue.

Dependencies

Matlab:

• developed under Matlab 2021b (earlier under 2018b)
  • Statistics and Machine Learning Toolbox
  • Optimization Toolbox
  • Global Optimization Toolbox
  • Parallel Computing Toolbox (to reduce wall clock time)
  • (only for testing: Deep Learning Toolbox (combvec))
• add to your path:
  • custom_FERUM: the entire repository
  • Statistics---Matlab: the content of the distribution_functions\univariate\ folder
  • Plotting-Matlab: the content of the distribution_functions\univariate\ folder (used to make prettier plots, non-essential)
  • export_fig

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Overview

The header names follow that of the folders.

pre_processing

model_uncertainty

• MatLab
• simple statistical analysis to infer model uncertainty based on experiments

random_variable_algebra

• Python
• generate pdf and cdf of the product of random variables

calibration

• MatLab
• reliability-based calibration
  • partial factor(s): main_calibration.m
  • representative value in semi-probabilistic format: main_calibration_Ck.m
• uses results from pre_processing

post_processing

• R (because MatLab is inconvenient for plotting)
• visualization of the results + shiny web server for quick and interactive data exploration
• A live version (not necessary the most up to date) of the visualization webserver is available from here.

Additional information may be found in dedicated README files in the respective folders.

On using the repository

• Running the code:
  • Matlab: run from the folder of the particular file.
  • R: run from the folder of the particular file (programatically ensured if RStudi is used).
  • python: to be run with the working directory set as the root directory of the repository: \shear_calibration\.
• Developed and tested under
  • Windows 10.
  • Python 3.x (pacal)
  • R 3.x
  • Matlab 2018a
• Install Python dependencies using the requirements.txt file.

If action (wind and snow) random variable inputs change:

1. compute product distributions using pacal (code\pre_processing\random_variable_algebra\pacal_product.py); output: *.txt files
2. Run code\pre_processing\random_variable_algebra\prepare_pacal_for_ferum.m; output: \code\calibration\tmp\*.txt
3. To reduce runtime copy of the content of the txt files from 2) into the relevant *_pdf.m and *_cdf.m files in \code\calibration\calibration_utils\reliability_analysis\

Notes on the probabilistic models

Click to expand!

General notes

to be added: pacal, etc.

Particular models

• traffic load:
  • model uncertainty (theta_T):
    • based on table 10.3 of ¹, considering all components but the load effect component because that we model separately (theta_E)
    • its mean is set to 1.0 because it is just a scaler, we scale the model/load during inverse design
    • our expert judgement: the representative value is assumed to be equal to the mean
  • time-dependent compoponent (T)
    • Gumbel, CV; based on ¹
    • the characteristic value of theta_T*T has a 1-1/1000 non-exceedance probability after ²
    • from the previous points the P_repr value of T can be computed (see pacal_product.py):
      • x_repr = F^{-1}_{theta_T*T}(1-1/100)
      • P_repr_T = F_{T}(x_repr)

Improvement ideas

• improve documentaton
• implement everything in one language (probably python would be the best choice)

Footnotes

1. Steenbergen, R. D. J. M., Morales Napoles, O., Vrouwenvelder, A.C.W.M. (2012). Algemene veiligheidsbeschouwing en modellering van wegverkeerbelasting voor brugconstructies. Retrieved from Delft ↩ ↩²

2. CEN. (2003a). Eurocode 1: Actions on structures - Part 2: Traffic loads on bridges. ↩