Diaphragm Design of Metal Clad Post Framed Buildings

5/24/2018 Diaphragm Design of Metal Clad Post Framed Buildings

1/11

ASAE EP484.1 DEC97

Diaphragm Design of Metal-Clad, Post-Frame RectangularBuildings

Developed by the ASAE Diaphragm Design of Metal-Clad, Post-FrameRectangular Buildings Subcommittee of the Structures Group; approvedby the Structures and Environment Division Standards Committee;

adopted by ASAE September 1989; revised December 1990; reaffirmedDecember 1994, December 1995, December 1996; reaffirmed for oneyear December 1997.

1 Purpose and scope1.1 This Engineering Practice standardizes the methods for testing andreporting the strength and stiffness of metal-clad, timber-framediaphragms and outlines engineering procedures for the diaphragmanalysis and design of metal-clad, post-frame rectangular buildings.

1.2 The provisions of this Engineering Practice are suitable for theanalysis and design of rectangular, metal-clad, post-frame buildingsusing roof and ceiling diaphragms, alone or in combination. Theprovisions are limited to the analysis of single-story buildings symmetricin design and construction with respect to the major axes of the building

and with endwalls sufficiently rigid to transfer roof shear loads to theground with negligible lateral deflection at the eave. The endwalls mayrequire supplemental reinforcement to replace lost strength and stiffnessdue to placement of doors and large openings in the endwalls.

2 Terminology (See Figs. 1, 2, 3, and 4)

2.1 Building diaphragm stiffness, ch: The stiffness of the entire roofdiaphragm assembly. The stiffness is obtained from test panel resultsand is adjusted for differences between the length of the test panel andthe roof diaphragm and for the slope of the roof.

2.2 Cantilever test: A load test arrangement for a diaphragm in whichthe diaphragm is supported along one edge and the shear load is appliedat a corner of the opposite edge and in the direction parallel to thedirection of the line of action of the supports (see Fig. 2).

2.3 Ceiling stiffness, cc: The stiffness of a horizontal diaphragmconsisting of the ceiling of the building.

2.4 Diaphragm: A structural assemblyincluding the timber framing(truss chords and purlins), metal cladding, fasteners and fasteningpatternscapable of transferring in-plane shear forces through thecladding and framing members.

2.5 Diaphragm design: The design of a post frame, including the rooftruss, sidewall posts, endwalls, shear connectors, chord splices andground anchorages, in which the diaphragm strength and diaphragm

stiffness are utilized to transfer applied horizontal loads to the ground.

Figure 1 Definition sketch for terminology

Figure 2 Cantilever test assembly

Figure 3 Simple beam test assembly

ASAE STANDARDS 1998 719


2/11

2.6 Diaphragm fastenings: The various fastenings and fasteningpatterns used to connect the several components of the diaphragm.These include the fastenings between the cladding and purlins, between

the diaphragm framing members, and between individual sheets ofcladding.

2.7 Diaphragm length, b: The test diaphragm dimension measured inthe direction of the corrugations.

2.8 Diaphragm shear stiffness, c: The shear stiffness, force per unitlateral in-plane displacement, of a diaphragm. It is defined as the slopeof the diaphragm load-shear displacement curve between zero load andthe load corresponding to the diaphragm design shear strength.

2.9 Diaphragm shear strength: The design shear strength (seeparagraph 3.3.6.2) of a diaphragm in the plane of the cladding.

2.10 Diaphragm width, a or 2a: The test diaphragm dimensionmeasured in the direction perpendicular to the corrugations.

2.11 Endwall diaphragm: The endwall of the building where theendwall cladding and framing are constructed so as to transfer in-plane

shear forces from the roof and/or ceiling diaphragm to the ground.

2.12 Frame stiffness, k:The horizontal stiffness to a load applied at theeave of the individual unclad post frames, including the truss, in each bayof the building.

2.13 Horizontal restraining force, R: The force applied at the leewardeave of the post frame to prevent translation due to design loads whendiaphragm action is not included.

2.14 Metal cladding: The metal exterior and interior coverings, usuallycold-formed aluminum or steel sheet, fastened to the timber framing.

2.15 Post frame: A structural frame consisting of a wood roof trussconnected to vertical timber columns.

2.16 Shear fastenings: The fastenings and fastening patterns used totransfer the shear forces between sheets of cladding, between thecladding and frame, and between roof or ceiling cladding to endwall orshearwall diaphragms.

2.17 Shear transfer: The transfer of the resultant shear forces betweenindividual sheets of cladding, between the edges of roof diaphragms andthe top of the endwalls, between the edges of ceiling diaphragms and theendwalls, or between the bottom of the endwall diaphragms and theground.

2.18 Shear wall: A vertical diaphragm in a structural framing system.The wall may be an endwall or an intermediate wall. In either case, thewall transfers shear forces from the roof or ceiling diaphragm to thegroundline.

2.19 Simple beam test: A load test arrangement for a diaphragm inwhich the diaphragm is loaded as a deep beam. Both ends of thediaphragm are supported to resist in-plane shear and one end issupported to resist perpendicular-to-plane movement. A singleconcentrated load is applied in the direction of the truss chords atmidspan (see Fig. 3).

