# Steel square

Last updated
Other names Framing squareCarpenter's square Type of square Carpentry hand tool

The steel square is a tool used in carpentry. Carpenters use various tools to lay out structures that are square (that is, built at accurately measured right angles), many of which are made of steel, but the name steel square refers to a specific long-armed square that has additional uses for measurement, especially of various angles. Today the steel square is more commonly referred to as the framing square or carpenter's square. It consists of a long, wider arm and a shorter, narrower arm, which meet at an angle of 90 degrees (a right angle). It can also be made of aluminum or polymers, which are light and resistant to rust.

## Contents

The longer wider arm is two inches (51 mm) wide, and is called the blade; the shorter narrower arm, is one and a half inches (38 mm) wide, and is called the tongue. The square has many uses, including laying out common rafters, hip rafters and stairs. [1] It has a diagonal scale, board foot scale and an octagonal scale. On the newer framing squares there are degree conversions for different pitches and fractional equivalents.

Framing squares may also be used as winding sticks.

In traditional timber frame joinery, mortises and tenons were typically two inches (51 mm) wide and two inches (51 mm) 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 (38 mm) 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.

## Use

### Stair framing

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.

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.

1. The rise (vertical measurement), and the run (horizontal measurement). Note that the stringer will rest partially on the horizontal surface.
2. This is a 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.
3. 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.
4. 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.

### Roof framing

18"17"16"15"14"13"12"10"9"8"
Common rafter length per foot run21.63"19.21"16.97"14.42"
Hip or valley rafter length per foot run24.74"22.65"20.78"18.76"
Difference in length of jacks 16 inch centers28.88"25.63"22.63"19.25"
Difference in length of jacks 24 inch centers43.25"38.44"33.94"28.88"
Side cut length of jack rafters6.69"7.5"8.5"10.00"
Side cut of hip rafter or valley rafter8.25"9.0"9.81"10.88"
This table shows five different types of rafter calculations and one table for marking an angle called the side cut or cheek cut.

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 slopes of the roof. Each column describes a different roof inclination (pitch) and contains the following information:

1. 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 distance (run).
2. 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.
3. 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.
4. 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.
5. Cutting hip and valley cripple rafters are all cut in a similar way.

### Octagon scale

The octagon scale allows the user to inscribe an octagon inside a square, given the length of the side of the square. The markings indicate half the length of the octagon's sides, which can be set to a compass or divider. Arcs drawn from the midpoints of the square's sides will intersect the square at the vertices of the planned octagon. All that remains is to cut four triangular sections from the square.

### Diagonal scale

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 post and beam.

### Calculators in roof framing

In addition to use the square tool, construction calculators 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.

### Side cut hip/valley rafter table

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 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.

 Legend ${\displaystyle c={\sqrt {12^{2}+12^{2}}}\,}$ ${\displaystyle L={\sqrt {c^{2}+P^{2}}}\,}$ ${\displaystyle tangent={\frac {c}{L}}\,}$ c= hypotenuseP= pitchL= rafter lengthZ= difference in L of jack rafter 16" OC

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 arc tan can be determined from any given pitch. Most power tools and angle measuring devices use 90° as 0° in construction. The complementary angles of the arc tan are used with tools like the speed square.

### Side cut of jack rafters

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.

 ${\displaystyle tangent={\frac {16}{z}}\,}$

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 devices 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.

Side cut angles versus pitch

This is a reference table for side cuts versus pitch. (only valid for 90 degrees eave angle) :

Pitch expressed in rise units / run units

Pitch 18/12 ==> 60,86 deg

Pitch 17/12 ==> 60,10 deg

Pitch 16/12 ==> 59,07 deg

Pitch 15/12 ==> 57,99 deg

Pitch 14/12 ==>  56,94 deg

Pitch 13/12 ==>  55,88 deg

Pitch 12/12 ==>  54,69 deg

Pitch 11/12 ==>  53,49 deg

Pitch 10/12 ==>  52,54 deg

Pitch 9/12 ==>  51,25 deg

Pitch 8/12 ==>   50,19 deg

Pitch 7/12 ==>   49,17 deg

Pitch 6/12 ==>   48,15 deg

Pitch 5/12 ==>   47,33 deg

Pitch 4/12 ==>   46,54 deg

Pitch 3/12 ==>   45,90 deg

Pitch 2/12 ==>   45,22 deg

Pitch 1/12 ==>   45,10 deg

Pitch 0/12 ==>  45,00 deg

### Plumb cut of jack and common rafters

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 .

 ${\displaystyle tangent={\frac {P}{b}}.\,}$

### Plumb cut of hip/valley rafters

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.

 ${\displaystyle tangent={\frac {P}{\sqrt {a^{2}+b^{2}}}}.\,}$

### Irregular hip/valley rafters

The only Framing Square that has tables for unequal pitched roofs is the Chappell Universal Square, (patent #7,958,645). There is also a comprehensive rafter table for 6 & 8 sided polygon roofs (first time ever on a framing square). The traditional steel square's rafter table (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 45°. The top plates can be 90° at the outside corners or various other angles. There are numerous irregular h/v roof plans.

## Carpenter's square

In carpentry, a square is a guide for establishing right angles (90° angles) or mitre angles, usually made of metal. There are various types of square, such as speed squares, try squares and combination squares.

## Related Research Articles

Stairs, a stairway, a staircase, a stairwell, or a flight of stairs is a construction designed to bridge a large vertical distance by dividing it into smaller vertical distances, called steps. Stairs may be straight, round, or may consist of two or more straight pieces connected at angles.

