Construction and Building Materials 94 (2015) 148–163

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Construction and Building Materials

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Comparison of models and tests on bottom rails in timber frame shearwalls experiencing uplift

http://dx.doi.org/10.1016/j.conbuildmat.2015.05.1250950-0618/� 2015 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +46 72 212 41 44.E-mail addresses: giuseppe.caprolu@ltu.se (G. Caprolu), ulf.arne.girhammar@ltu.

se (U.A. Girhammar), bo.kallsner@lnu.se (B. Källsner).

Giuseppe Caprolu a,⇑, Ulf Arne Girhammar a, Bo Källsner b

a Department of Civil, Environmental and Natural Resources Engineering, Division of Structural and Construction Engineering – Timber Structures, Luleå University of Technology,SE-971 87 Luleå, Swedenb Department of Building Technology, Faculty of Technology, Linnaeus University, Växjö, Sweden

h i g h l i g h t s

�We present a matching experimental study of three experiment’s programs.� We evaluate several fracture mechanics models able to evaluate the failure load of each failure mode.� The analytical models are compared with the test results.� We present models for each failure mode that show the best fitting with the experimental results.

a r t i c l e i n f o

Article history:Received 10 December 2014Received in revised form 26 May 2015Accepted 29 May 2015

Keywords:Bottom railSplitting of bottom railTimber shear wallsPartially anchoredFracture energyTensile strength perpendicular to the grain

a b s t r a c t

The authors present two different studies: one experimental study and one where analytical modelsdeveloped to calculate the splitting failure capacity of bottom rails in partially anchored timber frameshear walls are evaluated and validated. The experimental study was divided into three parts with spec-imens matched to each other: (1) first the splitting capacity and failure mode of bottom rails subjected touplift were studied; (2) then material properties such as tensile strength perpendicular to the grain; and(3) fracture energy were determined by testing specimens cut from the specimens belonging to study(1). The experimental results were compared with models based on a linear fracture mechanics approachpresented earlier, using as input values results from (2) and (3). Almost all tested models show goodagreement with the test results. The models showing the best agreement have been selected and pro-posed to be used as basis for calculation of the splitting failure capacity of bottom rails in partiallyanchored timber frame shear walls.

� 2015 Elsevier Ltd. All rights reserved.

1. Introduction

Shear walls are structural elements designed to transmithorizontal and vertical forces in their own plane. Shear walls areused, together with roof and floor diaphragms, to stabilisetimber-framed buildings against external loads. The structuralbehaviour of shear walls is to a large extent determined by thesheathing-to-framing joints and by the connection between wallsand the surrounding structure. Of particular importance is theanchoring of the shear wall to the floor/foundation, which is pro-vided by hold-downs and anchor bolts.

[1] pointed out the importance to understand the differencesbetween hold-downs and anchor bolts. Anchor bolts provide

horizontal shear continuity between the bottom rail and the foun-dation. Hold-downs serve as vertical anchorage devices betweenthe vertical end studs and the foundation. If the uplifting force isprevented at the leading stud by any means, the case correspond-ing to fully anchored shear walls, the vertical loads are directlytransferred to the substrate, resulting in a concentrated force atthe leading end of the wall, Fig. 1a. In this case the leading studfully interacts with the substrate and there is no vertical uplift ofthe studs of the walls.

When hold-downs are not provided, the correspondingtying-down forces may be replaced by vertical loads fromdead-weight or anchorage forces transferred from transverse walls.In the case of no such anchoring forces or devices or if they do notfully counteract the uplifting forces, the case corresponding to par-tially anchored shear walls, the bottom row of nails transmits thevertical forces in the sheathing to the bottom rail (instead of thevertical stud) where the anchor bolts will further transmit the

(a) (b)

(c) (d)Fig. 1. Structural behaviour of timber frame shear walls subjected to horizontal loading: (a) a fully anchored shear wall – concentrated anchorage of the leading stud tocounteract the uplifting force; (b) a partially anchored shear wall – distributed anchoring forces in the sheathing-to-framing joints along the bottom rail and through theanchoring bolts down to the substrate; (c) a crack opening from the bottom surface of the bottom rail; and (d) a crack opening from the edge surface of the bottom rail alongthe line of the sheathing-to-framing joints.

G. Caprolu et al. / Construction and Building Materials 94 (2015) 148–163 149

forces into the foundation. This results in a distributed force,Fig. 1b. Because of the eccentric load transfer, transverse bendingis created in the bottom rail and splitting may occur.

In [2], an experimental study is presented. Four types of par-tially anchored shear walls with varying nail size and spacing,and with small round or big square washers, were tested undertensile loading (perpendicular to the bottom rail) with three sam-ples per type of configuration. Splitting along the bottom side ofthe bottom rail was the predominant failure mode for shear wallswith small round washers, but in two of the nine tests, splittingalong the edge side of the bottom rail occurred. When squarewashers were used, splitting along the edge side of the bottom railwas the dominating failure mode. In one of the three tests, thesheathing-to-framing joints of the top rail failed. Thus, big squarewashers suppress the bottom rail cross-grain failure mode. Thesespecimens also showed an increased peak load.

In [3,4] two experimental programs on the splitting capacity ofbottom rails with single- and double-sided sheathing, respectively,were presented, and it has been shown that two brittle failuremodes may take place in the bottom rail: (1) a crack opening fromthe bottom surface of the bottom rail, according to Fig. 1c; and (2) acrack opening from the edge surface of the bottom rail along theline of the sheathing-to-framing joints, according to Fig. 1d.

In [5] a plastic model for the design of timber frame shear wallswas developed. The model covers only static loads and can be usedfor both fully and partially anchored shear walls. However, in orderto use the method, the bottom rail must not experience brittle fail-ure and a plastic behaviour of the sheathing-to-framing joints hasto be ensured. In [6] two models based on a linear fracturemechanics approach, one for each failure mode were presentedand evaluated. In [7] other analytical models, still based on a linearfracture mechanics approach, have been developed and evaluated.Some of those models were based on the assumptions in [6] whileothers were derived using the end-notched beam model in [8], thebeam model loaded perpendicular to the grain by a bolt locatedclose to the edge in [9] and a linear elastic fracture mechanicsmodel for a simply supported beam loaded perpendicular to thegrain by a single load at mid-span derived in [10].

When evaluating these models, the values of fracture energy, Gf ,and tensile strength perpendicular to the grain, ft,90, were taken

from literature. The failure modes found during the bottom railtests needed a Gf value in approximately the TR and RT planesand a ft,90 value in approximately the tangential and radial direc-tions, for failure mode 1 and 2, respectively. This is of course anapproximation. Due to the annual ring orientations, it is hard toexactly state the right orientation for each failure mode.However, it is possible to say that these orientations are dominat-ing with respect to the failure mode, even if in reality it is a mixturebetween TR and RT planes for Gf and T and R directions for ft,90. Dueto the orthotropic characteristics of the timber, it was hard to findthese values for the needed orientation and for the same timberspecies. [11] summarized the results of some studies on ft,90,namely [12–14]. He pointed out that ft,90 strongly depends on theannual ring orientations, the strain rates applied during the tests,the density, the moisture, the temperature and the volume of thespecimen.

The aim of the present study is as follows:

� to experimentally determine the splitting capacity and failuremodes of bottom rails subjected to uplift;� to experimentally determine the fracture energy Gf and the ten-

sile strength perpendicular to the grain ft,90 in the needed orien-tation for failure mode 1, vertical crack, and mode 2, horizontalcrack, from the same specimen tested in the bottom rail exper-imental program;� to evaluate the models presented in [6,7] using the material

properties determined above and compare the results withthe experimental results obtained in the tests of bottom railssubjected to uplift.

2. Material and methods

2.1. Matching test program

A comprehensive number of tests of bottom rails subjected to vertical uplifthave been reported in [3,4]. In order to obtain a deeper understanding of the timbermaterial properties used in the testing of the bottom rails, an additional experimen-tal program was decided to be run. The reason was to obtain more reliable informa-tion on material parameters that may be used in connection with the fracturemechanics analyses. In this new test series with matched specimens three typesof tests were run:

Table 1Test program for bottom rail tests. PD = pith downwards, PU = pith upwards,b = width of rail (notations as in Fig. 3). The series vary according to the anchorbolt position ‘‘bbolt’’, while the sets vary according to the distance ‘‘s’’.

