Shear Strength of Wood Beams

Douglas R. Rammer, Forest Products Laboratory, USDA Forest ServiceDavid I. McLean, Washington State University

AbstractExperimental shear strength research conductedcooperatively with the USDA Forest Service, ForestProducts Laboratory; Washington State University;and the Federal Highway Administration on solid-sawnbeams is summarized in this paper. Douglas Fir,Engelmann Spruce, and Southern Pine specimens weretested in a green condition to determine shear strengthin members without checks and splits. Sizes testedranged from nominal 51 by 102 mm to 102 by256 mm. Additional tests were conducted on air-driedsolid-sawn Douglas Fir and Southern Pine specimens.A three-point loading setup investigated the effectof splits and checks on shear strength and a five-pointloading setup investigated drying effect on beam shear.Based on the experimental tests, the following areconcluded: (1) shear strength of green solid-sawnwithout splits varies with size and may be characterizedusing a shear area or volume parameter (2) air-driedSouthern Pine shear strength free of splits is equivalentto that for Southern Pine glued-laminated timber;(3) tests on seasoned Douglas Fir and Southern Pinegave mixed results on the effect of splits and checks;and (4) fracture mechanics predictions of the shearstrength of artificially split Southern Pine wereconservative.

Keywords: Shear strength, beams, design, size effect,Engelmann Spruce, Douglas Fir, Southern Pine,fracture mechanics, splits, checks.

IntroductionShear design values for solid-sawn structural membersare currently derived from small clear, straight-grainspecimens (ASTM 1995a). Under typical conditions,wooden beams and columns sometimes develop splitsand checks (Fig. 1). These splits and checks are aresult of drying as the member equilibrates to thesurrounding moisture condition or from repeatedwet/dry moisture cycling that may be encountered inexposed timber bridge stringers. Because of theplacement of the member within a structure and thelocal climate, the occurrence and degree of splitting arevaried and unpredictable. Published shear design values(AFPA 1991b) account for this uncertainty byassuming a worst case scenario-a beam that has alengthwise split at the neutral axis. If the designengineer is confident that a member will not splitlengthwise, then the design shear value may bedoubled.

This approach may lead to an inefficiently designedbeam. To increase design accuracy for shear strength,typical beams, rather than small, clear specimens, mustbe studied. Structural members may or may notcontain splits or checks; therefore, an understandingof the shear strength of both unsplit/uncheckedand split/checked beams is critical to the designprocess.

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Figure 1—Deeply checked structural timberbeams and columns.

The overall purpose of this research was to improve theshear design criteria as it applies to wooden beams.Specific objectives were to

• Develop a beam shear strength database for differentsolid-sawn wood species;

• Determine the unsplit, unchecked shear strength forwood beams of different sizes and if strength varieswith size;

• Determine if the solid-sawn shear strengthfor unchecked, unsplit beams is similar to thatfor glued-laminated timber; and

• Determine the effect of checks and splits on beamshear strength.

These objectives were met through an experimentaltesting program and analysis of the experimentalresults.

BackgroundTwo approaches based on different failure criteria havehistorically been used for studying the shear strengthof wood beams: (1) a classical approach based on thestrength of an unsplit member and (2) a fracturemechanics approach based on the strength of a split orchecked member.

Unsplit Wood Shear StrengthIn the past, most shear research focused on the small,clear strength for various species using the standardASTM shear block test (ASTM 1995a). Alternativeshear test procedures have been proposed (Radcliffe andSuddarth 1955), but the shear block test is still theaccepted method for determining wood shear strength

values. However researchers have questioned theapplicability of shear block information to predict theactual strength of wood beams.

Huggins and others (1964) found that beam shearstrength and ASTM D143 shear strength were differentand that beam shear strength depends on the shearspan, defined as the distance from the support to thenearest concentrated load. A series of Canadian studiesinvestigated the effects of member size on shearstrength. Several of these studies experimentallyinvestigated shear strength using simply-supportedbeams (Longworth 1977, Quaile and Keenan 1978).Foschi and Barrett (1976, 1977) approached shearstrength with Weibull’s weak link theory. Theyshowed that shear strength varies with beam geometryand loading. Their work is the basis for the size effectrelationship in the Canadian building code.

