Post-Frame Building Design Manual

National Frame Builders Association

Post-Frame Building Design Manual

Chapter 1: INTRODUCTION TO POST-FRAME BUILDINGS 1.1 General

or masonry foundation. Figure 1.1 illustrates the structural components of a post-frame building.

1.1.1 Main Characteristics. Post-frame buildings are structurally efficient buildings composed of main members such as posts and trusses and secondary components such as purlins, girts, bracing and sheathing Snow and wind loads are transferred from the sheathing to the secondary members. Loads are transferred to the ground through the posts that typically are embedded in the ground or surface-mounted to a concrete

1.1.2 Use. Post-frame construction is wellsuited for many commercial, industrial, agricultural and residential applications. Post-frame offers unique advantages in terms of design and construction flexibility and structural efficiency. For these reasons, post-frame construction has experienced rapid growth, particularly in nonagricultural applications.

Roof cladding

Ridge cap

Purlin

Truss

Wall cladding

Doorway Pressure preservative treated post Pressure preservative treated splash board Concrete footing

Wall girt

Figure 1.1. Simplified diagram of a post-frame building. Some components such as permanent roof truss bracing and interior finishes are not shown.

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tion on post and foundation design (Knight, 1990). New roof panel constructions using highstrength steel and customized screw fasteners have dramatically improved diaphragm stiffness and strength.

1.2 Evolution 1.2.1 The concept of pole-type structures is not new. Archeological evidence exists in abundance that pole buildings have been used for human housing for thousands of years. In America, pole buildings began appearing on farms in the 19th century (Norum, 1967).

1.3 Advantages 1.3.1 Reliability. Outstanding structural performance of post-frame buildings under adverse conditions such as hurricanes is welldocumented. Professor Gurfinkel, in his wood engineering textbook, cites superior performance of post-frame buildings over conventional construction during hurricane Camille in 1969 (Gurfinkel, 1981). Harmon et. al (1992) reported that post-frame buildings constructed according to engineered plans generally withstood hurricane Hugo (wind gusts measured at 109 mph). Since post-frame buildings are relatively light weight, seismic forces do not control the design unless significant additional dead loads are applied to the structure (Faherty and Williamson, 1989; Taylor, 1996).

1.2.2 Pole-type construction resurfaced in 1930 when Mr. H. Howard Doane introduced the "modern pole barn" as an economical alternative to conventional barns (Knight, 1989). Mr. Doane was the founder of Doane's Agricultural Service, a firm specializing in managing farms for absentee owners. These early pole barns were constructed with red cedar poles that were naturally resistant to decay, trusses spaced 2 ft oncenter, 1-inch nominal purlins and galvanized steel sheathing. In the 1940s, pole barn construction was refined by using creosote preservative-treated sawn posts, wider truss and purlin spacings, and improved steel sheathing. Mr. Bernon G. Perkins, an employee of Doane's, is credited for many of the refinements to Doane's original pole barn. In 1949, Mr. Perkins applied for the first patent on the pole building concept through Doane's Agricultural Service, and the patent was issued in 1953. Rather than protecting their patent, they publicized the concept and encouraged its use throughout the world. In 1995, the post-frame building concept was recognized as an Historic Agricultural Engineering Landmark by the American Society of Agricultural Engineers.

1.3.2 Economy. Significant savings can be obtained with post-frame construction in terms of materials, labor, construction time, equipment and building maintenance. For example, postframe buildings require less extensive foundations than other building types because the wall sections between the posts are non-load bearing. Embedded post foundations commonly used in post-frame require less concrete, heavy equipment, labor, and construction time than conventional perimeter foundations. Additionally, embedded post foundations are better-suited for wintertime construction.

1.2.3 In the past two decades, post-frame construction has been further enhanced by the developments of metal-plate connected wood trusses, nail- and glue-laminated posts, highstrength steel sheathing, fasteners and diaphragm design methods. Composites such as laminated posts and structural composite lumber offer advantages of superior strength and stiffness, dimensional stability, and they can be obtained in a variety of sizes and pressure preservative treatments. Developments in metalplate connected wood truss technology allow clear spans of over 80 feet. Design procedures were introduced in the early 1980s to more accurately account for the effect of diaphragm ac-

1.3.3 Versatility. Post-frame construction facilitates design flexibility. Posts can be embedded into the ground or surface-mounted to a concrete foundation. Steel sheathing can be replaced with wood siding, brick veneer, and conventional roofing materials, to satisfy the appearance and service requirements of the customer. One-hour fire-rated wall and roof/ceiling constructions have been developed for wood framed assemblies. Exposed glued-laminated and solid-sawn timbers can be substituted for trusses made from dimension lumber to achieve desired architectural effects.

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ASAE: The Society for engineering in agricultural, food, and biological systems (formerly American Society of Agricultural Engineers).

1.4 Industry Profile 1.4.1 Post-frame construction has experienced tremendous growth since World War II. This growth was fueled by the abundant supplies of steel and pressure preservative-treated wood, together with the need for low-cost structures. In the 1950s and 1960s, the pole barn industry was characterized by large numbers of independent builders (Knight, 1989). During this time, pole builders were expanding from their traditional agricultural base into other construction markets. This expansion into code-enforced construction required rigorous documentation of engineering designs and more involvement in the building code arena.

Anchor Bolts: Bolts used to anchor structural members to a foundation. Commonly used in post-frame construction to anchor posts to the concrete foundation. ASCE: American Society of Civil Engineers. AWC: American Wood Council. The wood products division of the American Forest & Paper Association (AF&PA). AWPB: American Wood Preservers Bureau. Bay: The area between adjacent primary frames in a building. In a post-frame building, a bay is the area between adjacent post-frames.

1.4.2 NFBA. Approximately 20 builders met in 1969 to discuss challenges facing the postframe building industry. The group voted in favor of forming the National Frame Builders Association (NFBA). The NFBA became incorporated in 1971 and the first national headquarters was established in Chicago, Illinois. Today, the National Frame Builders Association is headquartered in Lawrence, Kansas and includes over 300 contractors and suppliers, with regional branches throughout the U.S. In addition, a Canadian Division of NFBA was created in 1984.

Bearing Height: Vertical distance between a pre-defined baseline (generally the grade line) and the bearing point of a component. Bearing Point: The point at which a component is supported. Board: Wood member less than two (2) nominal inches in thickness and one (1) or more nominal inches in width.

1.4.3 The post-frame industry has become one of the fastest growing segments of the total construction industry. Based on light-gauge steel sales, post-frame industry revenues are estimated to be from 2 to 2.5 billion dollars in 1990.

Board-Foot (BF): A measure of lumber volume based on nominal dimensions. To calculate the number of board-feet in a piece of lumber, multiply nominal width in inches by nominal thickness in inches times length in feet and divide by 12.

1.5 Terminology

BOCA: Building Officials & Code Administrators International, Inc. The organization responsible for maintaining and publishing the National Building Code.

AF&PA: American Forest & Paper Association (formerly National Forest Products Association). AITC: American Institute of Timber Construction.

Bottom Chord: An inclined or horizontal member that establishes the bottom of a truss.

ALSC: American Lumber Standard Committee. Bottom Plank: See Splashboard. ANSI: American National Standards Institute Butt Joint: The interface at which the ends of two members meet in a square cut joint.

APA: The Engineered Wood Association (formerly the American Plywood Association)

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Camber: A predetermined curvature designed into a structural member to offset the anticipated deflection when loads are applied.

Fascia: Flat surface (or covering) located at the outer end of a roof overhang or cantilever end. Flashing: Sheet metal or plastic components used at major breaks and/or openings in walls and roofs to insure weather-tightness in a structure.

Check: Separation of the wood that usually extends across the annual growth rings (i.e., a split perpendicular-to-growth rings). Commonly results from stresses that build up in wood during seasoning.

Footing: Support base for a post or foundation wall that distributes load over a greater soil area.

Cladding: The exterior and interior coverings fastened to the wood framing.

Frame Spacing: Horizontal distance between post-frames (see post-frame and post-frame building). In the absence of posts, the frame spacing is generally equated to the distance between adjacent trusses (or rafters). Frame spacing may vary within a building.

Clear Height: Vertical distance between the finished floor and the lowest part of a truss, rafter, or girder. Collars: Components that increase the bearing area of portions of the post foundation, and thus increase lateral and vertical resistance.

Gable: Triangular portion of the endwall of a building directly under the sloping roof and above the eave line.

Components and Cladding: Elements of the building envelope that do not qualify as part of the main wind-force resisting system. In postframe buildings, this generally includes individual purlins and girts, and cladding.

Gable Roof: Roof with one slope on each side. Each slope is of equal pitch. Gambrel Roof: Roof with two slopes on each side. The pitch of the lower slope is greater than that of the upper slope.

Diaphragm: A structural assembly comprised of structural sheathing (e.g., plywood, metal cladding) that is fastened to wood or metal framing in such a manner the entire assembly is capable of transferring in-plane shear forces.

Girder: A large, generally horizontal, beam. Commonly used in post-frame buildings to support trusses whose bearing points do not coincide with a post.

Diaphragm Action: The transfer of load by a diaphragm.

Girt: A secondary framing member that is attached (generally at a right angle) to posts. Girts laterally support posts and transfer load between wall cladding and posts.

Diaphragm Design: Design of roof and ceiling diaphragm(s), wall diaphragms (shearwalls), primary and secondary framing members, component connections, and foundation anchorages for the purpose of transferring lateral (e.g., wind) loads to the foundation structure.

Glued-Laminated Timber: Any member comprising an assembly of laminations of lumber in which the grain of all laminations is approximately parallel longitudinally, in which the laminations are bonded with adhesives.

Dimension Lumber: Wood members from two (2) nominal inches to but not including five (5) nominal inches in thickness, and 2 or more nominal inches in width.

Grade Girt: See Splashboard. Grade Line (grade level): The line of intersection between the building exterior and the top of the soil, gravel, and/or pavement in contact with the building exterior. For post-frame building

Eave: The part of a roof that projects over the sidewalls. In the absence of an overhang, the eave is the line along the sidewall formed by the intersection of the wall and roof planes.

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design, the grade line is generally assumed to be no lower than the lower edge of the splashboard.

Seismic Load: Lateral load acting in the horizontal direction on a structure due to the action of earthquakes.

Header: A structural framing member that supports the ends of structural framing members that have been cut short by a floor, wall, ceiling, or roof opening.

Snow Load: A load imposed on a structure due to accumulated snow. Wind Loads: Loads caused by the wind blowing from any direction.

Hip Roof: Roof which rises by inclined planes from all four sides of a building.

Lumber Grade: The classification of lumber in regard to strength and utility in accordance with the grading rules of an approved (ALSC accredited) lumber grading agency.

IBC: International Building Code. ICBO: International Conference of Building Officials. The organization responsible for maintaining and publishing the Uniform Building Code.

LVL: see Laminated Veneer Lumber. Main Wind-Force Resisting System: An assemblage of structural elements assigned to provide support and stability for the overall structure. Main wind-force resisting systems in post-frame buildings include the individual postframes, diaphragms and shearwall

Knee Brace: Inclined structural framing member connected on one end to a post/column and on the other end to a truss/rafter. Laminated Assembly: A structural member comprised of dimension lumber fastened together with mechanical fasteners and/or adhesive. Horizontally- and vertically-laminated assemblies are primarily designed to resist bending loads applied perpendicular and parallel to the wide face of the lumber, respectively.

Manufactured Component. A component that is assembled in a manufacturing facility. The wood trusses and laminated columns used in post-frame buildings are generally manufactured components.

Laminated Veneer Lumber (LVL) A structural composite lumber assembly manufactured by gluing together wood veneer sheets. Each veneer is orientated with its wood fibers parallel to the length of the member. Individual veneer thickness does not exceed 0.25 inches.

MBMA: Metal Building Manufacturers Association. NDS®: National Design Specification® for Wood Construction. Published by AF&PA. Mechanically Laminated Assembly: A laminated assembly in which wood laminations have been joined together with nails, bolts and/or other mechanical fasteners.

Loads: Forces or other actions that arise on structural systems from the weight of all permanent construction, occupants and their possessions, environmental effects, differential settlement, and restrained dimensional changes.

Metal Cladding: Metal exterior and interior coverings, usually cold-formed aluminum or steel sheet, fastened to the structural framing.

Dead Loads: Gravity loads due to the weight of permanent structural and nonstructural components of the building, such as wood framing, cladding, and fixed service equipment.

NFBA: National Frame Builders Association. NFPA: National Fire Protection Association

Live Loads: Loads superimposed by the construction, use and occupancy of the building, not including wind, snow, seismic or dead loads.

Nominal size: The named size of a member, usually different than actual size (as with lumber).

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Orientated Strand Board (OSB): Structural wood panels manufactured from reconstituted, mechanically oriented wood strands bonded with resins under heat and pressure.

Post-Frame Building: A building system whose primary framing system is principally comprised of post-frames. Post Height: The length of the non-embedded portion of a post.

Orientated Strand Lumber (OSL): Structural composite lumber (SCL) manufactured from mechanically oriented wood strands bonded with resins under heat and pressure. Also known as laminated strand lumber (LSL)

Pressure Preservative Treated (PPT) Wood: Wood pressure-impregnated with an approved preservative chemical under approved treatment and quality control procedures.

OSB: See Orientated Strand Board. Primary Framing: The main structural framing members in a building. The primary framing members in a post-frame building include the columns, trusses/rafters, and any girders that transfer load between trusses/rafters and columns.

Parallel Strand Lumber (PSL): Structural composite lumber (SCL) manufactured by cutting 1/8-1/10 inch thick wood veneers into narrow wood strands, and then gluing and pressing the strands together. Individual strands are up to 8 feet in length. Prior to pressing, strands are oriented so that they are parallel to the length of the member.

PSL: See Parallel Strand Lumber. Purlin: A secondary framing member that is attached (generally at a right angle) to rafters/ trusses. Purlins laterally support rafters and trusses and transfer load between exterior cladding and rafters/trusses.

Pennyweight: A measure of nail length, abbreviated by the letter d. Plywood: A built-up panel of laminated wood veneers. The grain orientation of adjacent veneers are typically 90 degrees to each other.

Rafter: A sloping roof framing member.

Pole: A round, unsawn, naturally tapered post.

Rake: The part of a roof that projects over the endwalls. In the absence of an overhang, the rake is the line along the endwall formed by the intersection of the wall and roof planes.

Post: A rectangular member generally uniform in cross section along its length. Post may be sawn or laminated dimension lumber. Commonly used in post-frame construction to transfer loads from main roof beams, trusses or rafters to the foundation.

Ridge: Highest point on the roof of a building which describes a horizontal line running the length of the building.

Post Embedment Depth: Vertical distance between the bottom of a post and the lower edge of the splashboard.

Ring Shank Nail: See threaded nail. Roof Overhang: Roof extension beyond the endwall/sidewall of a building.

Post Foundation: The embedded portion of a structural post and any footing and/or attached collar.

Roof Slope: The angle that a roof surface makes with the horizontal. Usually expressed in units of vertical rise to 12 units of horizontal run.

Post Foundation Depth: Vertical distance between the bottom of a post foundation and the lower edge of the splashboard.

SBC: Standard Building Code (see SBCCI).

Post-Frame: A structural building frame consisting of a wood roof truss or rafters connected to vertical timber columns or sidewall posts.

SBCCI: Southern Building Code Congress International, Inc. The organization responsible for maintaining and publishing the Standard Building Code.

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Secondary Framing: Structural framing members that are used to (1) transfer load between exterior cladding and primary framing members, and/or (2) laterally brace primary framing members. The secondary framing members in a post-frame building include the girts, purlins and any structural wood bracing.

span" for rafters and joists in conventional construction.

Self-Drilling Screw: A screw fastener that combines the functions of drilling and tapping (thread forming). Generally used when one or more of the components to be fastened is metal with a thickness greater than 0.03 inches

Overall Span: Total horizontal length of an installed horizontal or inclined member.

Out-To-Out Span: Horizontal distance between the outer faces of supports. Commonly used in specifying metal-plateconnected wood trusses.

SPIB: Southern Pine Inspection Bureau. Skirtboard: See Splashboard.

Self-Piercing Screw: A self-tapping (thread forming) screw fastener that does not require a pre-drilled hole. Differs from a self-drilling screw in that no material is removed during screw installation. Used to connect light-gage metal, wood, gypsum wallboard and other "soft" materials.

Splashboard: A preservative treated member located at grade that functions as the bottom girt. Also referred to as a skirtboard, splash plank, bottom plank, and grade girt. Splash Plank: See Splashboard.

SFPA: Southern Forest Products Association

Stitch (or Seam) Fasteners: Fasteners used to connect two adjacent pieces of metal cladding, and thereby adding shear continuity between sheets.

Shake: Separation of annual growth rings in wood (splitting parallel-to-growth rings). Usually considered to have occurred in the standing tree or during felling.

Structural Composite Lumber (SCL): Reconstituted wood products comprised of several laminations or wood strands held together with an adhesive, with fibers primarily oriented along the length of the member. Examples include LVL and PSL.

Shearwall: A vertical diaphragm in a structural framing system. A shearwall is any endwall, sidewall, or intermediate wall capable of transferring in-plane shear forces. Siphon Break: A small groove to arrest the capillary action of two adjacent surfaces. Soffit: The underside covering of roof overhangs.

Threaded Nail: A type of nail with either annual or helical threads in the shank. Threaded nails generally are made from hardened steel and have smaller diameters than common nails of similar length.

Soil Pressure: Load per unit area that the foundation of a structure exerts on the soil.

Timber: Wood members five or more nominal inches in the least dimension.

Span: Horizontal distance between two points.

Top Chord: An inclined or horizontal member that establishes the top of a truss.

Clear Span: Clear distance between adjacent supports of a horizontal or inclined member. Horizontal distance between the facing surfaces of adjacent supports.

TPI: Truss Plate Institute. Truss: An engineered structural component, assembled from wood members, metal connector plates and/or other mechanical fasteners, designed to carry its own weight and superimposed design loads. The truss members form a

Effective Span: Horizontal distance from center-of-required-bearing-width to centerof-required-bearing-width, or the "clear

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semi-rigid structural framework and are assembled such that the members form triangles. UBC: Uniform Building Code (see ICBO).

Harmon, J.D., G.R. Grandle and C.L. Barth. 1992. Effects of hurricane Hugo on agricultural structures. Applied Engineering in Agriculture 8(1):93-96.

Wane: Bark, or lack of wood from any cause, on the edge or corner of a piece.

Knight, J.T. 1989. A brief look back. Frame Building Professional 1(1):38-43.

Warp: Any variation from a true plane surface. Warp includes bow, crook, cup, and twist, or any combination thereof.

Knight, J.T. 1990. Diaphragm design - technology driven by necessity. Frame Building Professional 1(5):16,44-46.

Bow: Deviation, in a direction perpendicular to the wide face, from a straight line drawn between the ends of a piece of lumber.

Norum, W.A. 1967. Pole buildings go modern. Journal of the Structural Division, ASCE, Vol. 93, No.ST2, Proc. Paper 5169, April, pp.47-56.

Crook: Deviation, in a direction perpendicular to the narrow edge, from a straight line drawn between the ends of a piece of lumber.

Taylor, S.E. 1996. Earthquake considerations in post-frame building design. Frame Building News 8(3):42-49.

Cup: Deviation, in the wide face of a piece of lumber, from a straight line drawn from edge to edge of the piece. Twist: A curl or spiral of a piece of lumber along its length. Measured by laying lumber on a flat surface such that three corners contact the surface. The amount of twist is equal to the distance between the flat surface and the corner not contacting the surface. WCLIB: West Coast Lumber Inspection Bureau Web: Structural member that joins the top and bottom chords of a truss. Web members form the triangular patterns typical of most trusses. WTCA: Wood Truss Council of America. WWPA: Western Wood Products Association.

1.6 References Faherty, K.F. and T.G. Williamson. 1989. Wood Engineering and Construction Handbook. McGraw-Hill Publishing Company, New York, NY. Gurfinkel, G. 1981. Wood Engineering (2nd Ed.). Kendall/Hunt Publishing Company, Dubuque, Iowa.

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Chapter 2: BUILDING CODES, DESIGN SPECIFICATIONS AND ZONING REGULATIONS (SBCCI). These model building codes are commonly referred to as the UBC, BOCA and the Southern Building Code, respectively.

2.1 Introduction 2.1.1 Definition. A building code is a legal document that helps ensure public health and welfare by establishing minimum standards for design, construction, quality of materials, use and occupancy, location and maintenance of all buildings and structures.

2.2.2 Adoption. Most states have adopted (and enforce) all or a major portion of one of the three model building codes. As shown in figure 2.1, western states have adopted the UBC, northeastern states the BOCA code, and states in the southwest the Southern Building Code.

2.1.2 Model Versus Active Codes. A model code is a code that is written for general use (i.e., a code that is not written for use by a specific state, county, town, village, company or individual). An active code is a model or specially written code that has been adopted and is enforced by a regulatory agency such as a state or local government. It follows that in a given jurisdiction, acceptance of a model building code is voluntary until the model code becomes part of the active code in the jurisdiction.

2.2.3 Development. Model building codes are consensus documents continually studied and annually revised by building officials, industry representatives and other interested parties. 2.2.4 International Building Code. On December 9, 1994, the three model building code agencies (BOCA, ICBO and SBCCI) created the International Code Council (ICC). The ICC was established in response to technical disparities among the three major model codes. Since its founding, the ICC has worked to create a single model building code for the U.S. This code, which is entitled the International Building Code is now complete and will replace the three model codes over the next couple years. With all states adopting the same model code, it will be less difficult for building designers to work in different regions of the country.

2.1.3 Active Code Variations. The content and administration of active building codes varies not only between states, but frequently between municipalities within a state. Some states have established a hierarchy structure of state, county and township/village/city building codes. In this situation, more localized governing areas can modify the state (or county) codes, provided the changes result in more strict provisions. Despite local differences in content and administration, most active building codes share the common trait of regulating components of construction based on building occupancy and use.

2.3 Building Classification 2.3.1 General. Building codes give criteria for classifying buildings based on: (1) use or occupancy, and (2) type of construction.

2.2 Major Model Building Codes

2.3.2 Occupancy Classifications. Occupancy classifications include assembly, business, educational, factory and industrial, high-hazard, institutional, mercantile, residential and storage. Occupancy classifications have requirements on the number of occupants and building separation, height and area. Other limits exist, for example on lighting, ventilation, sanitation, fire

2.2.1 Current Codes. There are currently three primary model building codes in the United States. These are the Uniform Building Code (UBC) published by the International Congress of Building Officials, the National Building Code published by the Building Officials and Code Administrators International (BOCA) and the Standard Building Code published by the Southern Building Code Congress International

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Uniform Building Code (ICBO) National Building Code (BOCA)

Standard Building Code (SBCCI)

Figure 2.1. Approximate areas of model building code influence. Wisconsin and New York building codes are developed by their respective state code agencies and are not necessarily influenced by current model codes.

protection and exiting, depending on the specific classification and building code.

tain areas of noncombustible construction. The superior fire resistance of large timber members is recognized by the codes with the inclusion of a "heavy timber" classification. To qualify for heavy timber construction, nominal dimensions of timber columns must be at least 6- by 8inches and primary beams shall have nominal width and depth of at least 6- by 10-inches.

2.3.2 Types of Construction. Classification by type of construction is primarily based on the fire resistance ratings of the walls, partitions, structural elements, floors, ceilings, roofs and exits. Specific requirements vary somewhat between model building codes.

2.3.2.1 NFBA Sponsored Fire Test. In January of 1990, the National Frame Builders Association had Warnick Hersey International, Inc., conduct a one-hour fire endurance test on the exterior wall shown in figure 2.2. The wall met all requirements for a one-hour rating as prescribed in ASTM E119-88. The wall sustained an applied load of 10,400 lbf per column throughout the test. Copies of the fire test report can be obtained from NFBA.

There are two primary source documents for determining the fire resistance of assemblies: the Fire Resistance Design Manual, published by the Gypsum Association, and the Fire Resistance Directory, published by Underwriters Laboratories, Inc. The fire resistance of wood framed assemblies can generally be increased by using fire retardant treated (FRT) wood or larger wood members. Codes allow FRT wood to be used in cer-

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Attach metal cladding 12 in. o.c. with 1.5 in. hex head screws with neoprene washers

Metal cladding 29 gage

Section A-A

B

Gold Bond 5/8 in. Fireshield G Type X, attached with 1-7/8 in. cement coated nails (0.0195 in. shank, 1/4 head, 7 in. o.c.)

Unexposed nominal 2by 4-inch nailers 24 in. o.c.

Nominal 2- by 4-inch nailers, 24 in. o.c. Fire side nailers, nominal 2- by 4-inches 24 in. o.c.

A

A

10 ft

FIRE SIDE

4-1/16- by 5-1/4-inch glue-laminated column

Nominal 2- by 2-inch blocking between nailers (nailed to nominal 2- by 6-inch edge blocks)

3- by 24- by 48-inch mineral wool, attach with 3 in. square cap nails (3 per 48 in. width)

Nail-laminated column fabricated from 3 nominal 2- by 6-inch No. 2 KD19 SP members Nominal 2- by 4-inch blocking attached to column

Section B-B

B 1 ft

8 ft

1 ft

Figure 2.2. Construction details for exterior wall that obtained a one-hour fire endurance rating during a January 1990 test conducted for the National Frame Builders Association by Warnock Hersey International, Inc. Details of the test are available from NFBA upon request.

nical literature for wood design and construction is somewhat fragmented. New design specifications and standards are continually under development, and existing documents are periodically revised. Keeping abreast of this literature requires a determined effort on the part of the design professional. To assist in this effort, Table 2.1 gives a partial list of engineering design specifications, standards and other technical references specifically related to post-frame construction. The reader is encouraged to maintain communication with the organizations isted in Table 2.1 concerning new and revised publications.

2.4 Specifications and Standards 2.4.1 General. Design of buildings is covered in the model building codes either by direct provisions or by reference to approved engineering specifications and standards. Engineering specifications and standards provide criteria and data needed for load calculation, design, testing and material selection. They are based on the best available information and engineering judgment. 2.4.2 Wood Design Specifications. The tech

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Of the documents listed in Table 2.1, the primary engineering design specification cited by the model building codes for wood construction is the National Design Specification® for Wood Construction (NDS®), published by the American Forest & Paper Association (AF&PA). The NDS was first issued in 1944 and in 1992 it became a consensus standard through the American National Standards Institute (ANSI).

height, and density of population and activity. Zoning laws may also dictate building appearance and location on property, parking signs, drainage, handicap accessibility, flood control and landscaping. Typically land is zoned for residential, commercial, industrial or agricultural uses. 2.5.2 Development and Enforcement. Zoning laws are developed by municipalities. They (and building codes) are principally enforced by the granting of building permits and inspection of construction work in progress. Certificates of occupancy are issued when completed buildings satisfy all regulations.

2.5 Zoning Regulations 2.5.1 General. Zoning laws are established tocontrol construction activities and regulate land use, in terms of types of occupancy, building

Table 2.1. Partial list of technical references related to post-frame building design and construction Organization & Address Publications

AF&PA American Forest & Paper Association 1111 19th Street, N.W., Suite 800 Washington, D.C. 20036 http://www.awc.org/

Allowable stress design (ASD) manual for engineered wood construction National design specification® (NDS®) for wood construction NDS commentary Design values for wood construction (NDS supplement) Load and resistance factor design (LRFD) manual for engineered wood construction Wood frame construction manual (WFCM) for one-and twofamily dwellings Span tables for joists and rafters

AITC American Inst. of Timber Construction 7012 S. Revere Parkway, Suite 140 Englewood, CO 80112

Timber construction manual

ANSI American National Standards Institute 11 West 42nd Street New York, NY 10036 http://www.ansi.org/

ANSI/AF&PA National design specification for wood construction (see AF&PA) ANSI Standard A190 structural glued laminated

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Table 2.1. Partial list of technical references related to post-frame building design and construction Organization & Address Publications APA The Engineered Wood Association P.O. Box 11700 7011 South 19th Street Tacoma, WA 98411 http://www.apawood.org/

APA design/construction guide; residential and commercial Plywood design specification (PDS) Diaphragms and shear walls Performance standard for APA EWS I-joists Panel handbook & grade glossary

ASAE 2950 Niles Road St. Joseph, MI 49085-9659 http://asae.org/

ASAE EP288 Agricultural building snow and wind loads ASAE EP484.2 Diaphragm design of metal-clad, wood-frame rectangular buildings ASAE EP486 Post and pole foundation design ASAE EP558 Load tests for metal-clad, wood-frame diaphragms ANSI/ASAE EP559 Design requirements and bending properties for mechanically laminated columns

ASCE American Society of Civil Engineers 1801 Alexander Bell Drive Reston, Virginia 20191-4400 http://www.asce.org/

ASCE Standard 7 Minimum Design Loads for Buildings and Other Structures Standard for load and resistance factor design (LRFD) for engineered wood construction Guide to the use of the wind load provisions of ASCE 7-95

AWPA American Wood Preservers Assoc. P.O. Box 5690 Granbury, TX 76049

Standard C2 lumber, timbers, bridge ties and mine ties - preservative treatment by pressure processes Standard C15 wood for commercial-residential construction preservative treatment by pressure processes Standard C16 wood used on farms - preservative treatment by pressure processes Standard C23 round poles and posts used in building construction - preservative treatment by pressure processes Standard M4 standard for the care of preservative-treated wood products

AWPI American Wood Preservers Institute 2750 Prosperity Avenue, Suite 550 Fairfax, Virginia 22031-4312 http://www.awpi.org/

Answers to often-asked questions about treated wood Management of used treated wood products booklet

Gypsum Association 810 First St., NE, #510 Washington DC, 20002 http://www.gypsum.org/

Fire resistance design manual GA-600 Design data - gypsum board GA-530

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Table 2.1. Partial list of technical references related to post-frame building design and construction Organization & Address Publications ICC International Code Council http://www.intlcode.org/ BOCA International, Inc. 4051 West Flossmoor Road Country Club Hills, IL 50478-5794 http://www.bocai.org/ ICBO 5360 Workman Mill Road Whittier, CA 90601-2298 http://www.icbo.org/ SBCCI, Inc. 900 Montclair Road Birmingham, AL 35213-1206 http://www.sbcci.org/

International building code International energy conservation code International zoning code International property maintenance code commentary International property maintenance code International fuel gas code International mechanical code commentary International mechanical code International mechanical code supplement International private sewage disposal code International one and two family dwelling code International plumbing code commentary International plumbing code

MBMA Metal Building Manufacturers Assoc. 1300 Sumner Ave Cleveland, OH 44115-2851 http://www.mbma.com/

Low rise building systems manual Metal building systems

NFBA National Frame Builders Association 4840 W. 15th St., Suite 1000 Lawrence, KS 66049-3876 http://www.postframe.org/

Post wall assembly fire test

NFPA National Fire Protection Association 1 Batterymarch Park Quincy, MA 02269-9101 http://www.nfpa.org/

NFPA 1: Fire prevention code NFPA 13: Installation of sprinkler NFPA 70: National electrical code NFPA 72: National fire alarm code NFPA 101: Life safety code

SPIB Southern Pine Inspection Bureau 4709 Scenic Highway Pensacola, Fl. 32504-9094 http://www.SPIB.org/

Grading rules Standard for mechanically graded lumber Kiln drying southern pine

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Table 2.1. Partial list of technical references related to post-frame building design and construction Organization & Address Publications SFPA & Southern Pine Council Southern Forest Products Association P. O. Box 641700 Kenner, LA 70064-1700 http://www.southernpine.com/ http://www.SFPA.org/

TPI Truss Plate Institute 583 D'Onofrio Drive, Suite 200 Madison, WI 53719

Southern pine use guide Southern pine joists & rafters: construction guide Southern pine joists & rafters: maximum spans Post-frame construction guide Southern pine headers and beams Pressure-treated southern pine Permanent wood foundations: design & construction guide

ANSI/TPI 1-1995 National design standard for metal plate connected wood truss construction HIB-91 Summary sheet: handling, installing & bracing metal plate connected wood trusses HIB-98 Post frame summary sheet: recommendations for handling, installing & temporary bracing metal plate connected wood trusses used in post-frame construction HET-80 Handling & erecting wood trusses: commentary and recommendations DSB-89 Recommended design specifications for temporary bracing of metal plate connected wood trusses

UL Underwriters Laboratories, Inc. 333 Pfingsten Road Northbrook, IL 60062-2096 http://www.ul.com/

Fire resistance directory

WTCA Wood Truss Council of America One WTCA Center 6425 Normandy Lane Madison, WI 53711 http://www.woodtruss.com/

Metal plate connected wood truss handbook Commentary for permanent bracing of metal plate connected wood trusses Standard responsibilities in the design process involving metal plate connected wood trusses

WWPA Western Wood Products Association 522 SW Fifth Ave., Suite 500 Portland, Oregon 97204-2122 http://www.wwpa.org/

Western woods use book Western lumber span tables Western lumber grading rules

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Chapter 3: STRUCTURAL LOAD AND DEFLECTION CRITERIA approval process, and then must be adopted by the model building codes. Design professionals should check the governing building code for the latest adopted edition. For clarity of presentation, this manual uses and will refer to ASCE 793.

3.1 Introduction 3.1.1 Load Variations. Most structural loads exhibit some degree of random behavior. For example, weather-related loads such as snow, wind and rain fluctuate over time and locations. Extensive research has been conducted to characterize this load variation, and to refine procedures for determining design loads within the context of the intended building occupancy and use.

ASCE 7-93 is the primary technical source used by the model codes concerning dead, live, snow, wind, rain and seismic loads. Basically, the model codes attempt to distill the rigorous ASCE 7-93 procedures into a simpler, easy-touse format. Many specific load calculation procedures differ between the model codes; however, most of the basic concepts mimic ASCE 793. Background information on the wind load provisions in ASCE 7-88 (which are essentially the same as in ASCE 7-93) are given by Mehta et al. (1991).

3.1.2 Codes. Calculation procedures for minimum design loads are given in the model building codes. Buildings shall be designed to safely carry all loads specified by the governing building code. In the absence of a code, minimum design loads shall be calculated according to recommended engineering practice for the region and application under consideration.