Series Bolt position Set Distance sa Size of washer Numberof tests

bbolt [mm] [mm] PD PU

1 b/260 mm

1 40 40 � 40 � 15 3 32 30 60 � 60 � 15 3 33 20 80 � 70 � 15 3 34 10 100 � 70 � 15 3 3

2 3b/845 mm

1 25 40 � 40 � 15 3 32 15 60 � 60 � 15 3 33 5 80 � 70 � 15 3 3

3 b/430 mm

1 10 40 � 40 � 15 3 32 0 60 � 60 � 15 3 3

a Distance from washer edge to loaded edge of the bottom rail.

150 G. Caprolu et al. / Construction and Building Materials 94 (2015) 148–163

� Bottom rails subjected to uplift;� Tensile strength perpendicular to the grain for horizontal and vertical crack

direction;� Fracture energy for horizontal and vertical crack direction.

First the bottom rail was tested and then the two other specimens for the materialtesting were cut from the bottom rail specimen, in order to have all parametersneeded to evaluate the formulas given in [6,7] using the individual material proper-ties of each bottom rail. In [6,7] the analyses were carried out with bottom rail testresults from experimental programs run by the first author, but with values of ft,90

and Gf found in literature, which might have resulted in not so accurately results.The original boards from which the specimens were cut had a cross section of

120 � 45 mm and a length of about 5 m. Each board was cut into four parts; thentwo parts were used to build bottom rail specimens with expected failure mode1 and the other two to build bottom rail specimens with expected failure mode2, according to Fig. 2. Study A in [3] was used to foresee which kind of failure modewould occur in the bottom rail. In that study, the distance between the nails in thetimber-to-sheathing joints was 25 mm. This distance was chosen; despite it is not arealistic distance, in order to avoid failure due to yielding and withdrawal of thenails. For the bottom rail experimental program, as given in Table 1, the same char-acteristics were used as in study A in [3]. The plan was to test 15 specimens for Gf

tests for horizontal crack and 33 for vertical crack, and 15 specimens for ft,90 for hor-izontal crack and 33 for vertical crack. According to study A in [3] we can expectthat the vertical crack failure mode will occur for rails like the ones in Series 1,Set 1, 2 and 3 and that the horizontal crack failure mode will occur for rails likethe ones in Series 2, Set 3 and Series 3, Set 1 and 2, with the variation of series givenby the anchor bolt position and that of sets by the variation of the washer size,according to Table 1 and Fig. 3c.

For bottom rails with expected mode 2 failure, but where there was also somepossibility that failure mode 1 would occur, it was decided to test the fractureenergy and the tensile strength perpendicular to grain in the directions of both fail-ure modes. This was done to see if there were any relationships between the mate-rial properties and the failure modes and loads of the bottom rail.

2.2. Bottom Rail

2.2.1. Material propertiesThe specimens were built by hand using rails of length 900 mm with a cross

section of 45 � 120 mm, joined to a hardboard sheet of 900 � 500 mm by nails50 � 2.1 mm.

The details of the test specimens were as follow:

� Bottom rail: spruce (Picea Abies), C24 according to [15], 45 � 120 mm.� Sheathing: hardboard, 8 mm (wet process fibre board, HB.HLA2, [16], Masonite

AB).� Sheathing-to-timber joints: Annular ringed shank nails, 50 � 2.1 mm (Duofast,

Nordisk Kartro AB). The joints were nailed manually and the holes werepre-drilled, only in the sheet, 1.7 mm. The centre distance between nails was25 mm.� Anchor bolt: Ø 12 (M12). The holes in the bottom rails were pre-drilled, 13 mm.

2.2.2. Test programA total of 54 specimens, according to Fig. 3, were tested. The specimens were

divided into three different series, where each series was divided into different sets.The series were subdivided with regard to the position of the anchor bolt (bbolt) withrespect to the width ‘‘b’’ of the bottom rail (Fig. 3b and c). Knowing the anchor boltposition and the washer size, the distance s between the washer edge and the edgeof the bottom rail at the loaded side as shown in Fig. 3b and c, is defined. The setswere subdivided with regard to the distance s (Fig. 3b and c). The depth of the

Fig. 2. Scheme of how to cut and select the boards for the specimens (PU = pithupwards, PD = pith downwards). *Specimens with expected mode 1 failure. Theseboards were then selected and specimens for tests for Gf and ft,90 for the verticalcrack direction were cut. **Specimens with expected mode 2 failure. These boardswere then selected and specimens for test for Gf and ft,90 for the horizontal crackdirection were cut.

bottom rail is defined as h. Six specimens were tested in each set, three with thepith oriented downwards (PD) and three with the pith oriented upwards (PU).The test program is specified in Table 1.

2.2.3. Test set-upThe test set-up is shown in Fig. 3, for further details the reader should refer to

[3].The bottom rail was fastened to a supporting welded steel structure by two

anchor bolts. The distance between the bolts was 600 mm and the distancebetween bolt and the end of the bottom rail was 150 mm. A rigid square-orrectangular-shaped washer was inserted between the bottom rail and the bolt headthroughout all tests. The thickness of the washer (15 mm) was chosen so that therewould not arise any visible permanent deformations in the washers. A hydraulicpiston (static load capacity 100 kN) was attached to a steel bar, that was connectedto the upper part of the hardboard sheathing using C-shaped steel profiles and fourbolts Ø16. A hinge was used allowing the specimen to rotate, according to Fig. 3a.The distance between the nails in the sheathing-to-timber joint was 25 mm. Thereason to have such a small nail distance was to have strongsheathing-to-framing joints in order to avoid yielding and withdrawal of the nailsand have splitting failure in the bottom rails. A torque moment of 50 Nm was usedto tighten the bolts. A tensile load was applied to the upper part of the panel with adisplacement rate of 2 mm/min.

For each specimen the moisture content and density of the bottom rail weremeasured after the test, according to [17,18], respectively.

2.3. Tensile strength perpendicular to the grain

2.3.1. Material propertiesIn this section for specimen is meant the part needed to be tested, while for full

specimen is meant the specimen glued to the two timber pieces needed for thetests. The full specimens were built by hand using two different dimensions depen-dent on the direction tested. The specimen was glued to two pieces of timber1 month before testing and kept in a climate controlled chamber with relativehumidity RH 65%. The density of the specimens was measured before gluing; how-ever for few of them, by mistake, it was not measured. Once that the full specimenswere built, the surfaces were accurately prepared to ensure that they were plane.This was made with an electronic planer.

The details of the test specimens were as follow:

� Specimen: the timber was the same as for the bottom rail tests. The dimensionsof the specimen were as follow: 45 � 70 � 45 mm and 45 � 70 � 120 mm forhorizontal crack and vertical crack direction, respectively. Glue (two differentglues were used for the specimens):

1. Wood Glue PU Light 421 1-component moisture-curing polyurethane adhe-sive, water resistant according to [19,20] class D4;

2. CASCO Adhesive, Adhesive 1711 + Hardener 2520 (Phenol Resorcinol).� Reinforcement: Fiberglass.

2.3.2. Test programAccording to [21], the dimensions of a structural timber specimen for determi-

nation of the tensile strength perpendicular to grain should be as given in Fig. 4awith an area of 45 � 70 mm for the glued interface and with a depth e of180 mm. However, due to the small dimensions of the bottom rails studied it wasnot possible to follow these requirements.

The dimensions of the specimens used in the experimental program are speci-fied in Table 2. In Fig. 4b and c it is shown how the specimens were cut from thebottom rails.

Fig. 3. Test set-up and boundary conditions of sheathed bottom rails subjected to single-sided vertical uplift. (a) Boundary conditions: a hinge is used allowing the specimento rotate; (b) cross-section of the specimen. The distance s is the distance between the washer edge and the loaded edge of the bottom rail; and (c) series and set variation ofthe test program. The series vary according to the anchor bolt position ‘‘bbolt’’ and the set according to the distance ‘‘s’’. Units in mm.

