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| {{Redirect|Carpenter's square|the plant|Scrophularia marilandica}}
| | I am Giselle and was born on 13 December 1984. My hobbies are Racquetball and Games Club - Dungeons and Dragons, Monopoly, Etc..<br><br>Feel free to surf to my blog post; web site - [http://ce.mokpo.ac.kr/?document_srl=1511115 simply click the up coming document] - |
| [[Image:Steel Square-1.jpg|thumb|Steel square]]
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| The '''steel square''' is a tool that [[carpenter]]s use. They use many tools to lay out a "square" or right-angle, many of which are made of steel, but the title '''steel square''' refers to a specific long-armed square that has additional uses for measurement, especially of angles, as well as simple right-angles. Today the [[steel]] square is more commonly referred to as the '''framing square'''. It consists of a long arm and a shorter one, which meet at an [[angle]] of 90 degrees (a [[right angle]]). It can also be made of metals like [[aluminum]], which is light and resistant to rust.
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| The wider arm, two [[inch]]es wide, is called the '''blade'''; the narrower arm, one and a half inches wide, the '''tongue'''. The square has many uses, including laying out common [[rafter]]s, [[roof#Roof shapes|hip]] rafters and [[stairway|stairs]]. It has a [[diagonal]] scale, [[board foot]] scale and an [[octagon]]al scale. On the newer framing squares there are degree conversions for different pitches and fractional equivalents.
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| Carpenter's squares are very much like steel squares.
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| == Blade and tongue ==
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| In traditional [[timber frame]] joinery, [[Mortise and tenon|mortises and tenons]] were typically two inches wide and two inches from the edge of the timber when working with softwoods, giving rise to the width of the blade. Likewise, mortises and tenons were traditionally one and a half inches wide when working in hardwoods, explaining the width of the tongue. This allowed for quick layouts of mortise and tenon joints when working both hard and softwoods.
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| == Use in stair framing ==
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| [[Image:Stringer revised.jpg|thumb|right|250px|Theoretical rise and run of stringer, placement of square, marking of tread and rise, dropping the stringer, ABC=90°, total rise of stringer = 2R-T, total run of stringer = 2AB.]]
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| Stairs usually consist of three components. They are the stringer, the tread and the riser. The stringer is the structural member that carries the load of the staircase, the tread is the horizontal part that is stepped on, and the riser board is the vertical part which runs the width of the structure. There are many types of stairs: open, closed, fully housed, winding, and so on, to mention a few of them.
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| Laying out a staircase requires rudimentary math. There are numerous building codes to which staircases must conform. In an open area the designer can incorporate a more desirable staircase. In a confined area this becomes more challenging. In most staircases there is one more rise than there are treads.
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| # The ''rise'' (vertical measurement), and the ''run'' (horizontal measurement). Note that the stringer will rest partially on the horizontal surface.
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| # This is a [[dimensional lumber|two-by-twelve]] piece of lumber. A framing square is placed on the lumber so that the desired rise and tread marks meet the edge of the board. The outline of the square is traced. The square is slid up the board until the tread is placed on the mark and the process is repeated.
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| # The board is cut along the dotted lines, and the top plumb cut and the bottom level cut are traced by holding the square on the opposite side.
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| # The stringer in this example has two pieces of tread stock. This allows for a slight overhang. There is also a space in between the boards. The bottom of the stringer must be cut to the thickness of the tread. This step is called ''dropping the stringer''. After one stringer is cut this piece becomes the pattern that is traced onto the remaining stringers.
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| == Use in roof framing ==
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| {| class="wikitable"
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| |+Blade of steel square
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| ! !! 18" !! 17" !! 16" !! 15" !! 14" !! 13" !! 12" !! 10" !! 9" !! 8"
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| |-
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| | Common rafter length per foot run || 21.63" || || || 19.21" || || || 16.97" || || || 14.42"
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| | Hip or valley rafter length per foot run || 24.74" || || || 22.65" || || || 20.78" || || || 18.76"
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| | Difference in length of jacks 16 inch centers || 28.88" || || || 25.63" || || || 22.63" || || || 19.25"
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| | Difference in length of jacks 24 inch centers || 43.25" || || || 38.44" || || || 33.94" || || || 28.88"
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| |-
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| | Side cut length of jack rafters || 6.69" || || || 7.5" || || || 8.5" || || || 10.00"
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| |-
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| | Side cut of hip rafter or valley rafter || 8.25" || || || 9.0" || || || 9.81" || || || 10.88"
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| |-
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| | colspan="11" style="font-size:10px; font-style:italic;" | This table shows five different types of rafter calculations and one table for marking an angle called the side cut or cheek cut.
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| |}
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| There is a table of numbers on the face side of the steel square; this is called the '''rafter table'''. The rafter table allows the carpenter to make quick calculations based on the [[Pythagorean theorem]]. The table is organized by columns that correspond to various [[slope]]s of the roof. Each column describes a different roof inclination ([[roof pitch|pitch]]) and contains the following information:[[Image:Common rafter 12 pitch A.jpg|right|thumb|250px|This is a common rafter with the two different cuts. The plumb cut fits in the ridge board and the Bird's mouth fits on the wall plate.]]
