<jupyter_start><jupyter_text>Universidade Federal do Rio Grande do Sul (UFRGS)   Programa de Pós-Graduação em Engenharia Civil (PPGEC)    Project PETROBRAS (2018/00147-5):  Attenuation of dynamic loading along mooring lines embedded in clay---_Prof. <NAME>, Dr.techn._ [(ORCID)](https://orcid.org/0000-0001-5640-1020)  Porto Alegre, RS, Brazil ___[1.   Introduction](https://nbviewer.jupyter.org/github/mmaiarocha/Attenuation/blob/master/01_Introduction.ipynb?flush_cache=true)  [2.   Reduced model scaling](https://nbviewer.jupyter.org/github/mmaiarocha/Attenuation/blob/master/02_Reduced_model.ipynb?flush_cache=true)  [3.   Typical soil](https://nbviewer.jupyter.org/github/mmaiarocha/Attenuation/blob/master/03_Typical_soil.ipynb?flush_cache=true)  [4.   The R4 studless 120mm chain](https://nbviewer.jupyter.org/github/mmaiarocha/Attenuation/blob/master/04_R4_studless_chain.ipynb?flush_cache=true)  [5.   Dynamic load definition](https://nbviewer.jupyter.org/github/mmaiarocha/Attenuation/blob/master/05_Dynamic_load.ipynb?flush_cache=true)  [6.   Design of chain anchoring system](https://nbviewer.jupyter.org/github/mmaiarocha/Attenuation/blob/master/06_Chain_anchor.ipynb?flush_cache=true)  [7.   Design of uniaxial load cell with inclinometer](https://nbviewer.jupyter.org/github/mmaiarocha/Attenuation/blob/master/07_Load_cell.ipynb?flush_cache=true)  [8.   Location of experimental sites](https://nbviewer.jupyter.org/github/mmaiarocha/Attenuation/blob/master/08_Experimental_sites.ipynb?flush_cache=true)<jupyter_code># Importing Python modules required for this notebook
# (this cell must be executed with "shift+enter" before any other Python cell)
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt<jupyter_output><empty_output><jupyter_text>7. Design of uniaxial load cell with inclinometerThe uniaxial load cell is designed for a 7.1kN bottom scale times a safety margin 2,hence maximum admissible load is 15.2kN. Conditioning electronics shall map this maximum load to approximatelly 3V. The chain under test is connected to the chain anchor [(see section 6)](https://nbviewer.jupyter.org/github/mmaiarocha/Attenuation/blob/master/06_Chain_anchor.ipynb?flush_cache=true)through a _bottom load cell_ (BLC) and to the loading hoist through the a _top load cell_ (TLC).Both BLC and TLC shall have exactly the same design.All connections are accomplished with steel shackles of compatible strength.Each cell is provided with strain gages in full bridge configuration and also with a MEMSaccelerometer ADXL203. The accelerometer will provide the chain angle to vertical direction. The basic cell geometry is presented in the following figure:Special attention must be drawn to the following features:1. The circular lateral notches are designed to concentrate stresses at the gages position,   according to the following abacus:    2. The central area has only 4.5mm thickness, calculated to increase stresses to the    aimed magnitude.3. The 6mm depth channel to be machined at the left side will accomodate the 6 way shielded    cable, providing stress relief and allowing a lower profile for the epoxi waterproof    protection.4. The ADXL203 is a bi-axial accelerometer that will be used as as inclinometer. The   signal must low-pass filtered for only the mean (DC) acceleration value will be used.       The analog voltage output is factory calibrated as 1V/G.   Dimensions are $5\times 5$mm and less than 2mm thick, such that it can be   easily covered by the epoxi protection. 5. The load cell conditioning must be linear up to $\approx 100$Hz, what will be    accomplished with a INA118 instrumentation amplifier. The amplification gain must   be set as calculated at the end of this notebook.6. The 4mm hole close to the cable channel is intended for wire connections between   both sides of the cell.   The script below provides the expected stress levels:<jupyter_code>Fmax =  2*7.1                  # bottom scale design load (kN)

t    =  0.0125                 # maximum thickness
H    =  0.0220 + 0.0250        # maximum width equals chain link width (m)
r    =  0.00625                # radius of lateral notches

b    =  t - 2*0.004            # central thickness
h    =  H - 2*r                # central width
σn   =  Fmax/(b*h)             # central nominal stress

print('Ratio H/h is:           {0:6.2f}   '.format(H/h))
print('Ratio r/h is:           {0:6.2f}   '.format(r/h))
print('Nominal stress is:      {0:6.2f}MPa'.format(σn/1000))

ks   =  2.0
σmax =  ks*σn/1000

print('Stress concentration is {0:6.2f}   '.format(ks))
print('Concentrated stress is: {0:6.2f}MPa'.format(σmax))<jupyter_output>Ratio H/h is:             1.36   
Ratio r/h is:             0.18   
Nominal stress is:       91.47MPa
Stress concentration is   2.00   
Concentrated stress is: 182.93MPa<jupyter_text>Hence the maximum stress is less than 200MPa, what is acceptable for a stainless steel of any grade.A Poisson ration $\nu = 0.3$ is used for the two gages disposed orthogonally to theloading axis. The strain gages are assumed to have a $k = 2.1$ gage factor (with $R = 350\Omega$ for minimizing current). Young's modulus for steel is assumed as $E = 205$GPa. Expected bridge voltage unbalance is given by:$$ \frac{\Delta V}{V} = \left(2 + 2\nu\right) \frac{k \sigma_{\max}}{4E}$$The bridge source voltage will be approximatelly 5V. The script below is used to estimate the required amplification gain for maping the maximumforce to 3V.<jupyter_code>k  =  2.1           # gage factor
nu =  0.3           # Poisson ratio
E  =  205000        # Young's modulus (MPa)

dV =  5.*(2 + 2*nu)*k*σmax/E/4
G  =  3./ dV

print('Maximum bridge unbalance:    {0:8.5f}V'.format(dV))
print('Required amplification gain: {0:8.0f}x'.format( G))<jupyter_output>Maximum bridge unbalance:     0.00609V
Required amplification gain:      493x
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