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{
"cells": [
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"from scipy.stats import norm, t\n",
"\n",
"import matplotlib.pyplot as plt\n",
"import pandas as pd\n",
"plt.rcParams.update({'font.size': 22})\n",
"plt.rcParams['lines.linewidth'] = 3\n",
"\n",
"import check_lab02 as p"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"ME 3263 Introduction to Sensors and Data Analysis (Fall 2018)\n",
"=====================================\n",
"\n",
"Lab #2 - Static beam deflections with strain gage\n",
"=====================================\n",
"\n",
"# What is a Strain Gage?\n",
"\n",
"A strain gage consists of a looped wire that is embedded in a thin backing. Two\n",
"copper coated tabs serve as solder points for the leads. See Figure 1a. The\n",
"strain gage is mounted to the structure, whose deformation is to be measured. As\n",
"the structure deforms, the wire stretches (increasing its net length ) and its\n",
"electrical resistance changes: $R=\\rho L/A$, where $\\rho$ is the material\n",
"resistivity, $L$ is the total length of the wire, and $A$ is the cross sectional\n",
"area of the wire. Note that as $L$ increases, the cross sectional area changes as\n",
"well due to the Poisson contraction; the resistivity also changes."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"![Figure 1: a) A typical strain gage. b) One common setup: the gage is\n",
"mounted to measure the x-direction strain on the top surface. It's\n",
"engaged in a quarter bridge configuration of the Wheatstone bridge\n",
"circuit.](./figure_01.png)\n",
"\n",
"*Figure 1: a) A typical strain gage. b) One common setup: the gage is\n",
"mounted to measure the x-direction strain on the top surface. It's\n",
"engaged in a quarter bridge configuration of the Wheatstone bridge\n",
"circuit.*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Validate static strain gage measurements\n",
"\n",
"In this lab we will calibrate strain measurements using Euler-Bernouli beam theory\n",
"kinematics \\[1\\]. The axial strain in a beam is directly proportional to the distance\n",
"from the neutral axis and curvature as such"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$\\epsilon_x=-\\kappa z$. (1)\n",
"\n",
"The curvature of the beam is approximated as such\n",
"\n",
"$\\kappa=\\frac{d^2 w}{dx^2}$. (2)\n",
"\n",
"Equations 1 and 2 relate beam deflection to axial strain. These are called\n",
"kinematic equations because they define the geometry of the beam deflection. \n",
"\n",
"The Euler-Bernouli beam theory uses Newton's second law (kinetics) and Hooke's\n",
"law (constitutive) to derive the linear equations of motion for one dimensional\n",
"deformable objects \\[1,4\\]. The relation between a static applied force q(x) and static\n",
"deflection w(x) is as such\n",
"\n",
"$\\frac{\\partial^2}{\\partial x^2}\\left(EI\\frac{\\partial^2 w}{\\partial\n",
"x^2}\\right)=q(x)$ (3)\n",
"\n",
"where $E$ is the Young's modulus, $x$ is the distance along the neutral axis,\n",
"and $I$ is the second moment of area of the beam's cross-section. For a\n",
"rectangular cross-section $b \\times t$, width by thickness the second moment of\n",
"area is\n",
"\n",
"$I=\\frac{bt^3}{12}$. (4)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We will design our strain gage validation such that $E$ and $I$ are not necessary. The boundary conditions for a clamped beam that is\n",
"deflected by a distance $\\delta$ are $w(0)=0$, $w'(0)=0$, $w(L)=\\delta$, and\n",
"$w''(L)=0$. Therefore, the functions $w(x)$ and $w''(x)$ can be determined by\n",
"integrating equation 3 four times and using the four boundary conditions as such\n",
"\n",
"$w(x)=-\\frac{1}{2}\\left(\\frac{\\delta}{L^3}x^3-3\\frac{\\delta}{L^2}x^2\\right)$ (5a)\n",
"\n",
"and the curvature \n",
"\n",
"$w''(x)=-\\left(3\\frac{\\delta}{L^3}x-3\\frac{\\delta}{L^2}\\right)$ (5b)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Using equations 5a-b, the only quantities needed to determine strain at a given\n",