G. Caprolu et al. / Construction and Building Materials 94 (2015) 148–163 151

It is important to note that the difference in specimen size gives a difference inspecimen volume. As highlighted in [11] the perpendicular to grain tensile strengthis strongly size dependent and this should be taken into account when analysingthe results.

A total of 48 specimens, according to Fig. 5, were tested: 15 for the horizontalcrack direction and 33 for the vertical crack direction. For both the directions, afew trial tests were made. When the trial tests failed in the right way, they wereincluded in the test program. The dimensions of the test specimens differ withrespect to the direction tested. For the horizontal crack direction the specimenhad dimensions according to Fig. 5a and b while for the vertical crack directionthe specimen had dimensions according to Fig. 5d and e. The width ‘‘u’’, the thick-ness ‘‘v’’ and the depth ‘‘e’’ are also defined in Fig. 5b and e. The test program andspecimen sizes are specified in Table 2; where in the last row the dimensions ofthe specimens according to [21] are given.

2.3.3. Test set-upThe test set-up is shown in Fig. 5. Each specimen was glued to two pieces of

timber, with dimensions according to Table 2 and Fig. 5a and d, dependent onthe direction tested. The full specimen was then connected to steel bars which inturn were connected to the testing machine by dowels, as shown in Fig. 5g. Themachine used was a universal testing Machine UTM ‘‘Alwetron’’ TCT 50. The testswere performed under displacement control and a tensile load was applied by ahydraulic piston with a rate of 10 mm/min until a load of 20 N was reached andthen with a rate of 0.5 mm/min until failure. The displacement rate was chosenaccording to [21], where it is suggested that it shall be adjusted so that the maxi-mum load is reached within (300 ± 120) seconds. A few trial tests were performedin order to find the right displacement rate. During the trial tests the failure wasfound to occur in the glued interface instead of the specimen. Two measures were

then taken. For the specimens tested for the vertical crack direction, the volume ofthe specimen was reduced by two half circles, or here called waist, having a diam-eter of 18 mm. They were positioned at the middle of the specimen depth along theedges, as shown in Fig. 5a and d. The reason for this was to have a part of the spec-imen with a smaller cross section and to have the failure there. For the specimenstested for the horizontal crack direction the tensile strength perpendicular-to-grainwas found to be higher than that found for the other crack direction, therefore theaddition of the waist was not enough in order to get the failure within the speci-men. For that reason the glue lines were strengthened by addition of fiberglass (thiswas made also for a few specimens in tangential direction), as shown inFig. 5c and f. (It should be mentioned that due to the reduction of the area the fail-ure plane is directed to that area and then the Weibull theory to account for the vol-ume effect is not directly applicable under these circumstances. Also, the reducedarea creates some stress concentrations that can have some influence).

2.4. Fracture energy

2.4.1. Material propertiesThe preparation of the specimens was the same as for the specimens for the

tensile strength perpendicular to the grain in Section 2.3.1.The details of the test specimens were as follow:

� Specimen: the timber was the same as for the bottom rail tests. The dimensionsof the specimen were as follow: 45 � 45 � 45 mm for both vertical and horizon-tal crack orientation, with a notch length of 0.6 � 45 mm and a width of 2 mm.In order to obtain a stable curve after the peak load had been passed, the notchlength was increased by 3 mm with a razor blade. Glue (two different glueswere used for the specimens):

Fig. 4. Dimensions of test specimens for determination of tensile strength perpendicular to grain. (a) Specimen according to [21]; (b) specimen for determination of thetensile strength perpendicular to the vertical crack, corresponding to mode 1 failure; and (c) specimen for determination of the tensile strength perpendicular to thehorizontal crack, corresponding to mode 2 failure. Only the part to the right, surrounded by dashed lines, belongs to the specimen.

Table 2Test program of ft,90 tests (notation as in Fig. 5).

Series Direction of the crack Specimen size[mm]

Number of tests

u v e

1 Horizontal 70 45 45 18a

2 Vertical 70 45 120 34b

Specimen size as in [21] 70 45 180 –

a 15 tests were planned but the three trial tests have been added.b 33 tests were planned but one of the three trial tests has been added.

152 G. Caprolu et al. / Construction and Building Materials 94 (2015) 148–163

1. Wood Glue PU Light 421 1-component moisture-curing polyurethane adhe-sive, water resistant according to [19] and [20] class D4;

2. CASCO Adhesive, Adhesive 1711 + Hardener 2520 (Phenol Resorcinol).

2.4.2. Test programA total of 48 specimens, according to Fig. 6 and [22], were tested: 15 for the hor-

izontal crack orientation and 33 for the vertical crack orientation. For both thedirections, a few trial tests were made. The dimensions of the test specimens werechosen according to Fig. 6a and b. The width ‘‘c’’, the thickness ‘‘d’’ and the depthequal to ‘‘c’’ are also defined in Fig. 6a and b. The dimensions of the notch aredefined in Fig. 6b. The two different orientations tested are shown inFig. 6c and d, while in Fig. 6e and f details of the test set-up are shown. The test pro-gram is specified in Table 3.

2.4.3. Test set-upThe test set-up is shown in Fig. 6. The specimen was glued to two pieces of

timber, according to Fig. 6a. The dimensions were chosen according toFig. 6a and b. The tests were made according to [22]. The full test specimenwas simply supported at both ends by two steel cylinders, as shown in Fig. 6f,and loaded at midpoint through a cone connected to the load cell, accordingto Fig. 6e. A 1 mm thick rubber layers were placed between the wood test spec-imen and the supports. The same was done between the wood test specimenand the cone connected to the load cell. The machine used was the same asfor the tensile strength perpendicular to the grain tests; a universal testingMachine UTM ‘‘Alwetron’’ TCT 50.

The tests were performed under displacement control and a compression loadwith a rate of 1.30 mm/min until failure was applied by a hydraulic piston. The dis-placement rate was chosen according to [22], where it is suggested that it shall beadjusted so that collapse is obtained in about 3 ± 1 min. A few trial tests were per-formed in order to find the right displacement rate.

During the trial tests the load vs. deflection curve was found to be unstable. As asolution, the length of the notch was increased by 3 mm using a razor blade, accord-ing to Fig. 6e.

3. Results

3.1. Bottom rail

Two primary failure modes were found during the tests:

(1) Splitting along the bottom side of the rail according toFig. 7a.

(2) Splitting along the edge side of the rail according to Fig. 7b.

This is according to what was found during the other experi-mental programs related to bottom rail tests, [3,4], but where alsoa third failure mode, yielding and withdrawal of the nails in thesheathing-to-framing joints, was found. This third failure modedid not happen in this experimental program probably due to thesmall distance 25 mm between the nails, that we deliberatelychoose to use.

In Fig. 8, the number of observations of the two different failuremodes is graphically shown for the series of the study. It is notedthat the predominant failure mode is failure mode 1, splitting fail-ure along the bottom side of the rail. It is also possible to note aninfluence between the distance s and the failure mode. For smallvalues of distance s, failure mode 2 occurs.

The failure load for the two brittle failure modes is defined asthe load at which there is a first distinct decrease in the load car-rying capacity due to a propagating crack in the bottom rail. Theresults of the different tests are summarized in Table 4. The failureloads of the study are presented with respect to the pith orienta-tion. Mean failure load and mean density are presented withrespect to the failure mode. The dry density, defined as the ratiobetween the mass of the specimen after drying and the volumeof the specimen before drying at moisture content x, indicatedas q0,x, is shown in Table 4 as mean value per set and failure mode.The mean moisture content per set, indicated as x, is also shown.

For failure mode 1 the location of the crack initiation, the dis-tance bcrack1, somewhere between the middle of the width andthe loaded edge of the bottom rail, according to Fig. 7a, wasrecorded. For failure mode 2 the length of the horizontal crackbefore it changes in a more vertical direction, bcrack2, according toFig. 7b, was also recorded. These values, together with failure modeand load, are given in Table 5 for each specimen.