2.20 Tension fastenings: The fastenings required to transfer theresultant tensile forces in the flanges of deep beam diaphragms at pointswhere the flange members are spliced. In a roof diaphragm, the flangemembers are the edge purlins at the eave and ridge.

2.21 Test diaphragm: A diaphragm model of sufficient size to simulatethe behavior of the diaphragm in the building. Except for overall size, the

test diaphragm construction is functionally equivalent (see paragraph 3.1)to the building diaphragm and is supported in a manner similar to thatencountered in the building application.

3 Diaphragm strength and stiffness3.1 General provisions. This section outlines methods for determiningdiaphragm strength and stiffness for post-frame buildings. Unlessotherwise noted, this Engineering Practice assumes that the testdiaphragm construction is functionally equivalent to that used in thebuilding being designed. This requires that post spacing, purlin spacingand orientation, cladding type, cladding profile, cladding thickness,fastening type and pattern, and support patterns for both the claddingand diaphragm framing each be identical. Functional equivalence also

requires that the specific gravity and Group Number of both the purlinsand the chords used in the test diaphragm be equal to or greater than thespecific gravity and Group Number of the species used in the buildingconstruction. Group Number is defined by the National Forest ProductsAssociation Standard, National Design Specification for WoodConstruction, Table 8.1A (NDS, 1986).

3.2 Diaphragm tests.The shear strength and stiffness of wall, roof andceiling diaphragms are to be determined by shearing tests of diaphragmsor by other acceptable analysis methods. Testing may be accomplishedby either the cantilever test (see Fig. 2) or the simple beam test (see Fig.3).

3.2.1 Test apparatus

3.2.1.1 General. The test diaphragm shall meet all the functionalequivalence provisions of paragraph 3.1.

3.2.1.2 Frame size.The length,b, of the test frame shall not exceed thediaphragm length used in design. The width, a or 2 a, of the test frameshall not be less than the overall width of three sheets of cladding ineither the cantilever or simple beam test procedures. The frame width,a, shall also not be less than the width of one building bay (the distancebetween post frames) for the cantilever test or two bays for the simplebeam test.

3.2.1.3 Frame material requirements. The moisture content of allframing members shall be below 19% when the test section is fabricatedand shall not vary by more than 3% from the initial moisture contentwhen the section is tested. A specific gravity test per ASTM StandardD143-83, Method of Testing Small Clear Specimens of Timber, shall beconducted and recorded on all framing members immediately after thetest is completed.

3.2.1.4 Purlin and chord size and spacing. All test frames shall beconstructed with purlin size and spacing equal to those used in thebuilding design. Test frame chords shall have the same thickness andspacing as the chords in the building and shall have sufficient depth toaccommodate full penetration of all purlin to chord fasteners.

3.2.1.5 Support placement

3.2.1.5.1 Cantilever test (see Fig. 2). For the cantilever test, the frame

shall be supported at corner C(see Fig. 2) with a pinned connection toallow transfer of the horizontal forces into the supports. Frame corner

G (see Fig. 2) shall be supported with a roller type connection. Side

Figure 4 Diaphragm test results

720 ASAE STANDARDS 1998


3/11

DE shall be supported vertically by a series of rollers (for horizontalframe testing). A restraining force may be necessary to resist out-of-plane movement at corner E.

3.2.1.5.2 Simple beam test. For the simple beam test, the frame shallbe supported at corner G (see Fig. 3) with a pinned connection and atcorner Ewith a roller type connection. In addition, line HJ shall besupported in a manner similar to the supports along line DE in thecantilever test procedure. Restraining forces may be necessary to resistout-of-plane movement at corners C and E.

3.2.1.6 Loading and instrumentation

3.2.1.6.1 Calibration and accuracy. Loading equipment and

measurement devices shall be calibrated and verified in accordance withASTM Standard E4-83a, Practices for Load Verification of TestingMachines. All deflection and load measurement gages shall have anaccuracy within 2% of the respective design values.

3.2.1.6.2 Load application. Loading shall be applied parallel to and inthe plane of contact between the diaphragm and the frame. The methodof loading and relevant equipment shall accommodate a loading schemein which loads are continuously measured, and are applied in equalincrements from zero to failure. Proper load locations are illustrated inFigs. 2 and 3.

3.2.1.6.3 Deflection measurement.Deflections shall be recorded to thenearest 0.02 mm (0.001 in.). Deflection measurements shall be takensuch that the relative movement of the adjacent rafters is measured.Proper gage locations (numbered) are illustrated in Figs. 2 and 3.

3.2.2 Test procedures3.2.2.1 Number of tests and failure strength criteria. A minimum ofthree replications of each test diaphragm configuration shall be tested.Each replication requires construction of a new test frame. Evaluation oftest strength results shall be made based on the minimum failure valueof the three tests. Design stiffness shall be based on the average of thethree tests. The design failure value shall be based on the lower 33rdpercentile estimate according to the nonparametric point estimate, NPE,method described in ASTM Standard D2915-84, Method for EvaluatingAllowable Properties for Grades of Structural Lumber, (see paragraph4.5.4).

3.2.2.2 Loading procedure.The test diaphragm shall be loaded as perASTM Standard E564-76, Method for Static Load Test for ShearResistance of Framed Walls for Buildings; ASTM Standard E72-80,Method for Conducting Strength Tests of Panels for Building

Construction; and ASTM Standard E455-76(1984), Method for StaticLoad Testing of Framed Floor or Roof Diaphragm Constructions forBuildings.