"location on a linear, homogeneous beam are $z$, $\\delta$, $w(L)$, and $L$. \n",
"\n",
"![Figure 2: Diagram of the validation process. The strain gage is placed at a distance $x_{SG}$ from the cantilever support. A linear-elastic beam of length $L$ is deflected by distance, $\\delta$.](./figure_02.png)\n",
"\n",
"*Figure 2: Diagram of the validation process. The strain gage is placed at a distance $x_{SG}$ from the cantilever support. A linear-elastic beam of length $L$ is deflected by distance, $\\delta$.*\n",
"\n",
"- Apply a known tip displacement as seen in Figure 2. Measure and record the strain at your strain\n",
" gage location, the displacement, $\\delta$ and length where load was applied,\n",
" $L$.\n",
"\n",
"- Calculate the strain at the location of the strain gage using equations 1,2,\n",
" and 5a-b.\n",
" \n",
"Below are two functions that calculate displacement and curvature given a bar of length `L`, that is deflected by a distance, `delta`."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"def disp_at_x(x,L,delta):\n",
" '''returns the displacement w(x) given the position, x, \n",
" length of bar, L, and displacement at L, delta'''\n",
" wx=-1/2*(delta/L**3*x**3-3*delta/L**2*x**2)\n",
" return wx\n",
"\n",
"def k_at_x(x,L,delta):\n",
" '''returns the curvature w''(x) given the position, x, \n",
" length of bar, L, and displacement at L, delta'''\n",
" wx=-(3*delta/L**3*x-3*delta/L**2)\n",
" return wx\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"displacement of 400 mm bar deflected 10 mm, 20 mm from support =0.037 mm\n",
" curvature of 400 mm bar deflected 10 mm, 20 mm from support =0.178 1/m\n"
]
}
],
"source": [
"w20mm=disp_at_x(20,400,10)\n",
"k20mm=k_at_x(20,400,10)\n",
"print('displacement of 400 mm bar deflected 10 mm, 20 mm from support =%1.3f mm'%w20mm)\n",
"print(' curvature of 400 mm bar deflected 10 mm, 20 mm from support =%1.3f 1/m'%(k20mm*1000))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Problem 1\n",
"\n",
"If your beam is 400 mm long by 10 mm thick and it deflects 15 mm at the tip, determine the following:\n",
"\n",
"a. displacement `w400` of the beam 20 mm from the base\n",
"\n",
"b. the curvature `k400` of the beam 20 mm from the base \n",
"\n",
"c. the strain `e400` of the beam 20 mm pixels from the base"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# your work here\n",
"\n",
"p.check_p01(w400,k400,e400)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Shape of deflected cantilever beam')"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"x=np.linspace(0,400)\n",
"wx=disp_at_x(x,400,10)\n",
"plt.plot(x,wx)\n",
"plt.xlabel('position along beam (mm)')\n",
"plt.ylabel('deflection of neutral \\naxis w(x) (mm)')\n",
"plt.title('Shape of deflected cantilever beam')"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Curvature of deflected cantilever beam')"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"x=np.linspace(0,400)\n",
"kx=k_at_x(x,400,10)\n",
"plt.plot(x,kx*1000)\n",
"plt.xlabel('position along beam (mm)')\n",
"plt.ylabel('curvature of neutral \\naxis \\\\w(x) (1/m)')\n",
"plt.title('Curvature of deflected cantilever beam')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Problem 2\n",
"\n",
"If your beam is 400 mm long by 10 mm thick and it deflects 15 mm at the tip, determine the position along the beam for the following:\n",
"\n",
"a. Where is the maximum deflection in the beam? save as `x_max_defl`\n",
"\n",
"b. Where is the maximum curvature in the beam? save as `x_max_curv`\n",
"\n",
"c. Where is the maximum strain in the beam? save as `x_max_strain`"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"import check_lab02 as p\n",
"\n",
"p.check_p02(x_max_defl,x_max_curv,x_max_strain)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Measure constitutive properties\n",
"\n",
"## Constitutive Model\n",
