Preface: After successfully completing over 700 projects during more than a quarter century without such a document as this, one might ask “is there really a need for one”?
Does the question presume that all of those previous projects could not have been improved upon? Experience knows differently. With the possible exception of the Tabernacle and the Temple later, there has not ever been a work of man constructed without flaw. And of course, the builders of those exceptions had the Architect of the Universe as their PM! But some Laborers may remember a column slightly (but noticeably) out of plumb on project X. What about the droopy and misaligned entryway on project Y? Then there’s the roof sheathing that’s “spongy” when trod upon, on that facility in town Z, which also has a peculiar bump in one wall. You can observe flaws on any project (to say nothing of the wasted effort correcting mistakes, etc.).
Even slight improvements will add to the value, serviceability, and longevity of Laborers work. Every project is also a learning experience for participants. Lessons learned are of enduring value only if passed along. It is hoped this humble offering will encourage others to share knowledge for future builders, and add to the worth of the Laborers for Christ program in service to Our Lord. - Wayne Valentine, P.E. (Ret.).
Acknowledgments: Many thanks to those who contributed ideas and helpful criticisms. Special thanks to my long-time friend and former colleague Stan Skousen for his careful review, suggestions, and comments, and also to my generous neighbor and computer genius Tim Wolf, who unselfishly provided the graphical adornments to this project.
Wednesday, April 8, 2009
INTRODUCTION
Laborers who understand a few basic principles of engineering, mensuration, and lay out will be able to do a better job framing the more important structural members of buildings. This includes:
* positioning and aligning members accurately
* recognizing critical load paths
* assuring adequate bearing
* avoiding weakening cuts
* making effective connections
* providing adequate but not excessive nailing
* spotting and correctly using defective material
* placing material so as to use its greatest strength
* erecting safe and economical temporary framing
This understanding can add to the quality and economy of LFC work performed for Our Savior and LCMS congregations.
Here is a legal disclaimer: By law, competent Engineers or Architects must review the design of permanent load-bearing structural members and their connection details. This Primer is only intended to acquaint Laborers with a few fundamental technical concepts, thereby exposing the need for Professional assistance in questionable or complex situations.
Never-the-less, framing and structural problems often arise during construction, and need to be dealt with quickly to avoid work delays. They may occur for several reasons, such as unforeseen difficulties in remodeling projects, the need for temporary scaffolding or supports, or even because of incomplete or poorly conceived architectural plans or revisions. When the latter happens, it may be possible to provide solutions that will keep the work going in anticipation of a design professional’s review. Knowledge of a few fundamental engineering principles will help reduce delays and improve the utilization of time and materials.
Laborers for Christ should also understand and correctly use building terminology to effectively communicate with architects, suppliers, contractors, and with each other. Speaking the same language helps the building process. Remember the project at Babel? They were doing quite well until the Lord confused their speech. Let’s try to use proper terminology and use it correctly. After all, He does not want our projects to fail like theirs.
* positioning and aligning members accurately
* recognizing critical load paths
* assuring adequate bearing
* avoiding weakening cuts
* making effective connections
* providing adequate but not excessive nailing
* spotting and correctly using defective material
* placing material so as to use its greatest strength
* erecting safe and economical temporary framing
This understanding can add to the quality and economy of LFC work performed for Our Savior and LCMS congregations.
Here is a legal disclaimer: By law, competent Engineers or Architects must review the design of permanent load-bearing structural members and their connection details. This Primer is only intended to acquaint Laborers with a few fundamental technical concepts, thereby exposing the need for Professional assistance in questionable or complex situations.
Never-the-less, framing and structural problems often arise during construction, and need to be dealt with quickly to avoid work delays. They may occur for several reasons, such as unforeseen difficulties in remodeling projects, the need for temporary scaffolding or supports, or even because of incomplete or poorly conceived architectural plans or revisions. When the latter happens, it may be possible to provide solutions that will keep the work going in anticipation of a design professional’s review. Knowledge of a few fundamental engineering principles will help reduce delays and improve the utilization of time and materials.
Laborers for Christ should also understand and correctly use building terminology to effectively communicate with architects, suppliers, contractors, and with each other. Speaking the same language helps the building process. Remember the project at Babel? They were doing quite well until the Lord confused their speech. Let’s try to use proper terminology and use it correctly. After all, He does not want our projects to fail like theirs.
FRAMING (FORCES AND STRESSES)
FORCES AND STRESSES
Remember your high-school physics and Newton’s laws, which are actually connected to rules God uses to govern the motion of planets. You learned that forces act on a straight line and that for any object at rest, the forces acting on it are met with equal but opposite forces. On objects at rest, or in equilibrium, “For every action there is an equal but opposite reaction”. We expect our buildings to be “at rest” and not collapsing!
Remember your high-school physics and Newton’s laws, which are actually connected to rules God uses to govern the motion of planets. You learned that forces act on a straight line and that for any object at rest, the forces acting on it are met with equal but opposite forces. On objects at rest, or in equilibrium, “For every action there is an equal but opposite reaction”. We expect our buildings to be “at rest” and not collapsing!
Forces in buildings come from Loads that cause Internal Stress within individual structural members that are resisting the Loads. The usual forces (stresses) concerning us are:
1) Moment (bending),
2) Compression (pushing)
3) Shear (sliding or cutting),
4) Tension (pulling),
(There are other stresses but they are generally not of concern in buildings.)
Force is the amount of push, bend, pull, etc. applied to and resisted by a structural member. We usually measure force in pounds per square inch (psi) for compression, tension, and shear; and inch-pounds or foot-pounds for bending.
LOADS
Loads are from building materials, people, stuff, and nature; e.g. shingles, beams, folks, pianos, pews, and wind, snow, or earthquakes. We classify loads in several ways.
By duration:
* Dead Load (DL) is permanent or long-term, such as the structure itself and what it continuously holds up, e.g. the roof, ceiling, walls, etc. (Somewhat like original sin.)
* Live Load (LL) is short-term, intermittent and re-occurring such as snow, wind, or people. (Somewhat like actual sin.)
* Impact is very short term shock loading, such as when a piano is dropped. Not usually considered in buildings except in seismic design. (Unlike steel and concrete, wood has a remarkable capacity to absorb short-term loading.)
By distribution:
* Concentrated Loads act in narrowly defined areas, e.g. a safe, or a beam bearing on a pier. Measured in pounds.
* Distributed Loads are either actually spread evenly over a surface, e.g. snow, wind, or carpet; or assumed to be spread evenly over a surface, e.g. people. Measured in pounds per square foot (psf) of surface, or pounds per linear foot (plf) along a beam supporting the surface.
By how they act on structural members:
* Axial Loads act along and parallel with the long axis (dimension) of the member, and produce compression or tension forces.
* Transverse Loads act at 90 degrees (“normal” or perpendicular) to the member’s long axis, and produce shear and also bending, which is actually comprised of tension and compression stresses.
Loads operate in a straight line (obvious but often un-recognized); and forces resisting them also operate in a straight line. All loads are supported by continuous paths of resistance from the building foundation to the point of application. Be aware of paths of load resistance. Identify and examine load paths to clarify critical members and joints, and to locate questionable situations. (A column should not bear in the middle of a floor with no underlying pier, for example.)
Any individual force can be “resolved” (i.e. broken down) into two or more components acting along different force lines through the same point. For example, a brace leaning against a wall will have vertical and horizontal forces acting against its weight, at each end of the brace.
Building codes specify the applicable design loads for floors, roofs, wind, etc. for each geographic area. Some typical live floor loads are 100 psf for hallways, and 40 psf for classrooms. Roof live loads vary geographically and are determined by weather (wind and snow) and seismic forces. Roof dead loads are typically 15 psf to 20 psf. Lumber weighs between 3 and 4 pounds per board-foot, depending on species.
RESISTANCE OF BUILDING MATERIALS
Resistance of Building Materials
Framing materials resist loads according to their strength. Wood, steel, and concrete are our primary structural materials and their strength characteristics are well known. The load carrying capacity of individual elements is a function of the size, shape, and inherent strength of the material, usually stated as allowable stress, and measured in pounds per square inch (psi), or, for some manufactured elements (e.g. nails, hangers), as pounds.
For rough estimating, here are some typical conservative values of allowable stresses:
Steel: 18,000 psi in tension, compression, and bending.
Concrete (plain): 1350 psi in compression and zero in tension and bending.
Structural Lumber: 1200 to 2000 psi in bending, tension and compression parallel with the grain, and 400 psi in compression perpendicular (normal) to the grain, values depending on the species and grade.
Nails: Allowable lateral load (shear) for a 16-penny nail completely driven into side grain of sound seasoned wood is approximately 80 to 100 pounds; its withdrawal load from side grain is about 30 pounds per inch penetration, and next to nothing in withdrawal from end grain.
Actual yield (total) strength is much higher but held in reserve to provide a factor of safety for un-anticipated over-loads, defective material or fabrication. Technical handbooks provide more detailed information.
Framing materials resist loads according to their strength. Wood, steel, and concrete are our primary structural materials and their strength characteristics are well known. The load carrying capacity of individual elements is a function of the size, shape, and inherent strength of the material, usually stated as allowable stress, and measured in pounds per square inch (psi), or, for some manufactured elements (e.g. nails, hangers), as pounds.
For rough estimating, here are some typical conservative values of allowable stresses:
Steel: 18,000 psi in tension, compression, and bending.
Concrete (plain): 1350 psi in compression and zero in tension and bending.
Structural Lumber: 1200 to 2000 psi in bending, tension and compression parallel with the grain, and 400 psi in compression perpendicular (normal) to the grain, values depending on the species and grade.
Nails: Allowable lateral load (shear) for a 16-penny nail completely driven into side grain of sound seasoned wood is approximately 80 to 100 pounds; its withdrawal load from side grain is about 30 pounds per inch penetration, and next to nothing in withdrawal from end grain.
Actual yield (total) strength is much higher but held in reserve to provide a factor of safety for un-anticipated over-loads, defective material or fabrication. Technical handbooks provide more detailed information.
BEAMS (BENDING RESISTANCE)
Beams (bending resistance)
Along with columns and trusses, beams are critical structural members, and they are found in virtually every building. Beams carry transverse loads such as roofs, floors and interior walls, and also plumbing fixtures, refrigerators, desks, and people; they have important load carrying jobs. Their ability to perform can be impaired by careless placing, reckless fastening, and foolish carving or cutting. This can lead to squeaky or un-even floors, sagging and leaking roofs, cracked walls, increased seismic or storm risk, and other problems. Laborers can help guard against these problems by understanding how beams work.
Beams have special names because they are for special jobs or are made in special ways. See the appendix for a list.
Beam parts:
Beam parts are best identified by reference to the end of an I-beam. There are three special areas, namely the two Flanges, and the area in between them, called the Web. Each of these parts has a separate job in load carrying. A horizontal beam properly placed to carry a vertical load has one flange on top and one on the bottom. The line along the beam halfway between the top and bottom flanges is the beam centerline, called the “Neutral Axis”.
