St. Oswald's Bell Tower Struts first created 21/09/2005 Page Author: Ty Harness
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Figure 1a 1b- St. Oswald's Church - Photos by Ty Harness
St. Oswald's (Strubby. Lincolnshire) are renovating the church roof and the oak struts of the bell tower are beyond repair. The architect has specified stainless steel box section to replace the oak struts (The box section is then clad with oak).

My job is to work out the lengths and angles of the new struts (we haven't got the old ones to copy).
It can be very difficult to determine the cut length of box section angles from 2D drawings when the box section is cut at an oblique angle and the angle out of plane is also oblique. Below shows a 3D drawing of the struts - note the wall plate is not sitting level which complicates the job considerably.
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Figure 2a 2b - 2 box sections sitting on rafters and 2 on the wall plate. I made paper 1:1 paper templates that were used to wrap round the box section to mark-out the angles.

It's well known the length of a 3D vector is $l = sqrt(x^2+y^2+z^2)$ but that's only from point to point. I've made many-of-a-mistake cutting either the angles wrong and ending up being too short.

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Figure XX - The magnitude or length of a 3D vector
From the above figure the hypotenuse of the triangle in the XY plane is $sqrt(x^2 + y^2)$ (Pythagorean Theorem) and the triangle out of plane where l is the hypotenuse $l^2 = (sqrt(x^2 + y^2))^2 + z^2 = x^2 + y^2 + z^2$ and hence $l= sqrt(x^2+y^2+z^2)$

Ronnie Wilkinson and Andrew Darby (D&D Engineering, Lincolnshire) measured up the job and cut the box section right first time. The guys did make a jig to ensure everything was right and that all would go smooth on site. The stainless steel box section is very expensive, measure twice-cut once.
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Figure 3a 3b- Spot-on (photos by A. Darby)

When I get chance I hope to show the mathematics to solve this type of problem in general and I'll update this page when I can.


Here's some more pictures taken by Ronnie.
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