3.2.2 Low Rise Building Systems Manual. The Low Rise Building Systems Manual, published by the Metal Building Manufacturers Association (1986), is recognized by model building codes as an excellent technical resource document for calculating structural loads on lowrise buildings (e.g. post-frame buildings). This document will be referred to as MBMA-86 throughout this manual. Because wind and crane loads frequently control the design of lowrise metal buildings, the coverage of these loads within MBMA-86 is especially thorough. Another attractive feature of MBMA-86 is the extensive collection of example load calculations.

It is impractical to describe detailed load calculation procedures in this chapter because of differences between building codes and frequent revisions of these codes. Instead, general concepts and key references related to structural loads and deflection criteria are presented, with an emphasis on issues that apply to post-frame buildings.

3.2 Technical References on Structural Load Determination 3.2.1 ANSI/ASCE 7 Standard. The National Bureau of Standards published a report titled Minimum Live Load Allowable for Use in Design of Buildings in 1924. The report was expanded and published as ASA Standard A58.1-1945. This standard has undergone several revisions to become the current ASCE Standard ANSI/ASCE 7 Minimum Design Loads for Buildings and Other Structures. At the time this design manual was written, the most recent revision of ASCE 7 was 1999 (ASCE, 1999); however, the edition most commonly used is ASCE 7-93. The ASCE 7 standard is periodically revised and balloted through the ANSI consensus

3.2.3 ASAE EP288.5 Standard. Agricultural buildings generally fall into a separate class from other types of buildings due to the lower risks involved. The American Society of Agricultural Engineers publishes a snow and wind load standard, EP288.5, intended for agricultural buildings (ASAE, 1999). The major differences between agricultural and other types of buildings are that lower values are used for importance and roof snow conversion factors (due to relatively lower risk factors for property and nonpublic use). If the local governing building code applies to agricultural buildings, then the design load criteria in the code must be followed.

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Table 3.1. Approximate Weights of Construction Materials (from Hoyle and Woeste, 1989) Weight Material Material (lb/ft2) Ceilings Acoustical fiber tile Gypsum board (see Walls) Mechanical duct allowance Suspended steel channel system Wood purlins (see Wood, Seasoned) Light gauge steel (see Roofs) Floors Hardwood, 1-in. nominal Plywood (see Roofs) Linoleum, 1/4-in. Vinyl tile, 1/8-in. Roofs Corrugated Aluminum 14 gauge 16 gauge 18 gauge 20 gauge Built-Up 3-ply 3-ply with gravel 5-ply 5-ply with gravel Corrugated Galvanized steel 16 gauge 18 gauge 20 gauge 22 gauge 24 gauge 26 gauge 29 gauge Insulation, per inch thickness Rigid fiberboard, wood base Rigid fiberboard, mineral base Expanded polystyrene Fiberglass, rigid Fiberglass, batt Lumber (see Wood, Seasoned)

Roofs (continued) Plywood (per inch thickness) Roll roofing Shingles Asphalt Clay tile Book tile, 2-in. Book tile, 3-in Ludowici Roman Slate, ¼ in. Wood

1.0 4.0 2.0

4.0 1.0 1.4

Walls Wood paneling, 1-in. Glass, plate, 1/4-in. Gypsum board (per 1/8-in. thickMasonry, per 4-in. thickness Brick Concrete block Cinder concrete block Stone Porcelain-enameled steel Stucco, 7/8-in. Windows, glass, frame, and sash

1.1 0.9 0.7 0.6 1.5 5.5 2.5 6.5 2.9 2.4 1.8 1.5 1.3 1.0 0.8

Wood, Seasoned Cedar Douglas-fir Hemlock Maple, red Oak Poplar, yellow Pine, lodgepole Pine, ponderosa Pine, Southern Pine, white Redwood Spruce

1.5 2.1 0.2 1.5 0.1

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Weight (lb/ft2)

3.0 1.0 2.0 9.0-14.0 12.0 20.0 10.0 12.0 10.0 3.0

2.5 3.3 0.55 38.0 20.0 20.0 55.0 3.0 10.0 8.0 Density lb/ft3 32.0 34.0 31.0 37.0 45.0 29.0 29.0 28.0 35.0 27.0 28.0 29.0



3.3 Minimum Design Loads Technical Note

Horizontal Uniform Dead Load Calculation

Sections 3.4, 3.5, 3.6, 3.7, and 3.8 give general load requirements, sources of load data and references for making detailed load calculations. Detailed calculation procedures are not provided due to differences between the model codes and the frequency of code revisions.

Many structural analysis programs (e.g. Purdue Plane Structures Analyzer) require that the dead load associated with a sloping surface be represented as a uniform load, wDL, acting on a horizontal plane as shown in figure 3.1. For a given horizontal distance, bH, a sloping roof surface contains more material and is heavier than a flat one. Thus, wDL increases as roof slope increases.

3.4 Dead Loads 3.4.1 Definition. Dead loads are the gravity loads due to the combined weights of all permanent structural and nonstructural components of the building, such as sheathing, trusses, purlins, girts and fixed service equipment. These loads are constant in magnitude and location throughout the life of the building.

Load wDL is obtained by multiplying the unit weight of the roof assembly, wR, by the slope length, bS, and dividing the resulting product by the horizontal length, bH. Numerically, this is equivalent to dividing wR by the cosine of the roof slope.

3.4.2 Code Application. Minimum design dead loads shall be determined according to the governing building code. In the absence of a building code, dead load data can be found in ASCE 7-93, or actual weights of materials and equipment can be used.

Example: For a roof at a 4:12 slope, with materials weighing 4 lbm for each square foot of roof surface area, the equivalent load, wDL, to apply to the horizontal plane would be: wDL = (4 lbm/ft2)/(cos 18.4°) = 4.21 lbm/ft2

3.4.3 Special Considerations. Design dead loads that exceed the weights of construction materials and permanent fixtures are permitted, except for when checking building stability under wind loading. Using inflated design dead loads may lead to conservative designs for gravity load conditions; however, it would not be a conservative assumption for designing anchorage to counteract uplift, overturning and sliding due to wind loads. In the cases of wind uplift and overturning, the dead load used in design must not exceed the actual dead load of the construction.

wDL

Roof assembly with weight wR per unit area Rafter or truss top chord

3.4.4 Weights of Construction Materials. Table 3.1 lists approximate weights of materials. commonly used in post-frame construction.

bH

θ bS

Figure 3.1. Roof dead load represented by an equivalent uniform load acting on a horizontal plane.

3.5 Live Loads 3.5.1 Definition. Live loads are defined as the loads superimposed by the construction, maintenance, use and occupancy of the building, and therefore do not include wind, snow, seismic or dead loads.

3.5.2 Code Application. Design live loads shall be determined so as to provide for the service requirements of the building, but should never be lower than the minimum live load specified in

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the governing building code. In the absence of a governing building code, the minimum live loads found in ASCE 7-93 are recommended. The minimum roof live load recommended for agricultural buildings in ASAE Standard EP288.5 is 12 psf. Some agricultural buildings do not necessarily pose a "low risk", and the ASAE higher minimum live load reflects the possibility of highvalue agricultural constructions now common in the United States

3.6 Snow Loads 3.6.1 Code Application. Minimum design snow loads shall be determined by the provisions of the governing building code. The presentation of snow loads varies among the model codes, but they all follow the basic concepts presented in ASCE 7-93. In the absence of a building code, procedures given in ASCE 7-93 are recommended. For low-risk agricultural buildings, snow load calculation procedures given in ASAE EP288.5 are permitted.

Ce Ct I Cs Pg

= = = = =

roof snow load in psf, roof snow factor that relates roof load to ground snowpack, snow exposure factor, roof temperature factor, importance factor, roof slope factor, and ground snow load in psf (50-yr mean recurrence).

3.6.5 Special Considerations. Several factors, such as multiple gables, roof discontinuities, and drifting can cause snow to accumulate unevenly on roofs. These factors must be considered in the design. Specific recommendations and calculation procedures are given in the model codes and ASCE 7-93.

3.6.2 Ground Snow Load Maps. ASCE 7-93 presents ground snow load maps that correspond to a mean recurrence interval of 50 years. These maps do not give snow load values for areas that are subject to extreme variations in snowfall, such as western mountain regions. In some regions, the best and only reliable source for ground snow loads is local climatic records.

3.7 Wind Loads 3.7.1 Controlling Factors. Wind loads are influenced by wind speed, building orientation and geometry, building openings and exposure. Wind loading on structures is a complex phenomenon and is being actively researched.

3.6.3 Roof Snow Loads. Roof snow loads are influenced by a number of factors besides ground snow load. These factors include roof slope, temperature and coefficient of friction of the roof surface, and wind exposure. Snow loads are also adjusted by an importance factor to account for risk to property and people. The basic form of the snow load calculation found in ASCE 7-93 is: = R Ce Ct I Cs Pg

= =

The roof snow factor, R, varies from 0.6 for Alaska to 0.7 for the contiguous United States. The snow exposure factor in the model codes accounts for the combined effects of R and Ce given in Equation 3-1. The thermal factor defined in ASCE 7-93 varies from 1.0 for heated structures to 1.2 for unheated structures. The thermal factor is not included in the model building codes. The importance factors range from 0.8 to 1.2 depending on the specific building code. Roof slope factors vary linearly from 0 to 1 as roof slope increases from 15 to 70 degrees.

3.5.3 Reductions. In some cases, reductions are allowed for uniform loads to account for the low likelihood of the loads simultaneously occurring over the entire tributary area.

pf

pf R

3.7.2 Code Application. Minimum design wind loads shall be determined by the provisions of the governing building code. In the absence of a building code, procedures given in ASCE 7-93 or MBMA-86 are recommended. For low-risk agricultural buildings, wind load calculation procedures given in ASAE EP288.5 are permitted. 3.7.3 Design Wind Speed. ASCE 7-93 gives a map showing basic wind speeds throughout the United States that correspond to a mean recurrence interval of 50 years. Local weather rec-

(3-1)

where:

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ords should be used in regions that have unusual wind events. Detailed procedures and illustrations for calculating wind loads on low-rise buildings are given in MBMA-86.

model codes publish fewer exposure categories. Importance factors vary from 0.95 for agricultural buildings (25-year recurrence interval) to 1.07 for buildings that represent a high hazard to property and people in the event of failure (100year recurrence interval). Wind pressure is related to the square of its speed, therefore the terms V and I are squared in equation 3-2. The model building codes simplify the calculation in equation 3-2 by publishing tables of effective wind velocity pressures, Pb, for a base wind speed and various heights.

Technical Note

Wind Speed Wind speeds are derived from data which reflect both magnitude and duration. Wind speeds can be reported as peak gusts, or can be averaged over some time interval. The time interval may be fixed, as with mean hourly speeds, or variable, as with “fastest-mile” wind speeds. Fastest-mile wind speeds are used in ANSI/ASCE 793 to calculate design loads, and are defined on the basis of the period of time that one mile of wind takes to pass an anemometer at a standard elevation of 10 meters. The U.S. National Weather Service no longer collects fastest-mile wind speed data; instead, they record 3-second gust speeds. The 1995 and later revisions of ASCE-7 base wind loads on 3-second gust wind speeds.

3.7.5 Pressure Coefficients. Wind loads are calculated for each part of the building by multiplying the effective wind pressure by a pressure coefficient. The pressure coefficient, which may be different for each planar portion of the building, accounts for building orientation, geometry and load sharing. It also accounts for localized pressures at eaves, overhangs, corners, etc. Wind pressures, qi, for the ith building surface are calculated by: qi = Cpi qz

(3-3)

where: 3.7.4 Effective Wind Velocity Pressure. The first step in determining wind loads is to calculate the effective wind velocity pressure. The most severe exposure factors that will apply during the service life of the structure should be used. Wind velocity pressure is a function of the wind speed, exposure and importance. The equation for calculating wind velocity pressure, qz , is given by: qz =

0.00256 Kz (I V)2

Cpi = qz =

ith pressure coefficient, and wind velocity pressure.

The wind velocity pressure is based on the wall height for the windward wall and on the mean roof height for the leeward wall and roof. Wind pressures act normal to the building surfaces. Inward pressures are denoted with positive signs, while outward pressures (suction) are denoted with negative signs.

(3-2)

where: Technical Note

Kz = I V

= =

Components of Wind Load

velocity pressure exposure coefficient, importance factor, and basic wind speed in mph (50-year mean recurrence interval).

Many structural analysis programs require uniform loads to be entered in terms of their horizontal and vertical components. Wind loads act normal to building surfaces, so an adjustment is needed for sloping members such as roof trusses. The roof wind load, w, shown in figure 3.2a is equivalent to the horizontal and vertical components shown in figure 3.2b. The relationship depicted in figure 3.2 can be proven as follows:

The velocity pressure exposure coefficient is a function of height above ground and exposure category. Exposure categories account for the effects of ground surface irregularities caused by natural topography, vegetation, location and building construction features. ASCE 7-93 lists four wind exposure categories, whereas the

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these members have relatively large tributary areas, localized wind effects tend to be averaged out over the tributary areas. Pressure coefficients for main members reflect this averaging effect.

1. Convert the uniform wind load, w, to its resultant vector force. R = w (span)/(cos θ) 2. Multiply resultant force, R, by cos θ to obtain its vertical component.

3.7.7 Components and Cladding. Wind pressures are higher on small areas due to localized gust effects. This observation has been verified by wind tunnel studies (MBMA, 1986), as well as site inspections of wind-induced building failures (Harmon, et al., 1992). For this reason, components and cladding have higher pressure coefficients than main frames. Components and cladding include members such as purlins, girts, curtain walls, sheathing, roofing and siding.

Fy = R (cos θ) = w (span) 3. Divide the vertical component, Fy, by the span to obtain the horizontally projected uplift pressure, whoriz. whoriz = Fy /(span) = w (span)/(span) = w

3.7.8 Openings. Wind loads are significantly affected by openings in the structure. ASCE 793 and the model building codes specify internal wind pressure coefficients (or adjustments to external pressure coefficients) for structures with different amounts and types of openings. Each model code has slightly different definitions and wind load coefficients for open, closed and partially open buildings. In general, "openings" refer to permanent or other openings that are likely to be breached during high winds. For example, if window glazings are likely to be broken during a windstorm, the windows are considered openings. However, if doors and windows and their supports are designed to resist design wind loads, they need not be considered openings. It should be noted that internal wind pressures act against all interior surfaces and therefore do not contribute to sidesway loads on a building.

The vertically projected uniform load can be proven similarly. A common mistake is to multiply the normal pressure by sine and cosine of the roof slope to obtain the two components.

w

θ (a) w

w

θ

3.8 Seismic Loads

(b)

Figure 3.2. Illustration of wind load acting normal to inclined surface and equivalent horizontal and vertical load components. A common mistake is to multiply the normal load by sin(θ) and cos(θ) for the vertical and horizontal components, respectively.

3.8.1 Cause. Earthquakes produce lateral forces on buildings through the sudden movement of the building’s foundation. Building response to seismic loading is a complex phenomenon and there is considerable controversy as to how to translate knowledge gained through research into practical design codes and standards.

3.7.6 Main Frames. Different pressure coefficients are used to calculate wind loads on main frames as compared to components and cladding. Main frames include primary structural systems such as rigid and braced frames, braced trusses, posts, poles and girders. Since

3.8.2 Code Application. Seismic loads shall be determined by the provisions of the governing building code. In the absence of a building code, procedures given in ASCE 7-93 are recommended. Sweeping changes were made in the

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1993 revision of ASCE 7 with respect to seismic loads. The seismic provisions in ASCE 7-93 were based on work by the Building Seismic Safety Council under sponsorship of the Federal Emergency Management Agency.

3.9.2 Load Combinations. Except when applicable codes provide otherwise, the following load combinations shall be considered (as a minimum) and the combination which results in the most conservative design for each building element shall be used. Note that different load combinations may control the design of different components of the structure.

3.8.3 Lateral Force. Basic concept of seismic load determination for low-rise buildings is to calculate an equivalent lateral force at the ground line as follows: V = Cs W

Case 1: Snow) Case 2: Case 3: Case 4: Case 5:

(3-4)

where: V

=

W =

Cs = = Av = S

=

R T

= =

total lateral force, or shear, at the building base total dead load, plus other applicable loads specified in the code or ASCE 7-93. For most single-story post-frame buildings, the only other minimum applicable load is a portion (20% minimum) of the flat roof snow load. If the flat roof snow load is less than 30 psf, the applicable load to be included in W is permitted to be taken as zero. seismic design coefficient 1.2 Av S/(T2/3 R)

Dead + Floor Live + Roof Live (or Dead + Floor Live + Wind (or Seismic) Dead + Floor Live + Wind + ½ Snow Dead + Floor Live + ½ Wind + Snow Dead + Floor Live + Snow + Seismic

3.9.3 Floor Live Loads. Most post-frame buildings are single story and therefore would not have floor live loads acting on the post-frames. When a concrete floor is used in a single story building, consideration must be given to anticipated live and equipment loading. 3.9.4 Reductions. Reductions in some of the load terms in Cases 1 through 5 are permitted, depending on governing building code or reference document. With some exceptions, the model building codes permit allowable stresses used in allowable stress design to be increased one-third when considering wind or seismic forces either acting alone or when combined with vertical loads. The allowable stress increase for wind loading can be traced back to the New York City Building Code of 1904 (Ellifritt, 1977), and appears to be based on judgment rather than engineering theory. It should be noted that ASCE 7-93 does not include the one-third increase factor, but instead specifies load combination factors that are intended to account for the low probability of maximum live, seismic, snow and wind loads occurring simultaneously. The commentary of ASCE 7-93 implies the stress increase for wind and seismic found in codes is not appropriate if the combined load effects are also reduced by the load combination factors published in ASCE 7-93. Finally, the National Design Specification (NDS) for Wood Construction (NF&PA, 199) addresses the issue of load combination versus load duration factors by stating, “The load duration factors, CD, in Table 2.3.2 and Appendix B are independent of load combination factors, and both shall be permitted to be used in design calculations.”

coefficient representing effective peak velocity-related acceleration coefficient for the soil profile characteristics response modification factor fundamental period of the building

3.8.4 Seismic loads rarely control post-frame building design because of the relatively low building dead weight as compared with other types of construction (Taylor, 1996; Faherty and Williamson, 1989). For post-frame buildings, lateral loads from wind usually are much greater than those from seismic forces.

3.9 Load Combinations for Allowable Stress Design 3.9.1 Code Application. Every building element shall be designed to resist the most critical load combinations specified in the governing building code.

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flexibility of corrugated metal siding, girt deflections present no serviceability problems, and consequently, girt size is generally only stress dependent.

3.10 Load Duration Factors for Wood It is well documented that wood has the property of being able to carry substantially greater loads for short durations than for long durations of loading. This property is accounted for in design through the application of load duration factors to all allowable design values except modulus of elasticity and compression perpendicular to grain. Additional restrictions and details on load duration adjustments can be found in Chapter 2 and Appendix B of the NDS (AF&PA, 1997).

3.11.3 Time Dependent Deflection. In certain situations, it may be necessary to limit deflection under long term loading. Published modulus of elasticity, E, values for wood are intended for the calculation of immediate deflection under load. Under sustained loading, wood members exhibit additional time-dependent deformation (i.e. creep). It is customary practice to increase calculated deflection from long-term loading by a factor of 1.5 for glued-laminated timber and seasoned lumber, or 2 for unseasoned lumber (see Appendix F, AF&PA, 1997). Thus, total deflection is equal to the immediate deflection due to long-term loading times the creep deflection factor, plus the deflection due to the short-term or normal component of load. For applications where deflection is critical, the published value of E (which represents the average) may be reduced as deemed appropriate by the designer. The size of the reduction depends on the coefficient of variation of E. Typical values of E variability are available for different wood products (see Appendix F, AF&PA, 1997).

3.10.1 Snow Load. The cumulative duration of maximum snow load over the life of a structure is generally assumed to be two months. It should be emphasized that the two-month period does not necessarily mean that the design snow load from any one event would last two months. Rather, it means that the total time that the roof supports the full design snow load over the life of the structure is two months. If the cumulative full design load is two months, an allowable stress increase of 15 percent is allowed (AF&PA, 1997). However, in some situations, such as unheated or heavily insulated buildings in cold climates, longer snow load durations may occur and the stress increase may not be justified.

3.11.4 Shear Deflection. Shear deflection is usually negligible in the design of steel beams; however, shear deflection can be significant in wood beams. Approximately 3.4 percent of the total beam deflection is due to shear for wood beams of usual span-to-depth proportions (i.e. 15:1 to 25:1). For this reason, the published value of E in the Supplement to the National Design Specification is 3.4 percent less than the true flexural value (AF&PA, 1993). This correction compensates for the omission of the shear term in handbook beam deflection equations. For span-to-depth ratios over 25, the predicted deflection using the published E value will exceed the actual deflection. Similarly, for span-todepth ratios less than 15, predicted deflections will be significantly less than actual. This could lead to unconservative designs (with respect to serviceability) for post-frame members such as door headers. Practical information on the effects of shear deformation on beam design is given in Appendix D of Hoyle and Woeste (1989) for rectangular wood beams and Triche (1990) for wood I-beams.

3.10.2 Wind Load. The cumulative duration of maximum wind (and seismic) loads over the life of a structure is generally assumed to be 10 minutes (AF&PA, 1997), if design wind loads are based on ASCE 7-93, and the corresponding load duration factor is 1.6. Other load duration adjustments may be appropriate when design wind loads are based on earlier versions of ASCE 7-93 or other standards (with different wind gust duration assumptions).

3.11 Deflection 3.11.1 Code Application. Post-frame building components must meet deflection limits specified in the governing building code. 3.11.2 Exception to Code Requirements. Girts supporting corrugated metal siding are typically not subjected to deflection limitations unless their deflection compromises the integrity of an interior wall finish. Because of the inherent

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3.12 References American Forest & Paper Association (AF&PA). 1997. ANSI/AF&PA NDS-1997 - National Design Specification for Wood Construction. AF&PA, Washington, D.C. American Forest & Paper Association (AF&PA). 1993. Commentary to the National Design Specification for Wood Construction. AF&PA, Washington, D.C. ASAE. 1999. ASAE EP288.5: Agricultural building snow and wind loads. ASAE Standards 1999, 46th edition, ASAE, St. Joseph, MI. American Society of Civil Engineers (ASCE). 1993. Minimum design loads for buildings and other structures. ANSI/ASCE 7-93, ASCE, New York, NY. American Society of Civil Engineers (ASCE). 1999. Minimum design loads for buildings and other structures. ANSI/ASCE 7-99, ASCE, New York, NY. Ellifritt, D.S. 1977. The mysterious 1/3 stress increase. American Institute of Steel Construction Engineering Journal (4):138-140. Faherty, K.F. and T.G. Williamson. 1989. Wood Engineering and Construction Handbook. McGraw-Hill, New York, NY. Hoyle, R.J. and F.E. Woeste. 1989. Wood Technology in the Design of Structures. Ames, IA: Iowa State University Press. Mehta, K.C., R.D. Marshall and D.C. Perry. 1991. Guide to the Use of the Wind Load Provisions of ASCE 7-88 (formerly ANSI A58.1). American Society of Civil Engineers, New York, NY. Metal Building Manufacturers Association (MBMA). 1986. Low rise building systems manual. MBMA, Cleveland, OH. Taylor, S.E. 1996. Earthquake considerations in post-frame building design. Frame Building News 8(3):42-49.

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Chapter 4: STRUCTURAL DESIGN OVERVIEW and ceiling diaphragms are formed that can add considerable rigidity to the building. In many post-frame buildings, diaphragms and shearwalls are carefully designed and become an integral part of the main wind-force resisting system. Roof and Ceiling Diaphragms are covered in Section 4.9 and Shearwalls in Section 4.10.

4.1 Introduction 4.1.1 General. The aim of this chapter is to give a broad overview of post-frame building design, and then highlight unique aspects of post-frame that require special design considerations. Postframe is a special case of light-frame wood construction. Light-frame construction is accepted by all model building codes, and the design procedures are well documented. The design rules that apply to light-frame wood construction also apply to post-frame. However, there are some aspects of post-frame that are not as familiar to building designers, such as diaphragm design, interaction between post-frames and diaphragms, and post foundation design. Hence, Chapters 5, 6, 7 and 8 focus on these topics in more detail.

4.1.5 Limitations. The structural design of buildings involves making many judgments, such as determining design loads, structural analogs and analyses, and selecting materials that can safely resist the calculated forces. New research or testing could justify a change of design procedure for the industry or for an individual designer. The considerations presented here are not exhaustive, since many issues in a specific building design will require unique treatment.

4.1.2 Primary Framing. Primary framing is the main structural framing in a building. In a postframe building, this includes the columns, trusses (or rafters), and any girders that transfer load between trusses and columns. Each truss and the post(s) to which it is attached form an individual "post-frame". Post-frames collect and transfer load from roof purlins and wall girts to the foundation. In the context of wind loading in standards and building codes, post-frames are an integral part of the main wind-force resisting system. Specific sections dedicated to primary framing include: Section 4.2 Posts, Section 4.3 Trusses, Section 4.4 Girders, and Section 4.5 Knee braces.

4.2 Posts 4.2.1 General. The function of the wood post is to carry axial and bending loads to the foundation. Posts are embedded in the ground or attached to either a conventional masonry or concrete wall or a concrete slab on grade. Posts can be solid sawn, mechanically laminated, glued-laminated or wood composite. Any portion of a post that is embedded or exposed to weather must be pressure-treated with preservative chemicals to resist decay and insect damage. 4.2.2 Controlling Load Combinations. The load combination that usually controls post design is dead plus wind plus one-half snow; however, local codes may stipulate different load combinations. It is possible for any one of the combinations to be critical; therefore, they all should be considered for a specific building design. For example, maximum gravity load will govern truss-to-post bearing and post foundation bearing; whereas wind minus dead load will govern the truss-to-post connection (for uplift).

4.1.3 Secondary Framing. Secondary framing includes any framing member used to (1) transfer load between cladding and primary framing members, and/or (2) laterally brace primary framing members. The secondary framing members in a post-frame building include the girts, purlins and any structural wood bracing such as permanent truss bracing. Specific sections dedicated to secondary framing include: Section 4.6 Roof Purlins, Section 4.7 Wall Girts, and Section 4.8 Large Doors.

4.2.3 Force Calculations. The diaphragm analysis method presented in Chapter 5 is the most accurate method to determine design

4.1.4 Diaphragms and Shearwalls. When cladding is fastened to the wood frame of a post-frame building, large shearwalls and roof

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moments, and axial and shear forces in posts. Historically, some designers calculated the maximum post moment for embedded posts by using the simple structural analog of a propped cantilever (i.e. fixed reaction at the post bottom and pin reaction at the top). The implicit assumption of this analog is that the roof diaphragm and shearwalls are infinitely stiff. This model may be adequate for buildings with extremely stiff roof diaphragms and for conservatively estimating shear forces in the roof diaphragm; however, it may underestimate the maximum post moment for many post-frame buildings. The analysis procedures described in Chapter 5 are more reliable since they account for the flexible behavior of the roof diaphragm.

4.2.7 Connections. Truss-to-post connection must be designed for bearing as well as uplift. Connection design procedures are given in the NDS (AF&PA, 1997). This connection should be modeled as a pin unless moment-carrying capacity can be justified. Direct end grain bearing is desirable and is often achieved by notching the post to receive the truss. When designing the truss-to-post connection for uplift, it is important to accurately estimate the weights of construction materials if any counteracting credit is to be taken. For surface-attached posts, the bottom connection needs to be checked for maximum shear and uplift forces. For embedded posts attached to collars or footings, the connections must be properly designed to withstand gravity and uplift loads, and corrosion-resistant fasteners must be used.

If posts are embedded, generally two bending moments must be calculated - one at the groundline and the other above ground. Groundline bending moment and shear values are used in embedded post foundation design calculations. For surface-attached posts, the bottom reaction can be modeled as a pin, and generally only one bending moment is calculated.

4.2.8 Construction Alternatives. The posts in post-frame buildings can be solid sawn, mechanically-laminated, glued-laminated or wood composite. Allowable design stresses are published in the NDS or are available from the manufacturers. Treated wood is used for the embedded part of the post, but no treatment is required on the parts that are not in contact with the ground and are protected by the building envelope.

4.2.4 Combined Stress Analysis. Forces involved in post design subject the posts to combined stress (bending and axial) and must be checked for adequacy using the appropriate interaction equation from the NDS (AF&PA, 1997). In theory, every post length increment must satisfy the interaction equation, but in practice, a minimum of two locations are checked: the point of maximum interaction near the ground level (column stability factor, Cp, equal to 1.0) and the upper section of the posts where the maximum moment occurs in conjunction with column action (Cp<1.0).

4.2.9 Foundation. Post-frame building foundations include posts embedded in the ground or surface-attached on a concrete foundation. Embedded posts shall be designed to resist sidesway and overturning forces due to wind or seismic loads, as well as wind uplift, and gravity loads. Post foundation design is an important aspect of post-frame building design that is not well known in the structural engineering design community, and therefore Chapter 8 is dedicated to this subject. If a concrete slab is used, it only needs to be designed for interior loads since exterior building loads are transferred directly to the ground through the posts.

4.2.5 Shear Stress. The shear stress due to lateral loading (wind or seismic) rarely controls post design, but should always be checked as a matter of good practice. Other loads such as bulk loads from stored materials may influence final post design. 4.2.6 Deflection. A post deflection limit is not normally specified for post-frame buildings, but interior finishes may require it. Refer to the deflection criteria in Chapter 3.

Another option is to attach the posts to a concrete foundation. In this case, the concrete must be designed to carry the exterior building loads as well as interior. Connections must be designed to attach the posts to the concrete.

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4.2.10 Pressure Preservative Treatment (PPT). Treated foundation systems have been accepted by the model codes and have a history of successful performance in residential wood construction. The most common pressure preservative treatment used in post-frame construction is chromated copper arsenate (CCA). CCA can increase the potential for metal-fastener corrosion, and may require hot-dipped galvanized or stainless steel fasteners. The minimum waterborne treatment retention for structural posts used in post-frame buildings is 0.6 lb/ft3 (pcf) as defined in AWPA Standard C15 (AWPA, 1995a).

copper arsenate (ACA), and ammoniacal copper zinc arsenate. CCA is available in three formulations: CCA-A, CCA-B, and CCA-C. CCA-C is the most popular of the three formulations due to its increased resistance to leaching. Penta is an oil-borne preservative, and creosote is a coal-tar based preservative that is its own carrier. While penta and creosote offer superior resistance in high salt environments, waterborne preservatives are typically more popular since the final product has a clean surface, is paintable, and is relatively odorless. Waterborne preservatives do provide a strong potential for corrosion of metal connectors and fasteners; follow the manufacturers recommendations for the use of stainless or hot-dipped galvanized fasteners.

Technical Note

Wood Preservative Treatments

While the major building codes endorse the use of preservative-treated wood for foundation applications, it is imperative that the preservative retention guidelines be followed. The American Wood Preservers Association has published standards for the preservative treatment of wood for various applications (AWPA, 1991). Care must be taken that the appropriate standard is considered when specifying treatment for post foundation systems. For example, most waterborne preservative-treated lumber sold has a preservative retention level of 0.4 pcf (pounds of preservative per cubic foot of wood), which is the retention level specified by AWPA Standard C2 for lumber in contact with the ground. This differs, however, from the AWPA Standard C15 governing the treatment of structural posts used in foundations; the required preservative retention for waterborne preservatives under this standard is 0.6 pcf. The AWPA C15 required retention level for post foundations using penta as a preservative is 0.6 pcf, while the required retention level for creosote is 12.0 pcf.

When the moisture content of wood exceeds 20% on a dry weight basis in the presence of oxygen, it is vulnerable to attack by insects and decaying fungi. Although some species of wood (and the heartwood of other species) are naturally resistant to these types of attack, most structural woods used in North America are not. These structural wood species must be chemically treated to protect them from decay and maintain their strength throughout the structural design life. The chemicals used for preservative treatment of the wood are typically injected into the wood using pressure processes. Wood that has been chemically treated in this manner is accepted by all major building codes. The type of preservative treatment and the required amount of retention by the wood depends on the end use of the wood component. It is assumed that the designer is already familiar with the use of preservative treated wood for above-ground applications (such as wood decks); this section will concentrate specifically on preservative treatments and retention levels appropriate for use in post foundations.

The rate at which treatments are absorbed into wood, and the depth of penetration of the treatment, varies from wood species to wood species. Whereas Southern Pine species take treatment quite well, most other species must be incised to comply with AWPA retention requirements. Incising can adversely affect lumber strength properties. Consult AF&PA for specifications regarding the use of incised wood in structural applications.

Preservative chemicals abate wood decay by altering the wood as a potential food source for insects and fungi. The preservatives typically used in North America are waterborne arsenicbased, pentachlorophenol (penta) and creosote. Waterborne arsenic-based preservatives include chromated copper arsenate (CCA), ammoniacal

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Standard for Metal Plate Connected Wood Truss Construction.

Quality assurance is critical to the performance of treated wood. The treating industry has developed a quality control and treatment quality marking program accredited by the American Lumber Standards Committee. Any treated members specified for use in a post foundation should be stamped by an approved agency (e.g., AWPA, Southern Pine Inspection Bureau (SPIB), etc.) to assure that the members have been treated in accordance with AWPA Standard C15 and to the appropriate retention level.

4.3.2 Design Loads. The controlling load combination for truss design often is snow plus dead load. The unbalanced snow load case should be checked per the applicable building code, or for agricultural buildings, engineering practice ASAE EP288.5 (ASAE, 1999a) should be consulted. However, all other applicable load combinations must be checked. For example, a wind load combination may cause stress reversal in some truss elements as discussed later in this chapter.

Treated wood suppliers provide Material Safety Data Sheets (MSDS) or Consumer Information Sheets with the product. These sheets contain special instructions about the care, handling and disposal of treated wood. Federal law dictates that these sheets must be provided to all employees exposed to the materials.

Truss loads are normally represented by listing the top-chord live and dead, and bottom-chord live and dead loads, respectively. Truss design loads are typically expressed in units of pounds per square foot (psf). An example of truss loading would be 20-4-0-1 (psf is implied). Both live and dead loads apply to the vertically projected tributary areas of the top and bottom chords. Often, a bottom-chord live load is not required, so the preceding nomenclature would be shortened to 20-4-1 psf.

