Category Archives: Construction

I regularly encounter interesting math, particularly geometry, in my woodworking and remodeling projects.

CO2 Generation By Fuel Per Million BTUs of Heat

My year-round cabin in northern Minnesota needs a furnace, and a furnace needs fuel. My fuel options are fairly limited – fuel oil, liquid natural gas, or propane. I ended up choosing propane because the local propane gas supplier has a reputation for being reliable. While researching the fuels, I became curious about the amount of CO2 released into the atmosphere by the different fuel options for given amount of heat. Continue reading

Posted in Construction, General Science | 1 Comment

My New Cabin Construction

A number of folks have asked that I post pictures of my cabin construction project. The project actually consists of two separate activities: a large garage (started last fall) and a two-story cabin. I will start posting photos here as things progress. Continue reading

Posted in Construction, Personal | 10 Comments

Effect of Earth’s Curvature on Suspension Bridge Dimensions

I have received a number of questions recently on how the curvature of the Earth affects building construction. In general, the effects of the Earth’s curvature are ignorable because most man-made construction is on too small of a scale to notice the effects of the Earth’s curvature. One well documented exception is the Verrazano-Narrows bridge, whose design took into account that the bridge towers are 1 5/8 inch farther apart at the top than at the bottom. In this post, I will show how to compute this value. Continue reading

Posted in Construction, General Science | 27 Comments

Using Excel’s Solver and VBA For Repetitive Table Calculation

I will be providing some employee training on Excel in January, and I need an example of how to automate the use of Excel’s Solver add-in – a powerful optimization tool that few engineers use effectively. When I give a training seminar, I make a serious effort to show how I use Excel on real problems. While I generally use Mathcad for most optimization applications, Mathcad does not support integer programming – an optimization method where some or all variables are restricted to be integers. Here is where Solver shines – it supports integer programming. Continue reading

Posted in Construction, Excel | 9 Comments

Radius Measurement Using Roller Gages

This post will demonstrate how to measure the radius of an arc using two roller gages. While I am a very amateur machinist, I have on occasion needed to measure the radius of an arc (i.e. partial circle) and have not been sure how to approach that measurement. It turns out to be simple given two equal diameter roller gages and a surface plate. You can determine by taking one measurement and knowing the roller gage diameter. Continue reading

Posted in Construction, Geometry, Metrology | 3 Comments

Homemade Roof Pitch Protractor

As an amateur carpenter, I am always looking for simple and cheap construction tools. Recently, I have been working on improving my roof framing knowledge. During my reading on this topic, I saw this roof pitch protractor in a Journal of Light Construction (JLC) article . Notice how the template has a handle to make hauling it up a ladder easier. To get an accurate roof pitch, all you need to do is clamp a spirit level onto the template – simple, fast, accurate. Continue reading

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What R-Value Is Good Enough?

I plan on retiring at my lake home in Northern Minnesota. The first step in my retirement preparations is building a large garage on my retirement property that will allow me to work on my various projects – I have not mentioned it before, but I love doing auto body work. I am currently building a garage similar to that shown in Figure 1. Because northern Minnesota is quite cold in the winter, I needed to insulate and heat this structure. This post will review some observations that I made as to the value of insulation and of using modern ventilation systems with heat recovery capability. Continue reading

Posted in Construction | 4 Comments

Effective R Value of Common Wall Construction Methods

Because the winters are hard in this part of the country, I have become interested in the insulation value of different types of wall construction. My contractor has his preferred approach, and I am curious as to how it compares with other framing methods.

In this post, I will put together a simple model for computing the R-value of different types of wall construction. This analysis will provide me a quantitative basis for understanding which methods are the most economically sound. Continue reading

Posted in Construction | 1 Comment

Shimming and Trimming Stairs to Equalize the Risers

In this post, I will show how to generalize my previous stair solution to handle these three cases. I also present some illustrations of what is involved in adjusting the stairs. The general solution used a Mathcad program to compute both the final riser height and the thickness of the shims or trim cuts required for each step. In general, you may need a combination of shims and trim cuts to resolve a riser height problem caused by changes in flooring height. Continue reading

Posted in Construction | 2 Comments

Lateral Force Rating for Various Nails

I am an amateur carpenter, and I work hard to ensure that I always comply with the applicable building codes. The various codes include requirements for a properly nailed joint (examples). Since I like to understand where these requirements come from, I have been the reading some sections of the National Design Specification for Wood Construction (NDS) that address fastening. During my reading, I saw many interesting formulas associated with determining the NDS design ratings for nail withdrawal (covered here) and lateral force resistance – the subject of this post. Continue reading

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