3.2.2.2.1 Method of load application. (See ASTM Standard E72-80,Method for Conducting Strength Tests of Panels for BuildingConstruction) Load and unload the test diaphragm in three stages to 3.5,7.0, and 10.5 kN (800, 1600, and 2400 lbf) total load at a uniform rate.To provide data to meet performance requirements, other values of totalload may be included in the test procedure. Use the same rate of loadingfor all tests and report all results. At least 10 sets of uniformly-spaceddeflection readings shall be taken prior to failure to establish the load-deformation curve.

3.2.2.2.2 Load rate. Load rate should be applied continuouslythroughout the test at a uniform rate of motion of the loading deviceused. The rate of loading shall be such that the loading to 3.5 kN (800lbf) total load shall be completed in not less than two minutes from thestart of the test. Loading to 7.0 and to 10.5 kN (1600 and 2400 lbf) totalload and to failure shall occur at the same loading rate. The rate of theloading shall be such that that the anticipated full design load level will bereached in not less than 10 minutes.

3.2.2.2.3 Subsequent load cycles. (See ASTM Standard E72-80,Method for Conducting Strength Tests of Panels for BuildingConstruction) After the load of 3.5 kN (800 lbf) is placed on thespecimen, immediately remove all of the load at the same rate as loadingcommenced, wait five minutes and note any residual deflection (set) in

the diaphragm. Reload the specimen to 7.0 kN (1600 lbf) and againremove the load, wait five minutes and note any additional set. Reloadthe specimen to 10.5 kN (2400 lbf), remove the load, wait five minutesand note the set. Apply load continuously for each of the increment loadsspecified above and obtain load-deflection data. Obtain these data for atleast each 900 N (200 lbf) of loading. Obtain deflections during theloading and the unloading portion of the cycle.

3.2.2.2.4 Final load cycle. (See ASTM Standard E72-80, Method forConducting Strength Tests of Panels for Building Construction) After thespecimen is loaded as specified to 3.5, 7.0 and 10.5 kN (800, 1600 and2400 lbf), load it again to failure or until the adjusted deflection of the

diaphragm at pointEfor cantilever tests or point Jfor simple beam tests

equalsa/24 in cantilever test panels or 2 a/48 in deep beam test panels.Obtain readings of deflection for the same intervals of load as were usedfor the other loadings. In the event of test diaphragm failure before thefourth load cycle, use the results of the completed load cycles forevaluation of diaphragm strength and stiffness.

3.2.2.3 Failure definition. The ultimate failure load will be defined bythe serviceability limit. That is, any permanent failure of the cladding,framing or fastenings which would be objectionable based onappearance or performance.

3.3 Diaphragm test reports.The following information shall be reportedfor each diaphragm test panel. The report shall be sufficient to allow forthe incorporation of the test results into building design. See Fig. 4 for asample data sheet. The items noted with an asterisk are desirable but notrequired for design; they are required for research and theoreticalapplications.

3.3.1 General information. Sufficient information shall be provided touniquely identify each diaphragm tested, including:

3.3.1.1 Laboratory investigator. The laboratory and principalinvestigator shall be identified.

3.3.1.2 Test ID. An identifying number which uniquely references onetest replication.

3.3.1.3 Date of test. Date when the test was performed.

3.3.2 Test diaphragm configurations. The overall diaphragmconfiguration must be identified with the following information:

3.3.2.1 Length, b. Distance measured parallel to the sheets. Fordiaphragms utilizing a single-length sheet, this would be the sheet lengthunless the end fasteners are located more than 75 mm (3 in.) from theends of the sheets. The length is measured from the centerline of the

end fasteners when fasteners are more than 75 mm (3 in.) from the endsof the sheets.

3.3.2.2 Width, a or 2a. Distance measured perpendicular to the lengthof the sheets. The width is measured from the centerline of the outsideframing members.

3.3.2.3 Loading configuration.A sketch of the test configuration shallbe provided. Support types and locations, deflection measurementlocations, and load application locations shall be identified.

3.3.3 Lumber properties. For each framing component used toconstruct the test assembly (i.e., purlins, rafters, etc.), provide thefollowing information:

3.3.3.1 Number. Total number of pieces used in the test assembly.

3.3.3.2 Nominal size. Nominal order-entry size of the wood member.

3.3.3.3 Grade and species. The grade and species of lumber used.

3.3.3.4 Stiffness. The modulus of elasticity of each edge purlin pieceshall be measured prior to test panel fabrication. If a test machine isavailable, the method of ASTM Standard D198-84, Method for StaticTests of Timbers in Structural Sizes, using a continuous load-deflectiontrace is recommended. Alternately a flatwise measurement using twocenter-point deadweights can be used (Percival, 1981).

3.3.3.4.1 Span for flatwise E measurement.A recommended distancebetween supports is the diaphragm width, a, for the cantilever test butnot greater than 3.0 m (10 ft). For the simple beam tests, more than two



4/11

boards may be used as edge purlins. If only one board is used per edge,use a distance between supports of the test diaphragm width, 2 a, butnot greater than 3.0 m (10 ft). If two boards are used to form one edge(because of lapping or recessing purlins between truss chords) therecommended span is the truss spacing, a, but not greater than 3.0 m(10 ft).