For the past 10 years, the Forest Products Laboratoryhas increased its research focus on beam shear. Soltisand Gerhardt (1988) summarized and reviewed existingliterature on shear research. Rammer and Soltis (1994)investigated shear strength with a five-point loadingsetup for glued-laminated members. Leicester andBreitinger (1992) investigated beam shear testconfigurations. All this activity focused on determiningthe unsplit, unchecked beam shear strength. Researchcurrently underway is addressing the effects of splitsand checks after seasoning on shear strength.

Shear Failures In Actual StructuresPractitioners and scientists have long been interested inthe effect of splits and checks on residual shear strength.A bulk of the early research on the effects of splits andchecks in timber members came from the evaluationof stringers removed from railroad bridges. Railroadengineers are concerned with the proper time to replacethe member because of strength loss as a resultof checking, splitting, and deterioration.

The Santa Fe railroad system investigated thecondition of timbers removed from a 35-year-old bridgein Arkansas and two 20-year-old bridges in Oklahomaand Arizona. Strength of these timbers was comparedwith the strength of four virgin timbers to determinestrength loss. At the time of testing, all in-servicetimbers had moisture content levels less than 12% andthe virgin timbers had a moisture content levelof approximately 17%. Testing consisted of third-pointloading on a span-to-depth ratio between 10 and 11.All members showed signs of checking or splitting andsome had signs of deterioration. Of the 25 beamstested, 20 experienced shear failures that wereinfluenced by checks. Maximum shear strength losswas 72% for the timbers from Arizona andapproximately 40% to 50% for the timbers fromOklahoma and Arkansas (Santa Fe System 1921).

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McAlister (1930) reported on the strength tests of 12untreated 203- by 305-mm Douglas Fir timbersremoved from a bridge with 53 years of service life. Hisexperiments included bending and compression testson timbers and small, clear specimens. Of the 12specimens tested in three-point bending, five failed inhorizontal shear at a span to depth ratio of 10 and a14% moisture content. McAlister attributed the shearfailures to the degree of checking in the timbers.

Newlin and Heck (1934) tested the residual strengthoften 203- by 457-mm Douglas Fir stringers removedfrom a bridge that had been in service for 23 years.Two end-matched specimens were fabricated wheneverpossible from the original specimens, which weregreater than 9.14 m long. One specimen was tested ona 5.79-m span and the other on a 4.57-m span. Sevenof the ten 5.79-m specimens failed in horizontal shear,and all the 4.57-m specimens failed in shear. Theynoted that all shear failures occurred at checks, splits,or bolt holes. Small, clear specimens taken from thematerial showed no effects of service life, unlike thelarge timbers.

Wood (1954) investigated the residual strength of two101-year-old Eastern White Pine floor beams. Each

of the Western Hemlock timbers failed in shear. For theair-dried specimens, 50% of the Sitka Spruce and 66%of the Western Hemlock timbers failed in shear.Markwardt observed that the Sitka Spruce material wasof a higher grade than the Western Hemlock, becausethe Sitka Spruce members were cut from largerdiameter trees with few defects. Western Hemlockmembers were cut from small-diameter trees thatcontained heart rot, shakes, and decayed knots andmight have contributed to the increased occurrenceof shear failures.

To evaluate the effects of checks, Newlin and others(1934) conducted bending tests using a built-up beammade of Sitka Spruce. Additionally, they proposed atheory to explain the effect of checks or splits, which isincorporated into current design standards (AREA1991, AFPA 1991a), by the following, for aconcentrated load

beam was approximately 254 by 254 mm and wastested on a 3.96-m span in three-point loading. One In this theory, known as the two-beam theory, the

beam failed in bending, and the other failed in length and depth of checks are not considered, only the

horizontal shear along a plane containing deep checks. position x of the load, P from the support, beam depthd and the clear span lc are relevant. Researchers have

In all these cases, the failure mode in the existingtimber members tended to be governed by shear if adeep check or split was present. Checking and splittingwere a result of drying or cyclic environmental changesover the life of the member.