Saw cuts or drilled holes made after treatment may expose untreated wood. This problem is especially critical if the newly exposed wood is in the splash zone or in contact with the ground. When using nail-laminated posts, the cut end of the treated lumber should be placed upward, above the ground level; otherwise, brushapplied, soaked, or dipped field treatments are recommended. AWPA Standard M4 outlines procedures for field treatment; some chemicals require a certified pesticide applicators license to apply. The chemical suppliers should be consulted for application restrictions.

4.3.3 Design. This design manual does not present specifics of roof truss design. Metalplate-connected wood trusses in the United States are designed according to the provisions of ANSI/TPI 1-1995. Other designs are based on proprietary test information, along with design criteria from the NDS (AF&PA, 1997). Model building codes recognize either of these approaches.

4.3 Trusses

ANSI-TPI 1-1995 mentions two types of structural analyses. The “simplified method” is a type of pin joint analysis that has been calibrated to account for partial joint fixity. This method uses tables of factors to determine chord moments and member buckling lengths. The simplified method has been the predominate method for a number of years; however, it will eventually be phased out by TPI. The other type of analysis which is sometimes referenced as the “exact method”, is a stiffness matrix method of analysis. Plane frame structures analyzers are becoming more commonly used and provide for more sophisticated and accurate analyses. Regardless of analysis methods, structural modeling assumptions are important and can dramatically influence the design (Brakeman, 1994).

4.3.1 General. Together with posts, wood trusses are primary structural elements of postframe buildings. Two excellent sources of technical information on trusses are the Truss Plate Institute (TPI) and the Wood Truss Council of America (WTCA). Trusses must be properly designed, handled and installed. These responsibilities are shared by the building owner, contractor and designer, and the truss designer and manufacturer. The importance of a clear understanding of responsibilities among these parties cannot be overstated, and is covered in WTCA 1-1995 Standard Responsibilities in the Design Process Involving Metal Plate Connected Wood Trusses and ANSI/TPI-1-1995 National Design

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For example, partial fixity at truss plate joints as well as eccentricity at heel joints, can be modeled a variety of ways. The heel joint usually gets the most attention since heel joint modeling decisions can greatly influence truss design.

load. This load case may not frequently control the size of the truss chord lumber, but it makes compression in the bottom chord possible. This situation is one reason that lateral bracing of the bottom chord is required (TPI, 1989; 1991a; 1991b).

The size, and in some cases the orientation, of truss plates is dependent on proprietary design values. These values are available from the manufacturers or from research reports prepared by the model code agencies, Such as ICBO, SBCCI and BOCA.

4.3.6 Temporary Bracing. Temporary bracing is required to ensure stability of trusses during their installation and until permanent bracing for trusses and the building are in place. This area is the most difficult to manage in the field.

Trusses can be obtained pre-engineered from the manufacturer. It is important to consider wind loading on trusses as stress reversals can occur and overstress some members. This design is complicated by the fact that wind loads are influenced by building geometry, so this information must be communicated to the truss designer. Any structural bracing (e.g. knee braces) or redundant supports must be included in the truss design.

According to WTCA 1-1995 and ANSI/TPI 11995, determination and installation of temporary bracing is the responsibility of the building contractor. Truss Plate Institute (TPI) publication HIB-98 is a “summary sheet” that contains “recommendations for handling, installing and temporary bracing metal plate connected wood trusses used in post-frame construction.” Another TPI summary sheet (i.e., HIB-91) contains similar recommendation for trusses with on center spacings two feet or less and spans less than 60 feet. Both HIB-98 and HIB-91 are formatted as accident-prevention brochures for use by builders, building contractors, licensed contractors, erectors, and erection contractors.

4.3.4. Truss-to-Post Connection. The connection between the truss and post is critical. Designers must consider both gravity forces and uplift forces. With some truss-to-post connection designs, it might be necessary to examine the impact of the connection on the forces induced in the truss chords, heel joints, and post. Observations from several building investigations revealed that the individual trusses and posts were designed properly, but the connection between the two units was not. Many different methods and hardware have been used to design the connection, such as bolts, nails, truss anchors, and combinations of the same. Unless otherwise governed by a specific code, the design of this connection should meet NDS (AF&PA, 1997) requirements.

4.3.7 Permanent Bracing. Permanent truss bracing is critical to the performance of the roof system. Roof trusses are designed with the assumption that their elements are held sufficiently in-plane (ANSI/TPI, 1995). The primary function of permanent roof-truss bracing is to hold all trusses of the roof in the intended vertical plane. HIB-98, provides guidance for the placement of temporary truss bracing, which, if left in place, may function as part of the permanent bracing system. Building designers are responsible for designing permanent bracing. For trusses spaced 4 ft or less, DSB-89 (TPI, 1989) provides a calculation method for temporary and permanent bracing designs. For trusses spaced greater than 4 ft (1.22 m) on-center, similar principles can be used, but designers must consider that the longer lengths involved may cause the bracing members to buckle. A commentary covering permanent bracing of metal plate connected wood trusses is available from WTCA (1999).

4.3.5 Stress Reversal. The trusses used in post-frame buildings are typically long span and, consequently, have long webs. When the truss becomes part of a post-frame building, it is possible, under certain loading conditions, for a tension web in the truss design to become a compression web. Stress reversal can also occur in truss chords due to a wind uplift loading combined with dead

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the girder must be sized to handle additional stresses due to torsion.

4.4 Girders 4.4.1 General. Girders are heavy beams used to span large openings (e.g., doors) and to support trusses located between posts. For example, when roof truss spacing is less than the post spacing, girders (sometimes called headers) are needed to carry the intermediate trusses. This is a common occurrence over large door openings. These beams are considered main wind-force resisting members. Vertically nail-laminated lumber, structural composite lumber, glued-laminated beams and steel Ibeams are all commonly used as girders. There is an abundant supply of structural-composite lumber products from manufacturers who publish their own allowable stresses. Often, the critical load combination is dead plus snow load, although all applicable load combinations must be checked.

4.5 Knee Braces 4.5.1 General. Knee braces are intended to supplement the resistance of post frames under lateral loads, and can influence the unsupported length of columns. They have been used less and less in recent years. 4.5.2 Effectiveness. Knee brace effectiveness is highly dependent on the stiffness of its connections to the post and truss. If the connections at the ends of the brace are flexible or not very stiff due to the use of a few nails, the roof diaphragm carries the bulk of the load, and the brace is ineffective (Gebremedhin and Woeste, 1986). If the brace connections are made very stiff (by installing many nails or bolts) the brace could effectively resist the wind loading but could overload the truss.

4.4.2 Design Criteria. Girders are designed as bending members. Any one of the four criteria used for the design of bending members can control design (i.e. bending, shear, compression perpendicular to grain, and deflection). Shear can often control girder design. Also note that formulae found in most handbooks account for bending but not shear deflection. Designers should consider the impact of shear deflection on the total deflection of a girder. Hoyle and Woeste (1989) provide formulae for calculating shear deflection of wood beams.

4.5.3 Analysis. Knee braces induce primary bending moments in truss chords if attached between panel points. Knee braces induce secondary bending moments when attached directly to panel points. If knee braces are to be used in a post-frame design, load sharing among the truss, post, knee brace, connections, and diaphragm (when applicable) must be included in the structural analysis.

4.6 Roof Purlins

4.4.3 Vertically Laminated Lumber. The design of girders for a post-frame building is routine structural design except when a girder is fabricated by vertically laminating three or more pieces of dimension lumber. In this case, the allowable bending stress can be increased using the repetitive member factors published in ANSI/ASAE EP559 (ASAE, 1999b). These values are given in table 7.3.

4.6.1 General. Roof purlins are typically 2- by 4inch or 2- by 6-inch lumber, and are key structural elements of the roof assembly. They resist gravity loads, wind loads, roof diaphragm chord forces, and provide lateral bracing to truss top chords (or rafters). To fulfill the chord-bracing role, the purlins must be supported against lateral movement by attachment to sheathing or metal cladding that provides the needed roof diaphragm strength. Not all roof cladding materials provide diaphragm strength and/or purlin lateral support; one example is standing seam roofing, which is fastened with clips that allow adjacent sheets to slide.

4.4.4 Connections. Girder attachment to posts and individual roof trusses is a fundamental part of girder design. When designing girder-to-post connections, both uplift and gravity must be considered. When designing truss-to-girder connections, special consideration must be given to situations in which trusses are hung off the side of the girder. In such cases truss-togirder connections should be designed to prevent rotation between the trusses and girder, or

4.6.2 Classification. Purlins in post-frame buildings fall into the category of “component

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and cladding,” which is recognized by all three model building codes. Components and cladding collect the loads and distribute them to the primary structural elements, identified as the main wind-force resisting system. Wind loads are much greater at eaves, ridges, edges, corners and other discontinuities. Purlin spacing and fasteners are critical in these areas. If these areas fail under extreme wind loading, the building envelope will be breached, and internal wind pressures will change dramatically.

lins are recessed, and their capacity should be verified for the various loading cases. In general, the provisions of the NDS (AF&PA, 1997) apply for the connections and stress analysis.

4.7 Wall Girts 4.7.1 General. Girts are used to collect windinduced wall loads and distribute them to the post frames. For end walls, the wind loads are distributed to structural end-wall posts.

4.6.3 Orientation. Purlins are installed on-edge or flat. When they are used on-edge, they may be either placed on top of the truss or recessed between the trusses. Purlins placed on-edge are frequently overlapped and fastened together at the overlap. When used flat, purlins are installed on top of the trusses.

4.7.2 Classification. Girts belong to the “component and cladding” category for determining the design wind load. 4.7.3 Orientation. Girts are either installed flat on post faces or recessed between the posts. Girts recessed between posts are almost always orientated with the narrow edge facing the cladding, and in this position, are frequently used to support both interior and exterior cladding/sheathing.

4.6.4 Truss Chord Bracing. Purlin spacing is a factor in truss design since purlins provide lateral support to the truss top chord. In some cases, the slenderness ratio for weak-axis truss chord buckling between purlins can be greater than that for strong-axis buckling. Therefore, when specifying trusses, the building designer should inform the truss-design engineer of the planned purlin spacing.

4.7.4 Post Bracing. Girts provide lateral support to side-wall columns. With girts securely installed, the slenderness ratio of the post weak axis is greatly reduced. Therefore, posts can usually be designed to carry the axial loads using the slenderness ratio of the strong axis.

4.6.5 Design Loads. Purlin design often is controlled by the dead plus snow load combination, or dead plus wind load (especially in the edge zones of the roof). Dead loads used for design may exceed actual weights for gravity load calculations; however, inflated dead loads cannot be used to offset wind uplift or wind overturn moments. In these cases, offsetting loads cannot exceed actual weights of materials.

4.7.5 Design Loads. Girts are normally designed to resist only wind load. Wind loads are much greater at corners and other discontinuities. Girt spacing and fasteners are critical in these areas. If these areas fail, the building envelope will be breached, and internal wind pressures will change dramatically. The dead load of the girt and attached steel is normally negligible for girt design. Cladding is attached to the girts by nails or screws, and the stiffness of these connections does not allow the girts to undergo significant bending stress or deflection from the action of the small dead loads present. However, the wall dead load should be included in total dead load calculations for the post foundation.

4.6.6 Design Criteria. Purlins members should be checked for bending strength, shear capacity, and deflection. If the roof assembly is functioning as a structural diaphragm, purlins will also be subjected to axial forces. Purlins shall be designed to carry bending about both axes. Weak axis bending may be omitted if it can be demonstrated by test or analysis that the roof sheathing provides support. The connections between the purlins and rafters should be designed for both gravity loads and wind uplift forces. Purlin hangers are often used when pur-

Girts must be design to resist forces induced by stored materials, especially granular materials such as fertilizer or seeds/grain. Care should be

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taken to assure that the capacity of wall panels, fasteners and girts are not exceeded by these forces.

4.9.2 Design Properties. Diaphragm performance depends on factors such as the steel, steel sheet-to-sheet fasteners, steel-to-wood fasteners, and the wood frame. There is no standard steel panel construction, so diaphragm strength and stiffness depend on the specific construction used. Strength and stiffness data on laboratory test panels are generally required to derive design values. Most post-frame buildings have much greater spans than laboratory test panels; therefore, test data must be extrapolated to prac-tical building sizes as explained in Chapter 6.

4.7.6 Design Criteria. Girts are designed as bending members for which the usual bendingmember design criteria apply. The critical connections between the girts and the post should be checked for both wind pressure and suction. The top wall girt may be constructed to carry chord forces from the roof diaphragm and, if so, must be checked for the appropriate axial loads. The NDS (AF&PA, 1997) provisions apply for the connections and stress analysis.

4.10 Shearwalls 4.8 Large Doors 4.10.1 General. A large portion of the shear forces induced in roof and ceiling diaphragms is transferred to the building foundation by shearwalls. In many post-frame buildings, the only walls available to transfer this shear are exterior walls (i.e., endwalls and sidewalls). Where present, interior partition walls can be designed to transfer additional shear.

4.8.1 General. Large doors are common in post-frame buildings. Door components must be designed to withstand design wind loads, and are treated as “components and cladding” for such calculations. 4.8.2 Open Doors. It is not uncommon for building owners to leave large doors open, even during periods of high wind. If an owner anticipates that this will occur, the building must be designed accordingly. Note that a large opening on one side of the structure is generally associated with increased internal wind pressure coefficients, and thus can significantly increase roof uplift forces.

4.10.2 Endwalls. Endwalls in post-frame buildings resist wind loads perpendicular to the building end wall and simultaneously help transmit roof shears (due to parallel-to-end wall wind components) to the ground. In the diaphragm design procedure described in Chapter 5, maximum roof shears occur at the endwalls. The roof shear is transferred into the top truss chord or rafter of the endwall, through the endwall to the ground level, and finally to the ground by posts or to posts connected to a concrete slab. In addition to shear forces, the end wall is subject to overturning forces. Wirt et al. (1992) have published procedures for analyzing and designing end-wall foundations.

4.9 Roof and Ceiling Diaphragms 4.9.1 General. Roof and ceiling diaphragms are used to resist lateral (sidesway) forces applied to the building by wind, earthquake and stored material. Under lateral load, roof and ceiling diaphragms act as large stiff plates. These plates support and distribute loads to wall posts. Conceptually, diaphragm design is easy to understand, but the application of the procedure requires analysis tools and data.

4.10.3 Wall Openings. Allowances must be made for openings in shearwalls. One common practice in post-frame construction is to place large doorways in the building endwalls. Procedures for accounting for the opening and ways to reinforce the remaining wall are given in Chapter 5.

Diaphragms made from plywood are well documented, as well as those made entirely from steel. Less information is available about woodframed, metal-clad diaphragms which are prevalent in the post-frame building industry. This is a major factor in post-frame building design and is covered in more depth in Chapter 5.

4.10.4 Partitioning. Partitioning of the building into structural segments is one method to reduce maximum roof shears and endwall shears. For example, if it is not practical to reinforce an

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metal plate connected wood trusses. DSB-89. TPI, Madison, WI.

endwall that has a large door installed, the alternative is to install a structural partition in the center of the building. The structural partition must meet the shear requirements delivered by the roof diaphragm. Buttresses, inside or outside the walls, can be used to reduce the effective length of the building with respect to maximum roof and end-wall shears.

4.11

Truss Plate Institute (TPI). 1998. HIB-98 summary sheet. TPI, Madison, WI. Truss Plate Institute (TPI). 1995. ANSI/TPI 11995 National design standard for metal plate connected wood truss construction. TPI, Madison, WI.

References

ASAE. 1999a. ASAE EP 288.5: Agricultural building snow and wind loads. ASAE Standards, 46th edition. ASAE, St. Joseph, MI.

Wirt, D.L., F.E. Woeste, D.E. Kline and T.E. McLain. 1992. Design procedures for post-frame end walls. Applied Engineering in Agriculture 8(1):97-105.

ASAE. 1999b. ANSI/ASAE EP 559: Design requirements and bending properties for mechanically-laminated posts. ASAE Standards, 46th edition. ASAE, St. Joseph, MI.

Wood Truss Council of America (WTCA). 1995. Standard responsibilities in the design process involving metal plate connected wood trusses. WTCA 1-1995. WTCA, Madison, WI.

American Forest & Paper Association (AF&PA). 1997. National design specification for wood construction. AF&PA, Washington, D.C.

Wood Truss Council of America (WTCA). 1999. Commentary for permanent bracing of metal plate connected wood trusses. WTCA, Madison, WI.

American Wood-Preservers' Assc. (AWPA). 1995a. Wood for commercial-residential construction. Preservative treatment by pressure process, C-15. In Book of Standards. AWPA, Stevensville, MD. American Wood-Preservers’ Assc. (AWPA). 1995b. Lumber, timbers, bridge ties, and mine ties, pressure treatment, C2-90. In Book of Standards. AWPA, Stevensville, MD. American Wood-Preservers' Assc. (AWPA). 1995c. Care of pressure treated wood products, M4-90. In Book of Standards. AWPA, Stevensville, MD. Brakeman, D.B. 1994. Which truss design method is the correct one? Peaks 16(1):1-3. Gebremedhin, K.G., and F.E. Woeste. 1986. Diaphragm design with knee brace slip for postframe buildings. Transactions of the American Society of Agricultural Engineers 23(2):538-542. Hoyle, R.J. and F.E. Woeste. 1989. Wood technology in the design of structures. Fifth edition. Iowa State University Press, Ames, IA. Truss Plate Institute (TPI). 1989. Recommended design specifications for temporary bracing of

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Chapter 5: DIAPHRAGM DESIGN

post-frame relative to that of other post-frames and shearwalls. If a diaphragm is constructed in such a way that it is quite stiff in shear, diaphragm action will be enhanced and the diaphragm will transfer load from post-frames with low racking stiffness to shearwalls and postframes with high racking stiffness. However, if the shear stiffness of the diaphragm is relatively low, load transfer will be minimal and the behavior of the structure will be much more in accordance with the assumption of independently acting post-frames.

5.1 Introduction 5.1.1 2-D Frame Analysis. Prior to the 1980’s, the common method of analysis for post-frame structures in agricultural, commercial and light industrial applications was to consider the structure as a system of independently-acting, twodimensional (2-D) post-frames. Although a 2-D frame analysis method works well for designing frames under vertical loadings; it is often too conservative for designing buildings against sidesway. In addition, many 2-D frames offer little or no resistance to loads acting normal to the frames (e.g., wind acting normal to the endwalls).

Eave displacement

5.1.2 Diaphragm Action. A considerable portion of the horizontal load applied to many postframe structures is actually resisted by roof and ceiling diaphragms and shearwalls. As previously stated (section 4.9), roof and ceiling diaphragms are large plates that are formed when cladding is attached to roof and ceiling framing, respectively. These large plates help redistribute load throughout the structure. This redistribution of load by the diaphragms is called diaphragm action. A shearwall is any wall – interior or exterior – with a measurable amount of racking resistance. Most of the load to which a diaphragm is subjected, is transferred to the foundation by shearwalls orientated parallel to the direction of applied load. Figure 5.1 illustrates a situation in which wind load directed at a sidewall, is transferred via the roof diaphragm to the endwalls and one interior wall. Under this loading, the two endwalls and the one interior wall function as shearwalls. When the same wind load is directed toward the endwall, the sidewalls function as shearwalls in transferring the load from the roof diaphragm to the foundation system.

Wind load

Intermediate shearwall Roof diaphragm End shearwall Deformed structure Undeformed structure

Figure 5.1. Example of diaphragm action in which the roof diaphragm transfers load to three shearwalls – one interior and two exterior walls. 5.1.4 Endwall Loadings. Virtually all postframe buildings are longer than they are wide. It follows, that diaphragms in such buildings, when viewed from the endwall, appear as narrow, deep plates. For endwall loadings, these narrow, deep diaphragms are generally assumed to have an infinite shear stiffness, which means that every structural element attached to the diaphragm, shifts the same amount when the diaphragm shifts without rotating. For example, under an endwall loading, the roof diaphragm would ensure equal displacement of the top of endwall posts and the top of each sidewall.

5.1.3 Post-Frame Contributions. Whenever load is applied normal to the sidewall of a structure, any post-frame with measurable racking resistance functions like the interior shearwall in figure 5.1. The amount of load that an individual post-frame will transfer to the foundation is dependent on (1) the in-plane shear stiffness of the diaphragm, and (2) the racking stiffness of the

5-1



5.1.5 Diaphragm Design. When diaphragm action is accounted for in overall building design, the design process is referred to as diaphragm design. Diaphragm design is a relatively straight forward process when a diaphragm is (1) assumed to have infinite shear stiffness, and/or (2) only attached to two shearwalls/post-frames (as is generally the case with endwall loadings). When neither of these conditions applies (generally true with loads normal to the sidewall) diaphragm design is more complex. (a)

5.1.6 ASAE EP484.2. The current diaphragm design procedure is outlined in ANSI/ASAE EP484.2: Diaphragm Design of Metal-Clad, Wood-Frame Rectangular Buildings (ASAE, 1999a). This procedure, which is outlined in the following sections, can be broken into five steps: Step 1. Construct a finite element model of the building by breaking the structure into frame, shearwall, and diaphragm elements (Section 5.2) Step 2. Assign stiffness values to frames and shearwall elements (Section 5.3) and diaphragm elements (Section 5.4). Step 3. Calculate structural loads (i.e., eave loads) for the model (Section 5.5). Step 4. Determine the distribution of load to individual elements (Section 5.6). Step 5. Check to make sure that loads do not exceed allowable values (Section 5.7).

Diaphragm "a" Diaphragm "b"

Diaphragm "c"

(b)

2

1

3

4

5

1a

2a

3a

4a

1b

2b

3b

4b

5.2 Structural Model 5.2.1 General. The model developed in this section is only applicable for determining the distribution of loads that are applied parallel to individual post-frames (a.k.a., primary frames). As previously stated, an individual post-frame consists of an individual truss and any attached posts.

(c)

2

1

1c

5.2.2 Diaphragm Sectioning. The process of modeling a post-frame building for diaphragm design begins with the dividing of individual roof and ceiling diaphragms into sections, herein referred to as diaphragm sections. Diaphragm sectioning is a straight-forward process with interior post-frames, interior shearwalls, ridge lines and any other abrupt changes in roof and ceiling slopes servings as lines of demarcation between diaphragm sections.

3

4

3c

2c

5

4c

(d)

Figure 5.2. (a) Perspective view of a four-bay post-frame building with (b) roof and ceiling diaphragms. Sectioning of (c) roof diaphragms, and (d) ceiling diaphragm.

5-2



Figures 5.2a shows a post-frame building with three interior post-frames. Drawing a line along each interior frame and the ridge results in the eight (8) roof diaphragm sections shown in figure 5.2c, and the four ceiling diaphragm sections shown in figure 5.2d.

sent locations frame/shearwall.

at

the

eave

of

each

Horizontal components of applied building loads are typically uniformly distributed along the length of the building as shown in figure 5.3a. For modeling purposes, this uniform load is converted into a set of equivalent concentrated loads that are applied at the nodes as shown in figure 5.3b. Because of the location of their application, these forces are referred to as eave loads.

To avoid confusion when assigning properties to diaphragm sections, it is helpful to identify each diaphragm section with a two-digit identifier. The first digit identifies the bay associated with the section. Bays are generally numbered from leftto-right, as shown in figures 5.2c and 5.2d. The second digit identifies the specific roof or ceiling slope. In figure 5.2, letters have been used to identify these slopes, with letters “a” and “b” representing different roof slopes, and letter “c” used to identify ceiling sections.

2

1

5.2.3 Discretization. The process of breaking a structure into elements for analysis is referred to as discretization. For diaphragm design, a structure is broken into frame elements and diaphragm elements. Each post-frame is considered a separate frame element, as is each shearwall orientated in the same direction as the post-frames. The example building shown in figure 5.2 would be modeled with five (5) frame elements. These frame elements have been identified in figures 5.2c and 5.2d with the encircled numbers (as with individual bays, numbering is generally from left-to-right). Each diaphragm element models the diaphragm sections within a single bay. For example, diaphragm sections 1a, 1b, and 1c in figure 5.2 would be represented with a single diaphragm element. It follows that the number of diaphragm elements is equal to the number of building bays, which in turn, is one less than the number of frame elements. Discretization of a four-bay building is shown in figure 5.3a.

3

3

2

1

4

5

4

(a)

k1

Ch2

Ch1 r1

5.2.4 Spring Model. To determine the distribution of horizontally applied loads to individual diaphragm and frame elements requires only a single stiffness property for each element. For this reason, diaphragm and frame elements are generally represented with simple springs. As shown in figure 5.3b, frame elements are represented with springs of stiffness, k, and diaphragm elements are represented as springs with stiffness Ch. The element (or spring) connection points (a.k.a. nodes) are taken to repre-

r2

Ch3 r3

k5

k4

k3

k2

Ch4 r4

r5

(b)

Figure 5.3. (a) Top view of a four-bay building showing individual elements and applied horizontal loads. Encircled numbers identify frame elements, other numbers identify diaphragm elements. (b) Corresponding spring model.

5-3



Post stiffness, kp, is graphically defined in figure 5.5. For a post with a constant flexural rigidity (E x I) that is assumed to be fixed at the base, post stiffness is given as:

5.3 Frame Stiffness, k 5.3.1 Definition. To be compatible with a model in which nodes represent points along the eave line (figure 5.3b), frame element stiffness, k, must equal the force required for a unit displacement of the frame at the eave (figure 5.4). In equation form: k

=

P/∆

= = =

frame stiffness, lbf/in (N/mm) load applied at eave, lbf (N) lateral displacement at eave resulting from applied load P, in (mm)

kp =

(5-3)

where: kp =

(5-1)

where: k P ∆

3 E I / Hp3

E

=

I = Hp =

stiffness of post that is fixed at the base and pinned at the top, lbf/in (N/mm) modulus of elasticity of post, lbf/in2 (N/mm2) moment of inertia of post, in4 (mm4) post height from fixed base to truss connection post (see figure 5.5), in (mm)

∆ ∆

P k=P/∆

P

Hp

Figure 5.4. Definition of frame stiffness, k.

kp = P / ∆

5.3.2 Calculation. Frame stiffness is generally obtained with a plane-frame structural analysis program, e.g., PPSA (Purdue Research Foundation, 1993), METCLAD (Gebremedhin, 1987b), and SOLVER (Gebremedhin, 1987a). For post-frames in which (1) all posts are assumed to be pin-connected to the truss (or rafters), and (2) there are no special members (e.g., knee braces) connecting posts to the truss, frame stiffness can be calculated as:

Figure 5.5. Definition of post stiffness, kp. 5.3.3 Shearwalls. End shearwalls and intermediate shearwalls, like post-frames, are modeled as frame elements (see Section 5.2.3). Consequently, their stiffness, like that for post-frames, is defined as the ratio of a horizontal force, P, applied at the eave of the wall, to the resulting horizontal eave displacement, ∆.

n

k =

Σ kp,i

(5-2)

The stiffness of shearwalls can be obtained using validated structural models, or from tests of functionally equivalent assemblies. ASAE EP558 (1999b) gives laboratory test procedures that can be used to determine the stiffness of functionally equivalent walls. This topic is also discussed in Section 6.5.

i=1

where: kp,i = n =

Post -to-truss connection point

stiffness of post i, lbf/in (N/mm) number of posts in the post-frame

5-4



below grade. Meador (1997) developed similar equations, but unlike Bohnhoff, Meador assumed that soil stiffness was not a function of post width. Meador also investigated the assumption of infinite post stiffness below grade, and established limits for applicability of the equations he developed. McGuire (1998) used the work of both Bohnhoff and Meador to propose an analog where soil is modeled as a series of linear springs whose stiffness increases linearly below grade (figure 5.6c). McGuire verified Bohnhoff’s results and also showed that for the case of non-constrained posts, analogs like those shown in figure 5.6a may incorrectly predict the sense of base moment (see Chapter 8).

Technical Note Embedded Post Analogs When a post is embedded in the soil, calculated post stiffness (and consequently calculated frame stiffness) is highly dependent on how the embedded portion is modeled. Traditionally, engineers have ignored soil properties and have modeled embedded posts using the analogs shown in figures 5.6a and 5.6b. An inherent deficiency of these analogs is that the pin supports used to fix the post below grade do not allow the post to naturally displace. For this reason, post stiffness values predicted using the analogs should be applied with caution. It should also be noted that the analogs in figures 5.6a and 5.6b produce a reduced post stiffness when depth of embedment, d, is increased. In reality, anytime a post is embedded deeper into the ground, the stiffness associated with the post increases.

Current impediments to the wide spread adoption of analogs that account for soil stiffness include: (1) complexity of equations, and (2) unrealistically low post stiffness values obtained using published soil stiffness data.

To accurately model post movement below grade requires accounting for soil stiffness. Bohnhoff (1992) developed equations for predicting post stiffness assuming soil stiffness increased linearly with depth below grade and inversely with post width. Bohnhoff also assumed that the post had infinite flexural stiffness

It is important for the post-frame designer to realize that fixing the post at grade (figure 5.5) generally produces conservative values for post base moments, especially for the nonconstrained post case. Conversely, forces calculated in the diaphragm using this model might be non-conservative.

Hp

Hp

Hp

Ground surface Floor slab 0.34 d d

d

0.7 d

Springs used to model soil stiffness

d

0.1 d (a)

(b)

(c)

Figure 5.6. Structural analog traditionally used for (a) non-constrained and (b) constrained posts. (c) A more realistic non-constrained post analog that accounts for soil stiffness.

5-5



Ch =

5.4 Diaphragm Stiffness, Ch

ch,i =

5.4.1 Definition. As shown in figure 5.7, the stiffness of a diaphragm element is the horizontal load required to cause a unit shift (in a direction parallel to the trusses/rafters) of the roof/ceiling assembly over a frame spacing (a.k.a. bay width), s. This stiffness is commonly referred to as the total horizontal shear stiffness, Ch, of the diaphragm.

1

2

3

4

s1

s2

s3

s4

n

=

total horizontal shear stiffness of diaphragm element, lbf/in (N/mm) horizontal shear stiffness of diaphragm section i (from Section 6.4.4), lbf/in (N/mm) number of diaphragm sections comprising the diaphragm element

5.5 Eave Loads, R 5.5.1 Definition. For diaphragm design, building loads are replaced by an equivalent set of horizontally acting, concentrated (i.e., point) loads. These loads are located at the eave of each frame element (i.e., post-frame and end shearwall, and intermediate shearwall) and therefore are referred to as eave loads. Eave loads and applied building loads are equivalent when they horizontally displace the eave an equal amount.

(a) Roof Gravity Loads

P s x qwr

∆ i

s x qlr

R s xq ww

C h,i = P / ∆

Ceiling Gravity Loads

s xqlw

P

si

Figure 5.8. Typical structural analog for obtaining eave load, R.

(b)

Figure 5.7. (a) Top view of a four-bay building. (b) Definition of diaphragm stiffness, Ch, for a single diaphragm element.

5.5.2 Calculation by Plane-Frame Structural Analysis. A horizontal restraint (vertical roller) is placed at the eave line as shown in figure 5.8 and the structural analog is analyzed with all external loads in place. The horizontal reaction at the vertical roller support is numerically equal to the eave load, R. The vertical roller should always be placed at the same location that horizontal load P was placed when determine frame stiffness (see figure 5.4). The value of R is very dependent on the magnitude of forces with

5.4.2 Calculation. The total horizontal shear stiffness of a diaphragm element is simply equal to the sum of the horizontal shear stiffness values of the diaphragm sections that comprise the element. In equation form: n

Ch =

Σ ch,i

(5-4)

i=1

where:

5-6



horizontal components (i.e., wind and stored materials).

For symmetrical base restraint and frame geometry, equation 5-5 reduces to: R = s [hr (qwr – qlr) + hw f (qww – qlw)]

5.5.3 Calculation Using Frame-Base Fixity Factors. When: (1) posts are assumed to be pin-connected to trusses/rafters, (2) the only applied loads with horizontal components are due to wind, and (3) wind pressure is uniformly distributed on each wall and roof surface, then eave load, R, can be estimated as: R

=

s (hwr qwr – hlr qlr + hww fw qww – hlw fl qlw)

where: hr = hw = f =

(5-5)

= = =

hwr hlr hww hlw qwr

= = = = =

qlr = qww = qlw = fw

=

fl

=

roof height, ft (m) wall height, ft (m) frame-base fixity factor for both leeward and windward posts

5.6 Load Distribution

where: R s

(5-6)

5.6.1 General. The distribution of horizontal loads to frames, shearwalls, and various diaphragm sections can be determined after stiffness values have been assigned to each frame and diaphragm element, and eave loads have been established.

eave load, lbf (N) frame spacing for interior postframes and shearwalls, ft (m) one-half the frame spacing for endwalls, ft (m) windward roof height, ft (m) leeward roof height, ft (m) windward wall height, ft (m) leeward wall height, ft (m) design windward roof pressure, lbf/ft2 (N/m2) design leeward roof pressure, lbf/ft2 (N/m2) design windward wall pressure, lbf/ft2 (N/m2) design leeward wall pressure lbf/ft2 (N/m2) frame-base fixity factor, windward post frame-base fixity factor, leeward post

5.6.2 Analysis Tools. Any finite element or plane-frame structural analysis program can be used to analyze the structural model shown in figure 5.3b. However, to expedite this process, computer program DAFI was developed (Bohnhoff, 1992). Once eave loads and frame and diaphragm element stiffness values are input, DAFI calculates eave displacements, frame element loads and diaphragm element shear forces. DAFI can be downloaded at no cost from the NFBA web site (http://www.postframe.org/). An iterative method for hand-calculating load distribution was developed by Anderson and others (1989). This method, which is referred to as the force distribution method, is procedurally identical to the classical method of moment distribution.

Inward acting wind pressures have positive signs, outward acting pressures are negative (figure 5.8). In buildings with variable frame spacings, set s equal to the average of the frame spacings on each side of the eave load.

5.6.3 mS and mD Tables. Forces in the most highly loaded diaphragm and frame elements, can be calculated using tables 5.1 and 5.2 when all five of the following conditions exist: (1) all diaphragm elements have the same stiffness Ch, (2) all interior frame elements have the same stiffness, k, (3) both exterior frame elements (i.e., the two elements representing the endwalls) have the same stiffness, ke, (4) eave load, R, is the same at each interior frame, and (5) the eave load for each exterior frame is equal to one-half that for an interior frame. These five requirements are generally met in buildings with a fixed bay spacing, endwalls that are virtually identical in construction, and interior frames that

Frame-base fixity factors, fw and fl, determine how much of the total wall load is transferred to the eave, and how much is transferred directly to the ground. The greater the resistance to rotation at the base of a wall, the more load will be attracted directly to the base of the wall. For substantial fixity against rotation at the groundline, set the frame-base fixity factor(s) equal to 3/8. For all other cases, set the frame-base fixity factor(s) equal to 1/2.