Beams are supported by direct bearing on something else, e.g. a bearing wall, pier, truss, column, or shear through hardware connections. The number and place of supports are very important in determining a beam’s load carrying capacity. A beam supported only on its two ends is called “Simply Supported”. If there are more than two supports under a beam, it is called “Continuously Supported”. A beam overhanging a support and carrying a load on the overhang is “Cantilevered”. The distance between supports is the “Span”.
Along with columns and trusses, beams are critical structural members, and they are found in virtually every building. Beams carry transverse loads such as roofs, floors and interior walls, and also plumbing fixtures, refrigerators, desks, and people; they have important load carrying jobs. Their ability to perform can be impaired by careless placing, reckless fastening, and foolish carving or cutting. This can lead to squeaky or un-even floors, sagging and leaking roofs, cracked walls, increased seismic or storm risk, and other problems. Laborers can help guard against these problems by understanding how beams work.
Beams have special names because they are for special jobs or are made in special ways. See the appendix for a list.
Beam parts:
Beam parts are best identified by reference to the end of an I-beam. There are three special areas, namely the two Flanges, and the area in between them, called the Web. Each of these parts has a separate job in load carrying. A horizontal beam properly placed to carry a vertical load has one flange on top and one on the bottom. The line along the beam halfway between the top and bottom flanges is the beam centerline, called the “Neutral Axis”.
Beams are supported by direct bearing on something else, e.g. a bearing wall, pier, truss, column, or shear through hardware connections. The number and place of supports are very important in determining a beam’s load carrying capacity. A beam supported only on its two ends is called “Simply Supported”. If there are more than two supports under a beam, it is called “Continuously Supported”. A beam overhanging a support and carrying a load on the overhang is “Cantilevered”. The distance between supports is the “Span”.
HOW BEAMS WORK
How beams work:
Beam action demonstration: Take a Popsicle stick or tongue depressor and place it flat (wide face up) between two supports, e.g. a couple of thick books. You now have a simply supported beam (plank). Put your finger in the middle of the span and push down. You now have a loaded beam (plank), with a concentrated load at mid-span generating bending moment and shear within the beam. The beam will sag, or “deflect”. Push harder and the beam will break. Look at the break. The fibers at the top of the beam will not be severed, but the bottom fibers will be jagged and parted or broken. Now turn the beam over and repeat the exercise. This time the stick will break in two, with the fibers on both sides parted.
In each loading case, the fibers on the bottom were in tension, and the top fibers were in compression. Thus we see that a beam works by internal push in its top flange, and pull in its bottom flange. These are two opposing forces working together in harmony around the neutral axis. Sort of like the law and gospel around grace resisting the load of sin.
Your finger load also created a shearing force at the supports. But because the bending strength of the stick is weak when loaded as a plank, it failed by bending moment rather than shear.
Now, take another stick and repeat the exercise, but this time place the stick with the narrow edge on top. Unless you are as strong as Samson, you will not easily be able to break the stick, because loaded this way it is much stronger in bending. Thus we learn that a beam’s strength depends on the distance between (separation) of the flanges, or the depth of the web. This gives a basic rule of how beams work. “The flanges carry the moment, the web carries the shear”.
Beam action demonstration: Take a Popsicle stick or tongue depressor and place it flat (wide face up) between two supports, e.g. a couple of thick books. You now have a simply supported beam (plank). Put your finger in the middle of the span and push down. You now have a loaded beam (plank), with a concentrated load at mid-span generating bending moment and shear within the beam. The beam will sag, or “deflect”. Push harder and the beam will break. Look at the break. The fibers at the top of the beam will not be severed, but the bottom fibers will be jagged and parted or broken. Now turn the beam over and repeat the exercise. This time the stick will break in two, with the fibers on both sides parted.
In each loading case, the fibers on the bottom were in tension, and the top fibers were in compression. Thus we see that a beam works by internal push in its top flange, and pull in its bottom flange. These are two opposing forces working together in harmony around the neutral axis. Sort of like the law and gospel around grace resisting the load of sin.
Your finger load also created a shearing force at the supports. But because the bending strength of the stick is weak when loaded as a plank, it failed by bending moment rather than shear.
Now, take another stick and repeat the exercise, but this time place the stick with the narrow edge on top. Unless you are as strong as Samson, you will not easily be able to break the stick, because loaded this way it is much stronger in bending. Thus we learn that a beam’s strength depends on the distance between (separation) of the flanges, or the depth of the web. This gives a basic rule of how beams work. “The flanges carry the moment, the web carries the shear”.
BENDING STRESS (MOMENT)
Moment (bending stress)
The compression stress in the top flange converts to tension stress in the bottom flange. Think about how this happens. Compression within the beam is a maximum at the very top of the flange, but decreases within the beam, becoming zero at the neutral axis. From there, tension grows from zero to a maximum at the very bottom of the beam.
Therefore, bending stress is zero at the neutral axis, and maximum at the flanges! This is significant information for deciding where to poke holes in a beam. The “tension face” in a wooden member requires clear wood (i.e. knot-free), especially in the middle third of the span.
We have discovered how moment stress varies within the cross-section of a beam. Now let us look at how it varies along the beam. The beam broke in the middle, where the maximum moment stress occurred.
Therefore, the moment stress varies from a maximum in the middle of a simply supported beam to zero at the ends. This is more significant information, useful for strengthening a beam or avoiding weakening it.
The compression stress in the top flange converts to tension stress in the bottom flange. Think about how this happens. Compression within the beam is a maximum at the very top of the flange, but decreases within the beam, becoming zero at the neutral axis. From there, tension grows from zero to a maximum at the very bottom of the beam.
Therefore, bending stress is zero at the neutral axis, and maximum at the flanges! This is significant information for deciding where to poke holes in a beam. The “tension face” in a wooden member requires clear wood (i.e. knot-free), especially in the middle third of the span.
We have discovered how moment stress varies within the cross-section of a beam. Now let us look at how it varies along the beam. The beam broke in the middle, where the maximum moment stress occurred.
Therefore, the moment stress varies from a maximum in the middle of a simply supported beam to zero at the ends. This is more significant information, useful for strengthening a beam or avoiding weakening it.
VERTICAL SHEAR IN BEAMS
Vertical shear stress distribution in beams:
Remember that shear acts normal (perpendicular) to the beam. A simply supported beam with a concentrated load in the center of so many (say 10) pounds carries the load equally to the two supports, each taking half. Therefore, the vertical shear “up” (+) at the left support is one-half 10=5, and this shear is the same along the beam until the center. At the center, the “up” shear is decreased by the load 10 to equal 5 “down” (-) on the remaining portion of the beam over to the right support. Therefore, a beam carrying a concentrated load has large total shear at the load point.
Now let’s change the concentrated load into a uniform load spread along the beam. What happens to the shear stress in the beam? The load on the supports is the same, (the reaction), but now the shear stress decreases uniformly to zero at center span, where its “sign” changes and then its magnitude increases to the support.
Therefore the shear in a uniformly loaded simple span beam is zero at mid-span, but maximum at the supports. This is more significant information for deciding where (or if) to poke holes in the beam.
(Beams are also subject to horizontal shear developed by the opposing tension and compression forces. The shear plane is located at the neutral axis. Review of this stress must be made by a design professional.)
Summary of important stuff for placing and modifying beams:
For the most part, the beams we erect are considered to be uniformly loaded and simple span, in which the middle third of the span is the most critical area for moment stress, and the outer thirds are the most critical for vertical shear stress.
Beams should not be cut on the tension side in the center third.
The web should not be cut near the supports or load points of beams carrying heavy shear.
The web may be cut through at the neutral axis at mid-span.
Sawn lumber having loose knots, check, splits, or damage should be placed so these defects do not compromise strength.
Continuous beams have moment reversal over the interior supports. That is, the top flange is in tension there. Tension also appears in the top flange at the support in cantilevered beams. Rules for making cuts or holes in beams should be recognized in these situations.
Plywood, when loaded in beam action (as in roof sheathing or flooring) must be laid so that the face grain is perpendicular (normal) to the supporting beams. This placement provides the stiffest resistance to bending. Plywood is very weak in bending across the face grain. It is a bad mistake to lay up plywood improperly.
Remember that shear acts normal (perpendicular) to the beam. A simply supported beam with a concentrated load in the center of so many (say 10) pounds carries the load equally to the two supports, each taking half. Therefore, the vertical shear “up” (+) at the left support is one-half 10=5, and this shear is the same along the beam until the center. At the center, the “up” shear is decreased by the load 10 to equal 5 “down” (-) on the remaining portion of the beam over to the right support. Therefore, a beam carrying a concentrated load has large total shear at the load point.
Now let’s change the concentrated load into a uniform load spread along the beam. What happens to the shear stress in the beam? The load on the supports is the same, (the reaction), but now the shear stress decreases uniformly to zero at center span, where its “sign” changes and then its magnitude increases to the support.
Therefore the shear in a uniformly loaded simple span beam is zero at mid-span, but maximum at the supports. This is more significant information for deciding where (or if) to poke holes in the beam.
(Beams are also subject to horizontal shear developed by the opposing tension and compression forces. The shear plane is located at the neutral axis. Review of this stress must be made by a design professional.)
Summary of important stuff for placing and modifying beams:
For the most part, the beams we erect are considered to be uniformly loaded and simple span, in which the middle third of the span is the most critical area for moment stress, and the outer thirds are the most critical for vertical shear stress.
Beams should not be cut on the tension side in the center third.
The web should not be cut near the supports or load points of beams carrying heavy shear.
The web may be cut through at the neutral axis at mid-span.
Sawn lumber having loose knots, check, splits, or damage should be placed so these defects do not compromise strength.
Continuous beams have moment reversal over the interior supports. That is, the top flange is in tension there. Tension also appears in the top flange at the support in cantilevered beams. Rules for making cuts or holes in beams should be recognized in these situations.
Plywood, when loaded in beam action (as in roof sheathing or flooring) must be laid so that the face grain is perpendicular (normal) to the supporting beams. This placement provides the stiffest resistance to bending. Plywood is very weak in bending across the face grain. It is a bad mistake to lay up plywood improperly.
COLUMNS AND TIES
Columns AND TIES (Compression and tension resistance)
A Column is a member resisting axial compression forces. Column connections are usually in direct end bearing. Studs are columns, as are posts and struts. Length and condition of lateral (sideways) support classify columns as either “long” or “short”. Struts are short columns, resisting loads by pure compression strength.
Long columns are subject to buckling, in which the loaded column can be deflected out of line and fail by a combination of compression and bending. Loads on long columns are governed by what is called the L/d or “slenderness” ratio, i.e. the length of column that is laterally unsupported (L) divided by the least dimension (d) of the column. This ratio should be less than 50. Long column load capacity varies inversely as the square of this ratio, i.e. capacity decreases as the ratio increases. See the Column table for more data.
A tie is the reverse of a column, in that it resists axial tension forces. Temporary bracing is often in tension. Permanent tension members are common in trusses, uncommon elsewhere. Tie connections place shear on connecting hardware.
A Column is a member resisting axial compression forces. Column connections are usually in direct end bearing. Studs are columns, as are posts and struts. Length and condition of lateral (sideways) support classify columns as either “long” or “short”. Struts are short columns, resisting loads by pure compression strength.