Octagon houses were a unique house style briefly popular in the 1850s in the United States and Canada. They are characterised by an octagonal (eight-sided) plan, and often feature a flat roof and a veranda all round. Their unusual shape and appearance, quite different from the ornate pitched-roof houses typical of the period, can generally be traced to the influence of one man, amateur architect and lifestyle pundit Orson Squire Fowler. Although there are other octagonal houses worldwide, the term octagon house usually refers specifically to octagonal houses built in North America during this period, and up to the early 1900s.

A rafter is one of a series of sloped structural members such as wooden beams that extend from the ridge or hip to the wall plate, downslope perimeter or eave, and that are designed to support the roof shingles, roof deck and its associated loads. A pair of rafters is called a couple. In home construction, rafters are normally made of wood. Exposed rafters are a feature of some traditional roof styles.

Framing, in construction, is the fitting together of pieces to give a structure support and shape. Framing materials are usually wood, engineered wood, or structural steel. The alternative to framed construction is generally called mass wall construction, where horizontal layers of stacked materials such as log building, masonry, rammed earth, adobe, etc. are used without framing.

A tie, strap, tie rod, eyebar, guy-wire, suspension cables, or wire ropes, are examples of linear structural components designed to resist tension. It is the opposite of a strut or column, which is designed to resist compression. Ties may be made of any tension resisting material.

In building construction, roof pitch is the steepness of a roof quantified as a ratio or as the number of angular degrees that one 'exposure' surface deviates from horizontal level. A roof surface may be either 'functionally flat' or pitched.

A purlin is a longitudinal, horizontal, structural member in a roof. In traditional timber framing there are three basic types of purlin: purlin plate, principal purlin, and common purlin.

Domestic roof construction is the framing and roof covering which is found on most detached houses in cold and temperate climates. Such roofs are built with mostly timber, take a number of different shapes, and are covered with a variety of materials.

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In architecture, a vault is a self-supporting arched form, usually of stone or brick, serving to cover a space with a ceiling or roof. The simplest kind of vault is the barrel vault, which is generally semicircular in shape. The barrel vault is a continuous arch, the length being greater than its diameter. As in building an arch, a temporary support is needed while rings of voussoirs are constructed and the rings placed in position. Until the topmost voussoir, the keystone, is positioned, the vault is not self-supporting. Where timber is easily obtained, this temporary support is provided by centering consisting of a framed truss with a semicircular or segmental head, which supports the voussoirs until the ring of the whole arch is completed. With a barrel vault, the centering can then be shifted on to support the next rings.

A staircase jig is a woodworking tool that incorporates both a right angle and an acute angle in its design. The jig is easily transported due to its small size and light weight. Precise measurements are required to layout the diagonal locations.

Pole framing or post-frame construction is a simplified building technique adapted from the labor-intensive traditional timber framing technique. It uses large poles or posts buried in the ground or on a foundation to provide the vertical structural support, along with girts to provide horizontal support. The method was developed and matured during the 1930s as agricultural practices changed, including the shift toward engine-powered farm equipment and the demand for cheaper, larger barns and storage areas.

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A gable roof is the classic, most commonly occurring roof shape in those parts of the world with cold or temperate climates. It consists of two roof sections sloping in opposite directions and placed such that the highest, horizontal edges meet to form the roof ridge. The design of this type of roof is achieved using rafters, roof trusses or purlins. The pitch of the roof and the height of the gutters can vary greatly.

A Speed Square is a triangular carpenters' marking out tool manufactured and sold by Swanson Tool Co., Inc. The Speed Square combines common functions of the combination square, try square, and framing square into one. Carpenters use it to make basic measurements and mark lines on dimensional lumber, and as a saw guide for short 45 and 90 degree cuts.

A hip roof, hip-roof or hipped roof, is a type of roof where all sides slope downwards to the walls, usually with a fairly gentle slope. Thus, a hipped roof house has no gables or other vertical sides to the roof.

A post is a main vertical or leaning support in a structure similar to a column or pillar but the term post generally refers to a timber but may be metal or stone. A stud in wooden or metal building construction is similar but lighter duty than a post and a strut may be similar to a stud or act as a brace. In the U.K. a strut may be very similar to a post but not carry a beam. In wood construction posts normally land on a sill, but in rare types of buildings the post may continue through to the foundation called an interrupted sill or into the ground called earthfast, post in ground, or posthole construction. A post is also a fundamental element in a fence. The terms "jack" and "cripple" are used with shortened studs and rafters but not posts, except in the specialized vocabulary of shoring.

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## References

### Notes

1. Elliot, J. Hamilton (1910), Cobleigh, Rolfe (ed.), "Use of the Steel Square", Handy Farm Devices and How to Make Them, Orange Judd and Company.

### Bibliography

• Hodgson, Frederick T. (1880). The Carpenters' Steel Square and Its Uses. The Industrial Publication Company. LCCN   06036488.
• Siegele, H.H. (1981). The Steel Square. Sterling Publishing. ISBN   0-8069-8854-1.
• Ulrey, Harry F. (1972). Carpenters and Builders Library. No.3. Theodore Audel. LCCN   74099760.
• Schuttner, Scott (1990). . Taunton Press. ISBN   0-942391-44-6.
• Spence, William P. (2000). . Sterling Publishing. ISBN   0-8069-8101-6.
• Gochnour, Chris (February 2006). "11 Essential Measuring and Woodworking Tools". Fine Woodworking . Taunton Press (182): 75.
• Lanham, Wm. The Steel Square. Bath: E. A. Lovell.
• Falconer, John (1925). Ednie, John (ed.). The Steel Square. Carpentry and Joinery. Vol. V. Gresham.|volume= has extra text (help)
• Sobon, Jack (1994). Build a classic timber-framed house : planning and design, traditional materials, affordable methods. Pownal, Vt. : Storey Communications. ISBN   0882668420.