5-7



don’t vary in overall design. When tables 5.1 and 5.2 are applicable, the analysis tools discussed in Section 5.6.2 are generally not needed.

Q = mD = R

Input parameters required for tables 5.1 and 5.2 include: number of frame elements (i.e., the number of interior frames + 2); ratio of diaphragm element to interior frame element stiffness, Ch / k; and ratio of exterior to interior frame element stiffness, ke / k.

=

5.6.4 In-Plane Shear Force in a Diaphragm Section, Vp. The analysis tools discussed in Section 5.6.2 (and equation 5-7) output diaphragm element forces. In most cases, each element is comprised of two or more diaphragm sections. The in-plane shear force in each of these diaphragm sections is calculated as:

The most highly loaded diaphragm element (in any building that meets the preceding five conditions) is the element located adjacent to the endwalls. The maximum shear force in this diaphragm element, Vh, is equal to the appropriate shear modifier value, mS, from table 5.1, multiplied by the eave load, R, for an interior frame. In equation form:

Vp,i =

R mS

Vp,i =

(5-7) ch,i =

where: Vh = mS = R =

θi =

maximum diaphragm element shear force, lbf (N) shear force modifier from Table 5.1 eave load at interior frame, lbf (N)

The most highly loaded interior frame element (in any building that meets the preceding five conditions) is the element located closest to the building midlength. Because of diaphragm action, the total horizontal load that this critical frame must resist is reduced from that which it would have to resist without diaphragm action. The magnitude of this reduction is referred to the horizontal restraining force because in reality, it is a restraining force applied to the frame by the roof (and/or ceiling) diaphragms. Numerically, the horizontal restraining force, Q, is equal to the product of the eave load R, and the appropriate sidesway restraining force factor, mD from table 5.2. In equation form: =

R mD

(5-9)

in-plane shear force in diaphragm section i, lbf (N) horizontal shear force in the diaphragm element, lbf (N) horizontal shear stiffness of diaphragm section i, lbf/in. (N/mm) slope of diaphragm section i

5.6.5 Forces Applied to Frames by Individual Diaphragms. The horizontal movement of most building frames is resisted by roof/ceiling diaphragms. The total horizontal resisting force applied to an individual frame by the roof/ceiling diaphragms was previously defined as the sidesway restraining force, Q. To accurately model a frame with the resisting forces applied by the roof and ceiling diaphragms, requires that the sidesway restraining force, Q, first be divided up between the individual diaphragms (e.g., diaphragms a, b, and c in figure 5.2b). This is accomplished using the following equation:

The value obtained from equation 5-7 is simply equal to one-half of the total horizontal eave load that is not carried by the interior frames.

Q

(ch,i / Ch) Vh / (cos θ i)

where:

Vh = Vh =

sidesway restraining force, lbf (N) sidesway restraining force factor from Table 5.2 eave load at interior frame, lbf (N)

Qi =

Q (ch,i / Ch)

(5-10)

where: Qi = Q

=

Ch =

(5-8) ch,i =

where:

5-8

sidesway resisting force due to diaphragm i, lbf (N) total sidesway resisting force acting on the frame, lbf (N) horizontal shear stiffness for a width s of the roof/ceiling assembly, lbf/in. (N/mm) horizontal shear stiffness of diaphragm i with width s, lbf/in. (N/mm)