Fig. 5. Test set-up for the tensile strength perpendicular to grain tests. (a) Specimen glued to two pieces of timber for test for the horizontal crack direction; (b) dimensions ofthe test specimen for horizontal crack direction; (c) fiberglass reinforcement for specimen tested for horizontal crack direction; (d) specimen glued to two pieces of timber fortest for the vertical crack direction; (e) dimensions of the test specimen for vertical crack direction; (f) fiberglass reinforcement for specimen tested for vertical crackdirection; and (g) the connection between the specimen and the steel bars connected to the hydraulic piston.

Fig. 6. Test set-up for the fracture energy tests. (a) Specimen glued to two pieces of timber; (b) dimensions of the test specimen (annual ring oriented as in the case ofhorizontal crack); (c) annual ring orientation for specimens tested for the horizontal crack orientations; (d) annual ring orientation for specimens tested for the vertical crackorientations; (e) details of the test set-up (annual ring oriented as in the case of horizontal crack); and (f) details of the test set-up. The dashed lines in (c) and (d) show thepart of the rail from where the specimen was cut.

G. Caprolu et al. / Construction and Building Materials 94 (2015) 148–163 153

3.2. Tensile strength perpendicular to the grain

All curves were found to show a similar stiffness and a brittlefailure load, typical for timber loaded by a tensile load perpendic-ular to the grain. The results are presented in Table 6 with respectto the direction tested. Mean failure load, defined as the average ofthe maximum load reached during the tests, mean tensile strengthperpendicular to grain and mean density are presented.

3.3. Fracture energy

The load–deflection curve for each specimen has been recorded.They have been determined by measuring continuously corre-sponding values of load, F, and deflection or cross head movement,u. For the test to be valid it is required that the load deflectionresponse is stable, where by stable curve is meant a continuouscurve.

Table 3Test program of Gf tests (notation as in Fig. 6).

Series Crack orientation Specimensize [mm]

Number of tests

c d

1 Horizontal 45 45 152 Vertical 45 45 33

154 G. Caprolu et al. / Construction and Building Materials 94 (2015) 148–163

For specimens tested for the horizontal crack plane 6 curveswere stable, 4 almost stable and 5 unstable. For specimens testedfor the vertical crack plane 2 curves were stable, 6 almost stableand 25 unstable. In Fig. 9 one example of each type of curve isshown. The reason for this high number of unstable curves forthe vertical crack plane, which was already known before testing,is discussed below.

For specimens with vertical crack orientation most of the curveswere unstable. This is believed to be due to the annual ring orienta-tion, as shown in Fig. 10. In Fig. 10a the crack for specimens with hor-izontal crack orientation is shown. In this case most of the curveswere found to be stable or almost stable. The stability is probablydue to the annual ring orientation since the crack is able to developfollowing an annual ring. In Fig. 10b the crack has vertical orienta-tion. In this case most of the curves were found to be unstable. Thedifference in the crack path is noted with respect to the horizontalcrack orientation, since in this case the crack develops perpendicularto the annual ring ‘‘jumping’’ from one annual ring to another. It isbelieved that the drops of load in the post peak behaviour of the loaddisplacement curves are due to this.

The results of the tests are summarized in Table 7. The resultsare presented with respect to the direction tested. Mean failureload, mean fracture energy and mean density are presented.

3.4. Compilation of matched experimental results

Since the three types of tests are performed with specimenshaving matched material properties, it is interesting to show the

a) Mod

b) Mod

bcrack1

bcrack2

Fig. 7. (a) Splitting failure along the bottom side of the rail; and (b) splitting failure alonpith oriented downwards (PD = N) and the right column with the pith oriented upward

results of the three types of experiments with specimens cut fromthe same board, in order to see if, for example, due to an increase ordecrease of the bottom rail failure load correspond to an increaseor decrease of the fracture energy or tensile strength perpendicularto the grain. Tables 8 and 9 show the results of this correlation. Thetables are divided with regard to the pith orientation of the bottomrail, PD for Table 8, and PU for Table 9. Not all bottom rail speci-mens are presented but only those for which the fracture energyand the tensile strength were tested. The first number of the bot-tom rail ID refers to the series tested, the second number to theset and the third is just the progressive number of the specimen.When planning the experiments it was decided that for bottom railspecimens of series 1 the fracture energy and the tensile strengthwould be tested only for the vertical crack directions, since wewere sure that the failure mode would become failure mode 1.For bottom rail specimens of series 2 and 3, on the contrary, therewere the same possibilities to get failure mode 1 and 2, therefore, itwas decided to test the fracture energy and the tensile strength forboth cases. This was done also in order to see the possible influenceof these properties on the failure mode, since specimens of thesame set could fail in different ways. For each Gf – value the typeof curve characteristics is also listed in the last column.

4. Analysis

In [6,7], models based on a fracture mechanics approach havebeen presented and derived in order to calculate the load carryingcapacity of bottom rails in partially anchored shear walls. The for-mulas derived depend on the failure mode. In those papers theanalysis have been carried out using values of fracture energyand tensile strength perpendicular to the grain found in literature.However, due to the orthotropic characteristics of the wood mate-rial, it was hard to find proper values for the orientations wanted.With the values listed in Tables 8 and 9, the same formulas used in[6,7] are here used and their accuracy evaluated. When referring tomean values in this paper, the values listed in Table 10 below areused, where the ft,90 and Gf values are the mean values calculated

e 1

e 2

bcrack1

bcrack2

g the edge side of the rail. The left column of pictures refers to bottom rails with thes (PU = U).

Fig. 8. Recorded failure modes for the different test series and sets belonging to the experimental study (PU = pith upwards, PD = pith downwards). *Size of washer [mm].Mode 1: splitting along the bottom side of the rail and mode 2: splitting along the edge side of the rail.

Table 4Results from bottom rail tests with the pith oriented downwards (PD) and upwards (PU). Failure modes: (1) splitting along the bottom side of the rail; and (2) splitting along theedge side of the rail. q0,x = dry density with respect to volume at x = moisture content.

Series Set Number oftests

Mean failure load per failure mode Number oftests perfailure mode

q0,x Mean valueper failure mode[kg/m3]

x Meanvalue [%]

All failure modes (1) (2)

Mean[kN]

Std. dev.[kN]

COV[%]

Mean[kN]

Std. dev.[kN]

COV[%]

Mean[kN]

Std. dev.[kN]

COV[%]

(1) (2) All (1) (2)

Pith Down1 1 3 10.8 2.74 25.3 10.8 2.74 25.3 – – – 3 – 421 421 – 16.0

2 3 12.1 4.09 33.7 12.1 4.09 33.7 – – – 3 – 410 410 – 16.33 3 17.1 1.40 8.19 17.1 1.40 8.19 – – – 3 – 409 409 – 15.14 3 21.6 1.51 7.00 21.6 1.51 7.00 – – – 3 – 342 342 – 14.5

2 1 3 12.3 2.66 21.5 12.3 2.66 21.5 – – – 3 – 367 367 – 14.52 3 15.8 2.07 13.1 15.8 2.07 13.1 – – – 3 – 372 372 – 14.13 3 27.4 2.83 10.3 27.4 2.83 10.3 – – – 3 – 390 390 – 14.3

3 1 3 22.9 2.17 9.49 22.9 2.17 9.49 – – – 3 – 403 403 – 14.72 3 26.7 6.10 22.8 28.9 – – 22.5 – – 2 1 382 399 347 14.3

Meanvalue

388 390 347 14.9

Pith Up1 1 3 8.62 1.14 10.5 8.62 1.14 10.5 – – – 3 – 416 416 – 15.4

2 3 12.1 3.39 28.0 12.1 3.39 28.0 – – – 3 – 418 418 – 16.53 3 15.5 5.39 31.5 15.5 5.39 31.5 – – – 3 – 378 378 – 14.74 3 18.0 4.25 19.7 18.0 4.25 19.7 – – – 3 – 368 368 – 14.9

2 1 3 11.4 2.91 23.6 11.4 2.91 23.6 – – – 3 – 365 365 – 14.22 3 11.7 1.43 9.08 11.7 1.43 9.08 – – – 3 – 398 398 – 14.83 3 24.5 2.83 10.3 25.2 – – 23.2 – – 2 1 403 409 393 14.4

3 1 3 17.5 2.12 9.24 16.4 – – 19.7 – – 2 1 365 353 390 14.82 3 23.1 2.30 8.58 – – – 23.1 2.30 8.58 0 3 390 – 390 13.7

Meanvalue

389 389 391 14.8

G. Caprolu et al. / Construction and Building Materials 94 (2015) 148–163 155

from the tests presented in this paper and E and G according to [6],where E = E90 and G = GRT were used. The same E and G values havebeen here used for both failure modes 1 and 2, since their variationaccording to the failure mode is negligible. Other values listed inTable 10, and shown in Figs. 11,12 and 14,15, are the width b,the length l, and depth h of the bottom rail, the depth he of the‘‘cantilever beam’’ considered when deriving the formulas andthe shear correction factor bs.