Long columns are subject to buckling, in which the loaded column can be deflected out of line and fail by a combination of compression and bending. Loads on long columns are governed by what is called the L/d or “slenderness” ratio, i.e. the length of column that is laterally unsupported (L) divided by the least dimension (d) of the column. This ratio should be less than 50. Long column load capacity varies inversely as the square of this ratio, i.e. capacity decreases as the ratio increases. See the Column table for more data.
A tie is the reverse of a column, in that it resists axial tension forces. Temporary bracing is often in tension. Permanent tension members are common in trusses, uncommon elsewhere. Tie connections place shear on connecting hardware.
ROOF TRUSSES
ROOF TRUSSES
Even though it takes loads similarly to a beam, a truss is not a beam but a space frame with several connected members acting in either tension or compression. It is designed to carry heavy loads across long spans. Trusses can be thought of as open-webbed beams, in that the top flanges (chords) are in compression, and the bottom chords are in tension. These chords may also carry moment, depending on how load is transferred to the truss. The individual web pieces are either in tension or compression, depending on how the truss is configured. Connections at truss joints are critical; they should not be compromised through additional carpentry.
Since they are strong in one direction but weak in another, trusses, especially light trusses, must be handled with care. During erection, they can easily tip if not securely braced. When framed for loading, the top chords must be carefully aligned and straightened, uniformly spaced and parallel, and with the truss webs vertical or nearly so. Since the bottom chords will be in tension when fully loaded, less care needs to be given to aligning them. Obviously, the chords must not be damaged.
When placing roofing on trusses, try to keep the roofing operations more or less equal on each side, i.e. do not complete one side then do the other. Asymmetrical loading will introduce un-balanced horizontal thrust in the truss. This is more critical on steeper pitches.
Even though it takes loads similarly to a beam, a truss is not a beam but a space frame with several connected members acting in either tension or compression. It is designed to carry heavy loads across long spans. Trusses can be thought of as open-webbed beams, in that the top flanges (chords) are in compression, and the bottom chords are in tension. These chords may also carry moment, depending on how load is transferred to the truss. The individual web pieces are either in tension or compression, depending on how the truss is configured. Connections at truss joints are critical; they should not be compromised through additional carpentry.
Since they are strong in one direction but weak in another, trusses, especially light trusses, must be handled with care. During erection, they can easily tip if not securely braced. When framed for loading, the top chords must be carefully aligned and straightened, uniformly spaced and parallel, and with the truss webs vertical or nearly so. Since the bottom chords will be in tension when fully loaded, less care needs to be given to aligning them. Obviously, the chords must not be damaged.
When placing roofing on trusses, try to keep the roofing operations more or less equal on each side, i.e. do not complete one side then do the other. Asymmetrical loading will introduce un-balanced horizontal thrust in the truss. This is more critical on steeper pitches.
NAILED JOINTS
NAILED JOINTS
Joints connecting structural members are essential to the strength and performance of the building. They are usually the “weakest link”. Until framing anchors came along, nails were about the only way to hook two pieces of wood together cheaply and quickly. Framing anchors usually transfer loads through nails or screws in shear.
Side, toe, and end nailing are still common methods of connection. Nailing is actually a poor way to connect lumber, since it takes many nails to transfer the inherent strength of wood. Moreover, quality control is difficult, and there are many variables than cannot be evaluated. Never-the-less, we still nail because it is fast, economical, and most everyone can swing a hammer.
Nails should be placed in a triangular or staggered pattern. Avoid placing more that one nail into an individual growth ring. Beware of over-nailing. The last nail you place may end up splitting the piece, compromising the joint. Then what will you do?
When connecting temporary braces use a double headed nail; but if using a regular nails, try not to nail flush, instead leave about 1/8 inch proud for ease in withdrawal when dismantling. This has safety implications.
Edge nailing: When connecting members loaded in transverse shear (i.e. beams), be careful to avoid placing nails too close to the edge on the loaded side. Confine your nails to the “lower” 2/3 of the piece.
Toe nail or not toe nail? That is the question. You learned in high-school wood shop that toe nailing is a good thing. Maybe, maybe not. Remember that forces operate in a straight line. A nailed joint transfers loads by shear or withdrawal (tension). Nails driven straight (normal) into a joint provide better withdrawal resistance against normal loads than nails on a slant. Can you draw the force resolution to demonstrate this?
The power nailer is a mixed blessing. It is handy for placing nails without hammering, when hammering will disturb the joint arrangement. It is also faster than hand nailing. But it is dangerous to use, especially in the hands of the novice. Its ease and speed makes it the frequent cause of over-nailing, which can actually weaken joints. For temporary framing of braces, etc. it is a bane, since too many nails often are placed and usually placed too deeply for ease in dismantling.
Joints connecting structural members are essential to the strength and performance of the building. They are usually the “weakest link”. Until framing anchors came along, nails were about the only way to hook two pieces of wood together cheaply and quickly. Framing anchors usually transfer loads through nails or screws in shear.
Side, toe, and end nailing are still common methods of connection. Nailing is actually a poor way to connect lumber, since it takes many nails to transfer the inherent strength of wood. Moreover, quality control is difficult, and there are many variables than cannot be evaluated. Never-the-less, we still nail because it is fast, economical, and most everyone can swing a hammer.
Nails should be placed in a triangular or staggered pattern. Avoid placing more that one nail into an individual growth ring. Beware of over-nailing. The last nail you place may end up splitting the piece, compromising the joint. Then what will you do?
When connecting temporary braces use a double headed nail; but if using a regular nails, try not to nail flush, instead leave about 1/8 inch proud for ease in withdrawal when dismantling. This has safety implications.
Edge nailing: When connecting members loaded in transverse shear (i.e. beams), be careful to avoid placing nails too close to the edge on the loaded side. Confine your nails to the “lower” 2/3 of the piece.
Toe nail or not toe nail? That is the question. You learned in high-school wood shop that toe nailing is a good thing. Maybe, maybe not. Remember that forces operate in a straight line. A nailed joint transfers loads by shear or withdrawal (tension). Nails driven straight (normal) into a joint provide better withdrawal resistance against normal loads than nails on a slant. Can you draw the force resolution to demonstrate this?
The power nailer is a mixed blessing. It is handy for placing nails without hammering, when hammering will disturb the joint arrangement. It is also faster than hand nailing. But it is dangerous to use, especially in the hands of the novice. Its ease and speed makes it the frequent cause of over-nailing, which can actually weaken joints. For temporary framing of braces, etc. it is a bane, since too many nails often are placed and usually placed too deeply for ease in dismantling.
THREE B's
THREE B’s
(No, not those three Lutheran guys Beethoven, Brahms, and Bach. They weren’t famous for their carpentry.)
Blocking is installed in stud walls for several reasons. Blocks are placed to prevent “chimneys” for fire protection, and to provide a nailing surface for sheet rock, etc. Blocks add to wall strength by reducing the “L/d” ratio.
For sheet rock and other cladding, accurately spaced, parallel studs are necessary. Studs can easily be shoved out of parallel by careless blocking, with either too long or too short blocks. Because studs themselves may be warped, the block will often not fit snuggly. Measure the actual space between the stud pairs at the nearest plate to the block, and subtract 1/16 inch for the cut length. This will help maintain the studs parallel or nearly so after the whole wall section is blocked.
When possible, stagger the blocks around the line, with a 1/3 to ½ overlap. This permits direct end-nailing of blocks, in lieu of toe nailing.
Bridging enables neighbor beams to “share the load” under a floor or roof, and provides lateral stability. Bridging used to be made from two pieces and placed in an X pattern; this has given way to using solid sawn wood. As in blocking, achieving parallelism in the beams is important.
Bracing can be temporary or permanent. Remember that forces act in a straight line. Determine the direction of the force you are bracing against, and place the brace in direct linear opposition to it. Brace from “flimsy” to “stout”, not from “flimsy to flimsy”! Efficient bracing makes triangles, (sometimes imaginary) with two points of the triangle at the ends of the brace, and the third point at the intersection of a line along a solid base in the plane of the triangle.
Visualize how the force in a brace will resolve into horizontal and vertical components at the end points. A steeply sloping wall brace will have a smaller horizontal component than a flatter brace, but larger vertical component, and vice versa. A steep brace will have less resistance to the wall over-turning, but a flatter brace will be longer and heavier (assuming it’s attached to the wall at the same point). The best slope of the brace is about 45 degrees. Paradoxically, compression braces to a free-standing wall will actually introduce overturning forces into the wall, the same forces the brace is to resist, so be careful not to apply excessive lateral bending forces with the brace.
Braces in compression are less effective than braces in tension. Because a brace in compression acts as a column, its strength and stability is diminished unless it is stiffened along its side. Since temporary braces will be removed, avoid over nailing and remember to leave the nail head proud about 1/8 inch for ease in withdrawing.
Double cross (X) braces not connected at the crossing point will be unstable, unless the brace makes a complete triangle with all three end points fixed.
A final word on the Bs: Do not block the bottom chords of light trusses until they are fully loaded, or nearly so. Remember these chords are in tension and will straighten on their own. Premature blocking may inhibit this, and in extreme cases introduce unwanted tension or lateral stress in the chord.
Also, temporarily brace the top chords of TJIs, etc. against overturn, but it is foolish to waste time bracing their bottom chords.
(No, not those three Lutheran guys Beethoven, Brahms, and Bach. They weren’t famous for their carpentry.)
Blocking is installed in stud walls for several reasons. Blocks are placed to prevent “chimneys” for fire protection, and to provide a nailing surface for sheet rock, etc. Blocks add to wall strength by reducing the “L/d” ratio.
For sheet rock and other cladding, accurately spaced, parallel studs are necessary. Studs can easily be shoved out of parallel by careless blocking, with either too long or too short blocks. Because studs themselves may be warped, the block will often not fit snuggly. Measure the actual space between the stud pairs at the nearest plate to the block, and subtract 1/16 inch for the cut length. This will help maintain the studs parallel or nearly so after the whole wall section is blocked.
When possible, stagger the blocks around the line, with a 1/3 to ½ overlap. This permits direct end-nailing of blocks, in lieu of toe nailing.
Bridging enables neighbor beams to “share the load” under a floor or roof, and provides lateral stability. Bridging used to be made from two pieces and placed in an X pattern; this has given way to using solid sawn wood. As in blocking, achieving parallelism in the beams is important.
Bracing can be temporary or permanent. Remember that forces act in a straight line. Determine the direction of the force you are bracing against, and place the brace in direct linear opposition to it. Brace from “flimsy” to “stout”, not from “flimsy to flimsy”! Efficient bracing makes triangles, (sometimes imaginary) with two points of the triangle at the ends of the brace, and the third point at the intersection of a line along a solid base in the plane of the triangle.
Visualize how the force in a brace will resolve into horizontal and vertical components at the end points. A steeply sloping wall brace will have a smaller horizontal component than a flatter brace, but larger vertical component, and vice versa. A steep brace will have less resistance to the wall over-turning, but a flatter brace will be longer and heavier (assuming it’s attached to the wall at the same point). The best slope of the brace is about 45 degrees. Paradoxically, compression braces to a free-standing wall will actually introduce overturning forces into the wall, the same forces the brace is to resist, so be careful not to apply excessive lateral bending forces with the brace.