Table 5.1. Shear Force Modifier (mS) ke / k

Ch / k

5 5 5 5 5 5 5 5 5

Number of frames (endwalls are counted as frames) 3

4

5

6

7

8

9

10

11

12

13

14

15

16

5 10 20 50 100 200 500 1000 10000

0.88 0.89 0.90 0.91 0.91 0.91 0.91 0.91 0.91

1.14 1.19 1.22 1.24 1.24 1.25 1.25 1.25 1.25

1.33 1.42 1.48 1.51 1.53 1.53 1.54 1.54 1.54

1.45 1.59 1.68 1.74 1.76 1.77 1.78 1.78 1.79

1.53 1.72 1.85 1.93 1.97 1.98 1.99 2.00 2.00

1.59 1.82 1.98 2.10 2.14 2.16 2.18 2.18 2.19

1.62 1.89 2.08 2.23 2.29 2.32 2.34 2.35 2.35

1.65 1.94 2.16 2.35 2.42 2.46 2.48 2.49 2.50

1.66 1.98 2.23 2.45 2.53 2.58 2.61 2.62 2.63

1.67 2.00 2.29 2.53 2.63 2.69 2.73 2.74 2.75

1.68 2.02 2.33 2.60 2.72 2.79 2.83 2.84 2.86

1.68 2.04 2.36 2.67 2.80 2.87 2.92 2.94 2.95

1.68 2.05 2.39 2.72 2.87 2.95 3.01 3.02 3.04

1.68 2.06 2.41 2.77 2.93 3.02 3.08 3.10 3.12

10 10 10 10 10 10 10 10 10

5 10 20 50 100 200 500 1000 10000

0.91 0.93 0.94 0.95 0.95 0.95 0.95 0.95 0.95

1.23 1.29 1.33 1.35 1.36 1.36 1.36 1.36 1.36

1.46 1.58 1.66 1.70 1.72 1.73 1.74 1.74 1.74

1.62 1.81 1.94 2.02 2.05 2.07 2.08 2.08 2.08

1.73 1.99 2.17 2.30 2.35 2.37 2.39 2.40 2.40

1.81 2.13 2.36 2.55 2.62 2.65 2.68 2.68 2.69

1.86 2.23 2.52 2.76 2.86 2.91 2.94 2.95 2.96

1.89 2.31 2.66 2.96 3.08 3.14 3.19 3.20 3.21

1.91 2.36 2.76 3.12 3.27 3.36 3.41 3.43 3.45

1.92 2.40 2.85 3.27 3.45 3.56 3.62 3.64 3.66

1.93 2.44 2.92 3.40 3.61 3.74 3.82 3.84 3.87

1.93 2.46 2.98 3.51 3.76 3.90 4.00 4.03 4.06

1.94 2.48 3.03 3.61 3.89 4.06 4.17 4.20 4.24

1.94 2.49 3.06 3.70 4.01 4.20 4.32 4.37 4.41

20 20 20 20 20 20 20 20 20

5 10 20 50 100 200 500 1000 10000

0.93 0.95 0.96 0.97 0.97 0.97 0.98 0.98 0.98

1.28 1.35 1.39 1.41 1.42 1.42 1.43 1.43 1.43

1.54 1.68 1.76 1.82 1.84 1.85 1.86 1.86 1.86

1.73 1.95 2.09 2.20 2.23 2.25 2.27 2.27 2.27

1.85 2.16 2.38 2.54 2.60 2.63 2.65 2.66 2.67

1.94 2.33 2.62 2.85 2.95 2.99 3.02 3.03 3.04

2.00 2.45 2.83 3.14 3.26 3.33 3.38 3.39 3.40

2.03 2.55 3.00 3.39 3.56 3.65 3.71 3.73 3.75

2.06 2.62 3.14 3.62 3.83 3.95 4.03 4.06 4.08

2.07 2.67 3.25 3.83 4.09 4.24 4.33 4.37 4.40

2.09 2.71 3.35 4.01 4.32 4.50 4.62 4.66 4.70

2.09 2.74 3.43 4.17 4.54 4.75 4.90 4.95 5.00

2.10 2.76 3.49 4.32 4.74 4.99 5.16 5.22 5.28

2.10 2.78 3.54 4.44 4.92 5.21 5.41 5.48 5.55

50 50 50 50 50 50 50 50 50

5 10 20 50 100 200 500 1000 10000

0.95 0.97 0.98 0.99 0.99 0.99 0.99 0.99 0.99

1.31 1.38 1.43 1.45 1.46 1.47 1.47 1.47 1.47

1.59 1.74 1.83 1.90 1.92 1.93 1.94 1.94 1.94

1.79 2.04 2.20 2.32 2.36 2.38 2.40 2.40 2.40

1.93 2.28 2.52 2.71 2.78 2.82 2.84 2.85 2.86

2.03 2.46 2.80 3.08 3.18 3.24 3.28 3.29 3.30

2.09 2.61 3.04 3.42 3.57 3.65 3.70 3.72 3.74

2.14 2.72 3.25 3.73 3.93 4.04 4.12 4.14 4.16

2.16 2.80 3.41 4.01 4.27 4.42 4.52 4.55 4.58

2.18 2.86 3.55 4.26 4.60 4.79 4.91 4.96 5.00

2.19 2.91 3.67 4.50 4.90 5.14 5.29 5.35 5.40

2.20 2.94 3.77 4.70 5.18 5.47 5.66 5.73 5.80

2.20 2.97 3.84 4.89 5.45 5.79 6.02 6.11 6.19

2.21 2.99 3.91 5.06 5.69 6.09 6.37 6.47 6.57

100 100 100 100 100 100 100 100 100

5 10 20 50 100 200 500 1000 10000

0.95 0.97 0.98 0.99 0.99 0.99 1.00 1.00 1.00

1.32 1.40 1.44 1.47 1.48 1.48 1.48 1.48 1.49

1.61 1.76 1.86 1.92 1.95 1.96 1.97 1.97 1.97

1.82 2.07 2.24 2.36 2.40 2.43 2.44 2.45 2.45

1.96 2.32 2.58 2.77 2.85 2.89 2.91 2.92 2.93

2.06 2.51 2.87 3.16 3.27 3.33 3.37 3.39 3.40

2.13 2.67 3.12 3.52 3.68 3.77 3.83 3.85 3.86

2.17 2.78 3.34 3.85 4.07 4.19 4.27 4.30 4.32

2.20 2.87 3.52 4.16 4.44 4.61 4.71 4.75 4.78

2.22 2.93 3.67 4.43 4.79 5.00 5.14 5.19 5.23

2.23 2.98 3.79 4.69 5.13 5.39 5.56 5.62 5.68

2.24 3.02 3.89 4.91 5.44 5.76 5.98 6.05 6.12

2.24 3.05 3.98 5.12 5.73 6.12 6.38 6.48 6.56

2.25 3.06 4.05 5.30 6.01 6.46 6.78 6.89 7.00

1000 1000 1000 1000 1000 1000 1000 1000 1000

5 10 20 50 100 200 500 1000 10000

0.95 0.98 0.99 1.00 1.00 1.00 1.00 1.00 1.00

1.33 1.41 1.45 1.48 1.49 1.49 1.50 1.50 1.50

1.63 1.78 1.88 1.95 1.97 1.99 1.99 2.00 2.00

1.84 2.10 2.28 2.40 2.45 2.47 2.49 2.49 2.50

1.99 2.36 2.63 2.83 2.91 2.95 2.98 2.98 2.99

2.09 2.56 2.93 3.24 3.36 3.42 3.46 3.48 3.49

2.16 2.72 3.20 3.62 3.79 3.89 3.95 3.97 3.98

2.20 2.84 3.43 3.97 4.21 4.34 4.42 4.45 4.48

2.23 2.93 3.62 4.30 4.61 4.78 4.90 4.94 4.97

2.25 3.00 3.78 4.60 4.99 5.22 5.37 5.42 5.47

2.27 3.05 3.91 4.87 5.35 5.64 5.83 5.90 5.96

2.27 3.09 4.02 5.12 5.69 6.05 6.29 6.37 6.45

2.28 3.12 4.11 5.34 6.02 6.44 6.74 6.85 6.94

2.28 3.14 4.18 5.54 6.32 6.83 7.18 7.31 7.43

10000 10000 10000 10000 10000 10000 10000 10000 10000

5 10 20 50 100 200 500 1000 10000

0.96 0.98 0.99 1.00 1.00 1.00 1.00 1.00 1.00

1.33 1.41 1.45 1.48 1.49 1.50 1.50 1.50 1.50

1.63 1.79 1.89 1.95 1.98 1.99 2.00 2.00 2.00

1.84 2.10 2.28 2.40 2.45 2.48 2.49 2.50 2.50

1.99 2.36 2.63 2.84 2.92 2.96 2.98 2.99 3.00

2.09 2.57 2.94 3.25 3.37 3.43 3.47 3.49 3.50

2.16 2.72 3.21 3.63 3.80 3.90 3.96 3.98 4.00

2.21 2.85 3.43 3.98 4.22 4.35 4.44 4.47 4.50

2.24 2.94 3.63 4.31 4.62 4.80 4.92 4.96 4.99

2.26 3.01 3.79 4.61 5.01 5.24 5.39 5.44 5.49

2.27 3.06 3.92 4.89 5.37 5.66 5.86 5.93 5.99

2.28 3.10 4.03 5.14 5.72 6.08 6.32 6.41 6.49

2.28 3.12 4.12 5.36 6.05 6.48 6.78 6.88 6.98

2.29 3.14 4.19 5.57 6.35 6.87 7.23 7.36 7.48

5-9



Table 5.1. Shear Force Modifier (mS), cont. ke / k

Ch / k

5 5 5 5 5 5 5 5 5

Number of frames (endwalls are counted as frames) 17

18

19

20

21

22

23

24

25

26

27

28

29

30

5 10 20 50 100 200 500 1000 10000

1.69 2.06 2.43 2.81 2.98 3.09 3.15 3.18 3.20

1.69 2.07 2.44 2.84 3.03 3.14 3.22 3.24 3.27

1.69 2.07 2.46 2.87 3.07 3.19 3.28 3.30 3.33

1.69 2.07 2.46 2.89 3.11 3.24 3.33 3.36 3.39

1.69 2.07 2.47 2.92 3.14 3.28 3.38 3.41 3.45

1.69 2.08 2.48 2.94 3.18 3.32 3.43 3.46 3.50

1.69 2.08 2.48 2.95 3.20 3.36 3.47 3.51 3.54

1.69 2.08 2.49 2.97 3.23 3.39 3.51 3.55 3.59

1.69 2.08 2.49 2.98 3.25 3.42 3.55 3.59 3.63

1.69 2.08 2.49 2.99 3.27 3.45 3.58 3.63 3.67

1.69 2.08 2.49 3.00 3.29 3.48 3.61 3.66 3.71

1.69 2.08 2.49 3.01 3.30 3.50 3.64 3.70 3.74

1.69 2.08 2.50 3.01 3.32 3.52 3.67 3.73 3.78

1.69 2.08 2.50 3.02 3.33 3.54 3.70 3.75 3.81

10 10 10 10 10 10 10 10 10

5 10 20 50 100 200 500 1000 10000

1.94 2.50 3.09 3.77 4.12 4.33 4.47 4.52 4.57

1.94 2.50 3.12 3.84 4.21 4.45 4.61 4.66 4.72

1.94 2.51 3.14 3.89 4.30 4.56 4.74 4.80 4.86

1.94 2.51 3.15 3.94 4.38 4.66 4.86 4.93 4.99

1.94 2.51 3.16 3.99 4.45 4.76 4.97 5.05 5.12

1.94 2.52 3.17 4.02 4.52 4.84 5.08 5.16 5.24

1.94 2.52 3.18 4.06 4.58 4.92 5.18 5.27 5.36

1.94 2.52 3.19 4.09 4.63 5.00 5.27 5.37 5.47

1.94 2.52 3.19 4.11 4.68 5.07 5.36 5.47 5.57

1.94 2.52 3.20 4.13 4.72 5.13 5.44 5.56 5.67

1.94 2.52 3.20 4.15 4.76 5.19 5.52 5.65 5.76

1.94 2.52 3.20 4.17 4.80 5.25 5.60 5.73 5.86

1.94 2.52 3.21 4.18 4.83 5.30 5.67 5.81 5.94

1.94 2.52 3.21 4.19 4.86 5.35 5.73 5.88 6.03

20 20 20 20 20 20 20 20 20

5 10 20 50 100 200 500 1000 10000

2.10 2.79 3.58 4.56 5.08 5.42 5.65 5.73 5.81

2.10 2.80 3.62 4.65 5.24 5.61 5.88 5.97 6.06

2.10 2.80 3.64 4.74 5.38 5.80 6.09 6.20 6.30

2.10 2.81 3.66 4.82 5.51 5.97 6.30 6.42 6.54

2.10 2.81 3.68 4.88 5.62 6.13 6.50 6.64 6.77

2.10 2.81 3.69 4.94 5.73 6.28 6.69 6.84 6.98

2.10 2.82 3.71 4.99 5.83 6.42 6.87 7.03 7.20

2.10 2.82 3.71 5.03 5.91 6.55 7.04 7.22 7.40

2.10 2.82 3.72 5.07 5.99 6.67 7.20 7.40 7.60

2.10 2.82 3.73 5.11 6.07 6.79 7.36 7.58 7.79

2.10 2.82 3.73 5.14 6.13 6.90 7.51 7.74 7.97

2.10 2.82 3.74 5.16 6.20 7.00 7.65 7.90 8.15

2.10 2.82 3.74 5.18 6.25 7.09 7.78 8.06 8.33

2.10 2.82 3.74 5.20 6.30 7.18 7.91 8.21 8.50

50 50 50 50 50 50 50 50 50

5 10 20 50 100 200 500 1000 10000

2.21 3.00 3.96 5.20 5.92 6.39 6.71 6.83 6.94

2.21 3.01 4.00 5.33 6.13 6.66 7.04 7.18 7.31

2.21 3.02 4.03 5.45 6.33 6.93 7.36 7.52 7.68

2.21 3.02 4.06 5.55 6.51 7.18 7.67 7.85 8.03

2.21 3.03 4.08 5.64 6.67 7.41 7.97 8.18 8.38

2.21 3.03 4.10 5.72 6.83 7.64 8.26 8.50 8.72

2.21 3.03 4.11 5.79 6.97 7.85 8.54 8.80 9.06

2.21 3.03 4.12 5.85 7.10 8.05 8.81 9.10 9.39

2.21 3.03 4.13 5.90 7.21 8.24 9.07 9.40 9.72

2.21 3.04 4.14 5.95 7.32 8.42 9.32 9.68 10.04

2.21 3.04 4.14 5.99 7.42 8.59 9.57 9.96 10.35

2.21 3.04 4.15 6.03 7.51 8.75 9.80 10.23 10.66

2.21 3.04 4.15 6.06 7.59 8.90 10.03 10.50 10.97

2.21 3.04 4.16 6.08 7.67 9.04 10.25 10.75 11.27

100 100 100 100 100 100 100 100 100

5 10 20 50 100 200 500 1000 10000

2.25 3.08 4.10 5.46 6.26 6.79 7.16 7.30 7.43

2.25 3.09 4.14 5.61 6.50 7.10 7.54 7.70 7.85

2.25 3.10 4.18 5.74 6.72 7.41 7.91 8.10 8.28

2.25 3.10 4.21 5.85 6.93 7.69 8.27 8.49 8.69

2.25 3.11 4.23 5.95 7.12 7.97 8.62 8.87 9.11

2.25 3.11 4.25 6.04 7.29 8.23 8.96 9.24 9.51

2.25 3.11 4.27 6.12 7.45 8.48 9.29 9.61 9.92

2.25 3.11 4.28 6.19 7.60 8.72 9.62 9.97 10.32

2.25 3.11 4.29 6.24 7.74 8.94 9.93 10.33 10.72

2.25 3.12 4.30 6.30 7.86 9.15 10.24 10.67 11.11

2.25 3.12 4.30 6.34 7.98 9.35 10.53 11.01 11.50

2.25 3.12 4.31 6.38 8.08 9.54 10.82 11.35 11.88

2.25 3.12 4.31 6.42 8.18 9.72 11.10 11.68 12.27

2.25 3.12 4.31 6.45 8.27 9.89 11.37 12.00 12.64

1000 1000 1000 1000 1000 1000 1000 1000 1000

5 10 20 50 100 200 500 1000 10000

2.28 3.15 4.24 5.72 6.61 7.20 7.62 7.78 7.92

2.29 3.16 4.29 5.88 6.87 7.56 8.05 8.24 8.41

2.29 3.17 4.32 6.02 7.12 7.90 8.48 8.69 8.90

2.29 3.18 4.36 6.15 7.35 8.23 8.89 9.15 9.39

2.29 3.18 4.38 6.26 7.57 8.55 9.30 9.59 9.87

2.29 3.18 4.40 6.36 7.77 8.85 9.70 10.04 10.36

2.29 3.19 4.42 6.44 7.95 9.14 10.10 10.47 10.84

2.29 3.19 4.43 6.52 8.12 9.41 10.48 10.91 11.33

2.29 3.19 4.44 6.59 8.28 9.68 10.86 11.33 11.81

2.29 3.19 4.45 6.65 8.43 9.93 11.22 11.75 12.29

2.29 3.19 4.46 6.70 8.56 10.17 11.58 12.17 12.77

2.29 3.19 4.46 6.74 8.68 10.39 11.93 12.58 13.25

2.29 3.19 4.47 6.78 8.79 10.61 12.27 12.99 13.73

2.29 3.19 4.47 6.81 8.89 10.81 12.61 13.39 14.20

10000 10000 10000 10000 10000 10000 10000 10000 10000

5 10 20 50 100 200 500 1000 10000

2.29 3.16 4.25 5.75 6.64 7.24 7.67 7.83 7.98

2.29 3.17 4.30 5.91 6.91 7.60 8.11 8.30 8.47

2.29 3.18 4.34 6.05 7.17 7.95 8.54 8.76 8.97

2.29 3.19 4.37 6.18 7.40 8.29 8.96 9.22 9.46

2.29 3.19 4.40 6.29 7.62 8.61 9.38 9.67 9.96

2.29 3.19 4.42 6.39 7.82 8.92 9.78 10.12 10.45

2.29 3.19 4.43 6.48 8.01 9.21 10.18 10.57 10.94

2.29 3.20 4.45 6.56 8.18 9.49 10.57 11.01 11.44

2.29 3.20 4.46 6.62 8.34 9.76 10.96 11.44 11.93

2.29 3.20 4.46 6.68 8.49 10.01 11.33 11.88 12.42

2.29 3.20 4.47 6.73 8.62 10.26 11.70 12.30 12.91

2.29 3.20 4.48 6.78 8.74 10.49 12.06 12.72 13.40

2.29 3.20 4.48 6.82 8.86 10.71 12.41 13.14 13.89

2.29 3.20 4.48 6.85 8.96 10.91 12.75 13.55 14.38

5-10



Table 5.2. Sidesway Restraining Force Modifier (mD) ke / k

Ch / k

5 5 5 5 5 5 5 5 5

Number of frames (endwalls counted as frames) 3

4

5

6

7

8

9

10

11

12

13

14

15

16

5 10 20 50 100 200 500 1000 10000

0.75 0.78 0.80 0.81 0.81 0.82 0.82 0.82 0.82

0.64 0.69 0.72 0.74 0.74 0.75 0.75 0.75 0.75

0.52 0.59 0.64 0.67 0.68 0.69 0.69 0.69 0.69

0.43 0.52 0.58 0.62 0.63 0.64 0.64 0.64 0.64

0.34 0.44 0.51 0.56 0.58 0.59 0.60 0.60 0.60

0.28 0.39 0.46 0.52 0.54 0.55 0.56 0.56 0.56

0.22 0.33 0.41 0.48 0.50 0.52 0.52 0.53 0.53

0.18 0.28 0.37 0.44 0.47 0.48 0.49 0.50 0.50

0.14 0.24 0.33 0.41 0.44 0.46 0.47 0.47 0.47

0.12 0.21 0.30 0.38 0.41 0.43 0.44 0.45 0.45

0.09 0.18 0.26 0.35 0.38 0.41 0.42 0.42 0.43

0.08 0.15 0.24 0.32 0.36 0.38 0.40 0.40 0.41

0.06 0.13 0.21 0.30 0.34 0.36 0.38 0.39 0.39

0.05 0.11 0.19 0.28 0.32 0.35 0.36 0.37 0.37

10 10 10 10 10 10 10 10 10

5 10 20 50 100 200 500 1000 10000

0.83 0.86 0.88 0.90 0.90 0.90 0.90 0.90 0.91

0.73 0.79 0.83 0.85 0.86 0.86 0.86 0.86 0.86

0.60 0.70 0.76 0.80 0.81 0.82 0.82 0.83 0.83

0.51 0.63 0.70 0.75 0.77 0.78 0.79 0.79 0.79

0.41 0.54 0.64 0.71 0.73 0.75 0.75 0.76 0.76

0.34 0.48 0.58 0.66 0.70 0.71 0.72 0.73 0.73

0.27 0.41 0.52 0.62 0.66 0.68 0.70 0.70 0.70

0.22 0.36 0.48 0.58 0.63 0.65 0.67 0.67 0.68

0.17 0.30 0.43 0.55 0.60 0.63 0.64 0.65 0.66

0.14 0.26 0.39 0.51 0.57 0.60 0.62 0.63 0.63

0.11 0.22 0.35 0.48 0.54 0.57 0.60 0.61 0.61

0.09 0.19 0.31 0.45 0.51 0.55 0.58 0.59 0.59

0.07 0.16 0.28 0.42 0.49 0.53 0.56 0.57 0.58

0.06 0.14 0.25 0.39 0.46 0.51 0.54 0.55 0.56

20 20 20 20 20 20 20 20 20

5 10 20 50 100 200 500 1000 10000

0.87 0.91 0.93 0.94 0.95 0.95 0.95 0.95 0.95

0.78 0.85 0.89 0.91 0.92 0.92 0.93 0.93 0.93

0.65 0.76 0.83 0.87 0.89 0.90 0.90 0.91 0.91

0.56 0.69 0.78 0.84 0.86 0.87 0.88 0.88 0.89

0.45 0.60 0.72 0.80 0.83 0.85 0.86 0.86 0.87

0.38 0.54 0.66 0.76 0.80 0.83 0.84 0.84 0.85

0.30 0.46 0.60 0.72 0.77 0.80 0.82 0.82 0.83

0.25 0.41 0.55 0.69 0.75 0.78 0.80 0.81 0.81

0.19 0.35 0.50 0.65 0.72 0.76 0.78 0.79 0.80

0.16 0.30 0.46 0.62 0.69 0.73 0.76 0.77 0.78

0.13 0.26 0.41 0.58 0.66 0.71 0.74 0.75 0.76

0.10 0.22 0.37 0.55 0.64 0.69 0.72 0.74 0.75

0.08 0.19 0.33 0.51 0.61 0.67 0.71 0.72 0.73

0.07 0.16 0.30 0.48 0.58 0.65 0.69 0.71 0.72

50 50 50 50 50 50 50 50 50

5 10 20 50 100 200 500 1000 10000

0.89 0.93 0.96 0.97 0.98 0.98 0.98 0.98 0.98

0.81 0.88 0.93 0.95 0.96 0.97 0.97 0.97 0.97

0.68 0.80 0.88 0.93 0.94 0.95 0.96 0.96 0.96

0.59 0.73 0.83 0.90 0.93 0.94 0.95 0.95 0.95

0.48 0.65 0.77 0.87 0.90 0.92 0.94 0.94 0.94

0.40 0.58 0.72 0.84 0.88 0.91 0.92 0.93 0.93

0.32 0.50 0.66 0.80 0.86 0.89 0.91 0.92 0.93

0.26 0.44 0.61 0.77 0.84 0.88 0.90 0.91 0.92

0.21 0.38 0.55 0.73 0.81 0.86 0.89 0.90 0.91

0.17 0.33 0.51 0.70 0.79 0.84 0.88 0.89 0.90

0.13 0.28 0.46 0.66 0.76 0.82 0.86 0.88 0.89

0.11 0.24 0.41 0.63 0.74 0.81 0.85 0.87 0.88

0.09 0.21 0.37 0.59 0.71 0.79 0.84 0.86 0.87

0.07 0.18 0.34 0.56 0.69 0.77 0.83 0.85 0.87

100 100 100 100 100 100 100 100 100

5 10 20 50 100 200 500 1000 10000

0.90 0.94 0.97 0.98 0.99 0.99 0.99 0.99 0.99

0.82 0.90 0.94 0.97 0.98 0.98 0.98 0.98 0.99

0.69 0.82 0.89 0.94 0.96 0.97 0.98 0.98 0.98

0.60 0.75 0.85 0.92 0.95 0.96 0.97 0.97 0.98

0.48 0.66 0.79 0.89 0.93 0.95 0.96 0.97 0.97

0.41 0.59 0.74 0.86 0.91 0.94 0.96 0.96 0.97

0.32 0.51 0.68 0.83 0.89 0.93 0.95 0.95 0.96

0.27 0.45 0.63 0.80 0.87 0.91 0.94 0.95 0.96

0.21 0.39 0.57 0.76 0.85 0.90 0.93 0.94 0.95

0.17 0.34 0.52 0.73 0.83 0.88 0.92 0.93 0.95

0.14 0.29 0.47 0.69 0.80 0.87 0.91 0.93 0.94

0.11 0.25 0.43 0.66 0.78 0.85 0.90 0.92 0.94

0.09 0.21 0.39 0.62 0.75 0.84 0.89 0.91 0.93

0.07 0.18 0.35 0.59 0.73 0.82 0.88 0.91 0.93

1000 1000 1000 1000 1000 1000 1000 1000 1000

5 10 20 50 100 200 500 1000 10000

0.91 0.95 0.98 0.99 0.99 1.00 1.00 1.00 1.00

0.83 0.91 0.95 0.98 0.99 0.99 1.00 1.00 1.00

0.70 0.83 0.91 0.96 0.98 0.99 0.99 1.00 1.00

0.61 0.76 0.87 0.94 0.97 0.98 0.99 1.00 1.00

0.49 0.67 0.81 0.91 0.95 0.98 0.99 0.99 1.00

0.41 0.60 0.76 0.89 0.94 0.97 0.99 0.99 1.00

0.33 0.52 0.70 0.86 0.92 0.96 0.98 0.99 1.00

0.27 0.46 0.65 0.83 0.90 0.95 0.98 0.99 1.00

0.22 0.40 0.59 0.79 0.88 0.94 0.97 0.98 0.99

0.18 0.35 0.54 0.76 0.86 0.93 0.97 0.98 0.99

0.14 0.30 0.49 0.72 0.84 0.91 0.96 0.98 0.99

0.11 0.26 0.45 0.69 0.82 0.90 0.95 0.97 0.99

0.09 0.22 0.40 0.65 0.79 0.88 0.95 0.97 0.99

0.07 0.19 0.36 0.62 0.77 0.87 0.94 0.97 0.99

10000 10000 10000 10000 10000 10000 10000 10000 10000

5 10 20 50 100 200 500 1000 10000

0.91 0.95 0.98 0.99 1.00 1.00 1.00 1.00 1.00

0.83 0.91 0.95 0.98 0.99 1.00 1.00 1.00 1.00

0.70 0.83 0.91 0.96 0.98 0.99 1.00 1.00 1.00

0.61 0.76 0.87 0.94 0.97 0.99 0.99 1.00 1.00

0.49 0.68 0.81 0.92 0.96 0.98 0.99 1.00 1.00

0.42 0.61 0.76 0.89 0.94 0.97 0.99 0.99 1.00

0.33 0.53 0.70 0.86 0.93 0.96 0.98 0.99 1.00

0.27 0.46 0.65 0.83 0.91 0.95 0.98 0.99 1.00

0.22 0.40 0.59 0.79 0.89 0.94 0.98 0.99 1.00

0.18 0.35 0.54 0.76 0.87 0.93 0.97 0.99 1.00

0.14 0.30 0.49 0.72 0.84 0.92 0.96 0.98 1.00

0.11 0.26 0.45 0.69 0.82 0.90 0.96 0.98 1.00

0.09 0.22 0.40 0.65 0.80 0.89 0.95 0.98 1.00

0.07 0.19 0.37 0.62 0.77 0.87 0.95 0.97 1.00

5-11



Table 5.2. Sidesway Restraining Force Modifier (mD), cont. ke / k

Ch / k

5 5 5 5 5 5 5 5 5

Number of frames (endwalls counted as frames) 17

18

19

20

21

22

23

24

25

26

27

28

29

30

5 10 20 50 100 200 500 1000 10000

0.04 0.09 0.17 0.26 0.30 0.33 0.35 0.35 0.36

0.03 0.08 0.15 0.24 0.29 0.31 0.33 0.34 0.35

0.02 0.07 0.13 0.22 0.27 0.30 0.32 0.33 0.33

0.02 0.06 0.12 0.21 0.26 0.29 0.31 0.31 0.32

0.02 0.05 0.11 0.19 0.24 0.27 0.29 0.30 0.31

0.01 0.04 0.10 0.18 0.23 0.26 0.28 0.29 0.30

0.01 0.04 0.09 0.17 0.22 0.25 0.27 0.28 0.29

0.01 0.03 0.08 0.16 0.20 0.24 0.26 0.27 0.28

0.01 0.03 0.07 0.14 0.19 0.23 0.25 0.26 0.27

0.01 0.02 0.06 0.13 0.18 0.22 0.25 0.25 0.26

0.00 0.02 0.06 0.12 0.17 0.21 0.24 0.25 0.26

0.00 0.02 0.05 0.12 0.17 0.20 0.23 0.24 0.25

0.00 0.01 0.04 0.11 0.16 0.19 0.22 0.23 0.24

0.00 0.01 0.04 0.10 0.15 0.19 0.21 0.23 0.24

10 10 10 10 10 10 10 10 10

5 10 20 50 100 200 500 1000 10000

0.05 0.12 0.23 0.36 0.44 0.49 0.52 0.53 0.54

0.04 0.10 0.20 0.34 0.42 0.47 0.50 0.52 0.53

0.03 0.09 0.18 0.32 0.40 0.45 0.49 0.50 0.51

0.02 0.08 0.16 0.30 0.38 0.43 0.47 0.49 0.50

0.02 0.06 0.15 0.28 0.36 0.42 0.46 0.47 0.49

0.02 0.06 0.13 0.26 0.34 0.40 0.44 0.46 0.47

0.01 0.05 0.12 0.24 0.33 0.39 0.43 0.45 0.46

0.01 0.04 0.11 0.23 0.31 0.37 0.42 0.43 0.45

0.01 0.03 0.09 0.21 0.29 0.36 0.40 0.42 0.44

0.01 0.03 0.08 0.20 0.28 0.34 0.39 0.41 0.43

0.01 0.03 0.08 0.18 0.27 0.33 0.38 0.40 0.42

0.00 0.02 0.07 0.17 0.25 0.32 0.37 0.39 0.41

0.00 0.02 0.06 0.16 0.24 0.31 0.36 0.38 0.40

0.00 0.02 0.05 0.15 0.23 0.30 0.35 0.37 0.39

20 20 20 20 20 20 20 20 20

5 10 20 50 100 200 500 1000 10000

0.05 0.14 0.27 0.45 0.56 0.63 0.67 0.69 0.71

0.04 0.12 0.24 0.42 0.53 0.61 0.66 0.68 0.69

0.03 0.10 0.22 0.40 0.51 0.59 0.64 0.66 0.68

0.03 0.09 0.20 0.37 0.49 0.57 0.63 0.65 0.67

0.02 0.07 0.17 0.35 0.47 0.55 0.61 0.64 0.66

0.02 0.06 0.16 0.33 0.45 0.53 0.60 0.62 0.65

0.01 0.05 0.14 0.30 0.43 0.52 0.59 0.61 0.64

0.01 0.05 0.13 0.28 0.41 0.50 0.57 0.60 0.63

0.01 0.04 0.11 0.27 0.39 0.48 0.56 0.59 0.62

0.01 0.03 0.10 0.25 0.37 0.47 0.55 0.58 0.61

0.01 0.03 0.09 0.23 0.35 0.45 0.53 0.57 0.60

0.01 0.03 0.08 0.22 0.34 0.44 0.52 0.55 0.59

0.00 0.02 0.07 0.20 0.32 0.42 0.51 0.54 0.58

0.00 0.02 0.06 0.19 0.31 0.41 0.50 0.53 0.57

50 50 50 50 50 50 50 50 50

5 10 20 50 100 200 500 1000 10000

0.06 0.15 0.30 0.52 0.66 0.75 0.81 0.84 0.86

0.05 0.13 0.27 0.49 0.64 0.73 0.80 0.83 0.85

0.04 0.11 0.24 0.46 0.61 0.71 0.79 0.82 0.84

0.03 0.10 0.22 0.44 0.59 0.69 0.78 0.81 0.84

0.02 0.08 0.20 0.41 0.56 0.68 0.76 0.80 0.83

0.02 0.07 0.18 0.38 0.54 0.66 0.75 0.79 0.82

0.02 0.06 0.16 0.36 0.52 0.64 0.74 0.78 0.81

0.01 0.05 0.14 0.34 0.50 0.62 0.73 0.77 0.81

0.01 0.04 0.13 0.31 0.47 0.60 0.71 0.76 0.80

0.01 0.04 0.11 0.29 0.45 0.59 0.70 0.75 0.79

0.01 0.03 0.10 0.27 0.43 0.57 0.69 0.74 0.79

0.01 0.03 0.09 0.26 0.41 0.55 0.68 0.73 0.78

0.00 0.02 0.08 0.24 0.40 0.54 0.67 0.72 0.77

0.00 0.02 0.07 0.22 0.38 0.52 0.65 0.71 0.77

100 100 100 100 100 100 100 100 100

5 10 20 50 100 200 500 1000 10000

0.06 0.16 0.31 0.55 0.70 0.80 0.87 0.90 0.92

0.05 0.13 0.28 0.52 0.68 0.78 0.86 0.89 0.92

0.04 0.11 0.25 0.49 0.65 0.77 0.85 0.88 0.91

0.03 0.10 0.23 0.46 0.63 0.75 0.84 0.88 0.91

0.02 0.08 0.20 0.43 0.60 0.73 0.83 0.87 0.90

0.02 0.07 0.18 0.41 0.58 0.71 0.82 0.86 0.90

0.02 0.06 0.16 0.38 0.56 0.69 0.81 0.85 0.90

0.01 0.05 0.15 0.36 0.53 0.68 0.80 0.84 0.89

0.01 0.04 0.13 0.33 0.51 0.66 0.79 0.84 0.89

0.01 0.04 0.12 0.31 0.49 0.64 0.77 0.83 0.88

0.01 0.03 0.11 0.29 0.47 0.62 0.76 0.82 0.88

0.01 0.03 0.09 0.27 0.45 0.61 0.75 0.81 0.87

0.00 0.02 0.08 0.25 0.43 0.59 0.74 0.80 0.87

0.00 0.02 0.08 0.24 0.41 0.57 0.73 0.80 0.86

1000 1000 1000 1000 1000 1000 1000 1000 1000

5 10 20 50 100 200 500 1000 10000

0.06 0.16 0.33 0.58 0.74 0.85 0.93 0.96 0.99

0.05 0.14 0.29 0.55 0.72 0.84 0.93 0.96 0.99

0.04 0.12 0.26 0.52 0.69 0.82 0.92 0.95 0.99

0.03 0.10 0.24 0.49 0.67 0.80 0.91 0.95 0.99

0.02 0.09 0.21 0.46 0.64 0.79 0.90 0.94 0.99

0.02 0.07 0.19 0.43 0.62 0.77 0.89 0.94 0.98

0.02 0.06 0.17 0.40 0.60 0.75 0.88 0.93 0.98

0.01 0.05 0.15 0.38 0.57 0.74 0.87 0.93 0.98

0.01 0.05 0.14 0.35 0.55 0.72 0.86 0.92 0.98

0.01 0.04 0.12 0.33 0.53 0.70 0.85 0.92 0.98

0.01 0.03 0.11 0.31 0.50 0.68 0.84 0.91 0.98

0.01 0.03 0.10 0.29 0.48 0.66 0.83 0.90 0.98

0.00 0.02 0.09 0.27 0.46 0.65 0.82 0.90 0.98

0.00 0.02 0.08 0.25 0.44 0.63 0.81 0.89 0.98

10000 10000 10000 10000 10000 10000 10000 10000 10000

5 10 20 50 100 200 500 1000 10000

0.06 0.16 0.33 0.58 0.75 0.86 0.94 0.97 1.00

0.05 0.14 0.30 0.55 0.72 0.84 0.93 0.96 1.00

0.04 0.12 0.26 0.52 0.70 0.83 0.92 0.96 1.00

0.03 0.10 0.24 0.49 0.67 0.81 0.92 0.96 1.00

0.02 0.09 0.21 0.46 0.65 0.79 0.91 0.95 0.99

0.02 0.07 0.19 0.43 0.62 0.78 0.90 0.95 0.99

0.02 0.06 0.17 0.40 0.60 0.76 0.89 0.94 0.99

0.01 0.05 0.15 0.38 0.58 0.74 0.88 0.94 0.99

0.01 0.05 0.14 0.36 0.55 0.72 0.87 0.93 0.99

0.01 0.04 0.12 0.33 0.53 0.71 0.86 0.93 0.99

0.01 0.03 0.11 0.31 0.51 0.69 0.85 0.92 0.99

0.01 0.03 0.10 0.29 0.49 0.67 0.84 0.91 0.99

0.00 0.02 0.09 0.27 0.47 0.65 0.83 0.91 0.99

0.00 0.02 0.08 0.25 0.45 0.64 0.82 0.90 0.99

5-12



FRAME FRAME APPLIED HORIZONTAL LOAD RESISTED FRACTION OF NUMBER STIFFNESS LOAD DISPLACEMENT BY FRAME APPLIED LOAD --------------------------------------------------------------------1 10000.00 500.0 .1946696 1946.7 3.8934 2 100.00 1000.0 .3393392 33.9 .0339 3 100.00 1000.0 .3874022 38.7 .0387 4 100.00 1000.0 .3393392 33.9 .0339 5 10000.00 500.0 .1946696 1946.7 3.8934 DIAPHRAGM DIAPHRAGM SHEAR SHEAR NUMBER STIFFNESS DISPLACEMENT LOAD -------------------------------------------1 10000.00 .1446696 1446.7 2 10000.00 .0480630 480.6 3 10000.00 .0480630 480.6 4 10000.00 .1446696 1446.7 Figure 5.9. Sample output from computer program DAFI.

When requirements for use of tables 5.1 and 5.2 are met, equation 5-8 can be used to calculate the total sidesway resisting force, Q. In all other cases, analysis tools such as DAFI must be used to obtain Q. A copy of output from program DAFI for a 4-bay building with Ch fixed at 10000, ke at 10000, k at 100, and R at 1000 is shown in figure 5.9. Although the sidesway resisting force for each frame is not given in the DAFI output, it is numerically equal to the difference between the load applied to the frame, and the load resisted by the frame – two values that are listed in the program’s output. For example, Q for the critical middle frame (frame 3 in figure 5.9), would be equal to the difference between 1000.0 and 38.7 or 961.3.

Qp,i =

Q i / (cos θ i)

q p,i =

Q i / (d i cos θ i)

or (5-11)

where: Q pi = Qi =

θi = q p,i = di =

Since diaphragm construction typically doesn‘t change from one side of a frame to the other side of the frame, Ch and ch,i values associated with either of the two diaphragm elements (that are adjacent to the frame) can be used in equation 5-9.

in-plane force applied to frame by diaphragm i, lbf (N) sidesway resisting force due to diaphragm i, lbf (N) slope of diaphragm i in-plane force applied to the frame per unit length of diaphragm i, lbf/ft (N/m) slope length of diaphragm i, ft (m)

5.6.6 Simple Beam Analogy Equations. McGuire (1998) presented the concept of modeling the diaphragm as a simple beam with an applied load inversely proportional to deflection. This analogy resulted in the following equations for calculating diaphragm shear forces and lateral displacements for the special case when: (1) all diaphragm elements have the same stiffness Ch, (2) all interior frame elements have the same stiffness, k, (3) both exterior frame elements (i.e., the two elements representing the endwalls) have the same stiffness, ke, and (4) eave load, R, is the same at each interior frame.

Horizontal restraining forces calculated for the three diaphragms in figure 5.2b, are graphically illustrated in figure 5.10a. For post-frame component stress analysis, these restraining forces should be applied as in-plane forces as shown in figure 10b. In-plane forces are calculated from the horizontal forces as follows:

5-13



s y

Roof Gravity Loads

s x qwr

ye =

s x qlr

k Qa

= =

Qb

=

ke =

Qc

Ch = s xqlw

s xqww


L

=

sinh = cosh =

frame spacing, in. (mm) lateral displacement of diaphragm at a distance x from the endwall, in. (mm) lateral displacement of the endwall, in. (mm) stiffness of interior frames, lbf/in. (N/mm) stiffness of endwall frames (or shearwalls), lbf/in. (N/mm) horizontal shear stiffness for a width s of the diaphragm, lbf/in. (N/mm) Distance between endwalls, in. (mm) hyperbolic sine hyperbolic cosine

(a) Roof Gravity Loads

s x qwr

=

B

=

A ( 1 – cosh(α L)) sinh(α L)

D

=

ke sinh(α L) α Ch s (1 - cosh(α L))

5.7.1 General. All building components must be checked to ensure that actual loads do not exceed allowable design values. In this section, special attention is given to components that are involved in load transfer by diaphragm action.

(b)

Figure 5.10 (a) Frame with diaphragm resisting forces. (b) Resisting forces applied as uniformly distributed in-plane loads for frame component stress analysis. Vh = Chαs[A sinh(α x) + B cosh(α x)]

(5-12)

y = A cosh(α x) + B sinh(α x) + R/k

(5-13)

ye = R / [ k (1 – D)]

(5-14)

ye – R/k

5.7 Component Design

s xqlw


s xqww

A

q p,b q p,c

5.7.2 Diaphragms. The maximum shear in a diaphragm section, Vp,i, cannot exceed the allowable shear strength of the section, va,i, multiplied by the diaphragm length. Vp,i <

va,i d i

(5-15)

where: Vp,i =

where: Vh = x = R =

=

s x qlr

q p,a

( k / Ch )1/2 s

α

va,i = diaphragm shear force, lbf (N) distance from endwall, in. (mm) eave load, lbf (N)

di =

5-14

in-plane shear force in diaphragm section i from equation 5-9 lbf (N) allowable in-plane shear strength of diaphragm i (see Section 6.3.3), lbf/ft (N/m) slope length of diaphragm i, ft (m)



The bending moment applied to a roof/ceiling diaphragm assembly is resisted by axial forces (a.k.a. chord forces) in members orientated perpendicular to trusses/rafters. This includes roof purlins and analogous framing members in the ceiling diaphragm. For bending moment calculations, these members are referred to as diaphragm chords (figure 5.11a). Any connection in the chords, either between intermediate chord members or where they are connected to the endwalls, must be designed to resist the calculated axial force.

5.7.3 Diaphragm Chords. In addition to shear forces, a roof/ceiling diaphragm assembly must also resist bending moment. The magnitude of this bending moment is dependent on a number of factors. For design, this bending moment is assumed to be no greater than: Md =

Vh L / 4

(5-16)

where: Md = Vh = L

=

diaphragm bending moment, lbf-ft (N m) maximum total shear in roof/ceiling diaphragm assembly, lbf (N) distance between shearwalls, ft (m)

If the roof/ceiling assembly behaves as a single beam in resisting bending moment, the maximum chord force (which is located in the edge chords) can be calculated as:

Equation 5-16 treats the roof/ceiling assembly as a uniformly loaded beam that is simple supported by two shearwalls spaced a distance L apart. Each shearwall is assumed to be subjected to a force that is equal to the maximum total shear in the roof/ceiling assembly, Vh. The maximum total shear in the roof/ceiling assembly, Vh, can be obtained from computer output (e.g. figure 5.9), or equation 5-7 or 5-12 if applicable. The uniform load on the roof/ceiling assembly (w in figure 5.11a) is set equal to 2Vh/L. This quantity is multiplied by L2/8 to obtain Md.

Pe =

Md α / b

(5-17)

where: Pe = Md =

α

=

b

=

axial force in edge chord, lbf (N) diaphragm bending moment from equation 5-16, lbf-ft (N m) reduction factor dependent on chord force distribution horizontal distance between edge chords, ft (m)

w

L

Vh

Vh

Shearwall

Chords

Trusses/rafters (b)

(a)

(c)

Figure 5.11. (a) Plan view of a diaphragm under a uniform load, w. Chord force distributions when (b) moment resisted by edge chords only, (b) chord force distribution is linear, and (c) chord force distribution is linear, but diaphragm halves assumed to act independently in resisting moment.

5-15

(d)



The axial force in an edge chord is dependent on chord force distribution as indicated by the presence of α in equation 5-17. The current ASAE EP484 diaphragm design procedure (ASAE, 1999a) assumes that edge chords act alone in resisting bending moment (figure 5.11b). For this case, α is numerically equal to one (1). This is a conservative approach. Alternatively, many engineers assume a linear distribution of chord forces as shown in figure 5.11c. When a linear distribution is assumed, the reduction factor α is a function of chord location. If chords are evenly spaced, then α is given as:

α=

Table 5.3. Reduction Factor, α, for Axial Force in Edge Chords n* n* α α 2 1.000 22 0.249 3 1.000 23 0.239 4 0.900 24 0.230 5 0.800 25 0.222 6 0.714 26 0.214 7 0.643 27 0.206 8 0.583 28 0.200 9 0.533 29 0.193 10 0.491 30 0.187 11 0.455 31 0.181 12 0.423 32 0.176 13 0.396 33 0.171 14 0.371 34 0.166 15 0.350 35 0.162 16 0.335 36 0.158 17 0.314 37 0.154 18 0.298 38 0.150 19 0.284 39 0.146 20 0.271 40 0.143 21 0.260 41 0.139 * n is the number of chord rows, including the two rows of edge chords

(n – 1 )2 n/2

Σ (n – 2 i + 1)2

when n is even

i =1

α=

(n – 1 )2 (n-1)/2

Σ (n – 2 i + 1)2

when n is odd

i =1

where:

α

=

n

=

reduction factor when chords are evenly spaced and chord forces are linearly distributed number of chord rows, including the two rows of edge chords

Technical Note

Chord Forces

The preceding equations were used to calculate the values given in table 5.3.

The axial force induced in an individual chord by applied building loads is a function of many complex, interacting design variables. For this reason, designers have had to rely on simplifying assumptions in order to approximate chord forces.

If a linear distribution of chord force is assumed (figure 5.11c), and interior chords are evenly spaced, the load in an interior chord, Pi, is given as: Pi =

2 Pe x i / b

(5-18)

One common assumption is that the roof/ceiling assembly acts as a large deep beam that is simply supported by two end shearwalls. This assumption is used to calculate the maximum inplane bending moment to which a diaphragm is subjected. This assumption is conservative in that it neglects the resistance to in-plane bending contributed by sidewalls. Sidewalls help resist (and thereby reduce) in-plane bending moments in two ways. First they brace endwalls

where: Pi = Pe = b

=

xi =

axial force for chord in row i, lbf (N) axial force in edge chord from equation 5-17, lbf (N) horizontal distance between edge chords, ft (m) horizontal distance from center of diaphragm to chord row i.

5-16



and other shearwalls, which limits rotation of the diaphragm at these shearwalls. Second, they resist a change in eave length (and hence changes in eave chord forces) by virtue of their own in-plane shear stiffness.

moment in their models was resisted almost entirely by the edge purlins. Bohnhoff and others (1999) showed that as the shear stiffness of cladding is increased, interior purlins get more involved in resisting in-plane bending moments.

Because of the influence of sidewalls, the distribution of in-plane bending moment will not follow that for a typical simple supported beam (i.e., zero moment at the supports, and maximum moment at midspan). For this reason, Pollock and others (1996) recommend modeling the roof/ceiling assembly as a deep beam with fixed supports.

Chord force distribution has also been shown to depend on the degree of interaction between individual diaphragms. Figure 5.11d illustrates the distribution of chord forces when there is no interaction between individual diaphragms on both sides of a ridge. Note that interaction between individual diaphragms on opposites sides of a ridge is highly dependent on: (1) the spacing between ridge purlins, and (2) the rigidity of the ridge cap and other elements joining the two diaphragms.

Because of uncertainty surrounding variation in in-plane bending moment with building length, some designers will assign the maximum calculated in-plane bending moment (Md from equation 5-16) to every location along the length of the building. This is obviously a conservative approach.

5.7.4 Shearwalls. End and intermediate shearwalls must have sufficient strength to transmit forces from roof and ceiling diaphragms to the foundation system. In equation form:

Another major assumption that a designer must make involves the distribution of chord forces across a building. Three different chord force distributions are shown in figure 5.11b, 5.11c, and 5.11d. Whether or not edge chords resist virtually all of the in-plane bending moment (figure 5.11b), or a linear distribution of axial forces exists in chords between edge chords (figure 5.11c) is a question that is at the heart of ongoing research. In reality, the distribution of chord forces lies somewhere in between these two extremes, exactly where being dependent on specifics of the design and on the magnitude of the applied load (Note: at higher load levels, load distributions change due to geometric and material nonlinearities). Presently, there is very little research data to support one specific design procedure/assumption. The most extensive investigation of chord forces was by Niu and Gebremedhin (1997) who strain gauged purlins in a full-scale building and in a diaphragm test assembly. The data collected in this study does not strongly support any particular hypotheses regarding chord force distribution. The only other research of significance to chord force distribution was the comprehensive finite element analyses of diaphragm assemblies by Wright (1992) and Williams (1999). Both of these researchers found that in-plane bending

va >

Vs / (W – DT)

(5-19)

where: va = Vs = W = DT =

allowable shear capacity of shearwall, lbf/ft (N/m) force induced in shearwall, lbf (N) building width, ft (m) total width of door and window openings in the shearwall, ft (m)

The allowable shear capacity of end and intermediate shearwalls, va, is obtained from validated structural models, or from tests as outlined in ASAE EP558 (see Section 6.5). The total force in the shear wall, Vs, is obtained from computer output (e.g. figure 5.8), or equation 57 or equation 5-12 if applicable. The total width of door and window openings, DT, generally varies with height as shown in figure 5.12. At locations where DT is the greatest (section b-b in figure 5.12) additional reinforcing may be required to ensure that the allowable shear stress is not exceeded. The structural framing over a door or window opening will act as a drag strut transferring

5-17



shear across the opening. The header over the opening shall be designed to carry the force in tension and/or compression across the opening.

5.7.6 Shearwall Overturning. Diaphragm loading produces overturning moment in shearwalls. This moment induces vertical forces in shearwall-to-foundation connections that must be added to vertical forces resulting from tributary loads. In the case of embedded posts, increases in uplift forces may require an increase in embedment depth, and increases in downward force may require an increase in footing size (see Chapter 8).

a

a

5.8 Rigid Roof Design b

b

c

W

5.8.1 General. When diaphragm stiffness is considerably greater than the stiffness of interior post frames, the designer may want to assume that the diaphragm and shearwalls are infinitely stiff. Under this assumption, 100% of the applied eave load, R, is transferred by the diaphragm to shearwalls, and none of the applied eave load is resisted by the frames. Because all eave load is assumed to be transferred to shearwalls, no special analysis tools or design tables are required to determine load distribution between diaphragms and post-frames. This simplifies the entire diaphragm design process. This simplified procedure is referred to as rigid roof design (Bender and others, 1991).

c

Figure 5.12. Shearwall showing variations in opening width, DT, with height. Shearwall strength can easily be increased when the applied load exceeds shearwall capacity. For example, the density of stitch screws can be increased and additional fasteners can be added in panel flats (on both sides of each major rib is the most effective). If only one side of the wall has been sheathed, add wood paneling or metal cladding to the other side. Metal diagonal braces can also be added beneath any wood paneling or corrugated metal siding.

5.8.2 Calculation. When (1) the shearwalls and roof/ceiling diaphragm assembly are assumed to be infinitely rigid, (2) the only applied loads with horizontal components are due to wind, and (3) wind pressure is uniformly distributed on each wall and roof surface, then the maximum shear force in the diaphragm assembly is given as:

5.7.5 Shearwall Connections. Connections that fasten (1) roof and ceiling diaphragms to a shearwall, and (2) shearwalls to the foundation system, must be designed to carry the appropriate amount of shear load. The design of these connections may be proved by tests of a typical connection detail or by an appropriate calculation method.

Vh =

L (hwr qwr – hlr qlr + hww fw qww – hlw fl qlw) / 2

(5-20)

where:

At end shearwalls it is not uncommon to use the truss top chord to transfer load from roof cladding to endwall cladding. Sidewall steel is fastened directly to the truss chord, as is the roof steel when purlins are inset. In buildings with top-running purlins, roof cladding can not be fastened directly to the truss. In such cases, blocking equal in depth to the purlins is placed between the purlins and fastened to the truss. Roof cladding is then attached directly to this blocking.

Vh = L hwr hlr hww hlw

5-18

= = = = =

maximum diaphragm element shear force, lbf (N) building length, ft (m) windward roof height, ft (m) leeward roof height, ft (m) windward wall height, ft (m) leeward wall height, ft (m)


qwr = qlr = qww = qlw = fw

=

fl

=


Output from a DAFI analysis of a building with relatively high diaphragm and shearwall stiffness values is presented in figure 5.9. This output shows less than 3% of the total horizontal eave load being resisted by the interior frames.

design windward roof pressure, lbf/ft2 (N/m2) design leeward roof pressure, lbf/ft2 (N/m2) design windward wall pressure, lbf/ft2 (N/m2) design leeward wall pressure lbf/ft2 (N/m2) frame-base fixity factor, windward post frame-base fixity factor, leeward post

Although rigid roof design expedites calculation of maximum diaphragm shear forces, the design procedure does not provide estimates of sidesway restraining force for interior post-frame design.

5.9 References

Inward acting wind pressures have positive signs, outward acting pressures are negative (figure 5.8). As previously noted, frame-base fixity factors, fw and fl, determine how much of the total wall load is transferred to the eave, and how much is transferred directly to the ground. The greater the resistance to rotation at the base of a wall, the more load will be attracted directly to the base of the wall. For substantial fixity against rotation at the groundline, set the frame-base fixity factor(s) equal to 3/8. For all other cases, set the frame-base fixity factor(s) equal to 1/2.

Anderson, G.A., D.S. Bundy and N.F. Meador. 1989. The force distribution method: procedure and application to the analysis of buildings with diaphragm action. Transactions of the ASAE 32(5):1781-1786. ASAE. 1999a. EP484.2 Diaphragm design of metal-clad wood-frame rectangular buildings. ASAE Standards, 46th Ed., ASAE, St. Joseph, MI. ASAE. 1999b. EP558.1 Load tests for metalclad wood-frame diaphragms. ASAE Standards, 46th Ed., ASAE, St. Joseph, MI.

For symmetrical base restraint and frame geometry, equation 5-20 reduces to: (5-21)

Bender, D. A., T. D. Skaggs and F. E. Woeste. 1991. Rigid roof design for post-frame buildings. Applied Engineering in Agriculture 7(6):755-760.

roof height, ft (m) wall height, ft (m) frame-base fixity factor for both leeward and windward posts

Bohnhoff, D. R., P. A. Boor, and G. A. Anderson. 1999. Thoughts on metal-clad wood-frame diaphragm action and a full-scale building test. ASAE Paper No. 994202, ASAE, St. Joseph, MI.

Vh = L [hr (qwr – qlr) + hw f (qww – qlw)] / 2 where: hr = hw = f =

Bohnhoff, D. R. 1992. Expanding diaphragm analysis for post-frame buildings. Applied Engineering in Agriculture 8(4):509-517.

5.8.3 Application. The Vh value calculated using equation 5-20 (or 5-21) is always a conservative estimate of the actual maximum shear force (due to wind) in a diaphragm assembly. This estimate becomes increasingly conservative as the amount of load resisted by interior post-frames increases. It follows that equations 5-20 and 5-21 are most accurate when diaphragm stiffness is considerably greater than interior post-frame stiffness. This tends to be the case in buildings that are relatively wide and/or high, and in buildings where individual posts offer no resistance to rotation (i.e., the posts are more-or less pin-connected at both the floor and eave lines).

Gebremedhin, K.G. 1987a. SOLVER: An interactive structures analyzer for microcomputers. (Version 2). Northeast Regional Agricultural Engineering Service. Cornell University, Ithaca, NY. Gebremedhin, K.G. 1987b. METCLAD: Diaphragm design of metal-clad post-frame buildings using microcomputers. Northeast Regional Agricultural Engineering Service. Cornell University, Ithaca, NY.

5-19



McGuire, P.M. 1998. One equation for compatible eave deflections. Frame Building News 10(4):39-44. Meader, N.F. 1997. Mathematical models for lateral resistance of post foundations. Trans of ASAE, 40(1):191-201. Niu, K.T. and K.G. Gebremedhin. 1997. Evaluation of interaction of wood framing and metalcladding in roof diaphragms. Transactions of the ASAE 40(2):465-476. Pollock, D. G., D. A. Bender and K. G. Gebremedhin. 1996. Designing for chord forces in post-frame roof diaphragms. Frame Building News 8(5):40-44. Purdue Research Foundation. 1986. Purdue plane structures analyzer. (Version 3.0). Department of Forestry and Natural Resources. Purdue University, West Layfette, IN. Williams, G. D. 1999. Modeling metal-clad wood-framed diaphragm assemblies. Ph.D. diss., University of Wisconsin-Madison, Madison, WI. Wright, B.W. 1992. Modeling timber-framed, metal-clad diaphragm performance. Ph.D. diss. The Pennsylvania State University, University Park, PA.

5-20



Chapter 6: METAL-CLAD WOOD-FRAME DIAPHRAGM PROPERTIES

6.1 Introduction

mation of diaphragm strength and stiffness.

6.1.1 General. One of the first steps in diaphragm design is to establish in-plane shear strength and stiffness values for each identified diaphragm section. In most post-frame buildings, these diaphragm sections consist of corrugated metal panels that have been screwed or nailed to wood framing. Behavior of these metalclad wood-frame (MCWF) diaphragms is complex, and consequently, has been the subject of considerable research during the past 20 years. In addition to improving overall design, this research has led to improved methods for predicting metal-clad wood-frame diaphragm strength and stiffness.

6.1.3 ASAE EP558 and EP484. Construction specifications and testing procedures for diaphragm test assemblies are given in ASAE EP558 Load Test for Metal-Clad Wood-Frame Diaphragms (ASAE, 1999b). EP558 also gives equations for calculating diaphragm test assembly strength and stiffness. These calculations along with construction specifications and testing procedures from EP558 are outlined in Section 6.3: Diaphragm Assembly Tests. For additional details and further explanation of testing procedures, readers are referred to the ASAE EP558 Commentary (ASAE, 1999b). ASAE EP484, which was introduced in detail in Chapter 5, contains the equations for extrapolating diaphragm test assembly properties for use in building design. These calculations are presented in Section 6.4: Building Diaphragm Properties.

6.1.2 Predicting Diaphragm Behavior. There are essentially three procedures for predicting the strength and stiffness of a building diaphragm. First, an exact replica of the building diaphragm (a.k.a. a full-size diaphragm) can be built and tested to failure. Second, a smaller, representative section of the building diaphragm can be built and laboratory tested. The strength and stiffness of this test assembly are then extrapolated to obtain strength and stiffness values for the building diaphragm. Lastly, diaphragm behavior can be predicted using finite element analysis software. The latter requires that the strength and stiffness properties of individual component (e.g., wood framing, mechanical connections, cladding) be known.

6.2 Design Variables 6.2.1 General. Many variables affect the shear stiffness and strength of a structural diaphragm, including: overall geometry, cladding characteristics, wood properties, fastener type and location, and blocking. A short description of each of these variables follows. 6.2.2. Geometry. Geometric variables include: spacing between secondary framing members (e.g. purlins), spacing between primary framing members (e.g., trusses/rafters), and overall dimensions. With respect to overall dimensions, diaphragm depth is measured parallel to primary frames, diaphragm length is measured perpendicular to primary frames. In most structures, the overall length of a roof diaphragm is equal to the length of the building.

Of the three procedures for predicting metal-clad wood-frame diaphragm properties, only the second one – extrapolation of diaphragm test assembly data - is commonly used. This is because testing full-size diaphragms is simply not practical (a new test would have to be conducted every time overall dimensions changed), and finite element analysis of MCWF diaphragms is, for practical purposes, still in a developmental stage. The later can be attributed to the fact that the large number of variables affecting diaphragm structural properties, as well as the nonlinear behavior of some variables, has thus far precluded the development of a quick and reasonably accurate closed-form approxi-

6.2.3 Cladding. Cladding type (e.g., wood, metal, fiberglass, etc.) is a significant design variable. Coverage (and examples) in this design manual is limited to corrugated metal cladding. Important design characteristics of this type of cladding include: base metal (e.g., steel,

6-1



shear strength and stiffness of a diaphragm. Sheet-to-purlin fasteners are also defined by their location (i.e., end, edge, and field). A sheet-to-purlin fastener may be located in a rib or in the flat of a corrugated metal panel. Locating fasteners in the flat generally produces stronger and stiffer diaphragms. The nonlinear nature of fastener performance is one of the more complex variables affecting diaphragm stiffness.

aluminum), base metal thickness, panel profile, and individual sheet width and length. 6.2.4 Wood Framing. The species, moisture content and specific gravity of wood used in the framing system will not only affect the structural properties of the wood members, but also the shear stiffness and strength of mechanical connections between wood members and between wood members and cladding.

6.2.6 Blocking. When secondary framing members are installed above primary framing (e.g. top running purlins) or below primary framing (e.g. bottom-running ceiling framing), cladding can only be fastened directly to the secondary framing (see figure 6.1). In such cases, blocking is often placed between the cladding and primary framing to increase shear transfer between the components. This is commonly done at locations where diaphragms and shearwalls intersect.

6.2.5 Mechanical Connections. Type (screw or nail), size, and relative location of mechanical fasteners used to join components significantly impact diaphragm properties. Fasteners are primarily defined by what they connect. Major categories include purlin-to-rafter, sheet-topurlin, and sheet-to-sheet (see figure 6.1). Sheet-to-sheet fasteners are more commonly referred to as stitch or seam fasteners. Removing stitch fasteners can dramatically reduce the

Sheet-to-Purlin Fasteners (Field) Stitch Fastener Purlin-to-Rafter Fastener

Sheet-to-Purlin Fastener (Edge)

Sheet-to-Purlin Fasteners (End)

Sidelap Seam

Rake Board

Blocking between purlins

Corrugated Metal Cladding

Purlin

Rafter/Truss Top Chord

Figure 6.1. Components of a metal-clad wood-frame roof diaphragm.

6-2



Applied force, P F

Rafter / Truss chord

G

2

b = Test assembly length

Purlins

Direction of Corrugations

Cladding

4

E

Notes: 1. Force P may be alternately applied at point H 2. Locate gages 2 and 4 on the edge purlins 3. Locate gages 1 and 3 on the rafter / truss chord

H a = Test assembly width

1

Deflection gage location and direction of measured deflection (typ.)

3

(a)

3a = Test assembly width

Applied force, P/2 Rafter / Truss chord

F

I

Applied force, P/2 K

G

L

H

b = Test assembly length

Purlins

Direction of corrugations

Cladding

E

J 2 1

Notes:

3 Deflection gage location and direction of measured deflection (typ.)

4

1. The applied forces may alternately be applied at points J and L 2. Locate gages 1, 2, 3 and 4 on the rafters/ truss chords

(b) Figure 6.2. (a) Cantilever test configuration, and (b) Simple beam test configuration for diaphragm test assemblies.

6-3



When this reduction is not applied (as would be the case when test assembly failure is not initiated by wood failure), the NDS load duration factor, CD, can not be used to increase the allowable design shear strength during building design. Completely separate of the load duration factor adjustment is the 30% increase in allowable strengths allowed by most codes for wind loadings (see Section 3.9.4).

6.3 Diaphragm Test Assemblies 6.3.1 Construction. With the exception of overall length and width, a diaphragm test assembly is required to be identical to the diaphragm in the building being designed. Specifically, frame members must be of identical size, spacing, species and grade; metal cladding must be identical in composition, profile and thickness; and fastener type and location must be the same. ASAE EP558 has established minimum sizes for diaphragm test assemblies to ensure that there is not too great a difference between the size of a diaphragm test assembly and the actual building diaphragm.