4.1. Analysis for failure mode 1

The formulas used are listed below. For their derivation thereader should refer to [6,7]. All of them have been derived using

the compliance method, a branch of the linear elastic fracturemechanics theory (LEFM). In Fig. 11 the geometry used to deriveEqs. (1), (3–6) is shown. c is a length added to the ‘‘cantilever span’’be to account for the fact that fully clamped conditions at the edgeof the washer cannot be practically assumed.

Eq. (1) was derived considering a part the bottom rail as a can-tilever beam fully clamped at the crack position, according toFig. 11. The compliance has been calculated considering both flex-ural and shear deformations.

P ¼ lðh� aÞ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2GGf =be

12 GE

beh�a

� �2 þ bs

vuut ð1Þ

ble

5ea

sure

dcr

ack

data

for

spec

imen

sw

ith

the

pith

orie

nted

dow

nwar

ds(P

D)

and

upw

ards

(PU

).Fo

rfa

ilure

mod

e1

the

dist

ance

betw

een

vert

ical

crac

kan

dlo

aded

edge

ofth

ebo

ttom

rail

(bcr

ack

1)

isgi

ven.

For

failu

rem

ode

2th

ele

ngth

ofe

hori

zont

alcr

ack

befo

reit

chan

ges

dire

ctio

n(b

crac

k2)

isgi

ven.

End

1an

dEn

d2

indi

cate

the

two

bott

omra

ilen

ds,b

utno

dist

inct

ion

ishe

rem

ade

betw

een

them

.All

dist

ance

san

dcr

ack

leng

ths

are

give

nin

mm

,whi

lst

the

failu

relo

adgi

ven

inkN

.

Seri

es1

Seri

es2

Seri

es3

Set

1Se

t2

Set

3Se

t4

Set

1Se

t2

Set

3Se

t1

Set

2

M/L

aEn

d1

End

2M

/La

End

1En

d2

M/L

aEn

d1

End

2M

/La

End

1En

d2

M/L

aEn

d1

End

2M

/La

End

1En

d2

M/L

aEn

d1

End

2M

/La

End

1En

d2

M/L

aEn

d1

End

2

Pith

Dow

n1/

10.9

5358

1/12

.157

561/

15.7

5567

1/22

.155

701/

9.43

4250

1/14

.445

481/

27.8

4550

1/20

.915

–2/

22.5

12–

1/13

.555

581/

16.2

5360

1/18

.554

641/

22.8

6063

1/13

.040

631/

14.8

6060

1/24

.450

521/

25.2

2631

1/33

.740

–1/

8.04

5352

1/8.

0353

631/

17.0

5159

1/19

.952

621/

14.6

4552

1/18

.242

441/

30.0

2957

1–2/

22.6

b30

c–

1/24

.028

2831

d–

Pith

Up

1/9.

8962

581/

9.66

5865

1/17

.158

581/

17.2

8157

1/14

.750

421/

11.9

4152

1/22

.645

481/

15.5

3823

2/24

.721

–1/

7.69

7451

1/15

.965

561/

9.43

7044

1/22

.562

581/

9.44

4547

1/13

.060

341/

27.8

37–

2/19

.721

–2/

20.5

24–

1/8.

2860

581/

10.6

6930

1/19

.864

501/

14.1

4036

1/9.

9951

411/

10.2

4744

2/23

.222

–1/

17.3

3029

2/24

.235

–

aM

=fa

ilu

rem

ode

and

L=

fail

ure

load

.b

For

this

spec

imen

itw

asdi

fficu

ltto

dist

ingu

ish

the

fail

ure

mod

e.c

b cra

ck1

iffa

ilu

rem

ode

1is

con

side

red

asfa

ilu

rem

ode.

db c

rack

2if

fail

ure

mod

e2

isco

nsi

dere

das

fail

ure

mod

e.

156 G. Caprolu et al. / Construction and Building Materials 94 (2015) 148–163

Ta M th is

The crack length a, can be calculated using the initial cracklength acr, according to Eq. (2), given in [23]:

acr ¼EGf

pf 2t

ð2Þ

Simplified versions of Eq. (1) can be obtained assuming a smallcrack length (a ? 0), Eq. (3), assuming that bending deformationscan be ignored (G/E ? 0), Eq. (4), and assuming both small cracklength and that bending deformations can be ignored, Eq. (5).

P ¼ lh

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2GGf =be

12 GE

beh

� �2 þ bs

vuut ð3Þ

P ¼ lðh� aÞ

ffiffiffiffiffiffiffiffiffiffiffi2GGf

bebs

sð4Þ

P ¼ lh

ffiffiffiffiffiffiffiffiffiffiffi2GGf

bebs

sð5Þ

Eq. (6) was derived using the same geometry as Eq. (1).However, in this case is assumed that the cantilever is not com-pletely rigidly clamped at end, but some finite rotation occurs. In[7] the compliance was calculated and then Eq. (6) was derived.

P ¼ lðh� aÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2GGf =be

pffiffiffiffiffiffiffiffiffi12 G

E

qbe

h�aþffiffiffiffiffibs

p ð6Þ

Again, if a small crack length is considered, a simplified versionof Eq. (6), given by Eq. (7) can be obtained.

P ¼ lh

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2GGf =be

pffiffiffiffiffiffiffiffiffi12 G

E

qbeh þ

ffiffiffiffiffibs

p ð7Þ

Assuming negligible bending deformations or both small cracklength and negligible bending deformations would lead to Eqs.(4) and (5).

Eq. (8) has been derived using the end-notched beam model in[8], and the geometry according to Fig. 12. However, since thatmodel has different type of crack propagation compared to that offailure mode 1 of bottom rails, a different compliance has been used.

P ¼ lah

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2GGf =be

12 GE

beah

� �2 þffiffiffiffiffiffiffiffi185

GE

q4�3a�a3ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið1�aÞð1�a3Þp be

ahþ bs

vuuut ð8Þ

In Eq. (9), a simplified version, considering small crack length, ofEq. (8) is given.

P ¼ lh

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2GGf =be

12 GE

beh

� �2 þ 6ffiffiffiffiffiffi65

GE

qbeh þ bs

vuut ð9Þ

The formulas above have been used, together with the valueslisted in Table 10, to calculate the ‘‘root mean square error’’

(RMSE) values, RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið1=nÞ

Pn1D

2q

, where n is the number of

specimens tested and D is defined as the value of the differencebetween failure load from tests and failure load calculated accord-ing to the formulas above. The RMSE-values are calculated in twoways: (1) by using the individual values for Gf and ft,90 for each

specimen listed in Table 8 and 9, i.e. RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið1=nÞ

Pn1D

2ind

q, and

(2) by using the mean values for values for Gf and ft,90 as listed in

Table 10, i.e. RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið1=nÞ

Pn1D

2mean

q. These calculated

RMSE-values are listed in Table 11, where the values are dividedwith respect to the pith orientation.

(a)

(b)

(c)

0

20

40

60

80

100

0 2 4 6 8

Load

[N]

Displacement [mm]

0

20

40

60

80

100

0 2 4 6 8 10

Load

[N]

Displacement [mm]

0

40

80

120

160

200

0 2 4 6 8 10 12

Load

[N]

Displacement [mm]

Fig. 9. Examples of load–deflection curves. (a) Stable curve; (b) almost stable curve;and (c) unstable curve.