Braces in compression are less effective than braces in tension. Because a brace in compression acts as a column, its strength and stability is diminished unless it is stiffened along its side. Since temporary braces will be removed, avoid over nailing and remember to leave the nail head proud about 1/8 inch for ease in withdrawing.Double cross (X) braces not connected at the crossing point will be unstable, unless the brace makes a complete triangle with all three end points fixed.
A final word on the Bs: Do not block the bottom chords of light trusses until they are fully loaded, or nearly so. Remember these chords are in tension and will straighten on their own. Premature blocking may inhibit this, and in extreme cases introduce unwanted tension or lateral stress in the chord.
Also, temporarily brace the top chords of TJIs, etc. against overturn, but it is foolish to waste time bracing their bottom chords.
SUMMARY OF FRAMING RED FLAGS
SUMMARY OF FRAMING RED FLAGS
Beams: Protect the bottom flanges from cutting and other damage, and place sawn beams to take account of flaws (loose knots, splits, etc).
Trusses: Beware of pre-mature blocking of bottom chords. Be careful against damaging joints and cutting individual members. Be careful to avoid asymmetrical loading when installing roofing. Avoid using truss tension members as beams; if necessary to place heavy loads on the bottom of a truss, place the load point at or near a truss joint.
Plywood: For roofs and floors, be sure the face grain is normal to the support frame.
Re-roofing: Beware of roofing over an existing roof. Check dead loads.
Joints: Be careful not to over-nail.
Temporary Columns: Watch out for excessive un-supported length.
Double cross-braces: Be sure they are also connected together at the crossing point.
Manufactured members: Follow manufacturers’ recommendations for handling and temporary bracing.
Beams: Protect the bottom flanges from cutting and other damage, and place sawn beams to take account of flaws (loose knots, splits, etc).
Trusses: Beware of pre-mature blocking of bottom chords. Be careful against damaging joints and cutting individual members. Be careful to avoid asymmetrical loading when installing roofing. Avoid using truss tension members as beams; if necessary to place heavy loads on the bottom of a truss, place the load point at or near a truss joint.
Plywood: For roofs and floors, be sure the face grain is normal to the support frame.
Re-roofing: Beware of roofing over an existing roof. Check dead loads.
Joints: Be careful not to over-nail.
Temporary Columns: Watch out for excessive un-supported length.
Double cross-braces: Be sure they are also connected together at the crossing point.
Manufactured members: Follow manufacturers’ recommendations for handling and temporary bracing.
GEOMETRY: MISFITS AND DISTORTIONS
GEOMETRY
MISFITS AND DISTORTIONS
“All lumber should be cut to exact dimension and straight without warp, twist, wane, or split. Walls and columns should be exactly vertical. Floors should be perfectly flat and level. Foundations should be at the precise elevation, absolutely straight and level. Stairs and roofs should have exact slope or pitch. Joists and studs should be uniformly spaced and perfectly parallel. Door frames and corners should be square to within an arc-second. Trusses should be straight as a fiddle string. Square and bevel cuts should be right-on and straight clear through. All joints should fit snuggly without gaps or warping. All connections should join evenly for a smooth surface”.
Sadly, the above ideals cannot be achieved in this sinful world even individually, let alone all together! A skilled carpenter knows how to remedy flaws and recover from errors, without resorting to “Cut to fit, warp to connect, grind to bear, and paint to match” – hopefully this common solution will be used sparingly. A wise worker also pays attention to manufacturers recommendations when installing fixtures, etc. The common solution of “using a bigger hammer” to make things fit should be avoided!
Distortions from the desired geometry can be due to many factors. Sections built off-site have to be transported, which can stress and alter their shape. Tall, narrow sections are difficult to build true to square and parallelism. Wood changes dimension across grain, (but is stable along grain) and it warps and twists. Concrete cannot be placed absolutely flat. Plumb and level is hard to verify over long distance with only a spirit level.
Spirit levels, tapes, and string lines are the usual tools we use to layout, control, and check the geometry and construction. Optical and laser instruments are now found on many projects, and can provide greater accuracy. Unfortunately, these tools are often misused, their relative accuracy or reliability not understood, and the relative importance of geometrical elements is frequently not recognized. When things don’t fit right, what should give: line, grade, level, plumb, straight, flat, smooth, parallel, square, spacing, pitch, or dimension?
The best answer to this question will vary depending on several factors. Some things are critical, others of minor importance. There is distinction between what should be nearly perfect vs. what can be barely adequate. Is the defect potentially dangerous, just ugly, or merely annoying? What crooked piece is the likely cause of the trouble? What reference line or measurement mark is most susceptible of error or mistake in determination and therefore most suspicious?
Some parts that are especially critical are door posts, wall corners, and joists and studs to which sheathing is attached. Interior “non-edge” misaligned studs can be tolerated, providing they are securely blocked. Some things that are out of level, plumb, or square, may be tolerable if they are to be covered, are not critical structurally, and providing the defect is not too egregious.
It’s probably safe to say that most misfits occur because of defective measuring, sloppy marking and cutting, and careless fastening, abetted by warped lumber.
MISFITS AND DISTORTIONS
“All lumber should be cut to exact dimension and straight without warp, twist, wane, or split. Walls and columns should be exactly vertical. Floors should be perfectly flat and level. Foundations should be at the precise elevation, absolutely straight and level. Stairs and roofs should have exact slope or pitch. Joists and studs should be uniformly spaced and perfectly parallel. Door frames and corners should be square to within an arc-second. Trusses should be straight as a fiddle string. Square and bevel cuts should be right-on and straight clear through. All joints should fit snuggly without gaps or warping. All connections should join evenly for a smooth surface”.
Sadly, the above ideals cannot be achieved in this sinful world even individually, let alone all together! A skilled carpenter knows how to remedy flaws and recover from errors, without resorting to “Cut to fit, warp to connect, grind to bear, and paint to match” – hopefully this common solution will be used sparingly. A wise worker also pays attention to manufacturers recommendations when installing fixtures, etc. The common solution of “using a bigger hammer” to make things fit should be avoided!
Distortions from the desired geometry can be due to many factors. Sections built off-site have to be transported, which can stress and alter their shape. Tall, narrow sections are difficult to build true to square and parallelism. Wood changes dimension across grain, (but is stable along grain) and it warps and twists. Concrete cannot be placed absolutely flat. Plumb and level is hard to verify over long distance with only a spirit level.
Spirit levels, tapes, and string lines are the usual tools we use to layout, control, and check the geometry and construction. Optical and laser instruments are now found on many projects, and can provide greater accuracy. Unfortunately, these tools are often misused, their relative accuracy or reliability not understood, and the relative importance of geometrical elements is frequently not recognized. When things don’t fit right, what should give: line, grade, level, plumb, straight, flat, smooth, parallel, square, spacing, pitch, or dimension?
The best answer to this question will vary depending on several factors. Some things are critical, others of minor importance. There is distinction between what should be nearly perfect vs. what can be barely adequate. Is the defect potentially dangerous, just ugly, or merely annoying? What crooked piece is the likely cause of the trouble? What reference line or measurement mark is most susceptible of error or mistake in determination and therefore most suspicious?
Some parts that are especially critical are door posts, wall corners, and joists and studs to which sheathing is attached. Interior “non-edge” misaligned studs can be tolerated, providing they are securely blocked. Some things that are out of level, plumb, or square, may be tolerable if they are to be covered, are not critical structurally, and providing the defect is not too egregious.
It’s probably safe to say that most misfits occur because of defective measuring, sloppy marking and cutting, and careless fastening, abetted by warped lumber.
Tuesday, April 7, 2009
MEASURING AND LAYOUT
Measuring and Layingout
Reference Lines and Marks:
Arguably the most accurate and reliable reference line available is the plumb line, since it operates by gravity. Like God’s grace, gravity is constant, reliable, true, omnipresent and everywhere available. By definition, a level line is perpendicular to the plumb line and is usually gauged by a spirit level, which also operates by gravity. String and chalk lines, if carefully done and not deflected, tend to be reliable. Surveyors’ optical and laser tools provide excellent precision.
Establishing Vertical:
A plumb bob is better than a spirit level for critical verticals, i.e. wall corners and columns. Remember that gravity operates 24-7. Out of plumb is a bad thing that lasts for the life of the structure. When plumbing down from a high known point, allow the bob to oscillate freely and by eye note the center of the swing arc. When plumbing up from a known low point, establish a temporary reference point on the high piece, plumb down, determine the off-set of the down-plumbed point from the true spot and lay off this amount from the temporary reference. Modern laser equipment properly used will make this job easier.
Establishing Horizontal:
Messing up on the foundation and floor level will cause nothing but trouble for the rest of the job, and the whole building will be in danger of being out of whack.
The best tool for leveling, other than a surveyor’s instrument, is a long spirit level (at least 6-ft.). Check the bubble centering by rotating the level. Check the level’s quality by seeing how much the thickness of one penny (or dime) placed under one end will move the bubble. Your level should detect this error. The more the bubble moves with this test, the more sensitive the level. Sequential leveling, like sequential taping, is undesirable. Use a surveyor’s or builder’s optical or laser level to establish elevation over a long distance.
Establishing Right Angles:
A surveyor’s transit or theodolite is the most precise angle-measuring tool, but is impractical to use for short distances, where a tape is more convenient. Most every carpenter is familiar with the 3,4,5 sides of the right triangle. However, a much stronger and better combination is 20, 21, and 29 and its multiples, such as 100, 105, 145. This combination creates a nearly 45 degree angle at the acute corners thus providing a more accurate right angle.
Chalk and String Lines:
When chalking, make sure the line is taut and when snapping, be sure it’s pulled exactly perpendicular to the surface to be marked (especially important when marking across a sloped surface such as a roof). Do not use lengthy chalk lines since they often become misaligned when snapped; instead use a string or laser.
String or chalk all critical edges such as plates, wall sills, wall top plate, etc. Strings for alignment must be taken from accurate reference points; e.g. when stringing to straighten a wall, make sure the end-points of the string are anchored to accurately plumbed, secure corners. And do not lean ladders on the wall as you are trying to align it! Off set the reference line a small amount so as to keep it from being moved (string) or obscured (chalk). Use a gauge block to test conformance with the reference line.
Measurement and Marking Practice:
Linear measurements are made by reference to an “artificial” standard. Not all measurements are perfect to a zillionth of an inch, nor always mistake free. Since they are always susceptible to mistake and error, they are of less reliability. Right angles, when established by linear measures, also are of lesser reliability.
Your project may have been staked out by Surveyors, who usually measure in feet and decimals of a foot. Carpenters measure in feet, inches, and eighths (or sixteenths). It’s useful to remember that 1/100 a foot is nearly equal to 1/8 an inch.
Precision: Try to achieve +/- 1/8 inch in 100 ft. = 1:10,000 relative precision. Check diagonals of perimeter to 1/8 inch or 1/100 foot.