6.3.4 Shear Stiffness. The procedure for determining the effective shear modulus of a test assembly begins with calculation of the adjusted load-point deflection, DT. This value takes into account rigid body rotation/translation during assembly test and is calculated as follows:

6.3.2 Test Configurations. ASAE EP558 allows for two different testing configurations: a cantilever test and a simple beam test (figures 6.2a and 6.2b, respectively). In both figures 6.2a and 6.2b, variable “a” represents the spacing between rafters/trusses (a.k.a. the frame spacing). This spacing should be equal to, or a multiple of, the frame spacing in the building being designed.

(6-1)

Simple beam test: va = 0.40 Pu / (2b)

(6-2)

Pu = = b =

Simple beam test: DT = (D2 + D3 – D1 – D4) / 2

(6-4)

DT =

adjusted load point deflection, in. (mm) D1, D2, D3, and D4 = deflection measurements, in. (mm) (see figure 6.2) a = assembly width, ft (m) b = assembly length, ft (m)

The effective in-plane shear stiffness, c, for a diaphragm test assembly is defined as the ratio of applied load to adjusted load point deflection at 40% of ultimate load. In equation form:

where: va =

(6-3)

where:

6.3.3 Shear Strength. The allowable design shear strength, of a diaphragm test assembly is equal to 40% of the ultimate strength of the assembly. In equation form: Cantilever test: va = 0.40 Pu / b

Cantilever test: DT = D3 – D1 – (a/b) (D2 + D4)

allowable design shear strength, lbf/ft (N/m) ultimate strength, lbf (N) total applied load at failure assembly length, ft (m) (see figure 6.2)

Cantilever test: c = 0.4 Pu / DT,d

(6-5)

Simple beam test: c = 0.2 Pu / DT,d

(6-6)

where: c

If one or more of the test assembly failures were initiated by lumber breakage or by failure of the fastenings in the wood, then the allowable design shear stress must be adjusted to account for test duration. To adjust from a total elapsed testing time of 10 minutes to a normal load duration of ten years, divide va by a factor of 1.6.

=

DT,d =

effective in-plane shear stiffness, lbf/in. (N/mm) adjusted load-point deflection, DT, at 0.4 Pu, in. (mm)

The in-plane shear stiffness for the diaphragm test assembly, c, is converted to an effective shear modulus for the test assembly, G, as:

6-4


G = c (a/b)


(6-7)

6.4.4 Horizontal Shear Stiffness. The horizontal shear stiffness, ch, of a building diaphragm section is related to its in-plane shear stiffness as follows:

where: G

=

effective shear modulus of the test assembly, lbf/in (N/mm)

6.4.1 General. As described in Chapter 5, each building diaphragm is sectioned for analysis. Each of these sections must be assigned a horizontal stiffness value, ch, and an allowable load, va.

(6-8)

=

bS = s

=

bh =

θ

=

(6-11)

(6-9)

6.6 Tabulated Data

where: G

G bh cos(θ) / s

6.5.2 Shearwall Test Assemblies. ASAE EP558 also contains guidelines for construction and testing of shearwall test assemblies. With the exception of overall length and width, a shearwall test assembly is required to be identical to the shearwall in the building being designed. Specifically, frame members must be of identical size, spacing, species and grade; cladding must be identical; and fastener type and location must be the same.

or G bh s cos(θ)

ch =

6.5.1 General. The same procedure used to determine the strength and stiffness of building diaphragms is used to determine the strength and stiffness of building shearwalls. That is, representative test assemblies are loaded to failure, to determine their shear strength and stiffness. These properties are then linearly extrapolated to obtain strength and stiffness values for the building shearwall(s).

6.4.3 In-Plane Shear Stiffness. The in-plane shear stiffness, cp, of a building diaphragm section is calculated from the effective shear modulus, G, of the diaphragm test assembly using the following equation:

cp =

(6-10)

6.5 Building Shearwall Properties

6.4.2 Shear Strength The allowable design shear strength of a building diaphragm is equal to that calculated for the diaphragm test assembly. Consequently, to calculate the total in-plane shear load that a building diaphragm can sustain, simply multiply the allowable design shear strength, va, by the slope length of the building diaphragm.

G bs s

cp cos2(θ)

or

6.4 Building Diaphragm Properties

cp =

ch =

6.6.1 Sources. Testing replicate samples of diaphragm test assemblies can get expensive. For this reason, a designer may choose not to conduct his/her own diaphragm tests, relying instead on designs that have been previously tested by others. Information on many tested designs is available in the public domain. Cladding manufacturers may have additional test information on assemblies that feature their own products.

effective shear stiffness of test assembly, lbf/in (N/mm) slope length of building diaphragm section being modeled, ft (m) width of the building diaphragm section being modeled, ft (m) horizontal span length of building diaphragm section, ft (m) slope of the building diaphragm section, degrees

6.6.2 Example Tabulated Data. Table 6.1 contains design details and engineering properties for roof diaphragm tests assemblies. The information in this table represents a small percentage of available data.

Implicit in equation 6-8 is the assumption that the total shear stiffness of a building diaphragm is a linear function of length.

6-5



Table 6.1. Steel-Clad Roof Diaphragm Assembly Test Data Test Assembly Number Test Configuration Cladding Manufacturer/Trade Name Base Metal Thickness Gauge Major Rib Spacing, inches Major Rib Height, inches Major Rib Base Width, inches Major Rib Top Width, inches Yield Strength, ksi Overall Design Width, feet Length, b , feet Purlin Spacing, feet Rafter Spacing, feet Purlin Location Purlin Orientation Number of Internal Seams Wood Properties Purlin Size Purlin Species and Grade Rafter Species and Grade Stitch Fastener Type Length, inches Diameter On Center Spacing, inches Sheet-to-Purlin Fasteners Type Length, inches Diameter Location in Field Location on End Avg. On-Center Spacing in Field, in. Avg. On-Center Spacing on End, in. Purlin-to-Rafter Fastener Engineering Properties Ultimate Strength, Pu, lbf. Allowable Shear Strength, va, lbf/ft Effective In-Plane Stiffness, c ,lbf/in Effective Shear Modulus, G, lbf/in Reference

1 Cantilever

2 Cantilever

3 Cantilever

4 Cantilever

Wick Agri Panel 28 12 0.75 1.25 0.375 50

Wick Agri Panel 28 12 0.75 1.25 0.375 50

Wick Agri Panel 29 12 0.75 1.25 0.375 80

Midwest Manufacturing. 29 12 1.0 2.5 0.5 80

9 12 2 9 Top running On edge 2




2- by 4-inch No.1 & 2 SPF No. 1 SYP



2- by 4-inch No.2 SYP No. 1 SYP

None

Screw 1.0 #10 24

Screw 1.0 #10 24

EZ Seal Nail 2.5 8d 24

Screw 1.0 #10 In Flat In Flat 12 6 60d Threaded Hardened Nail



EZ Seal Nail 2.5 8d Major Rib In Flat 12 12 60d Threaded Hardened Nail

2140 71 1625 1220 Anderson, 1989

3390 113 2720 2040 Anderson, 1989

3220 107 2720 2040 Anderson, 1989

1930 64 1590 795 Wee & Anderson, 1990

6-6



Table 6.1. cont., Steel-Clad Roof Diaphragm Assembly Test Data Test Assembly Number Test Configuration Cladding Manufacturer/Trade Name Base Metal Thickness Gauge Major Rib Spacing, inches Major Rib Height, inches Major Rib Base Width, inches Major Rib Top Width, inches Yield Strength, ksi Overall Design Width, feet Length, b , feet Purlin Spacing, feet Rafter Spacing, feet Purlin Location Purlin Orientation Number of Internal Seams Wood Properties Purlin Size Purlin Species and Grade Rafter Species and Grade Stitch Fastener Type Length, inches Diameter On Center Spacing, inches Sheet-to-Purlin Fasteners Type Length, inches Diameter Location in Field Location on End Avg. On-Center Spacing in Field, in. Avg. On-Center Spacing on End, in. Purlin-to-Rafter Fastener Engineering Properties Ultimate Strength, Pu, lbf. Allowable Shear Strength, va, lbf/ft Effective In-Plane Stiffness, c ,lbf/in Effective Shear Modulus, G, lbf/in Reference

5 Cantilever

6 Cantilever

7 Cantilever

Grandrib 3

Grandrib 3

29 12 0.75 1.75 0.5 80

29 12 0.75 1.75 0.5 80





2- by 4-inch No.2 SYP No. 1 SYP

2- by 4-inch No.2 DFL No. 2 DFL

2- by 4-inch No.2 SPF No. 2 SPF

2- by 4-inch No.2 SYP 1950f1.7E SYP

EZ Seal Nail 2.5 8d 24

None

None

Screw 1.5 #10 24


Screw 1.0 #10 In Flat In Flat 12 6 1-60d Spike + 2-10d Toenails

Screw 1.0 #10 In Flat In Flat 12 6 1-60d Spike + 2-10d Toenails

Screw 1.5 #10 In Flat In Flat 12 and 18 12 60d Threaded Hardened Nail

3995 133 2980 1490 Wee & Anderson, 1990

3300 110 2920 2190 Lukens & Bundy, 1987

2775 93 2950 2210 Lukens & Bundy, 1987

4884 122 3890 2190 Bohnhoff and others, 1991

Midwest Manufacturing 29 12 1.0 2.5 0.5 80

6-7

8 Cantilever Walters STR-28 28 12 0.94

80



Table 6.1. cont., Steel-Clad Roof Diaphragm Assembly Test Data Test Assembly Number Test Configuration Cladding Type Base Metal Thickness Gauge Major Rib Spacing, inches Major Rib Height, inches Major Rib Base Width, inches Major Rib Top Width, inches Yield Strength, ksi Overall Design Width, feet Length, b , feet Purlin Spacing, feet Rafter Spacing Purlin Location Purlin length, ft Purlin Attachment

9

10

11

12

Regular Leg

Extended Leg

Simple Beam Regular Leg

Extended Leg 29 9 0.62 1.75 0.75 80

36 12 2 Pair of rafters every 12 feet (each pair spaced 6 in. apart) Top running and lapped Inset 13.2 and 12.0 11.25 To special blocking nailed beTo joist hanger attached to raftween each pair of rafters ters On edge 11

Purlin Orientation Number of Internal Seams Wood Properties Purlin Size 2- by 6-inch Purlin Species and Grade No.2 DFL and 1650f DFL Rafter Species and Grade No. 2 DFL Stitch Fastener* Type None Screw* None Screw* Length, inches 1.5 1.5 Diameter #10 #10 On Center Spacing, inches 24 24 Sheet-to-Purlin Fasteners Type Screw Length, inches 1.5 Diameter #10 Location in Field In Flat Location on End In Flat Avg. On-Center Spacing in Field, in. 9 Avg. On–Center Spacing on End, in. 9 Engineering Properties Ultimate Strength, Pu, lbf. 6950 7850 6400 6950 Allowable Shear Strength, va, lbf/ft 116 131 107 116 Effective In-Plane Stiffness, c ,lbf/in 4700 7500 3700 4400 Effective Shear Modulus, G, lbf/in 4700 7500 3700 4400 NFBA, 1996 Reference * Because of the extended leg, screws installed in the flat at overlapping seams function as stitch fasteners.

6-8



Table 6.1. cont., Steel-Clad Roof Diaphragm Assembly Test Data Test Assembly Number Test Configuration Cladding Manufacturer/Trade Name Base Metal Thickness Gauge Major Rib Spacing, inches Major Rib Height, inches Major Rib Base Width, inches Major Rib Top Width, inches Yield Strength, ksi Overall Design Width, feet Length, b , feet Purlin Spacing, feet Rafter Spacing, feet Purlin Location Purlin Orientation Number of Internal Seams Wood Properties Purlin Size Purlin Species and Grade Rafter Species and Grade Stitch Fastener Type Length, inches Diameter On Center Spacing, inches Sheet-to-Purlin Fasteners Type Length, inches Diameter Location in Field Location on End Avg. On-Center Spacing in Field, in. Avg. On-Center Spacing on End, in.

13 Simple Beam

14 Simple Beam

15 Simple Beam

Metal Sales Pro Panel II 30 9.0

Metal Sales Pro Panel II 30 9.0

McElroy Metal Max Rib 29 9.0 0.75 1.75

104

104

80

24 12 2.33 Pair of rafters every 12 feet (each pair spaced 6 in. apart) Top running On edge 8

24 12 2.33 Pair of rafters every 12 feet (each pair spaced 6 in. apart) Top running On edge 8

24 12 2

2- by 6-inch

2- by 6-inch

1650f 1.5E SPF

1650f 1.5E SPF

1650f 1.5E SPF

1650f 1.5E SPF

Mac-Girt steel hat section: 1.5 in. tall, 3.2 in. wide, 18 ga. 2250f 1.9E SP

Screw 0.625 #12 9

None

None

Screw 1.5

Screw 1.0

In Flat In Flat 9 4.5

Screw 1.5 #10 in field #14 in ends In Flat In Flat 9 4.5

9600 160 7680 7680 Townsend, 1992

6600 110 7100 7100 Townsend, 1992

#10

Purlin-to-Rafter Fastener Engineering Properties Ultimate Strength, Pu, lbf. Allowable Shear Strength, va, lbf/ft Effective In-Plane Stiffness, c ,lbf/in Effective Shear Modulus, G, lbf/in Reference

6-9

8 Top running NA 7

#14 In Flat In Flat 18 (3 screws/sheet) 9 (4 screws/sheet) Two - #12 x 1.6 in. screws/joint 8645 144 10700 7130 Myers, 1994



6.7 Example Calculations A designer wishes to find ch and va for roof diaphragm sections in a gable-roofed building with roof slopes of 4-in-12. Distance between eaves is 36 feet, and post-frame spacing, s, is 10 feet. A cantilever test of a representative diaphragm test assembly with a width, a, of 10 feet and a length, b, of 12 feet, yields an ultimate strength, Pu of 3900 lbf and an effective inplane stiffness, c, of 4000 lbf/in. The test assembly failure was not wood related, therefore the ultimate strength was not adjusted for load duration. Equation 6-1: va (test assembly) = 0.40 Pu / b va (test assembly) = 0.40 (3900 lbf) /12 ft = 130 lbf/ft Equation 6-7: G = c (a/b) G = (4000 lbf/in) (10 ft/12 ft) = 3333 lbf/in. Equation 6-11: ch = G bh cos(θ) / s ch = (3333 lbf/in) (36 ft / 2) (cos 18.4°) / 10 ft = 5690 lbf/in. The horizontal stiffness, ch of 5690 lbf/in represents a single diaphragm section that runs from eave to ridge and has a width of 10 feet. va (diaphragm) = 1.30 va (test diaphragm) = 1.3 (130 lbf/ft) = 169 lbf/ft As described in Section 3.9.4, the allowable strength of a diaphragm can generally be increased by 30% when wind or seismic loads are acting in combination with other loads.

Lukens, A.D., and D.S. Bundy. 1987. Strength and stiffnesses of post-frame building roof panels. ASAE Paper No. 874056. ASAE, St. Joseph, MI.

6.8 References Anderson, G.A. 1989. Effect of fasteners on the stiffness and strength of timber-framed metalclad roof sections. ASAE Paper No. MCR89501. ASAE, St. Joseph, MI.

Myers, N.C. 1994. McElroy Metal Post Frame Roof Diaphragm Test. Test Report 94-418. Progressive Engineering, Inc., Goshen, IN.

ASAE. 1999a. EP484.2: Diaphragm design of metal-clad, wood-frame rectangular buildings. ASAE Standards, 46th Edition. St. Joseph, MI.

NFBA. 1996. 1996 Diaphragm Test. National Frame Builders Association, Inc., Lawrence, KS.

ASAE. 1999b. ASAE EP558: Load tests for metal-clad wood-frame diaphragms. ASAE Standards, 46th edition. ASAE, St. Joseph, MI.

Townsend, M. 1992. Alumax test report: diaphragm loading on roofs and end wall sections. Alumax Building Products, Perris, CA.

Anderson, and P.A. Boor. 1991. Influence of insulation on the behavior of steel-clad wood frame diaphragms. Applied Engineering in Agriculture 7(6):748-754.

Wee, C.L. and G.A. Anderson. 1990. Strength and stiffness of metal clad roof section. ASAE Paper No. 904029. ASAE, St. Joseph, MI.

6-10



Chapter 7: POST PROPERTIES 7.1 Introduction

7.1, a post must be graded by an approved grading agency and stamped accordingly.

7.1.1 Types. Several different post types are currently used in post-frame construction. The most common of these are laminated lumber posts. Solid-sawn posts are still used by most builders, but not to the extent they were a decade ago. Parallel strand lumber (PSL) and laminated veneer lumber (LVL) products are gaining in popularity. Use of these and other engineered lumber products as posts in postframe buildings can only be expected to increase as the relative cost of these products decreases.

7.2.4 Current Demand. Solid-sawn post use in post-frame construction is on the decline, primarily because posts of acceptable size, length and quality are increasingly difficult to obtain. The scarcity of long posts in structural sizes has made laminated posts more price competitive. Additionally, laminated post prices are typically constant on a per-foot basis regardless of length, while the cost of solid-sawn posts increases exponentially with length.

7.3 Laminated Lumber Posts

7.1.2 Preservative Treatment. If posts are to be embedded, they must be preservative treated to avoid decay. General issues of preservative treatment have already been presented in Chapter 4. Discussion in this chapter will focus on the structural aspects of post selection and design.

7.3.1 General. Laminated lumber posts are posts that are fabricated by joining together individual pieces of dimension lumber, most commonly 2- by 6-inch, 2- by 8-inch and 2- by 10-inch members. Structural properties of the finished product vary significantly depending on the means of lamination and the presence or absence of joints in individual layers. Laminates are either glued together or joined together with mechanical fasteners (i.e., nails, screws, bolts, shear transfer plates, metal plate connectors).

7.2 Solid-Sawn Posts 7.2.1 Size. Post size varies considerably with building geometry and design loads. The most common sizes are 6- by 6-inch, 6- by 8-inch, and 4- by 6-inch. Although both S4S (Surfaced on 4 Sides) and rough sawn posts are available, most rough sawn posts are not graded and therefore are generally only used in code exempt applications.

7.3.2 Advantages. By combining individual laminates to build up a desired cross-section, the statistical probability that a strength-reducing characteristic of wood (such as a knot) would exist through the entire cross section is greatly diminished. Consequently, laminated posts have more uniform strength and stiffness properties than solid-sawn posts. This increased reliability results in higher allowable design values.

7.2.2 Wood Species. Species of wood used in posts depends on local availability and on preservative treatment needs. Commonly used species includes Southern Pine, Douglas Fir and Ponderosa Pine.

7.3.3 Laminate Orientation. Laminated post strength is dependent on orientation of individual laminates with respect to the principal load direction. If a post is designed (and positioned within the structure) to resist loads acting on the edge, or narrow face, of the laminates, the post is said to be vertically-laminated (figure 7.1a). If a post is oriented such that the applied load acts on the wide face of the laminates, the post is said to be horizontally-laminated (figure 7.1b).

7.2.3 Design Properties. NDS design values for species and grades typically used in postframe construction are given in table 7.1. These values have been adjusted for conditions of use in which wood moisture content exceeds 19% for extended time periods, as is the case for embedded posts. To apply the values in table

7-1



Table 7.1. Design Stresses for Selected Species and Grades of Solid-Sawn Posts *

Species and Grade

Bending, Fb

Design Values in Pounds per Square Inch (psi) Compression Shear Compression Tension Parallel to Parallel to Parallel to Perpendicular to Grain, Fc┴ Grain, Fv Grain, Fc Grain, Ft

Modulus of Elasticity, E

Douglas Fir-Larch Sel Str No. 1 No. 2

1500 1200 750

1000 825 475

85 85 85

420 420 420

1045 910 430

1,600,000 1,600,000 1,300,000

Northern Pine Sel Str No. 1 No. 2

1150 950 500

800 650 375

65 65 65

290 290 290

820 730 340

1,300,000 1,300,000 1,000,000

Ponderosa Pine Sel Str No. 1 No. 2

1000 825 475

675 550 325

65 65 65

360 360 360

730 635 295

1,100,000 1,100,000 900,000

Southern Pine Sel Str No. 1 No. 2

1500 1350 850

1000 900 550

110 110 100

375 375 375

950 825 525

1,500,000 1,500,000 1,200,000

*

From the National Design Specifications (NDS) for wood under wet-use conditions, AF&PA (1997b). Values are for lumber in the size category “Posts and Timbers”.

7.4 Glued-Laminated (Glulam) Posts Load

Load

H

V

V

V

7.4.1 Advantages. For a given species and grade of lumber, glued-laminated posts have higher allowable design values than solid-sawn posts and most spliced mechanically-laminated posts (see Section 7.6). Glued-laminated posts exhibit complete composite action, that is, the glue interface is of sufficient integrity that it is assumed that there is no slip between laminates regardless of load level. With no slip between layers, glued-laminated posts behave much like solid-sawn posts, and are very effective in carrying biaxial bending loads.

H

H

H

V

(a)

(b)

7.4.2 Vertical Lamination. Glued-laminated posts that have a rather square cross-section are typically designed as vertically-laminated components; that is, they are designed to resist primary bending moments about an axis perpendicular to the wide faces of individual laminations (Axis V-V, figure 7.1b). This class of posts

Figure 7.1. (a) Vertically laminated, and (b) horizontally laminated post cross-sections.

7-2



of curved members.

(cross-sectional aspect ratios less than 1.5) are commonly used as posts in post-frame buildings.

7.4.4 Design Properties. Design properties for both horizontally- and vertically-laminated glulams are published by American Institute of Timber Construction (AITC, 1985) and AF&PA (1997b). Values for selected vertically-laminated assemblies are listed in table 7.2. These values are for dry-use conditions and normal load duration. In actual application, glulam design values must be adjusted by applicable factors involving curvature, volume, beam stability and column stability. These factors (and direction regarding their application) can also be found in the two references cited in this paragraph.

7.4.3 Horizontal Lamination. In contrast to the glued-laminated posts commonly used in postframe construction, deep glulam beams (e.g. door headers) are generally designed as horizontally laminated components (figure 7.1a). Lumber is used more efficiently in these assemblies by placing higher grade lumber in outer laminates where bending stresses are higher, and using lower grade lumber near the center where bending stresses are low. In addition, horizontal lamination facilitates the manufacture

Table 7.2. Design Values for Vertically Glued Laminated Posts a

AITC Combin ation Symbol

Lumber Grade

MOE, million psi

Extreme Fiber in Bending, psi Bending about Bending V-V Axis. about 4 or H-H Axis. 3 Lams More Lams

Tension Parallel to Grain, psi

Compression Parallel to Grain, psi 2 or 3 Lams

4 or More Lams

Douglas Fir- Larch 13 Dense Sel Str 12 Sel Str 11 No. 1 Dense 10 No. 1 9 No. 2 Dense 8 No. 2

2.0 1.8 2.0 1.8 1.8 1.6

2300 1950 2100 1750 1800 1550

2400 2100 2300 1950 1850 1600

2200 1900 2100 1750 1600 1350

1600 1400 1500 1300 1150 1000

1950 1650 1700 1450 1350 1150

2300 1950 2300 1950 1800 1550

Hem-Fir 21 Sel Str 20 No. 1 19 No. 2

1.6 1.6 1.4

1650 1500 1300

1750 1550 1350

1500 1350 1150

1100 975 850

1350 1250 975

1450 1450 1300

Southern Pine 52 Dense Sel Str 51 Sel Str 50 No. 1 Dense 49 No. 1 48 No. 2 Dense 47 No. 2

1.9 1.7 1.9 1.7 1.7 1.4

2300 1950 2100 1750 1800 1550

2400 2100 2100 b 1850 b 1850 b 1600 b

2100 1750 1800 b 1550 b 1600 b 1350 b

1500 1300 1550 1350 1400 1200

1850 1600 1700 1450 1350 1150

2200 1900 2300 2100 2200 1900

0.833 0.80 0.80 0.80 0.80 0.73 0.73 Wet Service Factor, CM c a From the National Design Specifications (NDS), AF&PA (1997b). b Values reflect the removal of the more restrictive slope-of-grain requirements. c The tabulated values are applicable when in-service moisture content is less than 16%. To obtain wet-use values, multiply the tabulated values by the factors shown.

7-3



which nails, screws, bolts, and/or shear transfer plates (STPs) have been used to join individual laminates. Nails are the most commonly used mechanical fastener and posts that only feature nails are often referred to as nail-laminated posts. STPs are medium-gage metal plates that are stamped such that teeth protrude from both surfaces.

7.4.5 Manufacturing Requirements. For glulam design values apply, tight quality control must be maintained during the laminating process. The AITC has published standards for the design (AITC, 1985) and manufacturing (AITC, 1988) of glued-laminated members. Fabrication procedures for the members must conform to an additional standard (AITC, 1983), which covers physical construction issues as well as quality control, testing and marking procedures. The rigorous requirements for construction, as well as the planing that must be performed (individual laminates prior to lamination, and the finished member after lamination completion), combine to essentially eliminate the possibility of on-site fabrication. These factors also increase product price, however, for many applications, higher design properties justify the higher cost.

Mechanical fasteners that connect preservative treated lumber should be AISI type 304 or 316 stainless steel, silicon bronze, copper, hotdipped galvanized (zinc-coated) steel nails or hot-tumbled galvanized nails. 7.5.3 Advantages. Unspliced mechanicallylaminated posts generally cost less than solidsawn posts, and they are stronger than similarly sized solid-sawn posts when bent around axis V-V (figure 7.1a). As previously noted, this is due to the fact that strength reducing defects are spread out in laminated assemblies. Also, pressure preservative treatment retention is more uniform in the narrower laminates of a mechanically-laminated post than it is in wide solid-sawn posts.

7.4.6 End Joints. Posts of any length can be created by end-joining individual laminates. The most common glued end joint is the finger joint. Although finger joining is a common manufacturing process, only a few manufacturing facilities have the capability of producing finger joints that meet AITC quality standards for structural joints (i.e., the type of joints required in glulams). Joints that do not meet criteria established for structural joints are likely to fail when subjected to design level stresses.

7.5.4 Disadvantages. When mechanically-laminated posts are bent around axis H-H (figure 7.1b), there can be considerable slip between laminates. For this reason, the bending strength and stiffness of mechanically-laminated assemblies bent about axis H-H is relatively low. To compensate for this weakness, mechanicallylaminated posts are generally only used where: (1) there is adequate weak axis support (i.e., the posts are part of a sheathed wall), (2) cover plates can be added to increase bending strength and stiffness about axis H-H (figure 7.2), or (3) the bending moment about axis H-H is relatively low or non-existent.

7.4.7 Glulams for Post-Frame Buildings. A handful of companies now manufacture and market glulams specifically for use in post-frame buildings. These posts are intended for soil embedment, with pressure preservative treated wood on one end, and non-treated wood on the other. Fabrication of such posts requires special resins and procedures for joining and laminating treated wood to non-treated wood.

7.5 Unspliced MechanicallyLaminated Posts 7.5.1 General. The majority of posts used in post-frame construction with an overall length less than 18 feet are unspliced, mechanicallylaminated posts. An unspliced post is any laminated post that does not contain end joints. This means that each layer is comprised of a single uncut piece of dimension lumber.

Figure 7.2. Cover plates used to increase the bending capacity of a mechanically laminated post about axis H-H.

7.5.2 Fasteners. As previously noted, a mechanically laminated post is a laminated post in

7-4



wet use, load duration, temperature, and in certain cases, special preservative and fire treatments.

7.5.5 Bending About Axis V-V. Allowable design stresses for bending of unspliced mechanically-laminated posts about axis V-V are calculated in accordance with ANSI/ASAE EP559 Design Requirements and Bending Properties for Mechanically Laminated Columns (ASAE, 1999). The procedure outlined in ANSI/ASAE EP559 is identical to procedures outlined in the NDS (AF&PA, 1997a) with the exception of two adjustment factors: the repetitive member factor, Cr, and the beam stability factor, CL.

Table 7.3. Repetitive Member Factors* Number of laminations Visually graded

3

4

1.35

1.40

Mechanically graded 1.25 1.30 * For mechanically-laminated dimension lumber assemblies with minimum interlayer shear capacities as specified in Table 7.4. From ANSI/ASAE EP559 (ASAE, 1999).

7.5.5.1 Repetitive Member Factor. ANSI/ ASAE EP559 allows the use of the repetitive member factors in Table 7.3 when: (1) each lamination is between 1.5 and 2.0 inches, (2) all laminations have the same depth (face width), (3) faces of adjacent laminations are in contact, (4) the centroid of each lamination is located on the centroidal axis of the post (axis V-V in figure 7.1a), that is, no laminations are offset, (5) all laminations are the same grade and species of lumber, (6) concentrated loads are distributed to the individual laminations by a load distributing element, and (7) the mechanical fasteners joining the individual layers meet the criteria in table 7.4. Note that if one or more of these criteria are not met, the NDS repetitive member factor of 1.15 should be used if it applies.

Table 7.4. Minimum Shear Capacities*

Required

Interlayer

6

Minimum required interlayer shear capacity per interface per unit length of post, lb/in. 12

8

15

10

19

Nominal face width of laminations, inches

12 24 * For unspliced mechanically-laminated posts. From ANSI/ASAE EP559 (ASAE, 1999).

7.5.5.2 Beam Stability Factor. The beam stability factor, CL, is a function of the slenderness ratio, RB, which in turn, is a function of: beam thickness, b; depth, d; and effective span length, Le. ANSI/ASAE EP559 states that for mechanically-laminated posts being bent about axis V-V, thickness, b, shall be equated to 60% of the actual post thickness, and depth, d, to the actual face width of a lamination. The effective span length, Le, is a function of the unsupported length, Lu. The unsupported length shall be set equal to the on-center spacing of bracing that keeps the post from buckling laterally.

7.5.6 Bending About Axis H-H. When all laminates are the same size, species and grade of lumber, the allowable design bending strength about axis H-H is conservatively taken as the sum of the bending strengths of the individual layers. The bending strength of an individual layer is equated to the product of the “flatwise” section modulus of an individual laminate and the NDS adjusted design bending stress. For flatwise bending, the NDS adjusted design bending stress, Fb’, is equal to tabulated design bending stress, Fb, multiplied by the appropriate flat use factor, a repetitive member factor of 1.15, and all other applicable factors. Note that the beam stability factor is equal to 1.0 for flatwise bending.

7.5.5.3 Design Values. Tables 7.5a and 7.5b contain design values for assemblies fabricated from visually graded and machine stress rated dimension lumber, respectively. The design bending stresses have been adjusted for repetitive member use. They must be further adjusted to account for stability,

7-5



Table 7.5a Design Values for Unspliced Mechanically-Laminated Posts in Bending About Axis V-V. Extreme Fiber Bending Stress*, psi Modulus Nominal Width of Individual Layers, inches of 6 8 10 12 Elasticity, Number of laminations x 106 psi Grade 3. 4. 3. 4. 3. 4. 3. 4. Douglas Fir-Larch Sel Str 2540 2640 2350 2440 2150 2230 1960 2030 1.9 No. 1 & Better 2020 2090 1860 1930 1710 1770 1550 1610 1.8 No. 1 1760 1820 1620 1680 1490 1540 1350 1400 1.7 No. 2 1540 1590 1420 1470 1300 1350 1180 1230 1.6 Hem Fir Sel Str No. 1 & Better No. 1 No. 2

2460 1840 1670 1490

2550 1910 1730 1550

2270 1700 1540 1380

2350 1760 1600 1430

2080 1560 1410 1260

2160 1620 1460 1310

1890 1420 1280 1150

1960 1470 1330 1190

1.6 1.5 1.5 1.3

Southern Pine Dense Sel Str 3650 3780 3310 3430 2900 3010 2770 2870 1.9 Sel Str 3440 3570 3110 3220 2770 2870 2570 2660 1.8 Non-Dense SS 3170 3290 2840 2940 2500 2590 2360 2450 1.7 Dense No. 1 2360 2450 2230 2310 1960 2030 1820 1890 1.8 No. 1 2230 2310 2030 2100 1760 1820 1690 1750 1.7 Non-Den. No. 1 2030 2100 1820 1890 1620 1680 1550 1610 1.6 Dense No. 2 1960 2030 1790 1960 1620 1680 1550 1610 1.7 No. 2 1690 1750 1620 1690 1420 1470 1320 1370 1.6 Non-Den. No.2 1550 1610 1490 1540 1280 1330 1220 1260 1.4 * For dry posts under normal load duration. Size and repetitive member factors applied. For other applicable modification factors, see NDS (AF&PA, 1997a). Table 7.5b Design Values for Unspliced Mechanically-Laminated Posts in Bending About Axis V-V. Extreme Fiber Bending Stress*, psi Extreme Fiber Bending Stress*, psi Grade Grade 3 Laminates 4 Laminates 3 Laminates 4 Laminates 900f-1.0E 1130 1170 1950f-1.5E 2440 2540 900f-1.2E 1130 1170 1950f-1.7E 2440 2540 1200f-1.2E 1500 1560 2100f-1.8E 2630 2730 1200f-1.5E 1500 1560 2250f-1.6E 2810 2930 1350f-1.3E 1690 1760 2250f-1.9E 2810 2930 1350f-1.8E 1690 1760 2400f-1.7E 3000 3120 1450f-1.3E 1810 1890 2400f-2.0E 3000 3120 1500f-1.3E 1880 1950 2550f-2.1E 3190 3320 1500f-1.4E 1880 1950 2700f-2.2E 3380 3510 1500f-1.8E 1880 1950 2850f-2.3E 3560 3710 1650f-1.4E 2060 2150 3000f-2.4E 3750 3900 1650f-1.5E 2060 2150 3150f-2.5E 3940 4100 1800f-1.6E 2250 2340 3300f-2.6E 4130 4290 1800f-2.1E 2250 2340 * For dry posts under normal load duration. Repetitive member factors applied. For other applicable modification factors, see NDS (AF&PA, 1997a).

7-6



7.5.9 Field Fabrication. A distinct advantage of mechanically-laminated posts is that fabrication can be performed using tools and equipment readily available on the job site. With unspliced posts that will be embedded in the ground, it is common to construct the post so that an interior laminate is left shorter than the surrounding laminates. When the post is installed with this feature located on the top of the post, the truss can be set in the resulting pocket, enabling a double shear connection between the post and truss. The interior laminate is generally significantly shorter (approximately 1 foot) than needed to accommodate the truss. This is done to compensate for varying depths of embedment. After posts are installed, a spacer (or block) of the same cross-sectional size as the shortened laminate is placed in between the shortened laminate and the truss. A schematic of this procedure is shown in Figure 7.3.