3.3.3.5 Specific gravity. Specific gravity for each member shall bedetermined in accordance with ASTM Standard D143-83, Method ofTesting Small Clear Specimens of Timber. The average and range ofspecific gravity shall be reported for each assembly.

3.3.4 Metal cladding.The following information shall be reported for themetal cladding used in the test assembly:

3.3.4.1 Manufacturer.The name of the manufacturer of the cladding.

3.3.4.2 Profile. The commercial name of the profile which will uniquelyidentify the profile configuration.

3.3.4.3 Base metal. The type of metal used to form the panel (i.e.,aluminum, steel).

3.3.4.4 Grade or alloy. The specific grade or alloy of metal used (i.e.,Grade E Steel, 3004-H37 Aluminum).

3.3.4.5 Yield strength. The measured yield strength of the materialbeing used, or the yield strength from manufacturers data.

3.3.4.6 Thickness. The base metal thickness as reported by themanufacturer.

3.3.4.7 Section modulus.The elastic section modulus per unit width ofcladding based on the full section.

3.3.4.8 g/p ratio. The ratio of the total flat width of metal used to formone complete repeating corrugation to the pitch of the corrugation.

3.3.4.9 Profile dimensions. A sketch which includes all profiledimensions.

3.3.5 Fastenings. For each type of fastening used to construct theassembly, report the following (The items with an asterisk are desired butoptional):

3.3.5.1 Manufacturer.The name and address of the manufacturer ofthe fastenings.

3.3.5.2 Type. The brand name of each fastening and its general type(i.e., screw, nail, etc.).

3.3.5.3 Diameter.The shank diameter of the fastening.

3.3.5.4 Length. The nominal length of the fastening.

3.3.5.5 Thread spacing*. The spacing of threads for all screw typefastenings.

3.3.5.6 Washer type and size. The type washer (i.e., flat, domed, etc.)and the outside diameter.

3.3.5.7 Base metal*.The type metal used to form the shank part of thefastening.

3.3.5.8 Shear strength*. The tested ultimate shear strength of thefastening using a single-lap shear test in accordance with ASTMStandard D1761-77, Method of Testing Mechanical Fasteners in Wood.

3.3.5.9 Shear stiffness*. The tested shear stiffness of the fasteningusing a single-lap shear test in accordance with ASTM Standard D1761-77, Method of Testing Mechanical Fasteners in Wood.

3.3.6 Results. Report the following test results consistent with the

procedure outlined in paragraph 3.2 of this Engineering Practice:3.3.6.1 The load-deflection curves for each of the assemblies tested,indicating the scale.

3.3.6.1.1 Cantilever test. The ultimate strength, Pul t, equals themagnitude of the applied load at failure.

3.3.6.1.2 Simple beam test. The ultimate strength, Pul t , equals onehalf of the resultant of the applied load at failure.

3.3.6.2 Design shear strength. The long-term design shear strengthequals 0.4Pul t/LDF if the failure was initiated by lumber breakage or byfailure of the fastenings in the wood; otherwise design shear strength

equals 0.4 Pul t . The load duration factor, LDF, may conservatively betaken as 1.6 or be determined for actual test duration from NDS (1986).Shear strength per unit length may be reported as the design shear

strength divided by the diaphragm length, b.

3.3.6.3 Test diaphragm shear stiffness, c.

3.3.6.3.1 Cantilever test.The shear stiffness, c, for a test diaphragm isbased on the relatively linear portion of the load-deflection curve below0.4Pul t in accordance with the formula

cP

Ds

a

b

(1)

where

P 0.4 Pul tDs shear deflection of test diaphragm at 0.4 Pul ta/b aspect ratio of the frame shown in Fig. 2

3.3.6.3.1.1 The shear deflection,Ds, for the cantilever test diaphragm is

obtained from the deflection measurementsD1 , D2 , D3 , andD4 in Fig.2 and the following equations

DS DTDbDT D3D1a/bD2D4

Db Pa3/3EpIp (2)

EpIp EffectiveE Iof the panels contributed by the edge purlins. (Themoment of inertia contribution of the purlins about their own axes isneglected.) The following equation is recommended

EpIpby2A 1E1y

2A2E2 (3)

where

A1 ,A2 average area for each edge purlinE1 ,E2 average modulus of elasticity for each edge purlinb center to center distance between edge purlins

y bE1A 1/A 1E1A2E2

3.3.6.3.2 Simple beam test.The shear stiffness,c, for a test diaphragmis based on the relatively linear portion of the total load-midspandeflection curve below 0.4Pul t in accordance with the formula

c1

2

P

Ds

a

b (4)

where

P 0.4 Pul tDs shear deflection of test diaphragm at 0.4 Pul t

a/b aspect ratio of the frame shown in Fig. 33.3.6.3.2.1 The shear deflection, Ds, for the simple beam testdiaphragm is obtained from the deflection measurements D2 , D3 , andD4 in Fig. 3 and the following equations

DsDTDb

DT D21/2D3D4Db Pa

3/6EpIp (5)