"Now the strain gage should be calibrated. We need to determine the Young's modulus, $E$ and second moment of area, $I$. This measurement requires three components: kinematic (which we solved in the validation), kinetic ($\\sum{F}=0$), and a constitutive model (Hooke's Law). The constitutive equation for a linear-elastic beam subject to a moment is as such\n",
"\n",
"$M=EI\\kappa$. (6)\n",
"\n",
"In equation 6, $M$ is the applied moment, $E$ is the Young's modulus, $I$ is the second moment of inertia of the area of the beam, and $\\kappa$ is the curvature of the beam. The constant $I$ is based upon the geometry from equation 4. The material constant $E$ is unknown. \n",
"\n",
"Use the weights to apply forces at different distances, $r$, from the support as seen in Figure 3. Increasing the weight or the distance the weight is applied will increase the applied moment. Use Table 1 to record the trial no., strain, force, distance, and moment. Use at least two trials per measurement. \n",
"\n",
"![Figure 3: A linear-elastic beam of length $L$ has a force applied at distance, $r$. \n",
"The strain gage is placed at a distance $x_{SG}$ from the cantilever support.](./figure_03.png)\n",
"\n",
"*Figure 3: A linear-elastic beam of length $L$ has a force applied at distance, $r$. \n",
"The strain gage is placed at a distance $x$ from the cantilever support.*\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Fitting your data to your model\n",
"\n",
"Once you have filled in a number of data points for $\\kappa$ and $M$, you can use a linear regression to determine the slope of the data. The constitutive model in equation (6) predicts that the moment and curvature will be related by a proportional constant, $EI$. If we know $EI$, the total squared error is as such\n",
"\n",
"$SSE=\\sum_i^N{(M_i-EI\\kappa_i)^2}$ (7)\n",
"\n",
"where SSE is the sum of squares error between the predicted moment and measured moment for the $i^{th}$ measurement with $N$ total measurements [\\[2\\]](https://www.amazon.com/Numerical-Methods-Engineers-Steven-Chapra/dp/0073401064). We can choose a of $EI$ that minimizes $SSE$, but it will never be zero. Below is an example calculation for a linear least squares regression in python for a beam with cross-section $12\\times3$ mm."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"k=np.array([6.95685737e-07, 9.93992373e-06, 3.25200211e-05, 3.55750721e-05,\n",
" 5.32023782e-05, 7.48128585e-05, 7.61625461e-05, 8.54476229e-05,\n",
" 1.02089509e-04, 1.02841452e-04, 1.32351731e-04, 1.43996022e-04,\n",
" 1.45204793e-04, 1.56867759e-04, 1.73435915e-04, 1.95625232e-04,\n",
" 2.00670618e-04, 2.12900332e-04, 2.24582886e-04, 2.41141396e-04,\n",
" 2.45991618e-04, 2.55608426e-04, 2.76117673e-04, 2.96128593e-04,\n",
" 3.07157389e-04, 3.20509718e-04, 3.20363196e-04, 3.35535814e-04,\n",
" 3.53706984e-04, 3.64130433e-04])\n",
"M=np.array([ 0. , 23.82866379, 47.65732759, 71.48599138,\n",
" 95.31465517, 119.14331897, 142.97198276, 166.80064655,\n",
" 190.62931034, 214.45797414, 238.28663793, 262.11530172,\n",
" 285.94396552, 309.77262931, 333.6012931 , 357.4299569 ,\n",
" 381.25862069, 405.08728448, 428.91594828, 452.74461207,\n",
" 476.57327586, 500.40193966, 524.23060345, 548.05926724,\n",
" 571.88793103, 595.71659483, 619.54525862, 643.37392241,\n",
" 667.20258621, 691.03125 ])"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Best fit for Young's Modulus is 70.2 +/- 0.3 GPa\n"
]
},
{
"data": {
"text/plain": [
"Text(0, 0.5, 'Moment (N-mm)')"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from scipy.optimize import curve_fit\n",
"\n",
"def func(x,EI):\n",
" return EI*x\n",
"\n",
"EI,pcov=curve_fit(func, k, M)\n",
"EI_error=np.sqrt(pcov[0,0])\n",
"I=12*3**3/12.0\n",
"print(\"Best fit for Young's Modulus is %1.1f +/- %1.1f GPa\"%(EI/I*1e-3,EI_error/I*1e-3))\n",
"\n",
"plt.plot(k*1e3,M,'o',label='experiment')\n",
"plt.plot(k*1e3,func(k,EI),label='model')\n",
"plt.legend()\n",
"plt.xlabel('curvature (1/m)')\n",