Experimental Shear FailuresDocumented shear failures were noted in experimentalprograms as early as 1912. Cline and Heim (1912)summarized a large experimental testing program todetermine the mechanical properties of 11 woodspecies. Third-point bending specimens ranged in sizefrom nominal 51 mm by 51 mm by 0.46 m to203 mm by 406 mm by 4.6 m in a wet and air-driedcondition. Shear failures were noticed in both the greenand air-dried specimens. As the specimen sizedecreased, so did the percentage of shear failures. Ingeneral, the air-dried members had a higher percentageof shear failures at each size when compared with theirgreen counterparts.

In a study to determine the mechanical propertiesof Alaskan wood, Markwardt (1931) tested SitkaSpruce and Western Hemlock timbers in a green andair-dried condition. Members were tested in third-pointloading at a span-to-depth ratio of 11.25. Of the greenmaterial tested, 30% of the Sitka Spruce and 24%

since shown that the underlying assumptions of thistheory are incorrect (Keenan 1974, Soltis and Gerhardt1988).

Norris and Erickson (1951) conducted a pilot study onthe effect of splits on shear strength. They developed atheory based on the assumption that the stressconcentration at the tip of the split is approximated byan unknown function that relies on the split length tobeam depth ratio. This function can only be determinedempirically from test data. Fifteen tests with twodifferent loading patterns were conducted using SitkaSpruce. Based on these tests, the equation developedby Norris and Erickson to explain the effects of splits is

(2)

where τ c is the shear stress at the neutral axis; τ m is themaximum shear stress; a is the position of theconcentrated load; d is the beam depth; and c is thelength of the split.

Based on a survey of glued-laminated timber bridges,Huggins and others (1964) conducted a study on theeffect of delamination on the static and repeated loadstrength for glued-laminated beams. After testing 175small glued-laminated beams, of which 115 had

simulated splits or delamination, they concluded thatshear span influences strength and delamination reducesultimate strength. Additionally, they stated that shearstrength is less under repeated loading than staticloading, based on the 48 beams tested.

Fracture MechanicsOne method to evaluate the strength of a split, checked,or cracked beam is fracture mechanics. Fracturemechanics evaluates the state of stress at the end of acrack for three load cases. Mode I is an openingdisplacement; mode II is a sliding displacement; andmode III is a tearing displacement (Fig. 2).

Wood fracture was first investigated by Porter (1964).Since Porter’s first study, wood fracture investigationshave generally focused on mode I fracture with somelimited studies on modes II and III fracture. A problemwith mode II and III investigations is the lack of astandard test procedure to determine fracture properties.Recently, efforts have been made to standardize a testprocedure for mode II fracture. General details of the useof fracture mechanics in wood research is summarizedby Valentin and others (1991).

Barrett and Foschi (1977) numerically analyzed theinfluence of beam splits under concentrated and uniformloading. Based on their analysis, the following weredeveloped to express the mode II stress intensity factorK I I:

where τ is the shear stress in MPa; a is the splitlength; and H is a nondimensional factor thatcharacterizes the loading and beam geometry. Forconcentrated loading, H takes the following form:

(4)

Figure 2—Three modes of loading.

where A and B are functions depending on a/s and s/d,with s being distance from the load to the support andd the beam depth. Using Equation (3), Barrett andFoschi determined the critical stress intensity factor KIIc

value for select structural, No. 1, and No. 2 WesternHemlock.

Murphy (1979) used a boundary collocation method todevelop a simplified equation to evaluate the effectsof beam splits under concentrated and uniform loading.His equation for concentrated loading is

where R is the support reaction nearest the split; a isthe split length; d is beam depth; and b is the widthof beam. Murphy used the work of Norris and Erickson(1951) to validate Equation (5) for Sitka Spruce beams.

Equations (5) developed by Murphy and (3) by Barrettand Foschi are approximately equivalent for all sizedbeams.