3.4 Building diaphragm stiffness, ch.



5/11

3.4.1 Definition. The building diaphragm shear stiffness is defined bythe following equation

ChCcos2 b/a (6)

where

b/a aspect ratio of the roof diaphragm

roof slopeC test panel stiffness adjusted for diaphragm length

per equation 7

3.4.2 Diaphragm length adjustment. Shear stiffness, c, for a given

length test diaphragm may be corrected to shear stiffness, C

, for roofdiaphragms of different length by the following equation

CEt

21vg/pK2/bt2

(7)

where

E modulus of elasticity of cladding cladding thickness

cladding Poissons ratiog/p see paragraph 3.3.4.8b diaphragm length between end fastening along one

slope measured parallel to the corrugationsK2 constant for a given panel design

3.4.2.1 The constantK2 is determined by substituting the shear stiffnessof the test diaphragm calculated from equation 1 or 4 and otherdiaphragm geometric and material design values into equation 7.

3.4.2.2 Equation 7 is applicable for diaphragm lengths up to 1.5 timesthe length of the test diaphragm (see Section 5Commentary).

3.4.3 When full-size diaphragm stiffness test results are available, Cc.

4 Design procedures4.1 Diaphragm analysis of the building shall be performed in accordancewith the provisions of this section or by other acceptable structuralanalysis methods.

4.2 Assumptions

4.2.1 The stiffness, ch and/or cc , of the diaphragm is known.4.2.2 Uniform spacing and stiffness of frames.

4.2.3 Uniform roof stiffness.

4.2.4 Endwalls sufficiently rigid for negligible lateral shear and momentdisplacement at the eave under design loads.

4.2.5 The diaphragm length equals the length of one roof slope.

4.2.6 The building is rectangular and may have a flat or sloped roof thatconforms to the geometry illustrated in Figs. 1 and 5.

4.3 Calculation procedures for buildings without ceilings

4.3.1 Horizontal stiffness of the frame, k. A horizontal force, P, isapplied at the eave node of the post frame as shown in Fig. 6. The framestiffness is defined as the ratio of the applied force to the lateraldisplacement of the node,k P/.

4.3.2 Horizontal restraining force at the eave line, R. A horizontalrestraint (vertical roller) is placed at the eave line as shown in Fig. 7 andthe structural analog is analyzed with all external loads in place. Therestraining force,R, is the force required to prevent horizontal deflectionat the eave.

4.3.2.1 Design loads should be determined from approved standards orengineering practices.

4.3.2.2 Diaphragms help transfer only in-plane loads to endwalls.

4.3.3 Roof stiffness, ch. The roof stiffness is determined by themethods presented in Section 3Diaphragm strength and stiffness.

4.3.4 Stiffness ratio, k/ch. Calculate the ratio of the frame to roofstiffness.

4.3.5 Sidesway force modifier, mD. The sidesway force modifier is

calculated from the principles of compatibility of the lateral displacementof the frame and roof cladding at the eave line. Alternately, m D values

for a range of k/chvalues and number of frames between endwalls aregiven in Table 1. The number of frames include the framed endwalls.

4.3.5.1 As m Dapproaches 1.0, more load is carried by the diaphragm

to the endwalls. As m Dapproaches zero, more load is resisted by thepost frames. An mD value of zero is equivalent to a simple sideswayproblem. Anm Dvalue of 1.0 corresponds to zero sidesway movementat the eave.

4.3.6 Cladding shear force modifier, mS. The shear force modifier,mS, is calculated from the mDvalues. Alternately, mS values for arange ofk/chvalues and number of frames between endwalls are givenin Table 2. The number of frames include the framed endwalls.

4.3.7 Roof diaphragm sidesway resistance force, Q. This force is

calculated by multiplying the horizontal restraining force, R, at the eaveline by m D(see paragraph 4.3.2).

Figure 5 Definition sketch of rectangular, metal-clad, post-frame building

Figure 6 Definition sketch for frame stiffness, k



6/11

4.3.8 Shear force in roof cladding. The horizontal component of themaximum shear force, Vh, in the roof cladding is calculated bymultiplying the horizontal restraining force, R, at the eave line by mS(see paragraph 4.3.2).

4.3.8.1 The maximum shear force, V, in the cladding equals

Vh/cos

.4.3.8.2 The maximum shear force,V, in roof cladding must be less thanor equal to the design shear strength of the diaphragm. The design shearstrength, as defined in paragraph 3.3.6.2, may be increased by 33% byprovisions of most model building codes.

4.3.8.3 The largest shear value of the roof cladding occurs in the baynext to the framed endwalls.

4.3.9 Analysis of the post-frame building including roof diaphragmaction. Roof diaphragm action is included by applying the roofdiaphragm sidesway resistance force, Q, (see paragraph 4.3.7)distributed as a horizontal uniform load along the top chords of the trussin the direction of Ras illustrated in Fig. 8. The distributed force, q, inforce per unit length along the member, equals Qdivided by the lengthof both slopes of the roof diaphragm.

4.3.9.1 The critical frame on a building with symmetric shear walls isalways the one at or closest to the building midlength.

4.3.9.2 Appropriate changes in the post-frame design, including membersizes, stress grades, and frame geometry, are made until all limitingfactors for design are satisfied. Post strength, post-horizontal shear,shear force in roof cladding, truss-web buckling about the weak axis,bottom-chord lateral stability, strength and embedment of endwalls, etc.,can be limiting and critical factors in design.