"plt.ylabel('Moment (N-mm)')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Note:*\n",
"\n",
"The least-squares method used above can be used to fit any function to a data set. You would just need to update the `func` definition to return the desired function based upon your unkown fitting constants. \n",
"\n",
"The outout `popt` is the covariance matrix [\\[3\\]](./least_squares-error_with_covariance.pdf). In practice, we can use the square root of the diagonal terms to estimate the error in our least-squares fit. We make a few assumptions when performing this best-fit:\n",
"\n",
"1. There is a random error in the measured dependent variable (here the moment $M$). \n",
"\n",
"2. There is no error in the reported independent variable (here the curvature $\\kappa$).\n",
"\n",
"3. The measured dependent variables are uncorrelated with the measured error\n",
"\n",
"4. The random error has a mean of zero\n",
"\n",
"We can test assumption 4 by plotting the \"residuals\" of the fit i.e. the error. The plot below demonstrates that our data has a mean error of 0 and is uncorrelated with the random error. \n",
"\n",
"Our best-fit model has removed _systematic uncertainty_, but it cannot account for _random uncertainty._"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0,0.5,'Error=$M-EI\\\\kappa$')"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(k*1e3,M-func(k,EI),'o')\n",
"plt.xlabel('curvature (1/m)')\n",
"plt.ylabel(r'Error=$M-EI\\kappa$')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Problem 3\n",
"\n",
"If the thickness of the beam is not measured properly, you can have large systematic errors in your results. In the example above, the width of the beam was 12 mm and the thickness of the beam was 3 mm. On the line, \n",
"\n",
"`I = 12*3**3/12.0`\n",
"\n",
"Change the thickness to 3.1 mm and calculate `E31`\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
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"source": [
"import check_lab02.py as p\n",
"\n",
"p.check_p03(E31)"
]
},
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"source": [
"*Table 1: Fill in the measured and calculated values.*\n",
"\n",
"|trial|distance, $r$| force= $mg$|strain (mm/mm)|curvature (1/mm)|Moment=$r\\times F$|\n",
"|---|---|---|---|---|---|\n",
"|1|\n",
"|1|\n",
"|1|\n",
"|1|\n",
"|1|\n",
"|1|\n",
"|1|\n",
"|1|\n",
"|1|\n",
"|1|\n",
"|1|\n",
"|1|\n",
"|1|\n",
"|1|\n",
"|1|\n",
"|1|\n",
"|1|\n",
"|1|\n",
"|1|\n",
"|1|\n",
"|1|\n",
"|1|\n",
"|1|\n",
"|1|\n",
"|1|\n",
"|\n",
"|2|\n",
"|2|\n",
"|2|\n",
"|2|\n",
"|2|\n",
"|2|\n",
"|2|\n",
"|2|\n",
"|2|\n",
"|2|\n",
"|2|\n",
"|2|\n",
"|2|\n",
"|2|\n",
"|2|\n",
"|2|\n",
"|2|\n",
"|2|\n",
"|2|\n",
"|2|\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Your Report \n",
"\n",
"1. Introduction\n",
"\n",
" \n",
"\n",
"2. Procedure\n",
"\n",
"\n",
"3. Results and Discussion\n",
"\n",
"\n",
"4. Conclusion\n",
"\n",
"\n",
"### References\n",
"\n",
"References\n",
"\n",
"0. Sutton, M. A., Orteu, J. J., & Schreier, H. (2009). Image correlation for shape, motion and deformation measurements: basic concepts, theory and applications. Springer Science & Business Media.\n",
"\n",
"1. F.P. Beer and E.R. Johnson, Mechanics of Materials, 2nd Edition,\n",
"McGraw-Hill, 1992.\n",
"\n",
"2. S. Chapra, Numerical Methods for Engineers, ch. 14-15, 6th Edition, McGraw-Hill, 2009.\n",
"\n",
"3. [C. Salter, Error Analysis Using the Variance–Covariance Matrix, J. of Chem. Ed., 2000.](./least_squares-error_with_covariance.pdf)\n",
"\n",
"3. [Euler-Bernoulli Beam Theory - Wikipedia](https://en.wikipedia.org/wiki/Euler%E2%80%93Bernoulli_beam_theory) \n",
"\n",
"4. [Uncertainty\n",
"Notes courses.washington.edu](https://courses.washington.edu/phys431/uncertainty_notes.pdf)"
]
},
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"execution_count": null,
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"source": []
}
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