The previous two studies focused on end-split beams;however, a majority of actual defects are checks that areclassified as a mode III fracture problem. Murphy(1980) applied mode III fracture mechanics to predictthe effect of checks on beam strength. Correcting Sih’s(1964) mode III solution, Murphy developed anisotropic two-dimensional expression for mode IIIfracture and validated it with Newlin and others (1934)data. Murphy stated that this expression could notexplain the effects of shear span. Therefore, hedeveloped an empirical expression to address thisdeficiency.

In the fracture research previously discussed, the focuswas to determine the applicability of fracturemechanics to explain wood failure for simulated splits.In actual structural members, the geometry of the crockfront is highly irregular. Sometimes the beam iscompletely split but more often the beam is checked onone or both sides. Further investigation into theapplication of fracture mechanics is needed to explainthe effect of splits and checks.

Test ProgramAn investigation of shear strength is currentlyunderway through a cooperative study with the USDAForest Service, Forest Products Laboratory;Washington State University; and the Federal HighwayAdministration. This research was undertaken toinvestigate the green, unchecked shear strength, and theseasoned (checked or split) shear strength of solid-sawnbeams. Brief descriptions of the proceduresare discussed.

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Table 1—Nominal size and number of beam shear specimens used in this investigation.

Green Shear StrengthDouglas Fir, Southern Pine, and Engelmann Sprucespecimens with nominal sizes ranging from 51 by102 mm to 102 by 356 mm were tested to determineunchecked beam shear strength (Table 1). Allspecimens had moisture content levels of 20% or more.A total of 160 Douglas Fir, 183 Southern Pine, and187 Engelmann Spruce beams were tested.

A two-span, five-point loading test, with each spanlength equal to five times the member depth, wasselected to produce a significant percentage of beamshear failures. This test setup had been successfullyused to create shear failures by Langley Research Center(Jegly and Williams 1988), Purdue University(Bateman and others 1990), and the Forest ProductsLaboratory (Rammer and Soltis 1994). Informationrecorded included maximum load, type and location offailures, material properties, beam geometry, moisturecontent, and specific gravity. Further details of theDouglas Fir testing are published by Rammer andothers (1996) and the Southern Pine and EngelmannSpruce testing are published by Asselin (1995).

Dry or Seasoned Shear StrengthOnly Douglas Fir and Southern Pine specimens werestudied in a dry or seasoned condition at an averagemoisture content of 12%. Nominal specimen sizeranged from 102 to 102 mm to 102 by 356 mmfor both species (Table 1). All Douglas Fir specimenscontained natural splits and checks after 1½ years of airdrying and were tested in a single-span, three-pointloading setup with a center-to-center span length of fivetimes the member depth. A three-point configurationwas used to locate the split in the high shear forceregion.

Three different tests were conducted on the SouthernPine specimens that were air-dried for 1 year beforeconditioning to 12% moisture content (Table 1). First,a five-point loading setup was used to determine dryshear strength. Maximum shear force occurs between

the load points; therefore, only checks will influencethe results as splits are predominantly located at theends of the beam. Second, a three-point loading setup,with a center-to-center span length of five times themember depth, investigated the influence of naturalchecks and splits on shear strength. Finally, a three-point loading setup with saw kerfs at lengths of 0.5 d,d, and 1.5 d was conducted to examine the effectsof manufactured defects of known size on shear failures.

Details of the Southern Pine experiments are given byPeterson (1995), and Douglas Fir details will bepublished in a USDA Forest Service research paper byRammer.

Shear Block TestsSmall, clear ASTM D143 shear block specimens werecut in all the studies from each specimen after failure tobenchmark the results to published shear strengthvalues. Two shear block specimens were tested fromthe green, unchecked beam specimens. One specimenwas tested at the moisture condition of the beam andone at 12% moisture content. Only one shear blockspecimen at 12% moisture content was tested from theair-dried, seasoned beam specimens.

ResultsGreen Shear StrengthNot all of the five-point loading specimens failed in ashear mode; a significant number failed in tension orfrom local instability. Therefore, true shear strength isbest estimated by application of censored statistics.Censored statistics techniques were discussed andapplied by Rammer and others (1996) to adjust thegreen Douglas Fir results. This same technique wasapplied to the green Southern Pine and EngelmannSpruce data. Estimated true shear strength values andcoefficients of variation for these two species are listedin Table 2.