4.4 General calculation procedure for buildings with ceilings

4.4.1 The analysis of a post-frame with both ceiling and roof diaphragmsis accomplished from the principles of compatibility of the horizontaldisplacements of the frame, roof and ceiling diaphragms at the eave line.

4.4.2 Horizontal stiffness of the frame and horizontal restrainingforce. The horizontal stiffness of the frame, k, and the horizontal

restraining force,R, at the eave line are calculated per paragraphs 4.3.1and 4.3.2 for buildings without ceilings.

4.4.3 Ceiling stiffness, cc. Determined by the methods presented inSection 3Diaphragm Strength and Stiffness.

4.4.4 Ceiling and roof stiffness ratio, k/cT. Calculate the ratio of theframe stiffness to the sum of the stiffnesses of the ceiling, cc , and roof,cr.

cTcrcc

4.4.5 Modifiers, mD and mS. Use Tables 1 and 2 to select thesidesway force modifier,m D, and the shear force modifier, m S, basedon the k/cT ratio (see paragraph 4.4.4), and the number of framesbetween the endwalls of the building. The number of frames includes theframed endwalls.

4.4.6 Combined ceiling and roof diaphragm sidesway resistance

force, QT. This force is calculated by multiplying the horizontalrestraining force,R, at the eave line (see paragraph 4.3.2) by m D (seeparagraph 4.4.5).

4.4.7 Combined shear force in ceiling and roof diaphragms,VT. This

force is calculated by multiplying the horizontal restraining force, R, at

the eave line (see paragraph 4.3.2) by m S(see paragraph 4.4.5).4.4.7.1 Roof and ceiling diaphragm sidesway resistance forces, Qand Qc. These forces are calculated by multiplying the combinedresistance force, QT , by the ratio of stiffness of each diaphragm to thesum of stiffnesses of the roof, cr , and ceiling, cc , diaphragms, as

QcrcT

QT..... .... ..... .... ..for roof diaphragmand

QccccT QT .......................for ceiling diaphragm4.4.7.2 Shear forces in the roof and ceiling diaphragms, V andVc. These forces are similarly calculated as

VcrcT

VT...... .... ..... ..... ...for roof diaphragmand

VccccT VT .......................for ceiling diaphragm4.4.8 Analysis of post-frame building including roof and ceilingdiaphragm actions.Roof and ceiling diaphragm actions are included byapplying the roof diaphragm sidesway resistance force (see paragraph4.3.7), Q, distributed as a horizontal uniform load, q, along the topchords of the truss, and the ceiling diaphragm sidesway resistance force(see paragraph 4.4.6), Qc, distributed as a horizontal uniform load,

qc , along the bottom chord of the truss, respectively. These forces areillustrated in Fig. 9 and are applied in the direction of restraining force,R. The vertical roller introduced in paragraph 4.3.2 is removed at thisstep.

4.4.8.1 Check all limiting and critical factors in design as described inparagraph 4.3.9.2.

4.5 Shear transfer. Shear forces must be transferred through theindividual sheets of the diaphragm, through the connectors, through theconnections between the roof and ceiling diaphragms to the endwalls,and through the endwall diaphragm to the groundline in order to developdiaphragm action. These forces are illustrated in Fig. 11.

4.5.1 Roof diaphragm. The roof diaphragm allowable shear strengthmust be equal to or greater than the shear force, V, calculated inparagraph 4.3.8. (see Fig. 5).

4.5.2 Roof diaphragm-endwall connection. The fastenings betweenthe roof diaphragm and the endwall must be designed to transfer theshear force, V, calculated in paragraph 4.3.8 (see Fig. 5).

4.5.3 Ceiling diaphragm. The ceiling diaphragm allowable shearstrength must be equal to or greater than the shear force, Vc.

4.5.4 Ceiling diaphragm-endwall connections. The fasteningsbetween the ceiling diaphragm and the endwall must be designed totransfer the shear force, Vc, calculated in paragraph 4.4.7 (see Fig. 5).

4.5.5 Endwall diaphragm. The endwall diaphragm allowable shearstrength, must be equal to or greater than the sum of the horizontal

Figure 7 Definition sketch for horizontal restraining force at the eave



7/11


8/11


9/11

components of the diaphragm shear forces. The strength of the endwalldiaphragm is determined by the methods outlined in Section 3Diaphragm strength and stiffness.

4.5.5.1 The endwall diaphragm is only effective where the shear forcescan be transmitted to the base of the endwall columns and foundations.Therefore, a portion of the endwall shear may need to be transferred to

the column bases by other means (such as bracing) if the sum of thehorizontal components of the roof and ceiling shear forces, Vh Vc,exceeds the allowable shear strength of the endwall diaphragm.

4.5.5.2 The endwall post embedments must be able to resist the

overturning moment produced by the shear forces, Vand Vc(see Fig. 5).

4.6 Tensile force transfer. The flanges of the roof (edge purlins in Fig.1) and ceiling diaphragms must be designed to transfer the tensile force,T, developed from deep beam action (see Figs. 10 and 11).

