HW: Matplotlib

Purpose: Learn how to make graphs with different kinds of data.

Instructions

1. First, make a copy of the starter sheet here:

2. Rename it something like "(Your_Name)_HW_Matplotlib.ipynb"

3. Download each CSV to be used in parts 2 through 5:

   • 2013-2014-Pasadena-Temperature-Data.csv
   • June-2021-Provo-River-Streamflow-Rates.csv
   • Fremont-Bridge-Bicycle-Count.csv
   • 2012-US-Birth-Rates.csv

Part 1 - Shear and Moment Diagrams

For this exercise, we will be creating shear and moment diagrams for a simply supported beam. Such diagrams are used to better visualize the internal forces acting within the beam. The internal shear along the beam is represented by the variable \(V\), while the internal moment along the beam is represented by the variable \(M\). The shear diagram for the beam below is represented by the green graph while the moment diagram is represented by the red graph.

(image from https://mechanicalc.com/reference/beam-analysis)

We will be graphing the diagrams for the cantilevered simply supported beam shown below:

Where:

• \(L\) is the full length of the beam
• \(x\) is any point taken along the beam measured from its left end
• \(A\) is the pin support of the beam located at \(x=0 ft\)
• \(B\) is the roller support of the beam located at \(x=4 ft\)
• \(R_{A}\) is the reaction force of 170 \(lb\) associated with the pin support
• \(R_{B}\) is the reaction force of 410 \(lb\) associated with the roller support
• \(P_{1}\) is a point load of 100 \(lb\) acting at \(x=2 ft\)
• \(q_{1}\) is a distributed load of 120 \(lb/ft\) acting from \(x=0 ft\) to \(x=2 ft\)
• \(q_{2}\) is a distributed load of 120 \(lb/ft\) acting from \(x=4 ft\) to \(x=6 ft\)

After making a cut within the beam at a point of interest, the internal shear and moment equations can be solved by plugging in the above external forces and lengths into the following equilibrium equations:

\(\sum F_{y} = 0\)
\(\sum M = 0\)

The equations for the internal shear and moment forces are given to you. These can be modeled as piecewise functions with the functions changing at the points on the beam where the loads or supports change. You can then graph the results of these functions to create the shear and moment diagrams.

Here are the shear and moment equations

Shear

Moment

1. In the 'Part 1a - Shear Diagram' code block, define the following variables:

2. Define a variable x using np.linspace() with the following arguments:

• start: 0
• stop: \(L\)
• num: 500

3. Define a variable V using np.zeros_like() with x as the argument. This will create a list of zeros with the same length as x.
4. Create a for loop that loops over the length of x and defines V to be the following piecewise function under the respective boundary conditions:
   • A loop is easy to think about this, but you can use other methods if you prefer such as taking advantage of numpy's vector operations.

5. Using matplotlib, plot x against V and then replicate every element included in the graph below (the colors do not have to match exactly):

   

6. In the 'Part 1b - Moment Diagram' code block, copy and paste the variables defined in Part 1a.

7. Define a variable x using np.linspace() with the following arguments:

• start: 0
• stop: \(L\)
• num: 500

3. Define a variable M using np.zeros_like() with x as the argument.
4. Create a for loop that loops over the length of x and defines M to be the following piecewise function under the respective boundary conditions:

5. Using matplotlib, plot x against M and replicate every element included in the graph below (the colors do not have to match exactly):

   

Part 2 - Pasadena Temperature Data

You will now graph the temperature data from Pasadena, CA from 2013-2014.

1. In the 'Numpy Array Creation & Slicing' code block, create a numpy array from the CSV containing the temperature data. Use the code from the in-class as an example. Slice the array to create the x and y-axis values. These will correspond to the following columns in the CSV linked on readthedocs:

• x - Date
• y_1 - High Temperature
• y_2 - Low Temperature

2. In the 'Graphing the Data' code block, plot the data and replicate every element included in the graph below (the colors do not have to match exactly):

   

Part 3 - Provo River Streamflow Data

You will now graph the streamflow data of Provo River in June 2021.

1. In the 'Numpy Array Creation & Slicing' code block, create a numpy array from the CSV containing the streamflow data. Use the example code from the in-class exercise. Slice the array to create the x and y-axis values. These will correspond to the following columns in the CSV linked on readthedocs:

• x - Date
• y_1 - Site 10163000
• y_2 - Site 10155200
• y_3 - Site 10155500
• y_4 - Site 10154200
• y_5 - Site 10155000

2. In the 'Graphing the Data' code block, plot the data and replicate every element included in the graph below (the colors do not have to match exactly):

   

Part 4 - Fremont Bridge Bicycle Count Data

You will now graph bicycle count data over a bridge in Fremont, Seattle taken from 2013 to 2022.

1. In the 'Numpy Array Creation & Slicing' code block, create a numpy array from the CSV containing the Fremont bridge count data. Slice the array to create the x and y-axis values. These will correspond to the following columns in the CSV linked on readthedocs:

• x - Date
• y_1 - Fremont Bridge Total
• y_2 - Fremont Bridge East Sidewalk
• y_3 - Fremont Bridge West Sidewalk

2. In the 'Graphing the Data' code block, plot the data and replicate every element included in the graph below (the colors do not have to match exactly):

   

3. Write a comment in your code explaining why you think the bike count in later years are lower.

Part 5 - Average U.S. Daily Birth Data

You will now graph the average U.S. daily birth data taken from 2012 to 2013.

1. In the 'Numpy Array Creation & Slicing' code block, create a numpy array from the CSV containing the U.S. birth data. Then, slice the array to create the x and y-axis values. These will correspond to the following columns in the CSV linked on readthedocs:

• x - Date
• y_1 - Births

2. In the 'Graphing the Data' code block, plot the data and replicate every element included in the graph below (the colors do not have to match exactly. The arrow shapes also do not need to match exactly, but we do want curved arrows):

3. Write a comment explaining why you think the birth rate drops during the days we labeled on the graph.

Turning in/Rubric

REMINDER - For this class, you will only turn in the links to your colab notebooks. You will get a 0 for this assignment if you turn in a python file or a link that is not correct, wrong assignment, or does not give editor permission.

Rubric:

The following is not a part of the rubric, but specifies how you can lose points. For example: if you do not explain your code when using AI to help you create it or fail to share your link correctly.