7.5.7 Flexural Rigidity. To calculate deflections due to bending requires that the flexural rigidity of the member be known. The flexural rigidity of a solid-sawn member is equal to its modulus of elasticity times its moment of inertia about the axis it is being bent. The flexural rigidity of an unspliced laminated post when bent around axis V-V is simply equal to the sum of the flexural rigidities of the individual laminates about axis VV. In other words, the flexural rigidity about axis V-V is not dependent on the properties of the mechanical fasteners. This is not the case with respect to bending about axis H-H. The bending stiffness about axis H-H axis is highly dependent on the shear stiffness of the mechanical connections between the individual laminates. A high bound for flexural rigidity about axis H-H is obtained by assuming complete composite action between layers (no interlayer slip). A lower bound is obtained by assuming no composite action (no interlayer connections). In the latter case, the total flexural rigidity is equal to the sum of the flexural rigidities of the individual laminates. Special analysis procedures, such as that developed by Bohnhoff (1992) are available for more accurate estimates of deformation due to bending about axis H-H. Use of these programs requires knowledge of the shear stiffness properties of the mechanical connections.

Block Height

7.5.8 Compressive Properties. The allowable compressive load for an unspliced mechanically laminated post is typically calculated by treating the individual laminates as discrete columns. This method conservatively assumes no composite action between laminates. An allowable compressive stress is first calculated for each laminate for buckling about axis V-V. This allowable stress is then multiplied by the crosssectional area of the laminate to obtain an allowable load for buckling about axis V-V. This calculation is repeated for each layer, and the resulting individual laminate loads are summed to obtain a total allowable column load for buckling about axis V-V. The entire process is repeated to obtain a total allowable load for buckling about axis H-H.

Block

2. Truss set on 1. Post set, bottom of truss marked, and block block and bolted into place. height measured

3. Block nailed into place and top of outer layers cut off.

Figure 7.3. On-site truss placement in a mechanically laminated post.

7.6 Spliced Mechanically-Laminated Posts 7.6.1 Types. A spliced post is any post in which at least one laminate contains one or more endjoints (i.e., is comprised of two or more individual pieces of lumber). Major end-joint types used in spliced mechanically-laminated posts include: simple butt joints, reinforced butt joints, and glued finger joints. Butt joints are generally reinforced by pressing metal plate connectors into one or both sides of each joint.

The NDS (AF&PA, 1997a) presents methods for calculating a compressive load capacity that accounts for some composite action; however, connectors used in fastening the laminations must meet criteria outlined in the NDS.

7-7



Level line of sight

(a)

(b)

(c)

Figure 7.4. (a) Treated portions of 3-layer spliced posts are embedded in the soil. (b) Top of treated portions cut so that tops at same elevation. (c) Untreated post portions spliced to treated portions.

the upper portions will have the same overall length (figure 7.4c). This eliminates cutting and blocking like that associated with the special construction shown in figure 7.3.

7.6.2 Use. Virtually all mechanically-laminated posts with overall lengths exceeding 20 foot are spliced posts. 7.6.3 Advantages. Splicing enables the fabrication of long posts from shorter, less expensive lengths of dimension lumber. Splicing also enables the construction of posts with preservative treated lumber on only one end. This reduces the quantity of treated lumber used in a building, which in turn reduces the number of special corrosion-resistant fasteners needed to join treated lumber.

7.6.4 Disadvantages. Spliced mechanicallylaminated posts have the same disadvantages as unspliced mechanically-laminated posts (see Section 7.5.4). In addition, a simple (nonreinforced) butt joint can significantly reduce bending strength and stiffness in the vicinity of the joint. If a post contains a simple butt joint in each laminate, and these joints are all located within 1 or 2 feet of each other, engineers will often model that portion of the post as a hinge connection.

With simple butt joints, the attachment of nontreated lumber to treated lumber is sometimes done in the field. This attachment is done after the treated pieces have been laminated and embedded in the ground (figure 7.4a). Prior to attaching the untreated top-portion of each post, the embedded treated portions are all cut so that their tops are at the same elevations (note: because of differing depths-of-embedment, the top of each embedded section is generally at a different height above grade). With the embedded portions at the same elevation (figure 7.4b),

7.6.5 Design Properties. Design properties for spliced mechanically-laminated posts are highly dependent on the type and relative location of end joints, and on the type and relative location of mechanical fasteners, especially those located in the vicinity of end joints. Procedures for designing and determining the bending strength and stiffness of spliced nail-laminated posts are outlined in ANSI/ASAE EP559 (ASAE, 1999).

7-8



American Forest and Paper Association (AF&PA). 1997b. NDS Supplement - Design values for wood construction. American Forest and Paper Association, Washington, D.C.

The design portion of EP559 includes requirements for joint arrangement, overall splice length, nail strength, nail density, nail diameter, and nail location. If these design requirements are followed, the bending strength and stiffness of the nail-laminated post can be calculated using the equations in the EP. It is important to note that the intent of the EP559 design requirements is to maximize the bending strength of the splice region, while minimizing overall splice length. Overall splice length is defined as the distance between the two farthest removed end joints in a post that contains one end joint in each laminate. Reducing overall splice length generally reduces the amount of preservative treated lumber used in a post.

American Institute of Timber Construction (AITC). 1983. Structural glued laminated timber. ANSI/AITC A190.1-1983. Englewood, CO. American Institute of Timber Construction (AITC). 1985. Design standard specifications for structural glued laminated timber of softwood species. AITC 117.85. Englewood, CO. American Institute of Timber Construction (AITC). 1988. Manufacturing standard specifications for structural glued laminated timber of softwood species. AITC 117.88. Englewood, CO.

7.6.6 Laboratory Tests. Engineers must generally rely on laboratory tests to determine design properties for spliced posts that do not meet the design requirements of ANSI/ASAE EP559. In recognition of this, a laboratory test procedure specifically for spliced mechanically laminated posts is outlined in ANSI/ASAE EP559.

ASAE. 1999. ANSI/ASAE EP559: Design requirements and bending properties for mechanically laminated columns. ASAE Standards, 46th edition. ASAE, St. Joseph, MI. Bohnhoff, D.R. 1992. Modeling horizontally naillaminated beams. ASCE Journal of Strucutral Engineering 118(5):1393-1406.

7.6.7 Computer Modeling. Discontinuities at butt joints result in a post with a varying bending stiffness along its length. If the overall splice length is rather short (i.e., all joints are located within a distance equal to 1/4th the post length), the post is generally sectioned into three elements for computer frame analysis: a middle element that contains all the joints, and two “joint-free” outer elements. The joint-free elements are treated like unspliced mechanicallylaminated posts with flexural rigidities calculated as described in Section 7.5.7. The element containing the joints is assigned an effective flexural rigidity that will cause it to deform like actual laboratory tested posts. A procedure for “backing-out” an effective flexural rigidity from bending test data is given in ANSI/ASAE EP559. The EP also contains an equation for calculating the flexural rigidity of the splice region of any nail-laminated post that meets the design requirements of the EP.

7.7 References American Forest and Paper Association (AF&PA). 1997a. National Design Specifications for Wood Construction (NDS). American Forest and Paper Association, Washington, D.C.

7-9



7-10



Chapter 8 - POST FOUNDATION DESIGN The most comprehensive current design guideline is ASAE EP486 (ASAE, 1999a). The material in this chapter is largely based on this engineering practice.

8.1 Introduction 8.1.1 General. A distinct advantage of postframe construction is the opportunity to transfer structural loads to the soil via embedded posts, thereby eliminating the need for a traditional foundation.

B/2

8.1.2 Post Loads. Post loads (i.e., structurally induced shear, bending moment and axial loads) are obtained using procedures presented in Chapter 5. Most post foundation design equations require that post loads be specified at the ground surface.

CL

B/2

Post q 2.0B

1.5B 1.0B

1.0B 1.5B 2.0B 0.9q 0.8q

0.5B

0.7q 0.6q

8.1.3 Post Foundation Classification. Based on their depth, post foundations are categorized as shallow foundations. Shallow foundations exhibit behavior quite different from that of deeper systems such as pilings. Specifically, post deformation below grade is relatively insignificant compared to the deformation of the soil around the post. Soil deformation around a post is a three-dimensional phenomena. Figure 8.1 shows the lines of constant soil pressure (in a horizontal plane of soil) that form when a post moves laterally. The greater the distance between two posts, the less influence one post will have on the soil pressure near the other. For design purposes, individual embedded posts are considered isolated foundations when post spacing is six times greater than post width. Higher allowable lateral soil bearing pressures are justified for a foundation featuring isolated posts instead of a continuous foundation wall.

1.0B 0.5q 0.4q

0.1q

1.5B 0.3q

2.0B

0.2q

2.5B 3.0B 3.5B

Figure 8.1. Constant Pressure Lines in a Horizontal Plane of Soil.

8.2 Post Constraint 8.2.1 Nonconstrained Post. The most basic type of post foundation consists of a post simply embedded in the ground, with no attachments or additional support (figure 8.2). If the rotation and lateral displacement of the post are resisted solely by the soil, the post foundation is said to be non-constrained.

8.1.4 Design Variables. Factors that influence the strength and stiffness of a post foundation include: embedment depth, post constraint (Section 8.2), soil properties (Section 8.3), footing size (Section 8.4), collar size (Section 8.5), backfill properties (Section 8.6), and post dimensions (Section 8.7).

8.2.2 Constrained Post. If a post bears on (or is attached to) an additional “immovable” structural element such that the lateral displacement at some point at or above the ground surface is essentially equal to zero, the post foundation is said to be constrained. An example of a constrained post foundation would be when the post is installed immediately adjacent to a concrete slab floor in the building (figure 8.3).

8.1.5 Design Guides. The first design manual for post foundations was originally published by the American Wood Preservers Institute (Patterson, 1969). The basic design approach and guidelines for post embedment analysis have been accepted by several major building codes.

8-1



was pushing on the slab, the post would be considered constrained. However, if the wind were blowing in the opposite direction, the post would not be supported by the slab; hence, the post would be analyzed for that load case as nonconstrained.

8.2.3 Varying Constraint. It is important to note that a single post can be both constrained or non-constrained, depending on the load case. Using the previous example of a slab floor, and assuming that the post is not attached to the slab, if the wind loading was such that the post

Ma

Ground Level

do

Ma

Ground Level

Va

Resultant Soil Force

Post

Va

do d

d

Rotation Axis Resultant Soil Force

Rotation Axis

Soil Forces

Footing

Footing

LOAD CASE A

LOAD CASE B

Figure 8.2. Free body diagrams of non-constrained post foundations. Load Case A: groundline shear and moment both cause clockwise rotation of embedded portion of post. Load Case B: groundline shear and moment cause clockwise and counter clockwise rotation, respectively, of embedded portion of post. Ma Va

Ground Level

R

Floor d Resultant Soil Force

Post

Soil Forces

Footing

Figure 8.3. Free body diagram of a constrained post foundation.

8-2



8.3 Soil Properties 8.3.1 General. The capability of a soil to handle loads transmitted to it by a post depend on such characteristics as: particle size and size distribution (a.k.a. soil classification), moisture content, density, and depth below grade. These soil characteristics control the allowable vertical and lateral soil pressures. 8.3.2 Soil Classification. Soil is classified by the size of individual particles and the distribution of sizes within the sample. There are four major particle (grain) sizes: gravel, sand, silt, and clay. The most popular classification system in the U.S. (i.e., the Unified Soil Classification (USC) system) classifies gravels as grains between 0.2 and 3.0 inches, sands as particles between 0.003 and 0.2 inches, silts as grains between 0.003 and 0.00008 inches, and clays as all particles finer than 0.00008 inches. The distribution of these particles within a given soil has a major impact of soil behavior. A soil with a wide distribution of particle sizes is referred to as a well-graded soil. A poorly graded soil is comprised of similar sized particles. The best soils for foundation design are gravels and sands, with well-graded gravels and sands, better than poorly graded gravels and sands. Organic silt, peat and soft clay soils are not suitable for post foundations, as they have neither the strength nor the stability to support structural loads. 8.3.3 Soil Moisture Content. The effective shear strength of a soil can be reduced significantly when soil is allowed to saturate with water. To avoid water saturation of soils around posts, install rain gutters, and slope the finish grade away from the building. A minimum 2% slope for a distance of at least 6 ft (2 m) from the building walls is recommended. 8.3.4 Soil Density and Depth. Allowable vertical and lateral soil pressures increase with increases in soil density and depth. This is because soil confinement pressures increase as both of these variables increase. 8.3.5 Tabulated Design Values. Table 8.1

8-3

contains soil properties as tabulated in ASAE are referred to as presumptive values and should only be used if there is no active building code in effect, and site-specific soil properties are unavailable. The vertical soil pressures given in table 8.1 are for the first foot (300 mm) of footing width and first foot below grade. A twenty percent increase in allowable soil pressure is allowed for each additional foot (300 mm) of foundation width or depth, up to a maximum of three times the original value. The lateral soil pressure values in table 8.1 are per unit depth. To obtain the allowable lateral pressure at a point below grade, SL, multiple the lateral soil pressure value, S, by the distance below grade of the point in question. For example, the lateral pressure per unit depth, S, for a firm sandy gravel is 300 lbm/ft2 per foot of depth. This equates to an allowable pressure of 1200 lbf/ft2 (4 ft x 300 lbm/ft2 per ft x 1lbf/lbm) for points four feet below grade. [Note: use of variable SL to represent S when adjusted for depth, is unique to this design manual, and is done to avoid confusion between values that have and have not been adjusted for depth. It is important to realize that SL and S have different units.] 8.3.6 Soil Tests. Site-specific soil test results are often used to determine allowable soil pressures. Such calculations generally result in higher allowable design values than would be obtained using table 8.1. This is because presumptive values are the lowest values associated with a broad classification of soils, each at their minimum strength conditions. 8.3.7 Soil Sampling. Soil samples should be gathered from the applicable location in the soil profile: one-third the foundation depth for lateral soil pressure calculations for non-constrained posts; and at footing depth for lateral soil pressure calculations for constrained posts and for vertical soil pressure calculations. From each soil sample, the cohesion, c, angle of internal friction φ, and bulk density, w, must be determined.



Table 8.1. Presumed Soil Properties for Post Foundation Design (ASAE, 1999). For use in absence of codes or test. Class of Material

Density or Consistency ←

Lateral Pressure Per Unit Depth, S ↑ 2 kPa per lbf/ft per ft m

Lateral Sliding Coefficient →

Vertical Pressure, Sv ↓ lbf/ft

2

kPa

Friction Angle, degrees °

Density, w ± lbm/ft

2

kg/m

3

1.

Massive crystalline bedrock

-

1200

180

0.79

4000

200

-

-

-

2.

Sedimentary and foliated rock

-

400

60

0.35

2000

100

-

-

-

3.

Sandy gravel and/or gravel (GW and GP)

firm loose

300 200

45 30

0.35

2000

100

38 32

120 90

2000 1500

4.

Sand, silty sand, clayey sand, silty gravel and clayey gravel (SW, SP, SM, SC, GM, and GC)

firm

200

30

-

-

-

30

105

1750

loose

150

22.5

0.25

1500

75

26

85

1400

Clay, sandy clay, silty clay and clayey silt (CL, ML, MH and CH)

medium soft

130 100

20 15

″ -

1000

50

15 10

120 90

2000 1500

5.

← Firm consistency of class 4 and the medium consistency of class 5 can be molded by strong finger pressure, and the firm consistency of class 3 is too compact to be excavated with a shovel. ↑ The hydrostatic increase in lateral pressure per unit depth has been included in the equations of this chapter. Source: Table 29B UBC modified with the addition of firm and medium values from Hough (1969). → Sliding resistance source: Table 29-B UBC. ↓ Allowable foundation pressures are for footings at least 1 ft (300 mm) wide and 1 ft (300 mm) deep into natural grade. Pressure may be increased 20% for each additional 1 ft (300 mm) of width and/or depth to a maximum of three times the tabulated value. Source: Table 29-B UBC. ° Soil friction angle varies from soft to medium density for clay materials, and from loose to firm for sand and gravel materials. Source: Merritt (1976). ± Soil density varies from soft to medium density for clay materials, and from loose to firm for sand and gravel materials. Source: Hough(1969). 2 ″ Multiply an assumed lateral sliding resistance of 130 lbf/ft (6 kPa) by the contact area. Use the lesser of the lateral sliding resistance and one-half the dead load.

8.3.8 Allowable Vertical Soil Pressure From Soil Test Data. The allowable vertical soil pressure for round or square footings, Sv, can be estimated from site-specific soil test as: Sv = SBC / FS

c φ

= =

w g

= =

y

=

b

=

(8-1)

where: Sv = FS = SBC =

allowable vertical soil pressure, lbf/ft2 (kPa) factor of safety (2.3 to 3.0) ultimate soil bearing capacity, lbf/ft2 (kPa)

SBC = 0.6 g w b (Nq + 1) tan φ + (Nq - 1+ Nq tan φ)(g w y + c/tanφ) Nq =

soil cohesion, lbf/ft2 (Pa) soil angle of internal friction, degrees soil bulk density, lbm/ft3 (kg/m3) gravitational constant, 1 lbf/lbm (0.00981 kPa m2/kg) depth where soil allowable pressure is calculated, ft (m) footing diameter or length of one side, ft (m)

For shallow foundations, a factor of safety between 2.3 and 3.0 is typically applied to vertical soil pressure (Whitlow, 1995). Equation 8.2 is a modified Terzaghi-Meyerhoff equation taken from Whitlow (1995). Values compiled in table 8.2 can be used to facilitate calculation of the ultimate soil bearing capacity, SBC.

(8-2)

eπ tanφ tan2(φ/2 + 45)

8-4



For lateral earth pressures in drained soils, a factor of safety between 1.5 and 2.0 is typical (Whitlow, 1995). Equation 8-2 assumes drained soils (i.e., the water table is located below the top of the footing). Equation 8-2 does not account for soil cohesion, therefore the equation is conservative for clays. Values for the Rankine passive pressure are given in table 8.3.

Table 8.2. Ultimate Bearing Capacity* SBC = 0.6 w b T1 + φ T2(w y + c T3) Nq deg. T1 T2 T3 10 2.471 0.612 1.907 5.671 12 2.974 0.845 2.606 4.705 14 3.586 1.143 3.480 4.011 16 4.335 1.530 4.578 3.487 18 5.258 2.033 5.966 3.078 20 6.399 2.693 7.729 2.747 22 7.821 3.564 9.981 2.475 24 9.603 4.721 12.879 2.246 26 11.854 6.269 16.636 2.050 28 14.720 8.358 21.547 1.881 30 18.401 11.201 28.025 1.732 32 23.177 15.107 36.659 1.600 34 29.440 20.532 48.297 1.483 36 37.752 28.155 64.181 1.376 38 48.933 39.012 86.164 1.280 40 64.195 54.705 117.061 1.192 42 85.374 77.771 161.244 1.111 44 115.308 112.317 225.659 1.036 46 158.502 165.169 321.635 0.966 50 319.057 381.429 698.295 0.839 * See Equation 8.2 for variable descriptions.

Table 8.3. Rankine Passive Soil Pressures for Drained, Cohesiveless Soils SRP, lbf/ft2 per ft φ Soil Density, lbm/ft3 deg. 95 100 105 110 115 120 10 135 142 149 156 163 170 12 145 152 160 168 175 183 14 156 164 172 180 188 197 16 167 176 185 194 203 211 18 180 189 199 208 218 227 20 194 204 214 224 235 245 22 209 220 231 242 253 264 24 225 237 249 261 273 285 26 243 256 269 282 295 307 28 263 277 291 305 319 332 30 285 300 315 330 345 360 32 309 325 342 358 374 391 34 336 354 371 389 407 424 36 366 385 404 424 443 462 38 399 420 441 462 483 504 40 437 460 483 506 529 552 42 479 504 530 555 580 605 44 527 555 583 611 638 666 46 582 613 643 674 704 735 50 717 755 793 830 868 906

8.3.9 Allowable Lateral Soil Pressure From Soil Test Data. The allowable lateral pressure per foot of depth, S, can be estimated from sitespecific soil test data as: S = SRP / FS

(8-3)

where:

FS = SRP =

allowable lateral soil pressure, lbf/ft2 per ft, (kPa per m) factor of safety (1.5 to 2.0) Rankine passive pressure for drained, cohesiveless soils, lbf/ft2 per ft, (kPa per m).

SRP =

w g tan2(45 + φ/2)

w φ

= =

g

=

soil bulk density, lbm/ft3 (kg/m3) soil angle of internal friction, degrees gravitational constant, 1 lbf/lbm (0.00981 kPa m2/kg)

S

=

8.3.10 Adjustment to Allowable Vertical Pressure. Most codes allow for a 33% increase in the allowable vertical pressure values, Sv, when post loads result from wind and seismic forces acting alone or in combination with vertical forces (see Section 3.9.4). This adjustment would apply directly to the Sv value from equation 8-1, and is cumulative with the adjustments described in Section 8.3.5 for the presumptive Sv values listed in table 8.1. In this manual, a prime (‘) will be used to denote an allowable Sv value that has been adjusted (i.e., Sv Î Sv’).

(8-4)

8.3.11 Adjustment to Allowable Lateral Pressure. In addition to the 33% increase generally allowed when post loads result from wind

8-5



and seismic forces (acting alone or in combination with vertical forces), the allowable lateral pressure, S, can be doubled when posts have a spacing at least six times their width. This increase is due to the multi-dimensional nature of pressure distribution in the soil around isolated posts as depicted in figure 8.1, and described in Section 8.1.3. In this manual, a prime (‘) will be used to denote an allowable S value that has been adjusted (i.e., S Î S’).

when assessing the post lateral load resistance capabilities. Also, the friction between the post (and/or collar) and the surrounding soil are assumed to be negligible when assessing the vertical load-carrying capability of a given post foundation design.

8.5 Collars 8.5.1 General. When lateral soil pressures exceed allowable values, additional lateral surface area can be obtained by increasing post depth, or by adding a structural element called a collar. A collar is typically either concrete cast around the base of the post (and considered to be attached to the post) or built-up wood attached to the post. These structural elements are represented in figure 8.4.

8.4 Footings 8.4.1 General. Typically, the soil is not able to resist applied vertical loads when those loads are transferred through the post alone. Therefore, the post is set on some type of footing, which is installed in the hole prior to post placement. Footings in post-frame construction are usually poured concrete. This type of footing is depicted in Figure 8.4. Generally there is no mechanical attachment of the footing to the post.

8.5.2 Location. The collar increases the lateral load resistance capability of the post foundation by increasing the bearing area in the region of the post where lateral soil capability is relatively high. Collars are typically not placed at the top of the post foundation (at the surface of the ground) due to the possibility of frost heave.

8.4.2 Friction. A footing is assumed to only resist vertical loads; the friction between the footing and the post is assumed to be negligible

Ground level Post Original excavated post hole and backfill region

Poured concrete collar Built-up wood collar Footing

(a)

(b)

Figure 8.4. Examples of common post foundation elements with (a) a poured concrete collar, and (b) a built-up wood collar.

8-6



effective post width, b, which in turn, is a function of post size and shape.

8.5.3 Attachment. Whether poured concrete or wood, the collar must be attached to the post in a manner sufficient to carry the structural loads involved. As with any wood structural element exposed directly to the soil, appropriate preservatives and fastener systems must be employed to maintain structural integrity over the design life of the building.

For posts whose narrow face is pushing on the soil: b

=

1.4 B

(8-5)

= =

effective post width, ft (m) width of post face pushing on the soil, ft (m)

where:

8.6 Backfilling

b B

8.6.1 General. The details of backfilling are often overlooked by the designer, and with potentially dire consequences. After the footing and post are installed (and the collar, if required), the hole that was dug or drilled is backfilled. Essentially, the material used for backfill is the medium through which some, if not all, transverse loads are passed from the post to the virgin soil. Backfill material is subjected to higher pressures than the surrounding virgin soil due to its proximity to the post. Therefore, material used for backfill and its installation are critically important for the successful performance of a post foundation design.

For posts whose wide face is pushing on the soil, b is equal to the diagonal dimension of the post. For poles, the effective post width, b, is equal to the pole diameter.

8.7 Design for Lateral Loadings 8.7.1 General. Bending moments and post shears cause lateral movement of the post foundation. Designers must insure that this movement does not induce soil stresses that exceed allowable lateral soil pressures. If the allowable lateral soil pressure is exceeded, the designer must increase the lateral soil bearing area by adding a collar, by increasing embedment depth, d, and/or by increasing effective post width, b. In the majority of cases, the most economical way to increase bearing area is to increase post depth. For this reason, embedment depth, d, is the dependent variable in most design equations. Occasionally a designer will add an extra laminate to the embedded portion of a laminated post to increase effective width. More often, designers will backfill all or a portion of the hole with concrete, which is akin to adding a concrete collar.

8.6.2 Materials. Typical materials for backfill include concrete, well-graded granular aggregate, gravel, sand, or soil initially excavated from the post hole. These alternatives are listed in the order of decreasing stiffness. 8.6.3 Concrete. While concrete is the stiffest backfill material, it is also the most expensive. Concrete backfill essentially increases post width, b. It must be installed with attention to the possibility of frost heave (discussed later). 8.6.4 Excavated Soil. The most common backfill material is the excavated soil. If used as backfill, it should be free of topsoil and organic matter. Silt- or clay-based soils should be moist (not wet) and well packed.

8.7.2 Assumptions. Equations in 8.7.3 and 8.7.4 assume that only the post (and not the footing) resists lateral loads. This is because variations in vertical post loads make it impossible to rely on post-to-footing friction for lateral load resistance.

8.6.5 Compaction. Backfill materials should be tamped or vibrated upon backfill in maximum layers (a.k.a. lifts) of 8 inch (400 mm).

8.7 Post Dimensions

8.7.3 Required Embedment Depth for NonConstrained Posts Without Collars. Two different load cases for a non-constrained, noncollared post are shown in figure 8.2: The first

8.7.1 Effective Width. Design equations for lateral loading (Section 8.7) are a function of

8-7



load case (a.k.a. Load Case A ) represents conditions where groundline shear and groundline bending moment both cause the embedded portion of the post to rotate in the same direction. Load Case B represents conditions where groundline bending moment causes the embedded portion of the post to rotate in an opposite direction than the rotation caused by groundline shear. Minimum post embedment depth, d, for both Load Case A & B is calculated using one of the following equations.

where: A b d P h

SL’ =

From ASAE EP486 (1999a), AWPI (Patterson, 1969), and the UBC (ICBO, 1994): d 2=

7.02 Va + 7.65 Ma / d S’ b

6 Va + 8 Ma / d S’ b

(8-6)

To adjust equation T-1 so that it can be applied to posts subjected to a variety of loadings and “above-grade” constraint conditions, load P is replaced with an equivalent shear force and bending moment located at the ground surface. Using predefined nomenclature: Va is substituted into equation T-1 for P, and Ma is substituted for the product of P and h. In addition, the adjusted allowable lateral soil pressure at onethird the embedment depth, SL’, is replaced by the quantity S’ d / 3. This substitution eliminates having to recalculate SL’ every time the embedment depth changes. With these substitutions, equation T-1 appears in ASAE EP486 (1999a) as:

(8-7)

where: d = Va = Ma = S’ = b

=

minimum embedment depth, ft (m) shear force applied to foundation at ground surface, lbf (N) bending moment applied to foundation at ground surface, ft-lbf (N-m) adjusted allowable lateral soil pressure, lbf/ft per ft (kPa/m per m) effective post width, ft (m), see Section 8.7.1

Equations 8-6 and 8-7 must be solved by iteration. For Load Case B, Va and Ma must be input with opposing signs. Note that equation 8-6 is in a slightly different form than appears in any of the three referenced documents. See the following technical note on equation development for additional information.

d 2 = 3.51Va/(S’ b)[1+(1+(0.62 Ma S’ b d)/ Va2)1/2] Because it is somewhat confusing, the ASAE EP486 equation was rewritten for this design manual in the form of Equation 8-6. The first major revision to ASAE EP486 (due for release in 2000) will contain several changes, including a switch from equation 8-6 to equation 8-7. Equation 8-7 is based on five common assumptions: (1) only the post (and not the footing) resists lateral loads, (2) the post behaves as a rigid body below grade (3) soil type remains constant, (4) at a given depth, soil resisting pressure, q, is equal to the product of soil stiffness, k, and lateral post movement at that depth, and (5) soil stiffness, k, at a distance, y,

Technical Note Non-Constrained Post Equations Equation 8-6 for the embedment depth, d, of non-constrained, non-collared posts appears in most code documents as: d

=

0.5 A [1 + (1 + 4.36 h / A)1/2]

2.34 P / (SL’ b) effective post width, ft (m) post embedment depth, ft (m) applied lateral force, lbf (N) distance from ground surface to point of application of force P, ft (m) adjusted allowable lateral soil pressure at one-third the embedment depth, lbf/ft2 (kPa)

Equation T-1 was developed for point-loaded posts that behave as pure cantilevered beams. Unfortunately, posts in post-frame buildings are not point-loaded, and embedded posts are supported in such a way that they behave more like propped cantilevers.

From ASAE EP486.2 (1999b): d2=

= = = = =

(T-1)

8-8



below grade is equal to the product of the horizontal subgrade reaction, nh, and the distance below grade, y. In equation form, the soil resisting pressure, q, for a non-constrained, noncollared post is given by Meador (1997) as: q

=

nh ∆ (y – y2/do)

=

actual soil pressure at a depth y below grade, lbf/ft2 (kPa) constant of horizontal subgrade reaction, lbf/ft4 (N/m4) lateral post deflection at grade, ft (m) depth below grade, ft (m) distance from surface to point of post rotation in soil, ft (m), (see figure 8.2)

soil pressure, q, does not exceed the adjusted allowable lateral soil pressure, SL’ = S’ y. It can be shown that every time a designer does this, the depth at which the actual soil pressure is closest to the allowable pressure is right at the surface. In other words, for a non-constrained post, the designer does not need to compare S’ y and q from equation T-5 at every value of y, instead, the designer only needs to check it at y = 0. It follows that the embedment depth, d, needed to ensure that the actual soil pressure does not exceed the allowable soil pressure at the surface (or any point below the surface) is given as:

(T-2)

where: q

nh = ∆

=

y = do =

d 2 = (18 Va + 24 Ma / d )/(S’ b)

Equation T-6 is not used in practice as field and laboratory tests have shown that it is extremely conservative for non-constrained posts. This is because when actual soil pressures at the surface equal the allowable soil pressure, the actual soil pressure at points below the surface are below (and in most cases substantially below) allowable soil pressures. Consequently, nonconstrained post foundations are no where near failure when allowable soil pressures near the surface are exceeded. A more realistic embedment depth is obtained by replacing S’ in equation T-6 with 3S’. The resulting equation is equation 8-7. Note that when this equation is used, actual soil pressure will exceed allowable soil pressure for points between y = 0 and y = 2do/3, and for points deeper than y = 4do/3.

Equation T-2 is a parabolic function that produces the soil pressure profile shown in figure 8.2. If a summation of the horizontal forces in figure 8.2 is set equal to zero, and the bending moment around any point is equated to zero, the following two equations can be obtained for the grade deflection ∆, and distance to post rotation point, do. ∆ = (24 Ma + 18 Va d)/(d 3 nh b)

(T-3)

do = (3 Va d + 4 Ma)/(4 Va + 6 Ma /d)

(T-4)

(T-6)

Examination of equation T-4 shows that the point of post rotation is two-thirds the embedment depth when there is no shear in the post at the ground surface (Va = 0). When there is no moment in the post at the ground surface (Ma = 0), the point of post rotation is located at threequarters of the embedment depth. If both Va and Ma are positive and non-zero, the point of rotation is between two-thirds and three-fourths of the embedment depth.

For an in-depth discussion and greater detail on non-constrained post foundation equation development see Meador (1997).

8.7.4 Required Embedment Depth for Constrained Posts Without Collars. A free body diagram of a constrained, non-collared post is shown in figure 8.3. Minimum post embedment depth, d, for the constrained, non-collared case is calculated using one of the following equations.

Substitution of equation T-3 into equation T-2 yields the following equation for soil pressure: q = (18 Va + 24 Ma/d)(y – y 2/do)/(d 2 b) (T-5)

From ASAE EP486 (1999a), AWPI (Patterson, 1969), and the UBC (ICBO, 1994):

Typically, a designer selects a value for d, such that for all points below the surface, the actual

d=

8-9

4.25 Ma S’ b

1/3

(8-8)



From ASAE EP486.2 (1999b): 4 Ma d= S’ b

of these is a switch from equation 8-8 to equation 8-9. Equation 8-9 is based on the same assumptions as described for equation 8-7. These assumptions result in the following equation for actual soil resisting pressure, q, for a constrained, non-collared post (Meador, 1997):

1/3

(8-9)

where: d = Ma = S’ = b

=

minimum embedment depth, ft (m) bending moment applied to foundation at ground surface, ft-lbf (N-m) adjusted allowable lateral soil pressure, lbf/ft per ft (kPa/m per m) effective post width, ft (m), see Section 8.7.1

q

=

nh y 2 ∆ / d

=

actual soil pressure at a depth y below grade, lbf/ft2 (kPa) constant of horizontal subgrade reaction, lbf/ft4 (N/m4) lateral movement of post at a depth y = d, ft (m) depth below grade, ft (m)

where: q

nh = Note that equation 8-8 is in a slightly different form than appears in any of the three referenced documents. See the following technical note on equation development for additional information.

Equation 8-8 for the embedment depth, d, of constrained, non-collared posts appears in most code documents as: d

=

[4.25 P h / (SL’ b)]

= = =

post embedment depth, ft (m) applied lateral force, lbf (N) distance from ground surface to point of application of force P, ft (m) adjusted allowable lateral soil pressure at the full embedment depth, lbf/ft2 (kPa) effective post width, ft (m)

SL’ = b

=

=

y

=

∆ = 4 Ma /(d 3 nh b)

(T-1)

(T-3)

Substitution of equation T-3 into equation T-2 yields the following equation for soil pressure:

where: d P h

∆

Equation T-2 is a parabolic function that produces the soil pressure profile shown in figure 8.3. If the bending moment around any point in figure 8.3 is equated to zero, the following equation is obtained for the lateral movement, ∆, of the post at a depth, d.