4.6.1 Both flanges of a ceiling or roof diaphragm must be designed totransmit or transfer a tensile force, T, per the equation

TWL B2/8d (8)

where

LB

the building lengthddiaphragm length

Wdefined in paragraphs 4.6.1.1 and 4.6.1.2

4.6.1.1 In roof diaphragms, W is defined as 2 times the endwall shearforce, V, calculated in paragraph 4.3.8 divided by the building length,

LB, between endwalls or between endwalls and intermediate shearwalls.

4.6.1.2 In ceiling diaphragms,Wis defined as 2 times the endwall shearforce, Vc , calculated in paragraph 4.4.7 divided by the building length,

LB, between endwalls or between endwalls and intermediate shearwalls.

5 Commentary5.1 Commentary for Section 1Purpose and scope

5.1.1 This Engineering Practice is limited to the diaphragm analysis anddesign of rectangular, metal-clad, post-frame buildings. The proceduresare applicable to buildings with or without a ceiling diaphragm. Theendwalls are assumed to be nearly rigid endwalls; that is, their sway isnegligible under design loads. The endwalls must have adequate

Figure 8 Structural analog for a building with a roof diaphragm

Figure 9 Structural analog for a building with both a roof and a ceilingdiaphragm

Figure 10 Deep beam diaphragm schematic

Figure 11 Diaphragm metal roof/endwall wind bracing system for a rect-angular post frame building



10/11

strength and stiffness to transmit all the endwall shear forces from theroof and ceiling diaphragms to the ground with negligible sway.

5.2 Commentary for Section 3Diaphragm strength and stiffness

5.2.1 The test methods for determining the strength and stiffness ofdiaphragms are based primarily upon published ASTM Standards.Cantilever or simple beam (deep beam) test procedures can be used.The test diaphragm construction needs to be functionally equivalent tothe construction used in the building design in order to apply testdiaphragm results to the structural design of the buildings. Supportspacing should be the same as the post-frame spacing in the building.The diaphragm stiffness needs to be adjusted for roof slope, , and fordiaphragm length, b, by using the equations of Luttrell (1967). Equation7 in paragraph 3.4.2 has only been verified successfully for a 1.8 m (6 ft)difference in diaphragm length. However, it is believed that this equationcan with sufficient accuracy predict diaphragm stiffness for a 100%increase in diaphragm length over the test diaphragm. In cases where allfunctional equivalency requirements are met except the diaphragmlength exceeds 2.0 times the test diaphragm length, the followinganalysis procedure is suggested. For design of the building frame (postsand trusses), use the stiffness obtained by equation in paragraph 3.4.2for a diaphragm length of 2 times the test diaphragm length. For designof the roof, use the stiffness obtained from this equation for the actualslope length of the roof diaphragm. The former stiffness results in aconservatively designed frame; the latter stiffness results in aconservatively designed roof panel. Not following this two-step proceduremay result in an underdesigned frame or roof panel.

5.2.1.1 More research is required before this two-step analysisprocedure can be simplified for roof diaphragms more than 2.0 times thetest panel length. It has been demonstrated by Lukens and Bundy (1987)and can be shown by rational application of Davies and Bryansanalytical methods (Davies and Bryan, 1982) that the equation inparagraph 3.4.2 overestimates diaphragm stiffness when extendedbeyond 1.5 times the test panel length. Thus, the actual stiffness liessomewhere between the two stiffnesses defined in the previousparagraph.

5.2.2 Typical diaphragm strengths and stiffnesses are not included inthis Engineering Practice. Typical values may be found in numerouspublished articles on the subject. (Anderson, 1987; Conway and White,1979; Gebremedhin and Irish, 1984, 1986; Hausman and Esmay, 1975;Hoagland, 1981; Hoagland and Bundy, 1983; Lukens and Bundy, 1987;Turnbull, 1981; Turnbullet al., 1982; Whiteet al., 1977; White and Tocci,1978). Since diaphragm construction details will undoubtedly vary fromthose of the diaphragms in the literature, panel tests will likely have to beperformed in most instances. Other acceptable engineering analysismethods for predicting diaphragm strength and stiffness may be used inlieu of the provisions of Section 3Diaphragm strength and stiffness.Acceptable methods are those which have been documented by testingand peer review.

5.3 Commentary for Section 4Design procedures

5.3.1 The procedures outlined for structural analysis of a metal-clad,timber-framed diaphragm are based on the methods developed byGebremedhin et al. (1986). The post-frame structural analyses requiredare all statically indeterminate and are best performed with a computerprogram. The SOLVER and METCLAD programs developed byGebremedhin (1987a, 1987b) and PPSA III developed by the PurdueResearch Foundation (1986) are especially useful for analysis of the

timber post frames. Other acceptable structural analysis methods may beused in lieu of the provisions of Section 4Design Procedures.Acceptable methods are those which have been adequately validatedand peer-reviewed.

5.3.2 The need for adequate shear and tensile force transfer to developdiaphragm behavior is addressed in a general manner only. Thelocations and magnitudes of these forces are identified. Constructiondetails for transferring the forces are not included. The uniform loadshown in Fig. 10 is a good approximation for calculating the diaphragmmoment and chord tensile force if the wall cladding transfers the loaddirectly to the edge of the diaphragm or if the building is long and load

is transferred via posts. For short buildings point loads should replace thedistributed load for moment and chord tensile force calculations.

