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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"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\n",
"=====================================\n",
"\n",
"Lab #2 - Static beam deflections with strain gage\n",
"=====================================\n",
"\n",
"# What is a Strain Gage?\n",
"\n",
"[**A strain gage**](https://www.youtube.com/watch?v=Mts5Cr_BNCg&ab_channel=SkillLync) 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": [
"# Digital Image Correlation\n",
"\n",
"<https://github.com/dicengine/dice>\n",
"\n",
"![DICe Digital Image Correlation engine](https://cloud.githubusercontent.com/assets/15202746/26112065/167c12b0-3a14-11e7-8361-a4978dc54bf0.png)\n",
"\n",
"Digital image correlation (DIC) is a method to track movement of groups of pixels with sub-pixel accuracy used in solid mechanics \\[0\\]. A region of interest (ROI) is chosen, shown in green above, and groups of pixels are tracked in subsequent \"deformed\" images. \n",
"\n",
"In this lab, we will use DIC to determine the curvature $\\kappa$ in 1/pixels and multiply by the thickness in pixels to determine the strain on the surface of the beam. The kinematics is detailed in the next section \"Validate strain gage measurements\""
]
},
{
"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 $z$, $\\delta$, 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",
"- take a picture using a cross-hair to get the beam as close to horizontal as possible\n",
"\n",
"- Apply a known tip displacement by applying a load on the beam at multiple\n",
" locations 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",
"- take a picture of the deformed beam\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 6000 pixels long by 500 pixels thick and it deflects 700 pixels at the tip, determine the following:\n",
"\n",
"a. displacement `w300` of the beam 300 pixels from the base\n",
"\n",
"b. the curvature `k300` of the beam 300 pixels from the base \n",
"\n",
"c. the strain `e300` of the beam 300 pixels from the base"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Nice work!\n"
]
},
{
"data": {
"text/plain": [
"2"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# your work here\n",
"\n",
"p.check_p01(w300,k300,e300)"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Shape of deflected \\n cantilever beam')"
]
},
"execution_count": 33,
"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(r'deflection of neutral axis w(x) (mm)',wrap = 'True')\n",
"plt.title('Shape of deflected \\n cantilever beam')"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Curvature of deflected \\n cantilever beam')"
]
},
"execution_count": 34,
"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)',wrap=True)\n",
"plt.ylabel(r'curvature of neutral axis w(x) (1/m)')\n",
"plt.title('Curvature of deflected \\n cantilever beam')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Using DICe results files\n",
"\n",
"You can load the displacement calculated in DICe into your Python workspace for analysis. Included here is a folder \"results-dice\" with 2 images, the reference and the deformed image. The following creates two arrays from the two image analyses (reference = 0 and deformed = 1)\n"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fcd36cfcdf0>"
]
},
"execution_count": 7,
"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": [
"data0=pd.read_csv('./results-dice/DICe_solution_00.txt')\n",
"data1=pd.read_csv('./results-dice/DICe_solution_01.txt')\n",
"plt.plot(data0['COORDINATE_X']+data0['DISPLACEMENT_X'],data0['COORDINATE_Y']+data0['DISPLACEMENT_Y'],'o',label='reference')\n",
"plt.plot(data1['COORDINATE_X']+data1['DISPLACEMENT_X'],data1['COORDINATE_Y']+data1['DISPLACEMENT_Y'],'o',label='deformed')\n",
"\n",
"plt.xlabel('camera x-axis')\n",
"plt.ylabel('camera y-axis')\n",
"plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The raw data has two problems:\n",
"\n",
"1. The deformed image has poorly tracked regions\n",
"\n",
"2. The reference image is not a flat line (the camera is tilted)\n",
"\n",
"\n",
"\n",
"We fix these issues with two solutions:\n",
