Category Archives: Construction

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

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 | 5 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

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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

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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

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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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Layout Formula for a Balustrade

I am about to begin some construction on my cabin in northern Minnesota, and the design of the stairs has been on my mind. I consider well-designed stairs to be both beautiful and functional. A major factor in making a stairway beautiful is its balustrade – a railing with supporting spindles (aka balusters). The balustrade for a stairs is often referred to as a banister. Continue reading

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Withdrawal Force Rating for Various Nails

I have been reading some specifications on fastener requirements in carpentry. To ensure that I understand what I am reading, I decided to see if I could duplicate the design values for nailed connections. In this post, I will duplicate a table (Figure 1) for the withdrawal force ratings of various nails when used in a toe-nailed connection. In general, I try to avoid nails with a withdrawal load, but it is an allowed connection and it was easy to duplicate the results in a National Design Specification (NDS) document. I will be performing a similar computation for the lateral load rating in a later post. My Mathcad source and a PDF are stored here. Continue reading

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Stud Length Requirements

I usually use 92 5/8" studs when I am building standard 8' tall walls – they sit sit in piles at my nearby lumber yards next to piles of 8' long studs. I recently saw (example) that there are three pre-cut sizes available:

92-5/8" : used for 8' ceiling heights
104-5/8" : used for 9' ceiling heights
116-5/8": used for 10' ceiling heights

In this post, I thought I would take a look at these pre-cut sizes to (1) learn why these values are used, and (2) to decide if any of them would be appropriate for my building activities. Continue reading

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