Length of studs, plates, rafters, joists, etc. should be accurate to better than +/- 1/8 inch, down to +/- 1/16 inch.
Smaller details require comparatively more precise measures. 1/32 inch is probably the smallest practical limit (we’re not making furniture).
Check all the tapes. Make sure everyone on the crew has a tape that accurately conforms to a standard tape. For measuring long distances, steel tapes are preferred over woven or fiberglass types, which will stretch unacceptably. Replace damaged or kinked tapes.
When measuring, keep the tape straight. Make sure the tape has no twists, kinks, or “esses”. Watch the sag in the tape when measuring long dimensions. Put tension on un-supported tapes, at least 10 lbs.
When laying out stud intervals, etc. use the entire tape length instead of sequentially adding smaller segments.
If plan dimensions are horizontal, so should the layout measure be! Be careful not to incline the tape when measuring a horizontal dimension. Also, keep the tape plumb for vertical measurements.
When careful measures are needed, do not use the hook at the end of the tape, instead “bury” ten inches or a foot and read the gauge lines.
When measuring inside a closed space where the full tape cannot be stretched, measure in two directions to an intermediate temporary reference line, and add the two values.
Trim the ends off lumber to obtain a clean, sharp end from which to measure.
Mark carefully for cuts. The lead in a carpenter’s dull pencil is usually too fat to make narrow lines needed for precision cuts. The thinner the mark, the more precise the cut. For extra precision, mark the cut line with a sharp pencil or even with a knife. Place the marker at the dimension mark then slide the straight edge to it for striking the line, rather than vice-versa.
Cut to the line, (unless it marks the center of the saw kerf, in which case cut it out) and make sure the saw kerf is on the correct (waste) side! Radial arm, table, and chop saws are capable of more accurate cuts than hand-held “skill” saws.
Framing Square:
Most carpenters have retired the classic framing square and adopted instead the “speed-square.” This 45 degree triangle contains gauge lines for laying out angle cuts for common and jack rafters, and is simple to use and convenient to carry. Unfortunately, this handy gizmo cannot help with face angles, seat cuts, length of jacks, or odd pitches.
The framing square, with its mysterious number tables, is a useful tool that should be available on every project for solving unusual framing problems. Its use is really not that complicated. The key is to understand roof pitch (or slope) which is expressed as rise in inches per foot of horizontal run. On the body (the longer leg) of the square is a table of numbers arranged underneath individual inch marks. The inch value associated with the mark represents the pitch rise per foot of horizontal run and the corresponding table contains settings for marking various cuts of rafters and jack rafters for that pitch, using the tabulated value on one arm of the square, and the appropriate index (12 normal or 17 for 45 degrees) on the other arm.
Story Stick:
For short, frequent and repeated measurements, use a story stick cut to the proper length. For installing out-lookers and other short pieces placed at right angles to another member, use a story stick cut to the size of the diagonal of a right triangle, with the leg lengths marked on it. This is less cumbersome than a framing square and more accurate than a speed square.
Door Frames:
Properly operating doors require accurately installed frames. A frame that is out of square, or with a post out of plumb, or a door with the plane not coincident with the wall, or a frame with the top plate not level, will bind, swing or latch poorly, fit poorly with gaps, besides just looking bad.
To make the plane of the frame flat and in line with the wall, string a line from the frame’s top left corner to the bottom right corner, and another string from the top right corner to the bottom left corner. These two strings should barely touch where they cross. If not, the door frame is out of plane. After making one side post fixed and plumb, adjust the bottom and top corners of the other side until the strings just touch and the top plate is inline with the wall. Check the plumb of this last post and the level of the top plate, and fix in position. (Thanks to Bernie Gueldner for this tip.)
Trimming to Length:
Sometimes it’s difficult to make accurate measurements. Try measuring accurate lengths to fit studs for a new 12 foot wall that frames onto an old existing wavy ceiling! The amount to trim off a piece to be placed in an existing space is given by the formula C = d^2/2h, where C is amount to cut off, d is the distance by which the trial piece off sets or leans, and h is the nominal length.
Example: A 12ft. replacement stud is too long to fit between the top and bottom plates in an existing wall; when put nearly in place it leans over out of plumb by 8”. The trim cut is (8x8)/(2x12x12) = 32/144 = or about 0.2 inch for a snug vertical fit.
Reference Lines and Marks:
Arguably the most accurate and reliable reference line available is the plumb line, since it operates by gravity. Like God’s grace, gravity is constant, reliable, true, omnipresent and everywhere available. By definition, a level line is perpendicular to the plumb line and is usually gauged by a spirit level, which also operates by gravity. String and chalk lines, if carefully done and not deflected, tend to be reliable. Surveyors’ optical and laser tools provide excellent precision.
Establishing Vertical:
A plumb bob is better than a spirit level for critical verticals, i.e. wall corners and columns. Remember that gravity operates 24-7. Out of plumb is a bad thing that lasts for the life of the structure. When plumbing down from a high known point, allow the bob to oscillate freely and by eye note the center of the swing arc. When plumbing up from a known low point, establish a temporary reference point on the high piece, plumb down, determine the off-set of the down-plumbed point from the true spot and lay off this amount from the temporary reference. Modern laser equipment properly used will make this job easier.
Establishing Horizontal:
Messing up on the foundation and floor level will cause nothing but trouble for the rest of the job, and the whole building will be in danger of being out of whack.
The best tool for leveling, other than a surveyor’s instrument, is a long spirit level (at least 6-ft.). Check the bubble centering by rotating the level. Check the level’s quality by seeing how much the thickness of one penny (or dime) placed under one end will move the bubble. Your level should detect this error. The more the bubble moves with this test, the more sensitive the level. Sequential leveling, like sequential taping, is undesirable. Use a surveyor’s or builder’s optical or laser level to establish elevation over a long distance.
Establishing Right Angles:
A surveyor’s transit or theodolite is the most precise angle-measuring tool, but is impractical to use for short distances, where a tape is more convenient. Most every carpenter is familiar with the 3,4,5 sides of the right triangle. However, a much stronger and better combination is 20, 21, and 29 and its multiples, such as 100, 105, 145. This combination creates a nearly 45 degree angle at the acute corners thus providing a more accurate right angle.
Chalk and String Lines:
When chalking, make sure the line is taut and when snapping, be sure it’s pulled exactly perpendicular to the surface to be marked (especially important when marking across a sloped surface such as a roof). Do not use lengthy chalk lines since they often become misaligned when snapped; instead use a string or laser.
String or chalk all critical edges such as plates, wall sills, wall top plate, etc. Strings for alignment must be taken from accurate reference points; e.g. when stringing to straighten a wall, make sure the end-points of the string are anchored to accurately plumbed, secure corners. And do not lean ladders on the wall as you are trying to align it! Off set the reference line a small amount so as to keep it from being moved (string) or obscured (chalk). Use a gauge block to test conformance with the reference line.
Measurement and Marking Practice:
Linear measurements are made by reference to an “artificial” standard. Not all measurements are perfect to a zillionth of an inch, nor always mistake free. Since they are always susceptible to mistake and error, they are of less reliability. Right angles, when established by linear measures, also are of lesser reliability.
Your project may have been staked out by Surveyors, who usually measure in feet and decimals of a foot. Carpenters measure in feet, inches, and eighths (or sixteenths). It’s useful to remember that 1/100 a foot is nearly equal to 1/8 an inch.
Precision: Try to achieve +/- 1/8 inch in 100 ft. = 1:10,000 relative precision. Check diagonals of perimeter to 1/8 inch or 1/100 foot.
Length of studs, plates, rafters, joists, etc. should be accurate to better than +/- 1/8 inch, down to +/- 1/16 inch.
Smaller details require comparatively more precise measures. 1/32 inch is probably the smallest practical limit (we’re not making furniture).
Check all the tapes. Make sure everyone on the crew has a tape that accurately conforms to a standard tape. For measuring long distances, steel tapes are preferred over woven or fiberglass types, which will stretch unacceptably. Replace damaged or kinked tapes.
When measuring, keep the tape straight. Make sure the tape has no twists, kinks, or “esses”. Watch the sag in the tape when measuring long dimensions. Put tension on un-supported tapes, at least 10 lbs.
When laying out stud intervals, etc. use the entire tape length instead of sequentially adding smaller segments.
If plan dimensions are horizontal, so should the layout measure be! Be careful not to incline the tape when measuring a horizontal dimension. Also, keep the tape plumb for vertical measurements.
When careful measures are needed, do not use the hook at the end of the tape, instead “bury” ten inches or a foot and read the gauge lines.
When measuring inside a closed space where the full tape cannot be stretched, measure in two directions to an intermediate temporary reference line, and add the two values.
Trim the ends off lumber to obtain a clean, sharp end from which to measure.
Mark carefully for cuts. The lead in a carpenter’s dull pencil is usually too fat to make narrow lines needed for precision cuts. The thinner the mark, the more precise the cut. For extra precision, mark the cut line with a sharp pencil or even with a knife. Place the marker at the dimension mark then slide the straight edge to it for striking the line, rather than vice-versa.
Cut to the line, (unless it marks the center of the saw kerf, in which case cut it out) and make sure the saw kerf is on the correct (waste) side! Radial arm, table, and chop saws are capable of more accurate cuts than hand-held “skill” saws.
Framing Square:
Most carpenters have retired the classic framing square and adopted instead the “speed-square.” This 45 degree triangle contains gauge lines for laying out angle cuts for common and jack rafters, and is simple to use and convenient to carry. Unfortunately, this handy gizmo cannot help with face angles, seat cuts, length of jacks, or odd pitches.
The framing square, with its mysterious number tables, is a useful tool that should be available on every project for solving unusual framing problems. Its use is really not that complicated. The key is to understand roof pitch (or slope) which is expressed as rise in inches per foot of horizontal run. On the body (the longer leg) of the square is a table of numbers arranged underneath individual inch marks. The inch value associated with the mark represents the pitch rise per foot of horizontal run and the corresponding table contains settings for marking various cuts of rafters and jack rafters for that pitch, using the tabulated value on one arm of the square, and the appropriate index (12 normal or 17 for 45 degrees) on the other arm.
Story Stick:
For short, frequent and repeated measurements, use a story stick cut to the proper length. For installing out-lookers and other short pieces placed at right angles to another member, use a story stick cut to the size of the diagonal of a right triangle, with the leg lengths marked on it. This is less cumbersome than a framing square and more accurate than a speed square.
Door Frames:
Properly operating doors require accurately installed frames. A frame that is out of square, or with a post out of plumb, or a door with the plane not coincident with the wall, or a frame with the top plate not level, will bind, swing or latch poorly, fit poorly with gaps, besides just looking bad.
To make the plane of the frame flat and in line with the wall, string a line from the frame’s top left corner to the bottom right corner, and another string from the top right corner to the bottom left corner. These two strings should barely touch where they cross. If not, the door frame is out of plane. After making one side post fixed and plumb, adjust the bottom and top corners of the other side until the strings just touch and the top plate is inline with the wall. Check the plumb of this last post and the level of the top plate, and fix in position. (Thanks to Bernie Gueldner for this tip.)
