General solution Extent of beam path (1)Reference: https://en.wikipedia.org/wiki/Line-line_intersection Extent of beam path (2) Extent of beam path (3) Extent of beam path (4) Finite width beam (1) Finite width beam (2) Finite width beam (3) Finite width beam (3)

# Category: Mathematics

# Mathematics for Structural Engineers

1. I revisited calculus, and this solution to determine the moment of inertia of a circular cross-section. Moment of inertia of a circular cross-section 2. What is the strongest beam I can cut from a given log. Strongest beam statement Strongest beam solution Strongest beam diagram

# MIT Math Test 1876

Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 And here is the Jupyter notebook solving the problems using computer algebra (CA). The CA for the five problems was done using the Sympy module, the Python language, and a Jupyter notebook. Click on download to get the Jupyter notebook: (you might need to right […]

# Best of Seven Outcome Probability Dec 2020

Static Plots Using PLOTLY live plots Each chart series can be toggled off and on by clicking its legend entry. On a desktop device, reset the chart to full scale by reloading the web page. On a mobile device, reset the chart to full scale by double clicking. Team A Winning Outcomes The best of […]

# Structural Analysis, Finite Difference Method, Pythonista, and Plotly Oct 2020

Beam Problem — Hand Calculation PDF LINK — beam analysis — hand calculations The 5 page calculation in the PDF was done in 1983. The quidiagonal matrix solution was probably done with an HP-41 calculator program. Beam Problem — Plotly Graph LIVE LINK to HTML PAGE — using Plotly The Plotly graph shows deflections, shears, […]

# Gauss Profile Jun 2020

From the wiki https://en.wikipedia.org/wiki/Gaussian_function (go to wiki)

# Yield Line Theory — Rotation Angles Feb 2020

In this post, I provide derivations for the rotation angles between planes. We have two formulas: An exact formula [Eq 1] An approximate (easy and sufficient) formula [Eq 2] My link to my calculations Link to Blodgett Example

# The Lincoln Index — Software Bugs Jan 2020

John, Thanks for the presentation. https://www.johndcook.com/blog/2010/07/13/lincoln-index/ How many errors are left to find?

# Calculate Beta w for Single Angles Dec 2019

AISC v15.0 Shapes Database # NOTE # For enhanced readability and easier translation to other software, # exponents are indicated with the (mathematically) traditional caret symbol. # In Python, replace all carets with a double asterisk. # Get single angle properties a = np.arctan(my_angle.TANA) c = np.cos(a) s = np.sin(a) b = my_angle.B_LOWERCASE d = […]

# Three Blue One Brown Feb 2019

Here is a beautiful website by Grant Sanderson. 3blue1brown So many exciting insightful mathematics presentations. The craft and artistry are as impressive as the mathematical concepts. Take a look — even if you think you know the material — you will see a few new gems (I bet).

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