5.3.3 There are two potential computational difficulties associated withthe distributed loads, q and qc, in SOLVER and PPSA III. Thedistributed load q, as computed in paragraph 4.3.9, is the load per unitslope length. Many structural analysis programs are formatted such thatdistributed loads are inputted in load per unit horizontal and unit verticalprojected lengths. The distributed load, q, is converted to load per

vertical projected length on each slope by q* (slope length/verticalprojected length of the slope). The distributed load, qc , as computed inparagraph 4.4.8, cannot be defined as a distributed load in computerprograms formatted for distributed loads on the horizontal and verticalprojected lengths of a member (the vertical projected length of thehorizontal chord is zero). An alternative is to divide qc into a series ofconcentrated shear loads along the length of the lower chord of the truss.

References:

1. AISI. 1986. Cold formed steel design manual. American Iron and Steel Insti-tute, Washington, DC.

2. Anderson, G. A. 1987. Evaluation of light-gauge metal diaphragm behaviorand the diaphragms interaction with the post. M.S. Thesis. Iowa State Univer-sity.

3. Davies, J. M. and E. R. Bryan. 1982. Manual of stressed skin diaphragmdesign. John Wiley and Sons, New York, NY.

4. Gebremedhin, K. G. and W. W. Irish. 1984. An experimental investigation ofdiaphragm behavior of farm buildings. ASAE Paper No. 84-4511. ASAE, St.

Joseph, MI 49085.5. Gebremedhin, K. G., E. L. Bahler and S. R. Humphreys. 1986. A modifiedapproach to post-frame design using diaphragm theory. TRANSACTIONS ofthe ASAE 29(5):13641372.

6. Gebremedhin, K. G. and W. W. Irish. 1986. Ultimate load-deflection charac-teristics and failure modes of ceiling diaphragms for farm buildings. Wood andFiber Science 18(4):565578.

7. Gebremedhin, K. G. 1987a. SOLVER: An interactive structures analyzer formicrocomputers. (Version 2). Northeast Regional Agricultural EngineeringService. Cornell University.

8. Gebremedhin, K. G. 1987b. METCLAD: Diaphragm design of metal-clad post-frame buildings using microcomputers. Northeast Regional Agricultural Engi-neering Service. Cornell University.

9. Hausmann, C. T. and M. L. Esmay. 1975. Pole barn wind resistance designusing diaphragm action. ASAE Paper No. 75-4035. ASAE, St. Joseph, MI49085.

10. Hoagland, R. C. 1981. Strength and stiffness of screw-fastened roof panels

for pole buildings. M.S. Thesis. Iowa State University.11. Hoagland, R. C. and D. S. Bundy. 1983. Strength and stiffness of screw-fastened roof panels for pole buildings. TRANSACTIONS of the ASAE26(2):512-515.

12. Lukens, A. D. and D. S. Bundy 1987. Strengths and stiffnesses of post-framebuilding roof panels. ASAE Paper No. 87-4056. ASAE, St. Joseph, MI 49085.

13. Luttrell, L. D. 1967. Strength and behavior of light-gage steel sheardiaphragms. Cornell Engineering Research Bulletin 67-1, 41p.

14. NDS. 1986. National design specification for wood construction. NationalForest Products Association, Washington, DC, 87p.

15. Percival, D. H. 1982. Portable E-tester for selecting structural componentlumber. Forest Products Journal 31(2):3942.

16. Purdue Research Foundation. 1986. Purdue plane structures analyzer.(Version 3.0). Department of Forestry and Natural Resources. Purdue Univer-sity.

17. Turnbull, J. E. 1981. A summary of Canada plan service diaphragm design forwind bracing in farm buildings. ASAE Paper No. 81-4505. ASAE, St. Joseph,

MI 49085.18. Turnbull, J. E., K. C. McMartin and A. T. Quaile. 1982. Structural performanceof plywood and steel ceiling diaphragms. Canadian Agricultural Engineer24(2):135140.

19. White, R. N., C. Warshaw and J. Hart. 1977. Shear strength and stiffness ofaluminum diaphragms in timber-framed buildings. Research Report No. 370.Department of Structural Engineering. Cornell University.

20. White, R. N. and A. Tocci. 1978. Diaphragm action in aluminum-clad timberframing systems. Research Report No. 78-3. Department of Structural Engi-neering. Cornell University.



11/11

Cited Standards:

ASTM D143-83, Standard Method of Testing Small Clear Specimens ofTimber

ASTM D198-84, Standard Methods of Static Tests of Timbers in Struc-

tural Sizes

ASTM D1761-77, Standard Method of Testing Mechanical Fasteners in

Wood

ASTM E2915-84, Standard Method for Evaluating Allowable Properties

for Grades of Structural Lumber

ASTM E4-83a, Practices for Load Verification of Testing Machines

ASTM E72-80, Standard Method for Conducting Strength Tests of

Panels for Building Construction

ASTM E455-76(1984), Static Load Testing of Framed Floor or Roof

Diaphragm Construction for Buildings

ASTM E564-76, Standard Method of Static Load Test for Shear Resis-

tance of Framed Walls for Buildings


Diaphragm Design of Metal Clad Post Framed Buildings

Documents