"\n",
"1. Use a measure of how well the regions were tracked be the image correlation method\n",
"\n",
"2. Use best-fit lines to determine the shape of the "
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fcd3832b970>"
]
},
"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": [
"data0=data0[data1['UNCERTAINTY']>0.05]\n",
"data1=data1[data1['UNCERTAINTY']>0.05]\n",
"X0=data0['COORDINATE_X']+data0['DISPLACEMENT_X']\n",
"Y0=data0['COORDINATE_Y']+data0['DISPLACEMENT_Y']\n",
"X1=data1['COORDINATE_X']+data1['DISPLACEMENT_X']\n",
"Y1=data1['COORDINATE_Y']+data1['DISPLACEMENT_Y']\n",
"plt.plot(X0,Y0,'o',label='reference')\n",
"plt.plot(X1,Y1,'o',label='deformed')\n",
"\n",
"plt.xlabel('camera x-axis')\n",
"plt.ylabel('camera y-axis')\n",
"plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In the graph above all the points with 'UNCERTAINTY'<0.05 were removed. This is a measure made during the cross-correlation method \\[0\\]. "
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"from scipy.optimize import curve_fit\n",
"\n",
"def reference_line(x,A,B):\n",
" return A*x+B\n",
"\n",
"def deformed_line(x,A,B,C,D,E):\n",
" return A*x**4+B*x**3+C*x**2+D*x+E\n",
"\n",
"Al,pcov=curve_fit(reference_line, X0, Y0)\n",
"A0,B0=Al\n",
"Aq,pcov=curve_fit(deformed_line, X1, Y1)\n",
"A1,B1,C1,D1,E1=Aq[:]"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fcd36cf7340>"
]
},
"execution_count": 10,
"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": [
"Y0_fit=reference_line(X0,A0,B0)\n",
"Y1_fit=deformed_line(X1,A1,B1,C1,D1,E1)\n",
"x_fit=np.linspace(np.min(X0),np.max(X0))\n",
"\n",
"plt.plot(X0,Y0-Y0_fit,'o',label='reference')\n",
"plt.plot(X1,Y1-Y0_fit,'o',label='deformed')\n",
"plt.plot(X0,Y0_fit-Y0_fit,label='ref fit')\n",
"plt.plot(x_fit,deformed_line(x_fit,A1,B1,C1,D1,E1)-reference_line(x_fit,A0,B0),label='def fit')\n",
"\n",
"plt.xlabel('x-axis')\n",
"plt.ylabel('y-axis')\n",
"plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In the figure above, we have done 3 things:\n",
"\n",
"1. removed the untracked sections of the beam\n",
"\n",
"2. subtracted a line of best fit for the reference and deformed images\n",
"\n",
"3. plotted the displacement of the beam"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Problem 2\n",
"\n",
"Based upon the deformation from the reference to the deformed configuration, write a function that returns the strain on the surface of the deformed beam if the beam is 7 pixels thick. *Hint: you'll have to calculate the second derivative of the displacement and use $\\epsilon = -z\\kappa"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"def strain_in_beam(x,A,B,C,D,E):\n",
" '''function to return the strain in a beam that has the shape:\n",
" w(x) = A*x**4+B*x**3+C*x**2+D*x+E\n",
" the thickness of the beam is t=7 px in this case'''\n",
" t=7\n",
" # your work here e=...\n",
" \n",
" \n",
" return e\n"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Function output:strain in example locations\n",
"[0.0003892 0.0002422 0.0001708 0.0002548]\n",
"Actual output:strain in example locations\n",
"[0.0003892 0.0002422 0.0001708 0.0002548]\n",
"1.4103859859674254e-15\n",
"Nice work!\n"
]
},
{
"data": {
"text/plain": [
"2"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import check_lab02 as p\n",
"p.check_p02(strain_in_beam)"
]
},
{
"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": 13,
"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": 14,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[1895473.37722433]\n",
"75927572.83948949\n",
"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": 14,
"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",
"print(EI)\n",
"print(pcov[0,0])\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 measured dependent variable (here the moment )"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0, 0.5, 'Error=$M-EI\\\\kappa$')"
]
},
"execution_count": 15,
"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": [
"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": [
"*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)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}