Trimming to Length:
Sometimes it’s difficult to make accurate measurements. Try measuring accurate lengths to fit studs for a new 12 foot wall that frames onto an old existing wavy ceiling! The amount to trim off a piece to be placed in an existing space is given by the formula C = d^2/2h, where C is amount to cut off, d is the distance by which the trial piece off sets or leans, and h is the nominal length.
Example: A 12ft. replacement stud is too long to fit between the top and bottom plates in an existing wall; when put nearly in place it leans over out of plumb by 8”. The trim cut is (8x8)/(2x12x12) = 32/144 = or about 0.2 inch for a snug vertical fit.
SAFETY, a few words
You should have periodic meetings to discuss the usual dangers of working in the construction environment. The biggest concern with safety issues is, or should be, Protection of the Laborer, and not appeasing OSHA! The key risky parts of the Laborer, from bottom to top are:
Feet: Tennis shoes are popular foot gear but they offer very little foot protection. Consider hard-soled boots, maybe with steel toes. They don’t make Kevlar shoes, which is unfortunate, since they may be effective against the dreaded nail gun.
Legs: If you value your shins, please - no short pants.
Knees: Consider knee pads for those times you’ll be groveling.
Gloves: The modern construction gloves are a boon. They’ll help with blisters, splinters, and will tend to soften the finger smashing blows from errant hammers. Take them off when at the saw table.
Eyes: Eye protection is essential when engaged in activities where there are flying objects about.
Ears: Ear muffs or the soft rubber insert types will help preserve your hearing so you can listen to your PM, your Pastor’s sermons, the Choir, and your grand kids. Those noisy saws, air guns, Ram-Set devices, etc. inflict damage that is not repairable (unlike our work).
Head: Hard hats are a must and should always be worn, because the usual risk is you, running into things, as opposed to flying things hitting your head.
Entire Body: Ask your PM about ladder safety, and toe boards along the rim of the roof you’re working on. And if you don’t mind sky diving off the roof or out of a stinger-bucket, don’t bother with the restraining harness. Some times it’s a nuisance, but it’s better than a full body cast. Don’t forget to anchor it to something stout.
Project neatness is a safety concern. Work space littered with debris is dangerous and inefficient. Nails protruding from used lumber are a nasty hazard which should be assiduously eliminated.
Horseplay is not welcome on the job. But neither is Grouch nor Grim. A happy workforce is conducive to a safe work environment. The Lord, for whom we are working, loves a cheerful worker, and has promised His joyful blessing: “Delight thyself in the Lord, and He will give you the desire of your heart” (Ps 37:4). And remember to look out for your brother and sister laborer. We are one another’s keeper.
You should have periodic meetings to discuss the usual dangers of working in the construction environment. The biggest concern with safety issues is, or should be, Protection of the Laborer, and not appeasing OSHA! The key risky parts of the Laborer, from bottom to top are:
Feet: Tennis shoes are popular foot gear but they offer very little foot protection. Consider hard-soled boots, maybe with steel toes. They don’t make Kevlar shoes, which is unfortunate, since they may be effective against the dreaded nail gun.
Legs: If you value your shins, please - no short pants.
Knees: Consider knee pads for those times you’ll be groveling.
Gloves: The modern construction gloves are a boon. They’ll help with blisters, splinters, and will tend to soften the finger smashing blows from errant hammers. Take them off when at the saw table.
Eyes: Eye protection is essential when engaged in activities where there are flying objects about.
Ears: Ear muffs or the soft rubber insert types will help preserve your hearing so you can listen to your PM, your Pastor’s sermons, the Choir, and your grand kids. Those noisy saws, air guns, Ram-Set devices, etc. inflict damage that is not repairable (unlike our work).
Head: Hard hats are a must and should always be worn, because the usual risk is you, running into things, as opposed to flying things hitting your head.
Entire Body: Ask your PM about ladder safety, and toe boards along the rim of the roof you’re working on. And if you don’t mind sky diving off the roof or out of a stinger-bucket, don’t bother with the restraining harness. Some times it’s a nuisance, but it’s better than a full body cast. Don’t forget to anchor it to something stout.
Project neatness is a safety concern. Work space littered with debris is dangerous and inefficient. Nails protruding from used lumber are a nasty hazard which should be assiduously eliminated.
Horseplay is not welcome on the job. But neither is Grouch nor Grim. A happy workforce is conducive to a safe work environment. The Lord, for whom we are working, loves a cheerful worker, and has promised His joyful blessing: “Delight thyself in the Lord, and He will give you the desire of your heart” (Ps 37:4). And remember to look out for your brother and sister laborer. We are one another’s keeper.
APPENDIX (GLOSSARY AND DATA)
APPENDIX
GLOSSARY
Accuracy: Nearness to a true standard. Often confused with precision (q.v.).
Attitude Adjustment: A meeting at the close of each work session in which technical and job-related issues are discussed. Yah, sure.
Axial: Along the axis, or center-line of a structural member.
Beam: Structural member that carries loads by bending in a plane 90 degrees from its long axis, i.e. is loaded transversely. Following are specialty names for beams.
· Channel – rolled steel beam shaped like a sideways “u”
· Girder – built up steel beam for super heavy loads and long spans
· GluLam – manufactured wooden beam for heavy loads and long spans
· Header – commonly, a beam over the wall opening for doors or windows
· Horse – an inclined beam for stair tread support
· I-beam – describes the shape of a rolled steel or built up wooden beam
· Joist – for floor, ceiling, or roof support
· Ledger – beam parallel with and attached to a wall, that transfers load to the wall
· Girt – Heavier ledger receiving horizontal thrust besides vertical loads
· Lintel – another name for a header
· Mast – upright cantilever beam
· Purlin – beam supporting a roof between trusses or heavier beams
· Rafter – sloping beam for transferring roof loads, usually to a bearing wall
· Plank – a beam with the wide face up for load-bearing
· Stringer – longitudinal beam in bridge work
· T-beam – shape descriptor for a built-up beam, often composed of concrete and steel
· TJI (Not TGI) – brand name for an “I” beam manufactured from wood materials
Buck: Term suggested by Dan Baker. Next time you see Dan, ask him what it means.
Camber: Arching or bowing purposefully formed in a Glu-Lam or other beam. The purpose is to compensate for expected beam deflection. Be aware of this, if fastening to it another part of the structure that should appear level, such as a ceiling.
Cantilever: A beam anchored against bending at one end only, as apposed to a beam supported at two or more places. A tree limb is a cantilever beam.
Cement: Often mistaken as concrete (q.v.), but actually a constituent part thereof, when combined with water, sand and gravel. Discovered by Roman Engineers.
Column: Structural member that carries loads in compression along its long axis. A tree trunk is a column. (It’s also a cantilever when the wind blows.)
Compression: The force that resists loads by push.
Concrete: Often mistaken for cement. Concrete is placed, not poured, and cured, not dried. Invented by Roman Engineers.
Deflection: The amount of bend or sag in a beam when loaded.
Error: Not a mistake. An error is an unavoidable discrepancy from the true measure.
FBM: Foot Board Measure. Lumbermens’ speak for “board-foot”, 1” x 1” x 12”.
Footing: Bottom of a foundation, and wider than. Transfers loads to the earth.
Foot-Pound: A measure of bending stress or load. One pound push at the end of a restrained stick one foot from the restraint generates one foot pound of bending in the stick at the point of restraint.
Foundation: Stem wall extending up from the footing, upon which is placed and anchors the suprastructure.
Gismo: Thingamajig, only shorter.
Glossary: List of words with definitions, as understood by some Laborers.
Mistake: A flub. Reading “68” for “86”, for example. Everyone makes them, so don’t despair. Just rectify it, or design a work-around.
Moment: A fancy word for bending. Measured in foot-pounds (sometimes inch- pounds).
Normal: Perpendicular to a reference line.
Plate: The top or bottom end of a stud wall. The top plate is double, the bottom plate is single and of treated material when necessary. The bottom plate is also called the sill.
Power Nailer: A nasty tool invented for high speed anchoring of feet to a floor. The Romans did not have this, so they could wear sandals.
Precision: Refinement of measurement. Over precision wastes time, under precision wastes material and effort.
Project Manager. That guy who’s sometimes seen on the job, but most often on the phone. Some times he hollers. He prays a lot.
Psf: Pounds per square foot.
Psi: Pounds per square inch.
q.v.: Abbreviation of a Roman Engineering term which means “look it up”.
Shear: Cutting or sliding.
Shear wall: Wall especially anchored and constructed to resist seismic (earth quake) loads.
Sill: See Plate, above.
Strain: Amount of change in dimension (e.g. squashing or stretching) of a structural member due to load.
Stress: The internal force resisting an external load. The load imposed is limited by the capacity of the member, called the allowable stress. Direct stress is measured in pounds per square inch. Distinguished from strain.
Suprastructure: The correct spelling of “superstructure”. It comes from Latin, the lingo of Roman Engineers. Some of their stuff is still standing, which makes them “super”.
Tension: Pull; the opposite of compression.
Web: The interior parts of a beam or truss. The web members of a truss are usually in direct tension or compression.
GLOSSARY
Accuracy: Nearness to a true standard. Often confused with precision (q.v.).
Attitude Adjustment: A meeting at the close of each work session in which technical and job-related issues are discussed. Yah, sure.
Axial: Along the axis, or center-line of a structural member.
Beam: Structural member that carries loads by bending in a plane 90 degrees from its long axis, i.e. is loaded transversely. Following are specialty names for beams.
· Channel – rolled steel beam shaped like a sideways “u”
· Girder – built up steel beam for super heavy loads and long spans
· GluLam – manufactured wooden beam for heavy loads and long spans
· Header – commonly, a beam over the wall opening for doors or windows
· Horse – an inclined beam for stair tread support
· I-beam – describes the shape of a rolled steel or built up wooden beam
· Joist – for floor, ceiling, or roof support
· Ledger – beam parallel with and attached to a wall, that transfers load to the wall
· Girt – Heavier ledger receiving horizontal thrust besides vertical loads
· Lintel – another name for a header
· Mast – upright cantilever beam
· Purlin – beam supporting a roof between trusses or heavier beams
· Rafter – sloping beam for transferring roof loads, usually to a bearing wall
· Plank – a beam with the wide face up for load-bearing
· Stringer – longitudinal beam in bridge work
· T-beam – shape descriptor for a built-up beam, often composed of concrete and steel
· TJI (Not TGI) – brand name for an “I” beam manufactured from wood materials
Buck: Term suggested by Dan Baker. Next time you see Dan, ask him what it means.
Camber: Arching or bowing purposefully formed in a Glu-Lam or other beam. The purpose is to compensate for expected beam deflection. Be aware of this, if fastening to it another part of the structure that should appear level, such as a ceiling.
Cantilever: A beam anchored against bending at one end only, as apposed to a beam supported at two or more places. A tree limb is a cantilever beam.
Cement: Often mistaken as concrete (q.v.), but actually a constituent part thereof, when combined with water, sand and gravel. Discovered by Roman Engineers.