Table 6Results from testing of specimens in tensile strength perpendicular to grain. H = horizontal crack direction, V = vertical crack direction.

Series Crack direction Number of tests Failure load Tensile strength perpendicular to the grain ft,90 Mean density

Mean Min and max Std. dev. COV Mean Min and max Std. dev. COV [kg/m3]

[kN] [kN] [kN] [%] [MPa] [MPa] [MPa] [%]

1 H 18 4.73 3.266.45

0.83 17.4 2.28 1.543.10

0.40 17.4 467a

2 V 34 3.63 1.986.11

0.88 24.1 1.79 0.982.84

0.39 22.1 463b

a Result calculated with 9 specimens.b Result calculated with 31 specimens.

G. Caprolu et al. / Construction and Building Materials 94 (2015) 148–163 157

In the formulas above be = s + c, where s is the distance betweenthe edge of the washer and the loaded edge of the bottom rail andc, according to Fig. 11, is an additional length to the fictitiousclamped end. In this case c = 20 mm has been used.

From Table 11 it is noted that the difference betweenRMSE-values for individual test values and RMSE-values for meantest values is negligible, since the values are in the same order ofmagnitude. It is evident that the best agreement is given by theEqs. (7) and (9), for the case of RMSE-values for individual test val-ues, and by Eqs. (1), (7) and (9) for the case of RMSE-values formean test values.

In Fig. 13 the failure load versus distance s has been plotted,with the failure load curves calculated with Eqs. (1), (3–8). In thefigure only specimens failed in mode 1 are plotted, and an expo-nential trend-line for the test results is plotted. Fig. 13a and b referto specimens with pith oriented downwards and upwards, respec-tively, while in Fig. 13c all specimens failed in mode 1 are shownindependently of the pith orientation. The curves are plotted usingthe mean values listed in Table 10.

Eqs. (3) and (5) give values too high with respect to the testresults, while Eqs. (6) and (8) too low. The Eqs. (1), (4), (7) and (9)were found to give the best agreement. However, if graphical com-parison between them is made, is noted that Eq. (4) gives values toohigh for distance s > 10 mm and Eq. (1) follow the general beha-viour of the results but predicting low values. The best agreementis shown by Eqs. (7) and (9). Good agreement is also shown, withrespect to the test results, between the failure load and the distances, where the coefficient of determination is 0:56 6 R2

6 0:76.In [24], where an experimental study of bottom rails with

single- and double-sided sheathing was presented, an empiricalrelationship for the mean value of the load-carrying capacity ver-sus the distance s was given as Fmean ¼ 27:9e�0:0227s. Similar empir-ical relationships have been found in the present study: (1)Fmean ¼ 28:3e�0:0280s for specimens in Fig. 13a; (2)Fmean ¼ 21:9e�0:0224s for specimens in Fig. 13b; and (3)Fmean ¼ 25:8e�0:0227s for specimens in Fig. 13c.

4.2. Analysis for failure mode 2

For failure mode 2, a total of six equations, given in [6,7] havebeen tested. The equations are listed below.

Eq. (1), Eq. (10) was derived considering a part of the bottomrail as a cantilever beam fully clamped at the crack position andthe compliance was calculated in the same way considering bothflexural and shear deformations. In Fig. 14 the geometry used forthe derivations of Eqs. (10–13) is shown.

P ¼ l

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2GGf he

12 GE

ahe

� �2þ bs

vuut ð10Þ

Assuming small crack length (a ? 0) or assuming that bendingdeformation can be ignored as compared with the shear deforma-tions, (i.e. G/E ? 0) leads to a simplified version of Eq. (10):

P ¼ lffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2GGf he=bs

qð11Þ

Eq. (12) has been derived using again the model of splitting fail-ure of an end-notched beam derived in [8]. The difference with theprevious model is given by a different compliance, calculated tak-ing into account contributions from the part of the beam withdepth h and from additional rotation of the cantilever due to thefact that the stiffness of the beam with depth h cannot be fully acti-vated in the immediate vicinity of the corner of the notch. Thesolution given in [8], if used on a bottom rail, leads to Eq. (12).

(a)

(b)

Fig. 10. Examples of crack growth during the fracture energy tests. (a) Horizontal orientation of the crack; and (b) vertical orientation of the crack.

Table 7Results from fracture energy testing for horizontal and vertical crack direction, H and V, respectively.

Series Crack direction Number of tests Failure load Fracture energy Gf Mean density

Mean Min and max Std. dev. COV Mean Min and max Std. dev. COV [kg/m3][N] [N] [N] [%] [N/m] [N/m] [N/m] [%]

1 H 15 98.0 60.0169

27.4 27.9 322a 190476

86.7 26.9 455b

2 V 33 123 69.0192

29.7 24.2 303c 196432

66.5 21.9 474c

a Result calculated with 15 specimens.b Result calculated with 14 specimens.c Result calculated with 31 specimens.

Table 8Compilation of the matched experimental results. Bottom rail specimens with PD. Gf = fracture energy, ft,90 = tensile strength perpendicular to the grain. V = crack orientation forfailure mode 1 in bottom rail specimens and H = crack orientation for failure mode 2. S, A and U: stable, almost stable and unstable Gf curve, respectively. When two results aregiven in the column for the type of the Gf curve, the first refers to specimens with V crack orientation and the second to specimens with H crack orientation.

Bottom rail Bottom rail failure load Gf (V) Gf (H) ft,90 (V) ft,90 (H) Failure mode Type of Gf curveSpecimen ID [kN] [N/m] [N/m] [MPa] [MPa]

111 PD 10.9 231 – 1.44 – 1 U112 PD 13.5 237 – 1.82 – 1 U113 PD 8.04 356 – 1.93 – 1 AMean for set 10.8 265 – 1.73 – – –121 PD 12.1 251 – 1.89 – 1 U122 PD 16.2 432 – 2.14 – 1 S123 PD 8.03 285 – 1.49 – 1 UMean for set 12.1 323 – 1.84 – – –131 PD 15.7 279 – 1.70 – 1 A132 PD 18.5 225 – 1.36 – 1 U133 PD 17.0 364 – 1.69 – 1 UMean for set 17.1 289 – 1.58 – – –231 PD 27.8 – 352 1.75 2.15 1 –232 PD 24.4 366 441 1.37 2.53 1 A/U233 PD 30.0 316 371 2.34 2.06 1 U/AMean for set 27.4 341a 388 1.82 2.25 – –311 PD 20.9 266 381 1.71 3.10 1 U/U312 PD 25.2 245 225 1.24 1.88 1 U/S313 PD 22.6 233 310 1.40 1.75 1 U/UMean for set 22.9 248 305 1.45 2.24 – –321 PD 22.5 356 436 1.44 2.33 2 A/U322 PD 33.7 375 476 2.84 2.11 1 U/S323 PD 24.0 271 280 1.89 2.50 1 U/AMean for set 26.7 334 397 2.06 2.31 – –

a Result calculated with 2 specimens.

158 G. Caprolu et al. / Construction and Building Materials 94 (2015) 148–163

Table 9Compilation of the matched experimental results. Bottom rail specimens with PU. Gf = fracture energy, ft,90=tensile strength perpendicular to the grain. V = crack orientation forfailure mode 1 in bottom rail specimens and H = crack orientation for failure mode 2. S, A and U: stable, almost stable and unstable Gf curve, respectively. When two results aregiven in the column for the type of the Gf curve, the first refers to specimens with V crack orientation and the second to specimens with H crack orientation.