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Table 2—Estimated mean and coefficient of varia-tion (COV) green data considering censored data.

The size effect for the different species is compared byplotting the ratio of estimated mean beam shearstrength to mean ASTM shear block strength versuseither shear area or volume (Fig. 3). In these plots, thebeam and ASTM shear block strength values are notadjusted for moisture content or specific gravity. Inaddition, the mean beam shear strength and the 80%mean confidence limits are indicated to show thepotential variability in the mean results. In Figure 3,the relative shear strength ratio increases with adecrease in the shear area or volume parameter. Thesetrends are similar to glued-laminated beam shear results(Rammer and Soltis 1994, Longworth 1977). Plottedlines represent empirical relationships that relate beamshear strength to shear area (Rammer and Soltis 1994)and volume (Asselin 1995). In both cases, the curvepredicts the means of the large members well, butunderestimates the estimated average values for thesmall beams. This under estimation is a consequenceof performing a regression analysis of data that onlyfailed in shear and not considering the censored natureof the data. In almost every case, the empirical curvesare conservative.

Seasoned Five-Point Beam TestAir-dried Southern Pine was tested in a five-pointloading setup to determine the dry shear strength.Drying effects are most noticeable at the end of a beam;therefore, the five-point configuration results areinfluenced only by checks in the middle portion of thebeam and should give a good approximation of the dryshear strength. Censored statistical techniques wereagain used to estimate the mean and coeffecientof variation of the air-dried Southern Pine (Table 3).Mean values for solid-sawn and glued-laminated(Rammer and Soltis 1994) Southern Pine beams andthe 80% mean confidence levels are plotted in Figure 4.Comparison of the air-dried solid-sawn results withpreviously tested glued-laminated Southern Pineresults indicates similar trends, but the solid-sawnmaterial is slightly lower and more variable as a resultof checking effects.

Figure 3—Five-point beam shear to ASTMshear block ratio versus beam size:(top) shear area, (bottom) beam volume.

Table 3—Estimated mean and coefficient ofvariation (COV) 12% moisture contentSouthern Pine considering censored data.

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Figure 4—Comparison of seasoned solid-sawn and glued-laminated Southern Pineby five-point beam test.

Typically the dry/green shear strength ratios for theindividual Southern Pine species range between 1.45and 1.75 (ASTM 1995b), and Kretschmann and Green(1994) recently found a 1.47 increase for the generalSouthern Pine classification. An estimated dry/greenratio based on the estimated means for the SouthernPine five-point specimen at each size was calculatedwith the shear block dry/green ratio found by Asselin,as shown in Table 3. Beam shear dry/green ratiostended to be smaller than values published in ASTM(1995b), but similar to dry/green ratios found byAsselin in shear blocks cut from smaller beam sizes. Inthe 102- by 305-mm and 102- by 356-mm sizes, thebeam dry/green ratios are at the upper bound of theacceptable ASTM values and 20% lower than valuesdevelop from tested shear blocks.

Seasoned Three-Point Beam TestBoth Southern Pine and Douglas Fir beams withnatural defects (splits and checks) were tested in three-point loading to determine the effects of both splits andchecks on member strength. Of the 209 Southern Pinebeams tested, 73 failed in shear; of the 160 Douglas Firbeams tested, 76 failed in shear. It was difficult in bothstudies to predict which split or check was critical priorto testing so that critical pre-test information could begathered. After testing, beams were split open and theamount of lost area was calculated after testing. Lostarea was determined by observing the transition zonebetween the glossy weathered to newly formed dullsurfaces.

To show the effect of splits and checks on strength,shear strength versus lost area are plotted in Figure 5.Southern Pine beams showed little decrease in strength

Figure 5—Three-point shear strength resultsfor beams failing in shear of seasoned(a) Douglas Fir and (b) Southern Pine.

as a result of splitting or checking. Douglas Fir beams,on the other hand, visually showed a strongerdecreasing tend with increasing lost area. It alsoappears that the Douglas Fir members had a higherdegree of splitting and checking.