Column: Structural member that carries loads in compression along its long axis. A tree trunk is a column. (It’s also a cantilever when the wind blows.)
Compression: The force that resists loads by push.
Concrete: Often mistaken for cement. Concrete is placed, not poured, and cured, not dried. Invented by Roman Engineers.
Deflection: The amount of bend or sag in a beam when loaded.
Error: Not a mistake. An error is an unavoidable discrepancy from the true measure.
FBM: Foot Board Measure. Lumbermens’ speak for “board-foot”, 1” x 1” x 12”.
Footing: Bottom of a foundation, and wider than. Transfers loads to the earth.
Foot-Pound: A measure of bending stress or load. One pound push at the end of a restrained stick one foot from the restraint generates one foot pound of bending in the stick at the point of restraint.
Foundation: Stem wall extending up from the footing, upon which is placed and anchors the suprastructure.
Gismo: Thingamajig, only shorter.
Glossary: List of words with definitions, as understood by some Laborers.
Mistake: A flub. Reading “68” for “86”, for example. Everyone makes them, so don’t despair. Just rectify it, or design a work-around.
Moment: A fancy word for bending. Measured in foot-pounds (sometimes inch- pounds).
Normal: Perpendicular to a reference line.
Plate: The top or bottom end of a stud wall. The top plate is double, the bottom plate is single and of treated material when necessary. The bottom plate is also called the sill.
Power Nailer: A nasty tool invented for high speed anchoring of feet to a floor. The Romans did not have this, so they could wear sandals.
Precision: Refinement of measurement. Over precision wastes time, under precision wastes material and effort.
Project Manager. That guy who’s sometimes seen on the job, but most often on the phone. Some times he hollers. He prays a lot.
Psf: Pounds per square foot.
Psi: Pounds per square inch.
q.v.: Abbreviation of a Roman Engineering term which means “look it up”.
Shear: Cutting or sliding.
Shear wall: Wall especially anchored and constructed to resist seismic (earth quake) loads.
Sill: See Plate, above.
Strain: Amount of change in dimension (e.g. squashing or stretching) of a structural member due to load.
Stress: The internal force resisting an external load. The load imposed is limited by the capacity of the member, called the allowable stress. Direct stress is measured in pounds per square inch. Distinguished from strain.
Suprastructure: The correct spelling of “superstructure”. It comes from Latin, the lingo of Roman Engineers. Some of their stuff is still standing, which makes them “super”.
Tension: Pull; the opposite of compression.
Web: The interior parts of a beam or truss. The web members of a truss are usually in direct tension or compression.
PITCH TABLES
Pitch tables
Copy the appropriate table onto a hard piece of cardboard and place it into your tool belt for handy reference on the job.
To find an unknown dimension given a known dimension, multiply the known value by the tabulated factor appearing on the same line where the known factor is shown as one.
Example: For a 4:12 pitch, what is the slope distance given the vertical distance? From the table, find the line with “1” for the vertical, and multiply the known distance by 3.162 for the slope distance.
The angles shown are for jack rafters framed into a hip, with Tilt angle corresponding to the plumb cut, and Miter angle corresponding to the face cut. These angles assume the saw is indexed at Zero degrees on the table and 90 degrees on the miter gauge. If not, subtract the given value from 90 degrees for the correct saw angle setting.
Pitch 2 : 12 = 9.46^o, Hip length = 17.088” / ft. of common horizontal run.
Horizontal.....Vertical.....Slope
....1.................0.1667......1.014
....6.................1................6.083
....0.9864.......0.1644.......1
Difference in lengths of Jacks, 16” C-C = 16.221”, For Hips, Miter 44.5^o, Tilt 9.5^o
Pitch 4 : 12 = 18.435^o, Hip = 17.436” / ft. of common horizontal run.
Horizontal.....Vertical.....Slope
....1.................1/3.............1.054
....3.................1.................3.162
....0.949.......0.316............1
Diff. Jacks = 16.866”, Miter 43.5^o, Tilt 18.5^o
Pitch 6 : 12 = 26.56^o, Hip = 18.00” / ft. of common horizontal run.
Horizontal.....Vertical.....Slope
....1.................0.5..............1.118
....2.................1.................2.236
....0.8945......0.447...........1
Diff. Jacks = 17.889”, Miter 41 3/4^o, Tilt 26.5^o
Pitch 8 : 12 = 33.69^o, Hip = 18.762” / ft. of common horizontal run.
Horizontal.....Vertical.....Slope
....1.................2/3..............1.202
....1.5...............1.................1.803
....0.832.........0.555...........1
Diff. Jacks = 19.23”, Miter 39 3/4^o, Tilt 33 2/3^o
Copy the appropriate table onto a hard piece of cardboard and place it into your tool belt for handy reference on the job.
To find an unknown dimension given a known dimension, multiply the known value by the tabulated factor appearing on the same line where the known factor is shown as one.
Example: For a 4:12 pitch, what is the slope distance given the vertical distance? From the table, find the line with “1” for the vertical, and multiply the known distance by 3.162 for the slope distance.
The angles shown are for jack rafters framed into a hip, with Tilt angle corresponding to the plumb cut, and Miter angle corresponding to the face cut. These angles assume the saw is indexed at Zero degrees on the table and 90 degrees on the miter gauge. If not, subtract the given value from 90 degrees for the correct saw angle setting.
Pitch 2 : 12 = 9.46^o, Hip length = 17.088” / ft. of common horizontal run.
Horizontal.....Vertical.....Slope
....1.................0.1667......1.014
....6.................1................6.083
....0.9864.......0.1644.......1
Difference in lengths of Jacks, 16” C-C = 16.221”, For Hips, Miter 44.5^o, Tilt 9.5^o
Pitch 4 : 12 = 18.435^o, Hip = 17.436” / ft. of common horizontal run.
Horizontal.....Vertical.....Slope
....1.................1/3.............1.054
....3.................1.................3.162
....0.949.......0.316............1
Diff. Jacks = 16.866”, Miter 43.5^o, Tilt 18.5^o
Pitch 6 : 12 = 26.56^o, Hip = 18.00” / ft. of common horizontal run.
Horizontal.....Vertical.....Slope
....1.................0.5..............1.118
....2.................1.................2.236
....0.8945......0.447...........1
Diff. Jacks = 17.889”, Miter 41 3/4^o, Tilt 26.5^o
Pitch 8 : 12 = 33.69^o, Hip = 18.762” / ft. of common horizontal run.
Horizontal.....Vertical.....Slope
....1.................2/3..............1.202
....1.5...............1.................1.803
....0.832.........0.555...........1
Diff. Jacks = 19.23”, Miter 39 3/4^o, Tilt 33 2/3^o
SHEATHING CUT ANGLE AT VALLEY LINE
SHEATHING CUT ANGLES AT VALLEY LINE For roofs intersecting at 90 degrees
This angle is measured from a perpendicular to the ridge line, extending to the valley line. Often these angles are “eyeballed” and cut to fit by trial and error. The following table will help you avoid this frustrating, wasteful, and time consuming practice.
Roof pitches or slopes are measured in inches of vertical rise per foot of horizontal run. In the table, “S” equals the steepest roof pitch of the intersecting pair, and “F” equals the flattest. When the pitches are equal, obviously S = F. (Angle values in degrees.) Click picture for larger view; Click "back" to return
For combinations of other pitches, use the following equations to compute the angles:
S angle = ARCTAN [((S/F)12)/(S^2 +144)^0.5 ]
F angle = ARCTAN [12/(S^2(1+144/F^2))^0.5]
Example: A 3:12 roof intersects a 5:12 roof at 90 degrees. What is the cut angle for sheathing on the steepest roof?
S angle = ARCTAN [((5/3)12)/(5^2 + 144)^0.5]= ARCTAN [20/169)^0.5] = 57 degrees
Thanks to Dave Grazier and Martech Associates of Millheim, Pa. for this data.
This angle is measured from a perpendicular to the ridge line, extending to the valley line. Often these angles are “eyeballed” and cut to fit by trial and error. The following table will help you avoid this frustrating, wasteful, and time consuming practice.
Roof pitches or slopes are measured in inches of vertical rise per foot of horizontal run. In the table, “S” equals the steepest roof pitch of the intersecting pair, and “F” equals the flattest. When the pitches are equal, obviously S = F. (Angle values in degrees.) Click picture for larger view; Click "back" to return
For combinations of other pitches, use the following equations to compute the angles:
S angle = ARCTAN [((S/F)12)/(S^2 +144)^0.5 ]
F angle = ARCTAN [12/(S^2(1+144/F^2))^0.5]
Example: A 3:12 roof intersects a 5:12 roof at 90 degrees. What is the cut angle for sheathing on the steepest roof?
S angle = ARCTAN [((5/3)12)/(5^2 + 144)^0.5]= ARCTAN [20/169)^0.5] = 57 degrees
Thanks to Dave Grazier and Martech Associates of Millheim, Pa. for this data.
SHEATHING BEVEL ANGLE AT VALLEY LINE
SHEATHING BEVEL ANGLES AT VALLEY LINE (For butt joints)
Sheathing is often not beveled to make a butt joint at the valley line, since it may be considered a needless refinement. However, beveling makes for a neater and tighter joint. To make the bevel, cut on the back side and angle the skill saw table the amount shown in this table. Angle values in degrees.
Use the following formulas to calculate these angles for other roof combinations:
Bevel Angle for steep roof = ArcSin {{[S/(Cos Sangle(S^2 + 144)^0.5)] – [S/((S12/F)^2 + 144 + S^2)^0.5]}/Tan Sangle}Bevel Angle for flatter roof = ArcSin {{[F/(Cos Fangle(F^2 + 144)^0.5)] – [F/((F12/S)^2 +144+ F^2)^0.5]}/Tan Fangle}
Example: A 3:12 pitch roof intersects a 5:15 pitch roof. What is the bevel angle for the valley sheathing for the steepest roof?
Bevel Angle = ArcSin {{[5/(Cos 57.0^0(5^2 + 144)^0.5)] – [5/((5x12/3)^2 + 144 + 5^2)^0.5]}/Tan 57.0^0} = ArcSin {(0.706 – 0.21) /1.54} = 19 degrees
Thanks to Boiseans David Valentine and Bob Firman (famous Idaho Math Maven) for help with these equations.
Sheathing is often not beveled to make a butt joint at the valley line, since it may be considered a needless refinement. However, beveling makes for a neater and tighter joint. To make the bevel, cut on the back side and angle the skill saw table the amount shown in this table. Angle values in degrees.
Use the following formulas to calculate these angles for other roof combinations:
Bevel Angle for steep roof = ArcSin {{[S/(Cos Sangle(S^2 + 144)^0.5)] – [S/((S12/F)^2 + 144 + S^2)^0.5]}/Tan Sangle}Bevel Angle for flatter roof = ArcSin {{[F/(Cos Fangle(F^2 + 144)^0.5)] – [F/((F12/S)^2 +144+ F^2)^0.5]}/Tan Fangle}
Example: A 3:12 pitch roof intersects a 5:15 pitch roof. What is the bevel angle for the valley sheathing for the steepest roof?