Bottom rail Bottom rail failure load Gf (V) Gf (H) ft,90 (V) ft,90 (H) Failure mode Type of Gf curveSpecimen ID [kN] [N/m] [N/m] [MPa] [MPa]

111 PU 9.89 – – – – 1 –112 PU 7.69 – – 2.08 – 1 –113 PU 8.28 231 – 1.44 – 1 –Mean for set 8.62 – – 1.76a – – –121 PU 9.66 300 – 2.58 – 1 U122 PU 15.9 423 – 1.76 – 1 U123 PU 10.6 1032b – 1.90 – 1 SMean for set 12.1 362 – 2.08 – – –131 PU 17.1 345 – 1.99 – 1 A132 PU 9.43 196 – 0.98 – 1 U133 PU 19.8 373 – 1.98 – 1 UMean for set 15.4 305 – 1.65 – – –231 PU 22.6 233 – 2.05 2.75 1 U232 PU 27.8 328 – 2.40 1.54 1 U233 PU 23.2 212 352 2.11 2.15 2 U/UMean for set 24.5 258 – 2.19 2.15 – –311 PU 15.5 306 299 1.65 2.24 1 U/A312 PU 19.7 388 190 1.51 2.59 2 U/S313 PU 17.3 249 260 1.52 2.13 1 U/SMean for set 17.5 314 250 1.56 2.32 – –321 PU 24.7 316 331 1.34 1.99 2 U/S322 PU 20.5 246 231 1.65 2.44 2 U/S323 PU 24.2 390 243 1.80 2.10 2 U/AMean for set 23.1 317 268 1.60 2.18 – –

a Result calculated with 2 specimens.b This result is considered not trustable due to the difference with the other results.

Table 10Material properties and data used in the evaluation.

Material properties Values Unit

E = E90 500 MPaG = GRT 50 MPaft = ft,90,V

a 1.80 MPaft = ft,90,H

b 2.30 MPaGf = Gf,V

a 300 N/mGf = Gf,H

b 320 N/mb 120 mml 900 mmh 45 mmhe 22.5 mmbs 1.20

a Values calculated in the tests and used in equations for failure mode 1.b Values calculated in the tests and used in equations for failure mode 2.

Fig. 11. Geometry used to derive Eqs. (1), (3–6) for failure mode 1.

G. Caprolu et al. / Construction and Building Materials 94 (2015) 148–163 159

P ¼ lh

ffiffiffiffiffiffiGGf

h

qffiffiffiffiffiffiffiffiffiffi35

1�aa

qþ a

h

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi6 G

E ð 1a3 � 1Þ

q ð12Þ

A simplified version may be obtained in the special case of asmall crack or if assuming that the bending deformations are neg-ligible as compared with the shear deformations, giving Eq. (13):

Fig. 12. Geometry used to derive Eqs. (8) and (9).

P ¼ lC1

ffiffiffiffiffiffiffiffihe

1�heh

r

C1 ¼ffiffiffiffiffiffiffiffiffiffiffi53 GGf

q ð13Þ

Eq. (14) is based on the model derived in [9] where a beamloaded perpendicular to the grain by a bolt located close to theedge and close to the end is considered, according to Fig. 15. Thehorizontal crack in a bottom rail may be considered as a specialcase of that solution, namely for be ! 0.

P ¼ P01

2ffiffiffiffiffiffiffiffi2fþ1p

P0 ¼ 2lC1

ffiffiffiffiffihe

pC1 ¼

ffiffiffiffiffiffiffiffiffiffiffi53 GGf

qf ¼ C1

f t

ffiffiffiffiffiffiffiffiffiffiffiffiffiffi10 G

E1he

qð14Þ

(a)

0 5 10 15 20 25 30 35 400

5

10

15

20

25

30

35

40

45

50

Distance s [mm]

Fai

lure

load

[kN

]

Eq. (1)Eq. (3)

Eq. (4)

Eq. (5)

Eq. (6)Eq. (7)

Eq. (8)

Eq. (9)

ETLa) (R2 = 0.76)Exp. Data PD

Pith Downwards

(b)

(c)

0 5 10 15 20 25 30 35 400

5

10

15

20

25

30

35

40

45

50

Distance s [mm]

Fai

lure

load

[kN

]

Eq. (1)

Eq. (3)Eq. (4)

Eq. (5)

Eq. (6)

Eq. (7)

Eq. (8)

Eq. (9)

ETLa) (R2 = 0.56)

Exp. Data PU

Pith Upwards

0 5 10 15 20 25 30 35 400

5

10

15

20

25

30

35

40

45

50

Distance s [mm]

Fai

lure

load

[kN

]

Eq. (1)

Eq. (3)Eq. (4)

Eq. (5)

Eq. (6)

Eq. (7)

Eq. (8)

Eq. (9)

ETLa) (R2 = 0.65)

Exp. Data PD + PU

Pith Downwards + Pith Upwards

Fig. 13. Failure load versus distance s for specimen failed in mode 1. Curvesaccording to Eqs. (1), (3–8). (a) Specimens with pith downwards; (b) specimenswith pith upwards; and (c) all specimens independently on the pith orientation.aETL = Exponential trend line.

160 G. Caprolu et al. / Construction and Building Materials 94 (2015) 148–163

In [10], a linear elastic fracture mechanics model was derivedfor a simply supported beam loaded perpendicular to grain by asingle load at mid-span. For that model, if small edge distance

ðhe=h! 0Þ is considered, the failure load P ¼ P0, with P0 from Eq.(14). P0 may therefore be considered as a special case of the modelin [10]. A semi-empirical generalized version of Eq. (10) may beproposed, as in Eq. (15).

P ¼ clC1

ffiffiffiffiffiffiffiffihe

1�heh

rc ¼ 1ffiffiffiffiffiffiffiffi

2fþ1p

ð15Þ

In Table 12 the RMSE-values for individual test values and theRMSE-values for mean test values, as previously defined, are listed.The table shows values only for specimens with pith upwards,since for pith downwards only one specimen failed in mode 2and a statistical evaluation would not be meaningful.

The best agreement is given by the Eqs. (10), (11) and (15). InFig. 16 the failure load versus distance s has been plotted, withthe failure load calculated according to Eqs. (10–15). Only speci-mens failed in mode 2 are plotted, independently of their pith ori-entations, and the linear regression line for the test results isplotted only for specimens with pith upwards, since there was onlyone specimen with pith downwards failed in mode 2 The failureload has been calculated using the mean values listed in Table 10.

It is noted that the failure load for mode 2 is independent of thedistance s according to Eqs. (10–15). This would suggest that theupper surface is free from any washer and that the model is appli-cable only if the distance s is larger than the cantilever length a(s > a). However, it is obvious on the other hand that mode 2 com-pared to mode 1 occurs only for small s-values, which is confirmedby the experimental results where a weak trend with lower capac-ity for increasing values of distance s is found. This means that theside crack opens even when there is a washer within the distancea. This may due to the fact that large portions of the bottom railhave no washer on the upper side and that the cracks develop inthose areas and then later (or immediately) reach the area wherethe washers are located. There is a 3-dimensional effect. It is alsonoted that the anchor bolts and washers are discretely locatedalong the bottom rail in the experiments and, therefore, the thirddimension of the problem will have an effect on the initiation ofcracks.

Eq. (13) gives values too high with respect to the test results,while Eqs. (12) and (14) give too low values. This agrees with theresults listed in Table 12. The Eqs. (10), (11) and (15), which werefound to give the best agreement, are pretty close to test results.Eq. (10) gives lower values compared to Eqs. (11) and (15), whichgive more or less the same value (they have similar RMSE-values).

4.3. Combined design curves for mode 1 and mode 2

In the previous two sections Eqs. (7) and (15) have been foundto give the best RMSE-value with respect to the test results. A limitbetween the two formulas has been determined, according whichfailure mode 2 is applicable for s < 10 mm and mode 1 for s P 10mm. The limit is shown in Fig. 17, together with the test results.Figs. 17a and b show test results for specimens with pith down-wards and upwards, respectively, while Fig. 17c include all testresults independently on the pith orientations. Further theRMSE-value calculated for Eq. (7) versus test results of failuremode 1 for specimens with s P 10 mm and for Eq. (15) versus testresults of failure mode 2 for specimens with s < 10 mm, is shown.

5. Discussion

The results from the bottom rail experimental program are inline with the previous experimental programmes presented in[3,4]. For the details the reader should refer to those papers, hereonly a summary of the main findings is given. Two brittle failure

Fig. 14. Geometry used to derive Eqs. (10–13).