Technical Note Constrained Post Equations

1/2

(T-2)

q = 4 Ma y 2/(d 4 b)

(T-4)

The actual soil pressure increases at an increasing rate as y increases. The allowable lateral soil pressure, SL’, increases at a constant rate as y increases (note: SL’ = S’ y). This means that if a designer ensures that the actual soil pressure, q does not exceed the allowable pressure at a depth, y = d, then the actual stress will be less than the allowable for all points between the ground surface and y = d. In equation form:

Equation 8-8 is derived from equation T-1 by substituting bending moment, Ma, for the product of P and h, and replacing SL’ with the quantity S’d. This latter substitution eliminates having to recalculate SL’ every time the embedment depth changes.

S’ y > q = 4 Ma y 2/(d 4 b)

for y = d

(T-5)

Equation T-5 becomes equation 8.9 after it is rearranged so that d is the dependent variable.

As described in the previous technical note on non-constrained posts, the first major revision to ASAE EP486 will contain several changes. One

For an in-depth discussion and greater detail on constrained post foundation equation development see Meador (1997).

8 - 10



8.7.5 Required Embedment Depth for Posts With Collars. This design manual does not contain embedment equations for posts with collars. For such equations, see ASAE EP486 (1999a, 1999b) and Meador (1997).

Ground Level

Post

8.8 Design for Downward Loadings Ap

8.8.1 Required Footing Area. Downward forces are resisted by the footing. The footing area, A, required to resist these forces is: A

=

P / SV’

dT

φ

(8-10)

where: A = P = SV’ =

r / tan φ

required footing area, ft2 (m2) vertical foundation load, lbf (N) adjusted allowable vertical soil pressure, lbf/ft2 (kPa) (see Section 8.3.10)

Collar Footing 2r

8.9 Design for Uplift Loadings

Figure 8.5. Schematic of relevant uplift resistance components for post foundation with an attached circular collar.

8.9.1 General. If the net vertical force acting on a post is upward, either the footing or a collar must be attached to the post. When the footing or a collar is attached to the post, upward movement of the post foundation cannot occur without displacing a cone-shaped mass of soil. The mass of this of soil depends on foundation depth, footing (or collar) size, soil density, and soil internal friction angle.

Ground Level

Post

8.9.2 Skin Friction. An attached footing or collar is required to resist uplift forces because skin friction between a post and backfill cannot be relied on to resist such forces.

AP

8.9.3 Concrete Backfill. Concrete cast against undisturbed soil and mechanically fastened to the post adds uplift resistance of both the concrete mass and the skin friction between the concrete and soil. Note that this practice is not recommended in soils with a high susceptibility to frost heave

dT

φ

Collar l1

8.9.4 Volume of Displaced Soil. The volume of soil that must be displaced when pushed upward by a footing or collar is dependent on the shape of the footing or collar. Figures 8.5 and 8.6 show configurations for circular and rectangular foundation elements, respectively.

l2 Unattached Footing

Figure 8.6. Schematic of relevant uplift resistance components for post foundation with an attached rectangular collar.

8 - 11



The volume of displaced soil, VS, is calculated using the following equations:

forced upward. 8.10.2 Problems. Frost heave can induce large differential movements in the foundation. This differential movement can crack building finishes, and induce significant stress in structural connections and components. When ice lenses thaw, soil moisture content increases dramatically. The soil is generally in a saturated state with reduced strength. As soil water drains from the soil, effective soil stresses increase and the foundation will generally settle.

For circular footings and collars: VS =

π dT [r 2 + dT r tanφ + dT 2 tan2φ / 3] – dT Ap

For rectangular footings and collars: VS =

where: VS = dT = r

=

φ = Ap = l1, l2 =

dT (l1 l2 - Ap) + dT2 tanφ (l1 + l2) + dT 3π tan2φ / 3

8.10.3 Minimizing Frost Heave. Frost heave can be minimized by: (1) avoiding clays and silts, (2) extending footings below the frost line, and (3) providing good drainage.

volume of displaced soil, ft3 (m3) distance from ground surface to top of collar, or to top of footing if collar is not present, ft (m) radius of collar, or footing if collar is not present, ft (m) angle of internal soil friction post cross-sectional area, ft2 (m2) length and width of a rectangular collar or footing, ft (m)

8.10.3.1 No Silts and Clays. Fine grained soils such as clays and silts are more susceptible to frost heave because (1) water is drawn upward by the fine pores which function as capillaries, and (2) there is much more surface area in a unit volume of fine grained soil, and therefore more surface area for water adsoprtion.

8.9.5 Uplift Resistance, U. The resistance to uplift, U, is calculated as: U

=

g ( MF+ w VS )

8.10.3.2 Footing Depth. The most sure fire way to avoid frost heave problems is to locate the footing where water never freeze. It is for this reason that codes require foundations to be located below the frost line. Exceptions include footings on rock and floating foundation systems. A floating foundation is reinforced so that it can float as a monolithic unit as the soil swells and shrinks.

(8-11)

where: U = MF = w = dT = VS = g =

uplift resisting force, lbf (N) mass of all foundation elements that are attached to the post, lbm (kg) soil density, lbm/ft3 (kg/m3) distance from ground surface to top of collar, or to top of footing if collar is not present, ft (m) volume of displaced soil, ft3 (m3) gravitational constant, 1 lbf/lbm (9.81 N/kg)

8.10.3.3 Water Drainage. Proper surface and subsurface drainage can reduce frost heave. Drainage of surface waters from a builder is enhanced by installing rain gutters, adequately sloping the finish grade away from the building, and raising the building elevation to a level above that of the surrounding area. Subsurface drainage is achieved with the placement of drain tile or coarse granular material below the maximum frost depth, with drainage to an outlet. Such drainage lowers the water table and interrupts the flow of water moving both vertically and horizontally through the soil.

8.10 Frost Heave Considerations 8.10.1 General. Freezing temperatures in the soil result in the formation of ice lenses in the spaces (a.k.a. pores) between soil particles. Under the right conditions, these ice lenses will continue to attract water and increase in size. This expansion of the ice lenses increases soil volume. If this expansion occurs under a footing, or alongside a foundation element with a rough surface, that portion of the foundation will be

8 - 12



Merritt, F.S. 1976. Standard Handbook for Civil Engineers, pp. 7-53.

8.10.4 Concrete Floors. If the ground beneath a concrete floor can freeze, the floor should be installed such that its vertical movement is not restricted by embedded posts or by structural elements attached to embedded posts. While concrete shrinkage may break bonds between a floor and surrounding components, more proactive measures will ensure independent vertical behavior. For example, plastic film can be placed against surrounding surfaces prior to pouring the floor.

Patterson, D. 1969. Pole Building Design. American Wood Preservers Institute (AWPI), Washington D.C. Whitlow, R. 1995. Basic Soil Mechanics. 3rd edition. John Wiley & Sons, Inc. New York, NY

8.10.5 Concrete Backfill. The use of poured concrete as a backfill material may actually increase the likelihood of frost heave. The rough soil-to-concrete backfill interface provides the potential for significant vertical uplift forces due to frost heave. Also, the placement of concrete in holes that decrease in diameter with depth provide additional risk for frost heave. 8.10.6 Top Collars. Although common in past years, placement of collars at the ground surface (to increase lateral load resistance) has all but been abandoned due to frost heave considerations.

8.11 References ASAE. 1999a. ASAE EP486: Post and pole foundation design. Shallow post foundation design. ASAE Standards, 46th Edition. ASAE,. St. Joseph, MI ASAE. 1999b. ASAE EP486.2: Shallow post foundation design. In review. ASAE. St. Joseph, MI. Hough, B.K. 1969. Basic Soils Engineering, 2nd Edition. Ronald Press Co. Table 7-2, p. 249. International Conference of Building Officials (ICBO). 1994. Uniform Building Code, 1994 Edition. ICBO, Whittier, CA McGuire, P. M. 1998. Overlooked assumption in nonconstrained post embedment. ASCE Practice Periodic on Structural design and Construction, 3(1):19-24. Meador, N.F. 1997. Mathematical models for lateral resistance of post foundations. Trans of ASAE, 40(1):191-201.

8 - 13



8 - 14



Chapter 9: DESIGN EXAMPLE 9.1 Introduction

9.2 Step 1: Modeling

9.1.1 General. Structurally efficient post-frame buildings utilize the roof as a diaphragm to resist horizontal wind forces. This chapter presents an example of diaphragm design following the five steps outlined in Section 5.1.4.

9.2.1 General. The structural model for this example building follows that in Section 5.2. The frames are numbered from one to seven beginning on the left end. That portion of the roof diaphragm between each frame is broken into two discrete segments labeled 1a, 1,b, …6a, 6b. See Figure 9.1.

9.1.2 Building Specifications. Table 9.1 lists design parameters for the example building.

3

2

1 Table 9.1. Example Building Specifications Width (truss length) 36 ft Length (along ridge) 60 ft Height at post bearing 12 ft Roof slope 4/12 (18.43°) Bay spacing 10 ft Number of frames 7 (including end walls) Post embedment depth 4 ft Post grade & species No.2 S. Pine Post size Nom. 6- by 6-in. Roof snow load 30 psf Roof dead load 5 psf Concrete slab? Yes Ceiling? No

4

5

6

7

1a

2a

3a

4a

5a

6a

1b

2b

3b

4b

5b

6b

Figure 9.1. Identification of frame elements and roof diaphragm segments.

9.3 Step 2: Stiffness Properties 9.3.1 Frame Stiffness, k. One reliable way to determine frame stiffness is to use a planeframe analysis program such as the PPSA program mentioned in Section 5.3.2. In this example, all posts will be considered fixed at the grade line and pin connected to trusses (figure 5.5). Consequently, the stiffness of each embedded post can be calculated using equation 53 which is given as:

9.1.3 Wind Loads. It is assumed that the example building is located in a jurisdiction that has adopted the 1994 Uniform Building Code. Design wind loads calculated according to this code are presented in Table 9.2

kp =

Table 9.2. Wind Loads Wind speed 80 mph Exposure category B Windward wall, qww 8.13 psf Leeward wall, qlw -5.08 psf * Windward roof, qwr 3.05 psf Leeward roof, qlr -7.12 psf * * Negative loads act away from the surface in question. Positive loads act toward the surface in question.

3 E I / Hp3

For the nominal 6- by 6-inch No. 2 Southern Pine posts: E

=

I = Hp =

1.2 x 106 lbf/in.2 (No adjustment for wet conditions is necessary for Southern Pine timbers. It is generally required for laminated posts.) 76.26 in.4 144 in.

Thus, kp = 91.9 lbf/in.

9-1



Frame stiffness, k, is obtained by summing individual post stiffness values (equation 5-2). This summation yields: k

=

9.3.3 Shearwall Stiffness, ke. There are no large doors in the endwalls of the example building. Lacking a specific tested endwall assembly, the 12 ft high endwalls will be assumed to have the same shear stiffness as an 8 ft section of the roof diaphragm; that is, ke will be set equal to Ch or 12,640 lbf/in.

184 lbf/in.

9.3.2 Diaphragm Stiffness, Ch. The diaphragm assembly used in this example is Test Assembly 11 in Table 6.1. Its properties are summarized in Table 9.3.

9.4 Step 3: Eave Loads 9.4.1 Windward Roof Pressures. As noted in Section 9.1.3, this example uses wind loads calculated in accordance with the 1994 UBC. Pressure coefficients (from UBC table 16-H) for windward roof slopes between 2/12 and 9/12 are -0.9 (outward) and 0.3 (inward). It is important to recognize the significant impact that wind direction (inward or outward) has on calculated eave loads. The 3.05 psf design windward roof pressure listed in table 9.2 was calculated using the 0.3 pressure coefficient. When combined with the negative pressure of 7.12 psf on the leeward roof, the net lateral roof pressure is 10.17 psf. If the –0.9 pressure coefficient would have been used, the net lateral roof pressure would have been –2.03 psf.

Table 9.3. Diaphragm Properties Metal thickness 29 gage Assembly width, 3 x a 36 ft Assembly length, b 12 ft Allowable shear strength, va 107 lbf/ft Effective in-plane shear 3700 lbf/in. stiffness, c Effective shear modulus, G 3700 lbf/in. In-plane shear stiffness for a single diaphragm section is calculated using equation 6-9, which is given as. cp

=

G bh s cos(θ)

9.4.2 Fixity Factors, f. Based on the assumption of a post fixed at the groundline (see Section 9.3.1), a fixity factor of 3/8 is appropriate for this example.

Substitution of appropriate values yields: cp

=

cp

=

(3700 lbf/in.)(18 ft) (10 ft)(cos(18.43))

9.4.3 Eave Load, R. Since this example uses symmetrical base restraint and frame geometry, equation 5-6 may be used.

7020 lbf/in.

The horizontal shear stiffness, ch, of a single diaphragm section is calculated using equation 6-10 which is given as: ch =

R

=

s [hr (qwr – qlr) + hw f (qww – qlw)]

hr hw s f

= = = =

(36 ft /2) (4/12) = 6 ft 12 ft 10 ft 0.375

R

=

10 ft [6 ft (3.05 psf + 7.12 psf) + 12 ft (.375)(8.13 psf + 5.08 psf)]

R

=

1205 lbf

where:

cp cos2 (θ)

Substitution of appropriate values yields: ch = (7020 lbf/in.) cos2(18.43°) = 6320 lbf/in. or

Total horizontal shear stiffness of a diaphragm element, Ch, is found by summing the stiffness values of the two sections that comprise each diaphragm element (see equation 5-4). Ch = 6320 + 6320 = 12,640 lbf/in.

9-2



Q

For later calculations, it is convenient to calculate R in terms of its components – roof, windward wall and leeward wall.

mD R = 0.90(1205 lbf) = 1085 lbf

The difference between eave load, R, and the horizontal restraining force, Q, is the amount of the eave load that is transferred by the center post-frame to the foundation.

RR = 10(6)(3.05 + 7.12) = 610.2 lbf RW = 10(12)(.375)(8.13) = 365.8 lbf RL = 10(12)(.375)(-5.08) = -228.6 lbf RR + RW – RL = 1205 lbf

R – Q = 120 lbf The eave deflection, ∆, for a post-frame with stiffness, k, subjected to an eave load, R, and horizontal restraining force, Q, is given as:

9.5 Step 4: Load Distribution 9.5.1 Introduction. For this example problem, diaphragm shear stiffness, Ch, frame stiffness, k, endwall stiffness, ke, and eave load, R, are all constant. Consequently, in addition to analysis methods such as DAFI, load distribution can be determined using the ANSI/ASAE EP484.2 tables (Section 5.6.3) and the simple beam analogy equations (Section 5.5.6). For comparison purposes, all three methods are demonstrated here (Sections 9.5.2 – 9.5.4). The information obtained from these analyses is then used to determine the maximum diaphragm shear force (Section 9.5.6) and maximum post forces (Section 9.5.7).

∆

=

(R – Q) / k

Eave deflection for the center post-frame is given as: ∆

=

(1205 lbf – 1085 lbf) / 184 lbf/in.

∆

=

0.652 in.

9.5.3 Simple Beam Analogy Equations. As previously noted, the simple beam analogy equations for diaphragm shear force, Vh, and diaphragm displacement, y, can be used when R, k, ke and Ch are constant. These two equations are given in Section 5.6.6 as:

9.5.2 ANSI/ASAE EP484.2 Tables. In this design manual, the ANSI/ASAE EP484.2 tables are tables 5.1 and 5.2. Table 5.1 contains shear force modifiers or “mS” values. The product of this modifier and eave load, R, is the maximum shear force in the diaphragm, Vh. Table 5.2 contains sidesway restraining force modifiers or “mD” values. The product of this modifier and eave load, R, is referred to as the horizontal restraining force, Q, which is the amount of eave load transferred away from the center postframe(s) by the diaphragm.

Vh = Ch α s [A sinh(α x) + B cosh(α x)] y = A cosh(α x) + B sinh(α x) + R/k Input parameters and calculated equation constants for the simple beam analogy equations have been compiled for this example analysis in Table 9.4. Maximum diaphragm shear is calculated by setting x = 0 in., or:

Use of tables 5.1 and 5.2 requires two ratio: ke/k and Ch/k. For this example analysis, both ratios are equal to 69 (12640/184). Using linear interpolation, the mS value from table 5.1 is 2.77, and the mD value from table 5.2 is 0.90.

Vh = 12,640 lbf/in.(1.0054x10-3 in.-1) •(120 in.)[-6.286 in.(0) + 2.181 in.(1)] Vh = 3326 lbf Maximum diaphragm displacement is calculated by setting x = L/2 = 360 in. , or:

The maximum diaphragm shear force, Vh, which occurs adjacent to each endwall, is given as: Vh =

=

mS R = 2.77(1205 lbf) = 3340 lbf

The horizontal restraining force, Q, that must be applied to the center post frame (i.e., frame 4 in figure 9.1) is given as:

9-3

y

=

-6.286 in.( 1.0662) + 2.181 in.( 0.3699) + 1205 lbf/(184 lbf/in.)

y

=

0.6535 in.



The force transferred to the foundation by the center frame (frame 4) is equal to the product of eave displacement, y, and frame stiffness, k, or:

Table 9.4. Parameters for Simple Beam Analogy Equations 1205 lbf R 120 in. s 720 in. L 12,640 lbf/in. ke 184 lbf/in. k 6.549 in. R/ k 12,640 lbf/in. Ch 1.0054x10-3 in.-1 * α 0.7239 αL 1.2737 cosh(α L) 0.7888 sinh(α L) -23.890 * D 0.2631 in. * ye -6.286 in. * A 2.181 in. * B cosh(0) 1 sinh(0) 0 1.0662 cosh(α 360 in.) 0.3699 sinh(α 360 in.) * Equations for calculation of these values are given in Section 5.6.6.

yk =

0.6535 in. (184 lbf/in.) = 120.2 lbf

The horizontal restraining force, Q, for the frame 4 is equal to the difference between the eave load, R, and the 120.2 lbf, or Q

=

1205 lbf – 120.2 lbf = 1084.8 lbf

Note that ye in table 9.4 is the eave displacement of the endwall. 9.5.4 DAFI. As previously mentioned, DAFI is a computer program specifically written for determining load distribution between diaphragms and frames. DAFI can be downloaded free from the NFBA web site (www.postframe.org). The maximum shear force in the diaphragm. Vh, is numerically equal to the load resisted by the endwall frame. In figure 9.2, this value is given as 3353.2 lbf. Note that this value is more precise than the 3340 lbf value calculated from the mS values in table 5.1 because the values in table 5.1 are only given to three significant figures. It is important to note that the shear load

FRAME FRAME APPLIED HORIZONTAL LOAD RESISTED FRACTION OF NUMBER STIFFNESS LOAD DISPLACEMENT BY FRAME APPLIED LOAD --------------------------------------------------------------------1 12640.00 602.5 .2652868 3353.2 5.5655 2 184.00 1205.0 .4829074 88.9 .0737 3 184.00 1205.0 .6122254 112.6 .0935 4 184.00 1205.0 .6551232 120.5 .1000 5 184.00 1205.0 .6122254 112.6 .0935 6 184.00 1205.0 .4829074 88.9 .0737 7 12640.00 602.5 .2652867 3353.2 5.5655 DIAPHRAGM DIAPHRAGM SHEAR SHEAR NUMBER STIFFNESS DISPLACEMENT LOAD -------------------------------------------1 12640.00 .2176206 2750.7 2 12640.00 .1293180 1634.6 3 12640.00 .0428978 542.2 4 12640.00 .0428979 542.2 5 12640.00 .1293180 1634.6 6 12640.00 .2176206 2750.7

Figure 9.2. Output from computer program DAFI for example building.

9-4



Diaphragm elements 1 and 6 are both subjected to the maximum horizontal shear, Vh, of 3350 lbf. Consequently, the in-plane shear force in diaphagm sections 1a, 1b, 6a and 6b is given as:

listed for each diaphragm in the DAFI output is essentially an average shear load in the diaphragm. For example, the average shear load in diaphragm 1 is listed as 2750.7 lbf. To calculate the maximum shear load in each diaphragm element, simply add the quantity R/2 to the average value. For this example analysis, half the eave load is 602.5 lbf. Adding this to the average shear load in diaphragm 1 yields the expected maximum shear force in the diaphragm of 3353.2 lbf.

Vp

Vp =

1766 lbf

vp =

1766 lbf /(18 ft / cos (18.43°))

vp =

93.1 lbf/ft

9.5.7. Post Forces. The most critical posts from a design perspective are those associated with the most heavily loaded frame. In the example building this is the center post-frame (a.k.a. frame 4).

9.5.5 Comparison of Methods. The ANSI/ ASAE EP484.2 tables (tables 5-1 and 5-2), simple beam analogy equations, and program DAFI yield identical values for maximum diaphragm shear, horizontal restraining force, and eave deflections. Again, it is important to note that the ANSI/ASAE EP484.2 tables and the simple beam analogy equations are restricted to designs with fixed values of Ch, k, R, and ke. Although DAFI is more versatile, a DAFI analysis requires computer access. The simple beam analog equations can be quickly solved with a hand calculator that supports hyperbolic trigonometric functions.

There are two basic methods for determining post forces. The first is to analyze the frame with a plane-frame structural analysis program, the second is to assume the truss is rigid and then use a series of equations to calculate post forces. A structural analog for a plane-frame structural analysis of frame 4 is shown in figure 9.3a. Post forces obtained with this analog are given in figure 9.3b. For this example analysis, the load combination of “full dead + full wind + ½ snow “ was used, with a roof dead load of 5 psf and a roof snow load of 30 psf (Note: in practice, the building designer must check all applicable load cases). The force applied to the frame by the diaphragm, qp, was applied as a force of 30.12 lbf per foot of top chord. This force was obtained by first combining equations 5-10 and 5-11 into the following equation:

9.5.6 Diaphragm Shear. The maximum inplane shear force, Vp, in a diaphragm section is calculated from the maximum horizontal shear force, Vh, in the diaphragm elements using equation 5-9 which is given as: (ch,i / Ch) Vh / (cos θ i)

For this example analysis, all six diaphragm elements have the same Ch, and all twelve of the diaphragm sections shown in figure 9.1 have the same horizontal stiffness, ch and slope, θ, that is: Ch = ch,i = θ =

6320 lbf/in (3350 lbf) 12,640 lbf/in (cos 18.43°)

Dividing the in-plane shear force by the slope length of a diaphragm section yields the in-plane shear force on a unit length basis, vp.

The amount of eave load transferred to the foundation by each frame is listed in figure 9.2 under the column heading “load resisted by frame.” The difference between this value and the eave load, R, is the horizontal restraining force, Q. The load resisted by the most heavily loaded frame (i.e., frame 4) is 120.5 lbf. This equates to a horizontal restraining force for frame 4 of 1084.5 lbf (1205 lbf – 120.5 lbf).

Vp,i =

=

q p,i =

Q (c h,i / Ch ) / b i

(9-1)

where: Q is the horizontal restraining force (1084.5 lbf for frame 4); ch,i is the horizontal stiffness of diaphragm segment i (6320 lbf/in); Ch is the horizontal stiffness of diaphragm element i (12,640 lbf/in); and bi is the horizontal span of diaphragm segment i (18 ft).

12,640 lbf/in. 6320 lbf/in. 18.43°

9-5



s x (5 psf + 30 psf /2) 3820 lbf

s

sx

psf .05 x 3

30.1 2

ft lbf/ 12 30.

2650 lbf

0 in.-lbf

0 in.-lbf

7.1 2p sf

313 lbf

161 lbf

Windward post lbf/f

Leeward post

t

s x 5.08 psf

s x 8.13 psf

662 lbf

449 lbf 25100 in.-lbf 3821 lbf

20700 in.-lbf 2646 lbf

(a)

(b)

Figure 9.3. (a) Structural analog for frame 4 of the example building (s = 10 ft). (b) Resulting forces on post ends. Lateral deflection at the top of the windward and leeward posts were 0.572 and 0.735 inches, respectively.

Roof dead + 1/2 snow = 7200 lbf Vertical component of windward roof pressure = 549 lbf + Vertical component of diaphragm restraining force = 180.75 lbf

Vertical component of leeward roof pressure = -1281.6 lbf + Vertical component of diaphragm restraining force = -180.75 lbf 9 ft

Horizontal component of windward roof pressure = 183 lbf + Horizontal component of diaphragm restraining force = -542.25 lbf

9 ft

9 ft

9 ft

3 ft

3 ft

3 ft

3 ft Vtl

Vtw

Pw = 3821 lbf

Horizontal component of leeward roof pressure = -427.2 lbf + Horizontal component of diaphragm restraining force = 542.25 lbf

Pl = 2646 lbf

Figure 9.4. Resultant of forces applied to truss of frame 4.

In lieu of a computer analysis, post axial forces for a two-post frame can be obtained by drawing a free-body diagram of the truss and summing forces about each truss-to-post connection. Such a free-body diagram for frame 4 of the example building is shown in figure 9.4. The axial forces (Pw and Pl) obtained in this manner are identical to those obtained via the computer analysis (figure 9.3).

To obtain post shears and bending moments without reliance on a computer is a straight forward process if the truss is assumed to be completely rigid. When this assumption is made, the lateral movement, ∆, of all posts at their truss attachment point will be equal to that obtained using the methods outlined in Sections 9.5.2, 9.5.3 and 9.5.4. Post shear and post bending

9-6



Using equation 9-2, the shears at the top, Vt, and bottom, Vb, of the windward post of frame 4 are:

moment can then be calculated using the following equations which assume zero bending moment at the top of the post. = kp ∆ – R i + s q (Hp – y)

Vy

Vt

(9-2)

= (91.9 lbf/in.)(0.655 in.) – 365.8 lbf + (10 ft)(8.13 psf) (12 ft – 12 ft)

My = (s q / 2)(Hp – y)2 + Vt (Hp – y) (9-3) Vt =

Mmax = - Vt2 / (2 s q)

Vb


Vb

= 670.0 lbf

where: Vy = kp = ∆ = Ri = = = s = q = Hp = y = My = Vt = Mmax =

–305.6 lbf

(9-4)

post shear at distance y from base, lbf (N) post stiffness, lbf/in. (N/mm) lateral movement of post top, in. (mm) contribution of wall pressure to eave load, lbf (N) RW for windward wall RL for leeward wall frame spacing wall pressure, lbf/ft2 (N/m2) post height, ft (m) distance from post base, ft (m) bending moment in post at distance y from base, lbf-ft (N-m) Vy at y = Hp, lbf (N) bending moment at y = Hp + Vt /(sq) (i.e., at the point of zero post shear)

and the shears at the top, Vt, and bottom, Vb, of the leeward post of frame 4 are: Vt


Vt =

–168.4 lbf

Vb


Vb

= 441.2 lbf

Equation 9-3 yields bending moments at the base of the windward and leeward posts of 26200 and 19640 lbf-in., respectively. The difference between these values and those in figure 9.3b are due to the rigid truss assumption.

Positive sign conventions for the preceding variables are illustrated in figure 9.5.

According to equation 9-4, bending moments at the point of zero shear in the windward and leeward posts are 6890 and 3350 lbf-in., respectively.

∆

9.6 Step 5: Check Allowable Values s xq

y

9.6.1 Diaphragm Shear. The actual maximum diaphragm shear stress of 93.1 lbf/ft (Section 9.5.6) is less than the allowable of 107 lbf/ft (table 9.3) so the diaphragm has sufficient strength.

Vy Hp

My Vy

9.6.2 Windward Post Stresses. Posts are subject to combined bending and compression and must be checked per the requirements of the 1997 NDS Section 3.9.2 and NDS equation 3.93. This equation, simplified for uniaxial bending is:

Figure 9.5. Positive sign convention for variables used in equations 9-2 and 9-3.

9-7


CSI

= ( fc / Fc’ )2 + f b / {Fb’ [ 1 – ( fc / FcE)]} < 1.0


(9-5)

CD =

where:

CM =

CSI fc fb Fc’

= = = = = Fb’ = = FcE = =

combined stress index actual compressive stress actual bending stress allowable compressive stress Fc •CD •CM •CF •Ci •CP allowable bending stress Fb •CD •CM •CF •Ci •CL•Cr •Cf •CV critical buckling design stress K E’ I / ( le / d )2

CF = Ci = CL = Cr =

and: Fc = Fb = CD = CM = CF = Ci = CP = CL = Cr = Cf = CV = E’ = I = le /d = K = =

tabulated compressive stress tabulated bending stress load duration factor wet service factor size factor incising factor column stability factor beam stability factor repetitive member factor form factor volume factor E •CM •Ci moment of inertia slenderness ratio 0.3 for visually graded lumber 0.384 for machine evaluated lumber

Cf = CV = CP =

CP =

It follows that at the base of both the windward and leeward posts: Fc’ = Fb’ = FcE =

Actual stresses for the windward post are: fc

= =

PW / A = 3821 lbf / (30.25 in.2) 126 lbf/in.2

fb = =

M / S = 26200 lbf-in. / (27.73 in.3) 945 lbf/in.2 (at the base)

fb = =

6890 lbf-in. / (27.73 in.3) 248 lbf/in.2 (at point of zero shear)

( 525 lbf/in.2)(1.60) = 840 lbf/in.2 ( 850 lbf/in.2)(1.60) = 1360 lbf/in.2 A very large number if the effective buckling length, le, is assumed to be very small because of support at the base. As a result, the ratio fc / FcE in equation 9-5 is assumed to equal zero.

and at the base of the windward post: CSI = ( 126 / 840 )2 + ( 945 / 1360 ) = 0.02 + 0.70 = 0.72 < 1.0 OK

For No. 2 Southern Pine timber, the tabulated compression and bending stresses and modulus of elasticity are: Fb = Fc = E =

1.60 since the shortest duration load in the combination of loads is wind 1.00 for modulus of elasticity, compression and bending of Southern Pine timber regardless of moisture content 1.00 for nominal 6- by 6-inch No.2 Southern Pine 1.00 since Southern Pine does not need to be incised for pressure treatments 1.00 since post is square 1.00 because post spacing exceeds 24 inches. Note that this value is non-zero for mechanically laminated posts 1.00 since posts are rectangular 1.00 since posts are not gluedlaminated 1.00 at the base of the post where support is provided in both directions is less than 1.00 at locations removed from supports that keep the post from buckling. For such cases, CP is calculated using NDS equation 3.7-1.

The other critical location to check the combined stress index (CSI) is at the point of maximum bending moment (point of zero shear) in the upper portion of the post. At this location, the column stability factor is generally based on an effective column buckling length of 0.8 Hp (see

850 lbf/in.2 525 lbf/in.2 1,200,000 lbf/in.2

Applicable adjustment factors are:

9-8



NDS Appendix G), which results in the following slenderness ratio:

The minimum embedment depth, d, is:

le / d = 0.8 (144 in.) / 5.5 in. = 20.9

d =

4.25 (2180 lbf-ft) (532 lbf/ft3) (0.64 ft)

d

3.00 ft < 4 ft OK

1/3

thus: FcE = =

2

0.3 (1200000 lbf/in. ) / (20.9) 820 lbf/in.2

9.6.4 Leeward Post Stresses. Because (1) the axial force and maximum bending moments associated with the leeward post are all less than those for the windward post, (2) the windward and leeward posts are similarly supported, and (3) the windward post is not overstressed, there is not need to check stresses in the leeward post.

The ratio of FcE / Fc is 0.976. This yields a Cp of 0.682, resulting in the following allowable compressive stress, Fc’. Fc’ = =

( 525 lbf/in.2)(1.60)(0.682) 573 lbf/in.2

9.6.5 Leeward Post Embedment. Unless the post-frame designer makes special provisions to tie the base of the leeward post to the floor slab, it will be non-constrained. Since this is a UBC jurisdiction, embedment depth will be checked using equation 8-6, which is given as follows:

The CSI at the point of maximum moment in the upper portion of the post is: CSI = ( 126 / 573 )2 + 248 / [1360 (1 - 126/820)] = 0.05 + 0.22 = 0.27 < 1.0 OK

d2 =

9.6.3 Windward Post Embedment. The windward post is constrained by the floor slab. Since our example building is in an UBC jurisdiction, embedment depth will be checked using equation 8-8 which is given as: 4.25 Ma S’ b

d=

1/3

(200 lbf / ft2 / ft)(1.33)(2) 532 lbf / ft2 / ft

The effective width of the post, b, is: =

d2 =

7.02(441 lbf) + 7.65(1640 lbf-ft)/d (532 lbf/ft3) (0.64 ft)

d

4.22 ft > 4 ft

=

At this point, the post-frame designer must apply engineering judgement. It is important to remember that the analogs in this example produce conservative values for base moments and shears, especially for the non-constrained case. The designer must also consider what is known about the soil type and its variability on the building site. If an embedment of 4 ft rather than 4.22 ft satisfies uplift requirements as calculated elsewhere (not included in this example) an experienced post-frame designer could validly judge that an embedment of 4 ft. is OK.

As previously calculated, the moment at grade is 26200 lbf-in or 2180 lbf-ft.

b

7.02 Va + 7.65 Ma / d S’ b

Solution of this equation is an iterative process. The values for S’ and b are as determined for the windward post. Leeward post base shear and bending moment where previously calculated as 441 lbf and 1640 lbf-ft, respectively

For this example, the soil is assumed to be a firm silty sand which puts it in class 4 (firm) of Table 8.1 – a soil with a tabulated lateral soil pressure of 200 lbf/ft per foot of depth. In accordance with the UBC, the tabulated lateral pressure can be adjusted for wind loading by a factor of 1.33. Since the posts are more than six diameters apart, the allowable lateral pressure can also be doubled for isolated conditions. Thus, the allowable lateral soil bearing pressure is: S' = =

=

2

(1.4)(5.5 in)/12 = 0.64 ft

9-9



9.7 Example Summary There are many items that the post-frame designer must still check. These include but are not limited to: • • • • • • • •

The interconnection between diaphragms and shearwalls Diaphragm chords Footings for gravity loads Uplift checks for embedded posts All secondary members and headers The connections of all members, especially truss to post End wall posts Diaphragms and shearwalls for wind against the endwall

This example has focused solely on those items that are unique to post-frame. The post-frame designer should be able to perform the remaining checks and designs using commonly accepted practices and techniques.

9-10

Post-Frame Building Design Manual

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