Bevel Angle = ArcSin {{[5/(Cos 57.0^0(5^2 + 144)^0.5)] – [5/((5x12/3)^2 + 144 + 5^2)^0.5]}/Tan 57.0^0} = ArcSin {(0.706 – 0.21) /1.54} = 19 degrees
Thanks to Boiseans David Valentine and Bob Firman (famous Idaho Math Maven) for help with these equations.
COLUMN LOADS
COLUMN LOADS
The Table below provides information for building temporary scaffolds and other uses where compression members are needed.
Note the dramatic increase in load capacity with the “T” shape ( a double 2x4 in “T” shape has about 50% greater capacity than double 2x4’s flat, and nearly the same capacity as double 2x6’s nailed flat). This is primarily because the “T” addition increases the rigidity of the column by lowering the “L/d” slenderness ratio.
Also note the decrease in load capacity where the unsupported length is increased. The unsupported length can be reduced somewhat when “X” bracing temporary columns, by placing braces for the narrow dimension a foot or two below or above the top or bottom respectively of the column.
Note that single 2x4’s should not be used as columns much longer than 6 feet to prop up any appreciable load.
Allowable Column Loads in Pounds (Structural Lumber Only)
Column Type ..dbl2x4....dbl2x4"T"....2x6......dbl2x6"sq".....2x6&2x4
Column Shape..Square.......Tee............................Square................Tee
Unsupported
length, ft.
...6......................6620*.......9010*.......1300........1040*........16880*
...7......................4860.........6620*.......................7640*.......16880*
...8......................3720.........5070*.........................5850.......13290*
..10.....................2380.........3240...........................3740.........8510*
..12.....................1650..........2250..........................2600.........5910*
..14........................................1650.........................1910..........4340
..16...........................................................................................3320
* These loads will crush wood if bearing perp. to grain and require metal shoe or concrete bearing for column support.
The Table below provides information for building temporary scaffolds and other uses where compression members are needed.
Note the dramatic increase in load capacity with the “T” shape ( a double 2x4 in “T” shape has about 50% greater capacity than double 2x4’s flat, and nearly the same capacity as double 2x6’s nailed flat). This is primarily because the “T” addition increases the rigidity of the column by lowering the “L/d” slenderness ratio.
Also note the decrease in load capacity where the unsupported length is increased. The unsupported length can be reduced somewhat when “X” bracing temporary columns, by placing braces for the narrow dimension a foot or two below or above the top or bottom respectively of the column.
Note that single 2x4’s should not be used as columns much longer than 6 feet to prop up any appreciable load.
Allowable Column Loads in Pounds (Structural Lumber Only)
Column Type ..dbl2x4....dbl2x4"T"....2x6......dbl2x6"sq".....2x6&2x4
Column Shape..Square.......Tee............................Square................Tee
Unsupported
length, ft.
...6......................6620*.......9010*.......1300........1040*........16880*
...7......................4860.........6620*.......................7640*.......16880*
...8......................3720.........5070*.........................5850.......13290*
..10.....................2380.........3240...........................3740.........8510*
..12.....................1650..........2250..........................2600.........5910*
..14........................................1650.........................1910..........4340
..16...........................................................................................3320
* These loads will crush wood if bearing perp. to grain and require metal shoe or concrete bearing for column support.
Saturday, April 4, 2009
REFERENCE EQUATIONS AND EXAMPLES
Reference Equations
1) Safe column load psi = P/A = E(0.3)/(L/d)^2 < f. Doug Fir lumber E = 1,210,000,
f = 1250. Check supporting bearing.
2) The maximum bending moment M in foot-pounds due to uniform load “w” pounds per foot is M= (1/8)wl^2, where l is the span in feet (simple support).
3) If the load W is concentrated at mid span, M =(1/4) (W l)
4) The stress in psi due to bending moment is f = 12 M / S
5) S is a “shape factor” depending on the dimensions of the beam. For a rectangular beam, S = b d^2/ 6 with b = the beam width and d = the beam depth, in inches.
2x4 S = (1.5x3.5x3.5)/6 = 3.06, M capacity = 3.06 x 1250 = 3825 in-lbs or 319 ft lbs
2x6 S = (1.5x5.5x5.5)/6 = 7.56, M capacity = 7.56 x 1250 = 9450 in-lbs or 787 ft lbs
2x8 S = (1.5x7.5x7.5)/6 = 14.1, M capacity = 14.1 x 1250 = 17578 in-lbs or 1465 ft lb
Handbooks give the value of S for non-rectangular shapes.
Examples:
1) You are remodeling a building and need to temporarily support the end of a purlin that is holding up a section of asphalt shingle roof that has three layers of shingles. You need to shore up one end of the purlin at 15 ft. height. The purlins are spaced six feet on center, and span 22 feet. What is the load on the purlin, and what is the size of post needed? Assume the total existing roof dead load is 15 psf.
Total roof load = 6 x 22 x 15 = 1980 lbs
Load on each end of the purlin = half = 990 lbs, use a double 2 x 4 post in T shape.
2) It is planned to add another layer of shingles onto the existing roof of example one. The new shingles will add 5 psf dead load. Is the existing purlin with S = 50 adequate? Assume the allowable f = 1250 psi.
Existing distributed load along the purlin = 1980/22 = 90 plf
Existing maximum bending moment = 1/8 (90 x 22 x 22) = 5445 ft-lbs
Existing bending stress = 12 x 5445/50 = 1307 psi, which is greater than allowable. The purlin appears to be a bit over-stressed under current loading. Existing shingles must be removed.
3) Scaffolding is needed along side a building, at 14 foot height. You want to use 2 each, 2x12x10’ planks, spanning 8 feet. Assume a concentrated live load at mid span of 300 lbs. per plank. Is this a safe span for these planks? What is the best 14 foot column to use? What should be used as a cross beam to support the planks?
S value per plank (actual size 1.5x11) is bdd/6 = (11x1.5x1.5)/6 = 4.125
M due to concentrated load W is (¼) 300x 8 = 600 ft-lbs = 600x12 =7200 inch-pounds
Ignoring dead load, bending stress f is M/S = 7200/4.125 = 1745 psi. This is greater than allowable, which will lead to excessive deflection and “springiness”. The planks can be stiffened by fastening a 2x4 “T” underneath along the centerline. Reducing the load or span also are options.
Each scaffold bay will be supported by four corner posts. The live load at each corner post will be ¼ of 600 pounds, or 150 pounds per single bay, or twice that for posts at double bays, i.e. 300 pounds. Notice from the column table that if a single 2x post is used, it must be braced at half-height, because L/d exceeds 50. A double 2x4 post will support this load securely.
The cross beam to support 4 planks at a double bay must carry 600 lbs live load, plus the weight of the planks themselves. At 3 pounds per FBM, each 2x12 plank weighs roughly 10x2x1x3 = 60 lbs. Therefore total load per beam is 720 lbs, assumed uniformly distributed over a span of (say) 4 feet. M = 1/8wl^2 = 1/8 (720/4)16 = 360 ft-lbs. A 2x6 is adequate. Shear at each beam end will be half 720 lbs = 360 lbs, requiring at least a four 16 penny nail connection to each post. Nail in a random pattern, with no more than one nail per growth ring. Avoid nailing close to the top edge of the beam.
1) Safe column load psi = P/A = E(0.3)/(L/d)^2 < f. Doug Fir lumber E = 1,210,000,
f = 1250. Check supporting bearing.
2) The maximum bending moment M in foot-pounds due to uniform load “w” pounds per foot is M= (1/8)wl^2, where l is the span in feet (simple support).
3) If the load W is concentrated at mid span, M =(1/4) (W l)
4) The stress in psi due to bending moment is f = 12 M / S
5) S is a “shape factor” depending on the dimensions of the beam. For a rectangular beam, S = b d^2/ 6 with b = the beam width and d = the beam depth, in inches.
2x4 S = (1.5x3.5x3.5)/6 = 3.06, M capacity = 3.06 x 1250 = 3825 in-lbs or 319 ft lbs
2x6 S = (1.5x5.5x5.5)/6 = 7.56, M capacity = 7.56 x 1250 = 9450 in-lbs or 787 ft lbs
2x8 S = (1.5x7.5x7.5)/6 = 14.1, M capacity = 14.1 x 1250 = 17578 in-lbs or 1465 ft lb
Handbooks give the value of S for non-rectangular shapes.
Examples:
1) You are remodeling a building and need to temporarily support the end of a purlin that is holding up a section of asphalt shingle roof that has three layers of shingles. You need to shore up one end of the purlin at 15 ft. height. The purlins are spaced six feet on center, and span 22 feet. What is the load on the purlin, and what is the size of post needed? Assume the total existing roof dead load is 15 psf.
Total roof load = 6 x 22 x 15 = 1980 lbs
Load on each end of the purlin = half = 990 lbs, use a double 2 x 4 post in T shape.
2) It is planned to add another layer of shingles onto the existing roof of example one. The new shingles will add 5 psf dead load. Is the existing purlin with S = 50 adequate? Assume the allowable f = 1250 psi.
Existing distributed load along the purlin = 1980/22 = 90 plf
Existing maximum bending moment = 1/8 (90 x 22 x 22) = 5445 ft-lbs
Existing bending stress = 12 x 5445/50 = 1307 psi, which is greater than allowable. The purlin appears to be a bit over-stressed under current loading. Existing shingles must be removed.
3) Scaffolding is needed along side a building, at 14 foot height. You want to use 2 each, 2x12x10’ planks, spanning 8 feet. Assume a concentrated live load at mid span of 300 lbs. per plank. Is this a safe span for these planks? What is the best 14 foot column to use? What should be used as a cross beam to support the planks?
S value per plank (actual size 1.5x11) is bdd/6 = (11x1.5x1.5)/6 = 4.125
M due to concentrated load W is (¼) 300x 8 = 600 ft-lbs = 600x12 =7200 inch-pounds
Ignoring dead load, bending stress f is M/S = 7200/4.125 = 1745 psi. This is greater than allowable, which will lead to excessive deflection and “springiness”. The planks can be stiffened by fastening a 2x4 “T” underneath along the centerline. Reducing the load or span also are options.
Each scaffold bay will be supported by four corner posts. The live load at each corner post will be ¼ of 600 pounds, or 150 pounds per single bay, or twice that for posts at double bays, i.e. 300 pounds. Notice from the column table that if a single 2x post is used, it must be braced at half-height, because L/d exceeds 50. A double 2x4 post will support this load securely.
The cross beam to support 4 planks at a double bay must carry 600 lbs live load, plus the weight of the planks themselves. At 3 pounds per FBM, each 2x12 plank weighs roughly 10x2x1x3 = 60 lbs. Therefore total load per beam is 720 lbs, assumed uniformly distributed over a span of (say) 4 feet. M = 1/8wl^2 = 1/8 (720/4)16 = 360 ft-lbs. A 2x6 is adequate. Shear at each beam end will be half 720 lbs = 360 lbs, requiring at least a four 16 penny nail connection to each post. Nail in a random pattern, with no more than one nail per growth ring. Avoid nailing close to the top edge of the beam.
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