Fig. 15. Geometry used to derive Eqs. (14) and (15).

Table 11Comparison between mean values of individual RMSE-values and RMSE-values using mean values of Gf and ft,90 for failure mode 1.

Eq. (1) [kN] Eq. (3) [kN] Eq. (4) [kN] Eq. (5) [kN] Eq. (6) [kN] Eq. (7) [kN] Eq. (8) [kN] Eq. (9) [kN]

RMSE-values for individual test values PD 7.87 8.54 6.68 15.4 10.2 3.33 10.0 3.39PU 4.49 9.19 6.54 16.4 7.01 3.13 6.70 3.19

RMSE-values for mean test values PD 4.48 8.94 5.88 16.0 8.48 3.02 8.15 3.21PU 3.44 11.3 8.48 18.7 5.74 4.88 5.49 4.89

0 5 10 15 20 25 30 35 400

5

10

15

20

25

30

35

40

Distance s [mm]

Fai

lure

load

[kN

]

Eq. (10)

Eq. (11)Eq. (12)

Eq. (13)

Eq. (14)

Eq. (15)

LTLa) (R2 = 0.33)Exp. Data PD

Exp. Data PU

Pith Downwards + Pith Upwards

Fig. 16. Failure load versus distance s for specimen failed in mode 2. Failure loadcalculated according to Eqs. (10–15). All specimens independent on the pithorientation. aLTL = Linear trend line.

G. Caprolu et al. / Construction and Building Materials 94 (2015) 148–163 161

modes were found during the experimental program: (1) a crackopening from the bottom surface of the bottom rail; and (2) a crackopening from the edge surface of the bottom rail along the line of

the sheathing-to-framing joints. In comparison with [3,4], in thisstudy, the yielding and withdrawal of the nails in thesheathing-to-framing joint was not found, due to the deliberatelysmall distance chosen between the nails: 25 mm. The failure modeis dependent on the distance s between the washer edge and theloaded edge of the bottom rail; in fact for s P 10 failure mode 1is the only failure mode, while for s 6 10 mm failure mode 2appears. The failure load was also found to be dependent on thedistance s, and increases when s is decreased. Further, such asthe previous experimental programmes, the failure load of bottomrails with the pith oriented downwards is higher than for speci-mens with the pith oriented upwards. Since the density and mois-ture content of all the specimens are similar, it is believed that thisis an effect of the initial cupping of the bottom rail due to the ani-sotropic shrinkage from drying or a consequence of the anisotropicmaterial properties in the radial-tangential plane of the timber.

The tensile strength perpendicular to the grain was found to behigher for specimens with horizontal crack direction than thatwith vertical. Results of [14] discussed in [11], show that ft,90

increases with increasing density and decreases with the increas-ing moisture content and temperature. However, the influence ofthese parameters do not explain the difference found between val-ues for different crack direction, since the mean density has beenfound to be similar for the specimens tested in the two directionsand the moisture and temperature were kept constant for all tests.

One reason for the difference between radial and tangentialdirection could be the different volumes between the two speci-mens, which is commonly explained by the weakest link of theoryof Weibull. However, for such small specimens and small differ-ence in volume, and, as mentioned earlier, with the presence ofthe waist in the specimens, it is not believed that the volume hasany major influence. Hence it can be concluded that the differencebetween ft,90 in the two direction is just due to the orthotropiccharacteristic of wood. [12] has presented results of ft,90 strengthof Scots pine at various load directions and his results also showthat the strength value for the horizontal crack direction is higherthan that for vertical crack direction in agreement with the resultspresented in this paper. It is noted that the tensile strength valuesare lower for both directions, than the values used earlier in [6,7]. Itis believed that the tensile strength together with the fractureenergy, are the governing parameters for the failure capacity ofthe bottom rail. From this point of view, the results of the tensilestrength tests are important.

The reliability of the fracture energy test results could be ques-tioned, since most of the curves were found to be unstable oralmost stable and just a few were stable. However, the results havebeen compared with fracture energy values of previous experi-ments such as those in [27] and those shown in [26] referred toby [25], where similar values were found, meaning that even ifthe curves are not stable the Gf values calculated from them arenot far from the values found in literature. Further, similar valueshave already been used in [6,7].

When the values have been used in the analysis in the previoussection, not all formulas gave results in agreement with the testresults. Regarding failure mode 1, the RMSE-values in Table 11

Table 12Comparison between mean values of individual RMSE-values and RMSE-values usingmean values of Gf and ft,90 for failure mode 2.

Eq.(10)[kN]

Eq.(11)[kN]

Eq.(12)[kN]

Eq.(13)[kN]

Eq.(14)[kN]

Eq.(15)[kN]

RMSE-values forindividual testvalues

PU 4.30 2.85 9.56 6.36 8.06 2.46

RMSE-values formean testvalues

PU 2.94 2.03 8.66 9.04 6.92 2.00

Fig. 17. Limit between failure mode 1 and 2 for Eqs. (7) and (15). (a) Specimenswith pith oriented downwards; (b) specimens with pith oriented upwards; and (c)all specimens independent on the pith orientation.

162 G. Caprolu et al. / Construction and Building Materials 94 (2015) 148–163

shows a rather good agreement for almost all formulas, with theexception of Eq. (5). This was expected, since that equation is asimplified version of Eq. (1), which was one of those giving the bestagreement, where the initial crack length and the bending defor-mations were ignored. Eq. (7) was found to give the best agree-ment. The results here confirm the good agreement with bottomrail test results as already found in [6,7].

Regarding failure mode 2, the results for pith downwards can beomitted, since only one specimen failed in mode 2 and hence it isnot statistically reliable. The RMSE-values in Table 12 shows thatthe best agreement is given by Eq. (15), which is a simplified ver-sion of Eq. (14) Also in this case the results confirm the good agree-ment with bottom rail test results, as already found in [6,7].

6. Conclusions

Fracture mechanics models for the splitting capacity of bottomrails in partially anchored shear walls are compared to results fromconducted full-scale bottom rail tests, where also matching testresults for the main fracture mechanics parameters were obtained.Tests on the splitting capacity of the bottom rail, fracture energyand tensile strength perpendicular to the grain have been con-ducted. The results of the bottom rail tests confirm the behaviourpresented in previous studies presented in [3,4]. Results of tensilestrength tests show a tensile strength higher for specimens withhorizontal crack direction than those with vertical. This confirmsresults from a previous study found in the literature. It is notedthat the resulting values are lower than the values used in [6,7].Since it is believed that the tensile strength together with the frac-ture energy, are the governing parameters with respect to the fail-ure capacity, the results of this study are considered veryimportant. The results of the fracture energy tests instead are ques-tionable due the high number of unstable curves. However, sincethe mean values from the tests have been found to be in goodagreement with literature values, they have been consideredreliable.

Most formulas investigated in this paper, show good agreementwith the tests results. The formulas giving the best agreement, oneper failure mode, have been chosen and it is believed that they canbe used for calculating the splitting failure capacity of the bottomrail. If the splitting failure capacity can be calculated and, hence,these brittle failure modes can be avoided and the plastic beha-viour of the sheathing-to-framing joints can be ensured, the plasticdesign method proposed in [5] can then be applied.

7. Future work

This paper concerns the splitting failure capacity of bottom railsin partially anchored shear walls, both experimentally and analyt-ically. In this paper the equations believed to be the best for calcu-lating this capacity have been compared.

G. Caprolu et al. / Construction and Building Materials 94 (2015) 148–163 163

The present two-dimensional models do not consider someinfluencing factors such as the friction under the bottom rail, thecupping of the bottom rail, the effect of the pretension force andthe discretely placed washers. In order to study in more detailthe influence of these parameters and, especially, the effect ofthe third dimension, a future work based on an XFEM (ExtendedFinite Element Method) analysis, is planned and, in fact, alreadyhas started.

Acknowledgements

The authors would like to express their sincere appreciation forthe financial support from the County Administrative Board inNorrbotten, the Regional Council of Västerbotten and theEuropean Union’s Structural Funds – The Regional Fund.

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