Based on research to be published later in a ForestProducts Laboratory report, Douglas Fir materialchecks dominated the 102-mm specimens; in contrast,splits dominated the shear failures in the 51-mmspecimens. As indicated by Murphy (1980), theinfluence of checks on beam shear strength,characterized by mode III fracture, occurs when checkshave depths greater than 15% of the cross sectionalwidth.

Three-Point Beam Test With Saw KerfsPeterson’s (1995) third testing series evaluated theeffects of saw kerfs on shear strength. Application of a

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Figure 6—Comparison of saw kerf SouthernPine beam with Equation (5). Solid linerepresents 51- by 102-mm strengthprediction. Dashed line represents102- by 356-mm strength prediction.

saw kerf increased the percentage of shear failures from35% in the seasoned material to 68% in the cutspecimens. To compare fracture mechanics approaches,a critical mode II (KIIc) stress intensity property isneeded. Kretschmann and Green (1992) determined theKIIc for Southern Pine at several moisture levels using acenter-split beam. At 12% moisture content, the KIIc

value is 2060 kN•m-3/2. Using this value of KIIc inMurphy’s Equation (5), mode II fracture yields aprediction for the shear strength of the beams. For thistest configuration, Murphy’s Equation (5), and Barrettand Foschi’s Equation (3), yield similar results. Figure6 compares the experimental and predicted shearstrength to the split length to beam depth ratio.

The predicted values for the split beam shear strengthwere conservative at all sizes. This conservatism wasprobably because the derived solutions assume tractionforces were not applied over the crack surfaces. Peterson(1995) observed crack closure and contact as the loadwas applied. This action could develop surface tractionand frictional forces along the crack. To correctly modelthis type of fracture, crack closure should be considered.

Concluding RemarksSeveral studies were conducted to determine the shearstrength of wood beams. These studies were conductedon various member sizes of Douglas Fir, Engelmann

Spruce, and Southern Pine beams. As a result of thisresearch, the following are concluded.

• Unsplit, unchecked shear strength for all speciesvaried with beam size and had similar trendsafter estimated beam strength was divided byASTM shear block values to normalize materialeffects. An empirical expression based on bothshear area and volume gave conservative results atsmaller beam sizes after censored statisticstechniques were applied.

• Air-dried Southern Pine material tested in a five-point loading configuration gave similar results toSouthern Pine glued-laminated shear strength data.This is likely due to the lower incident of splitsand checks as a result of drying in the regionof maximum shear in a five-point configuration.The application of dry/green ratios for shearstrength design should be further investigated. Forlarger-sized members, dry/green ratios developedfrom the beam shear tests were at least 20% lessthan ASTM dry/green ratios.

• Tests on naturally split and checked beamsshowed mixed results for Southern Pine andDouglas Fir specimens. Southern Pine specimensshowed little change with increasing lost area. Incontrast, Douglas Fir specimens indicated adecreasing trend with an increase in defected area.In both materials, shear failures were difficult toreplicate and these tends are based on limitedsample sizes. Further testing is needed to betterconclude the effect of natural defects.

• Finally, a comparison of shear strength obtainedon artificially split Southern Pine beams withpredicted strength based on existing mode IIfracture theories revealed the predictionsare conservative.

References

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AcknowledgmentsThis research was funded in part through a cooperativeresearch agreement between the Federal HighwayAdministration (FP–94-2266) and the USDA ForestService, Forest Products Laboratory. We thank thefollowing from the Forest Products Laboratory: LarrySoltis, Michael Ritter, and the researchers who laboredin the laboratory Cathy Scarince, Javier E. Font, andDan Winsdorski. At Washington State University, wethank Steve Asselin and Jason Peterson.

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In: Ritter, M.A.; Duwadi, S.R.; Lee, P.D.H., ed(s). Nationalconference on wood transportation structures; 1996 October23-25; Madison, WI. Gen. Tech. Rep. FPL- GTR-94.Madison, WI: U.S. Department of Agriculture, Forest Service,Forest Products Laboratory.