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| #Common rafter per foot of run The common rafter connects the peak of a roof (the ''ridge'') to the base of a roof (the plate). This number gives the length ([[hypotenuse]]) of the common rafter per twelve units of [[Horizontal plane|horizontal]] distance (''run'').
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| #Hip or valley rafter per foot of run The hip or valley rafter also connects the ridge to the plate, but lies at a 45-degree angle to the common rafter. This number gives the length of the hip or valley rafter per seventeen units of run.
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| #Difference in lengths jacks The jack rafters lie in the same plane as the common rafter but connect the top plate (the wall) or ridge board to the hip or valley rafter respectively. Since the hip or valley rafter meets the ridge board and the common rafter at angles of 45 degrees, the jack rafters will have varying lengths when they intersect the hip or valley. Depending on the spacing of the rafters, their lengths will vary by a constant factor—this number is the common difference.
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| #This angle can be cut on the fly by aligning this given number on the blade of the steel square and the twelve-inch mark on the tongue, and drawing a line along the tongue.
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| #Cutting hip and valley criple rafters are all cut in a similar way.
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| <gallery> | |
| Image:hip jack and common rafter.jpg|The relationship between hip, jack and common rafters, and how they tie into the ridge and bottom plate. The rafters are fastened to the horizontal ridge board at the peak of the roof.
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| Image:Hip Rafter Side and Level Cut.jpg| The side cut is the beveled angle of the hip or valley rafter that fits into the ridge board in this image.
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| Image:Common rafter layout.jpg|Common and jack rafters all use twelve as the common reference to mark the plumb cut.
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| Image:Side cut jack rafter revised.jpg|Hip and jack rafters use twelve as a common reference while aligning the desired pitch in the side cut column.
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| Image:Plumbcuts new.jpg| Hip and valley rafters use seventeen as the common reference for marking the plumb cut of a rafter.
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| </gallery>
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| == Use of the octagon scale ==
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| <gallery>
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| Image:Octagon Table.jpg|Octagon Table located on the front side of the Steel square.
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| Image:Calculation Table A.JPG| Octagon table viewed from an aluminum square.
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| Image:Scribe an Octagon.jpg|Octagon made from the Octagon scale. A protractor can accomplish the same task.
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| </gallery>
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| ==Use of the Diagonal scale==
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| Knee bracing is a common feature in [[timber framing]] to prevent racking under lateral loads. The diagonal scale is useful for determining the length of the a knee brace desired for a given distance from the joint between the bost and beam.
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| <gallery>
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| Image:Diagonal calculations A.JPG|This is the location of the diagonal scale on the square.
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| Image:Diagonal Scale revised.jpg|The diagonal scale gives the ''diagonal'', or the hypotenuse, for the different legs of the triangle for which a brace is to be cut.
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| </gallery> | |
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| ==Using calculators in roof framing==
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| [[Image:flat hip roof.jpg|90px|right]]
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| In addition to use the square tool, construction [[calculator]]s are also used to verify and determine roofing calculations. Some are programmed to calculate all side cuts for hip, valley and jack regular rafters to be exactly 45° for all rafter pitches. The rafter table is expressed in inches, and the higher the numerical value of the pitch, the greater the difference between side cut angles within a given pitch. Only a level roof, or a 0 pitch will require a 45° angle side cut (cheek cut) for hip and jack rafters.
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| ==Side cut hip/valley rafter table==
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| If a [[right triangle]] has two angles that equal 45° then the two sides are equidistant. The rafter is the hypotenuse and the legs or [[cathetus|catheti]] of the triangle are the top wall plates of the structure. The side cut is located at the intersection of the given pitch column and the side cut of the hip/valley row. The regular hip/valley rafter runs at a 45° angle to the main roof and the unit of measurement is 16.97 inches of run. Regular hip/valley and jack rafters have different bevel angles within any given pitch and the angle decreases as the pitch increases.
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| <table border = "1">
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| <tr>
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| <td><math> c = \sqrt{12^2 + 12^2}. \,</math></td>
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| <td><math> L= \sqrt{c^2 + P^2}. \,</math></td>
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| <td><math>tangent = \frac{c}{L}.\,</math></td>
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| <table style="float: right; margin-left: 1em; margin-bottom: 0.5em; width: 242px; border: #99B3FF solid 1px">
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| <tr><td><center>'''Legend'''</center></td></tr>
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| <tr><td>c= hypotenuse</td></tr>
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| <tr><td>P= pitch</td></tr>
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| <tr><td>L= rafter length</td></tr>
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| <tr><td>Z= difference in L of jack rafter 16" OC<tr>
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| </table>
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| The side cut of the hip/valley rafter = (Tangent)(12) = side cut in inches. The side cuts in the rafter table are all in a base 12. The [[Inverse trigonometric functions|arc tan]] can be determined from any given pitch. Most power tools and angle measuring devises use 90° as 0° in construction. The [[complementary angle]]s of the arc tan are used with tools like the [[speed square]].
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| ==Side cut of jack rafters==
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| The side cut is located at the intersection of the side cut of jack rafters row and the pitch column on the Steel square. There is a row for the difference in length of jacks, 16 and 24 inch centers on the blade. The tangents are directly proportional for both centers.
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| <table border = "2">
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| <tr>
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| <td><math>tangent = \frac{16}{z} \,</math></td>
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| </tr>
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| </table>
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| The tangent is in a base 12. The tangent x 12 = side cut of jack rafters. This corresponds to the side cut on the Steel square. The complementary angles of the arc tan are used on most angle measuring devises in construction. The tangent of hip, valley, and jack rafters are less than 1.00 in all pitches above 0°. An eighteen pitch has a side cut angle of 29.07° and a two pitch has a side cut angle of 44.56° for jack rafters. This is a variation of 15.5° between pitches.
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| ==Plumb cut of jack & common rafters==
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| The plumb cut for jack and common rafters are the same angles. The level cut or seat cut is the complementary angle of the plumb cut. The notch formed at the intersection of the level and plumb cut Is commonly referred to as the bird’s mouth .
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| <table border = "1">
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| <tr>
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| <td><math> tangent = \frac{P}{b}.\,</math></td>
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| </table>
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| ==Plumb cut of hip/valley rafters==
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| The plumb cut of the hip/valley rafter is expressed in the formula. The level cut is the complementary angle or 90° minus the arc tan.
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| <table border = "1">
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| <tr>
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| <td><math> tangent = \frac{P}{\sqrt{a^2 + b^2}}. \,</math></td>
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| </table>
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| == Irregular hip/valley rafters ==
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| <span>
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| The only Framing Square that has tables for unequal pitched roofs is the [[chappellsquare.com|Chappell Universal Square]], ([http://patft.uspto.gov/netacgi/nph-Parser?Sect2=PTO1&Sect2=HITOFF&p=1&u=/netahtml/PTO/search-bool.html&r=1&f=G&l=50&d=PALL&RefSrch=yes&Query=PN/7958645 patent #7,958,645]). There is also a comprehensive rafter table for 6 & 8 sided polygon roofs (first time ever on a framing square).
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| The traditional steel square's rafter table ([http://www.google.com/patents/US672455 patented April 23,1901]) is limited in that it does not have tables that allow for work with unequal pitched roofs. Irregular hip/valley rafters are characterized by plan angles that are not equal or 45º. The top plates can be 90° at the outside corners or various other angles. There are numerous irregular h/v roof plans.
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| </span>
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| <gallery>
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| Image: Irregular roof plan rev.jpg| irregular hip/valley gable roof plan.
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| Image:Irregular roof plan.jpg|irregular roof plan.
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| Image:Irregular roof plan d.jpg| Intersecting irregular hip/valley gable roof plan.
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| </gallery>
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| == Carpenter's square ==
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| In [[carpentry]], a '''square''' or '''set square''' is a guide for establishing right angles (90° angles), usually made of metal and in the shape of a right triangle.
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| == See also ==
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| *[[Combination square]]
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| *[[Hip Roof]]
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| *[[Try square]]
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| == Bibliography ==
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| * {{cite book
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| |title=The Steel Square
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| |last=Siegele |first=H.H.
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| |publisher=Sterling Publishing
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| |year=1981
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| |isbn= 0-8069-8854-1
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| }}
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| * {{cite book
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| |last=Ulrey |first=Harry F.
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| |series=Carpenters and Builders Library |volume=No.3
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| |publisher=Theodore Audel
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| |year=1972
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| |LCCN=74099760
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| }}
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| * {{cite book
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| |title=Basic Stairbuilding,
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| |last=Schuttner |first=Scott
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| |year=1990
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| |isbn= 0-942391-44-6
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| |publisher=[[Taunton Press]]
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| }}
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| * {{cite book
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| |title=Constructing Staircases Balustrades & Landings
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| |last=Spence |first=William P.
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| |publisher=Sterling Publishing
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| |year=2000
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| |isbn=0-8069-8101-6
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| }}
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| * {{cite journal
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| |title=11 Essential Measuring and Woodworking Tools
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| |last=Gochnour |first=Chris
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| |journal=[[Fine Woodworking]]
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| |pages=75
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| |publisher=Taunton Press
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| |issue=182
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| |date=February 2006
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| }}
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| * {{cite book
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| |title=The Steel Square
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| |last=Lanham |first=Wm.
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| |publisher=E. A. Lovell |location=Bath
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| }}
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| * {{cite book
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| |last=Falconer |first=John
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| |editor=Ednie, John (editor)
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| |title=The Steel Square
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| |series=Carpentry and Joinery |volume=Vol. V
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| |publisher=Gresham
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| |year=1925
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| }}
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| * {{cite book
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| |title=Build a classic timber-framed house : planning and design, traditional materials, affordable methods
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| |last=Sobon |first=Jack
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| |publisher=Pownal, Vt. : Storey Communications
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| |year=1994
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| |isbn=0882668420
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| }}
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| {{Measuring and alignment tools}}
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| [[Category:Woodworking measuring instruments]]
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| [[Category:Dimensional instruments]]
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| [[Category:Woodworking hand tools]]
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