experimental study on loading capacity of glued-laminated

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Experimental Study on Loading Capacity of Glued-LaminatedTimber Arches Subjected to Vertical Concentrated Loads

Citation for published versionZhou J Li C Ke L He J amp Wang Z 2020 Experimental Study on Loading Capacity of Glued-LaminatedTimber Arches Subjected to Vertical Concentrated Loads Advances in Civil Engineering vol 20207987414 httpsdoiorg10115520207987414

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Download date 18 May 2022

Research ArticleExperimental Study on Loading Capacity of Glued-LaminatedTimber Arches Subjected to Vertical Concentrated Loads

Jiale Zhou1 Chuanxi Li1 Lu Ke 1 Jun He12 and Zhifeng Wang 3

1Key Laboratory of Bridge Engineering Safety Control by Department of EducationChangsha University of Science and Technology Changsha 410114 China2Institute for Infrastructure and Environment Heriot-Watt University Edinburgh Currie EH14 4AS UK3Department of Civil Engineering and Mechanics Central South University of Forestry and Technology Changsha 41004 China

Correspondence should be addressed to Lu Ke clkelustucsusteducn and Zhifeng Wang 13607431423163com

Received 27 December 2019 Revised 2 May 2020 Accepted 4 May 2020 Published 22 May 2020

Academic Editor Jorge Branco

Copyright copy 2020 Jiale Zhou et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Glued-laminated timber arches are widely used in gymnasiums bridges and roof trusses However studies on their mechanicalbehaviours and design methods are still insufficient is paper investigates the in-plane loading capacity of circular glued-laminated timber arches made of Douglas fir Experiments were conducted on four timber-archmodels with different rise-to-spanratios under concentrated loads at mid-span and quarter-point locations e structural responses failure modes and loadingcapacity of the timber arch specimens were obtained e results show that the timber arches presented symmetric and anti-symmetric deformation under mid-point and quarter-point loading conditions respectively e downward shifting of theneutral axis of the cross section was observed under mid-point loading condition which contributes to higher loading capacitycompared to that under quarter-point loading condition e loading condition significantly affects the ultimate loads and thestrain distribution in the cross section Based on the design formula in current standards for timber structures an equivalentbeam-columnmethod was introduced to estimate the loading capacity of the laminated timber arches under vertical concentratedloads e moment amplification factor in the formula was compared and discussed and the value provided in the NationalDesign Specification for Wood Construction was recommended with acceptable accuracy

1 Introduction

Glued-laminated (glulam) timber which is made of gluedlayers of solid sawn lumber (timber lamellae) has numerousadvantages such as high strength-to-weight ratio excellentsustainability of sources and superior designability [1] eglued-laminated timber arches (glulam arches) have beenwidely used in many large-span structures such as gymnasi-ums bridges and roof trusses [2ndash6] However the failuremechanism of glulam arches subject to external loads has notbeen sufficiently studied many problems are still not wellunderstood It is of importance to understand the failuremechanism and design method for glulam arches underconcentrated loads e loading capacity of glulam arches isinfluenced by many factors such as the rise-to-span ratiolateral supports [7] creep of timber material [8] and rein-forcement measures [5 9ndash11]

Regarding the research on glulam arches Rodman et al[7] investigated the stability of glulam arches subjected tovertical distributed loads finding that the rise-to-span ratiosignificantly affects the lateral buckling capacity of glulamarches e lateral deformation is no longer crucial whensufficient lateral supports were provided Zhu and Zhou [8]analyzed the influence of creep of the timber material on theloading capacity of glulam arches under full-span uniformloads through theoretical analysis they revealed that thecreep is the crucial factor affecting the loading capacityOlsson [12] analyzed the influence of the load distributionon the internal forces in the glulam arches e results showthat the internal force distribution of glulam arches issensitive to the load distribution Kannar et al [13] analyzedthe global bending and shear strength of timber structuresfinding that the use of thinner lamella enables producingmore homogeneous glulam structures Ostrycharczyk and

HindawiAdvances in Civil EngineeringVolume 2020 Article ID 7987414 9 pageshttpsdoiorg10115520207987414

Malo [4] proposed a radial network pattern as a modificationof a radial pattern to improve the performance of thenetwork arch especially the bending capacity of the archesRammer and Line [14] experimentally and analytically in-vestigated the behavior of a full-scale three-hinged Tudorarch under service and ultimate loads e results showedthat the main arch structure was in an elastic state andplastic deformation was only observed in the baseconnections

Typical load patterns on circular arches include dis-tributed vertical load and concentrated vertical load Forexample the main arch rib of an open-spandrel arch bridgewas mainly subjected to concentrated loads from the pillarse equivalent beam-column method was an effectivemethod to calculate the loading capacity of the arches [15]However limited research has been performed on the failuremechanisms and loading capacity calculation methods forglulam arches under concentrated load According to theequivalent beam-column design method the arches inmany existing studies are considered as columns subjectedto both axial force and bending moment e interactionformula was usually used to analyse their loading capacityCurrently the main timber standards have provided in-teraction equations to calculate the loading capacity ofglulam arches such as GBT 50708-2012 [16] NationalDesign Specification for Wood Construction (NDS) [17]and Eurocode 5 [18] However the formulas of momentamplification factors which describe the second-order effectof axial force are quite different in these standards usmore studies are needed to verify which moment amplifi-cation factor calculation method is the most suitable one forevaluating the loading capacity of glulam arches

e objective of this paper is to investigate the failuremechanisms and loading capacity of glulam arches subjectedto vertical concentrated loads First the structural responsesfailure modes and loading capacity of the timber-archspecimens were obtained through experimental investiga-tion en based on the design formula in current timberstructure standards an equivalent beam-column methodwas introduced to estimate the loading capacity of laminatedtimber arches under mid-span and quarter-span loadconditions Finally based on the experimental results themoment amplification factor calculation methods werecompared and discussed to propose somerecommendations

2 Materials and Specimens

21 Materials In this study North American Douglas firlumbers (botanical name Pseudotsuga menziesii Franco)(Western Wood Structures Inc Tualatin OR USA) andphenol resorcinol formaldehyde resin adhesive (NanjingSkybamboo Science amp Technology Industry Co LtdNanjing China) were used to fabricate the timber arches

According to GB50005-2017 [19] the Douglas fir lumberwas selected according to the results of visual stress gradinge quality grade of the lumber materials is Ic e tensionand compression tests of timber were conducted accordingto the Standard for Test Methods of Timber Structures [20]

e elastic modulus (E) tensile ultimate strength (ft) andcompressive strength (fc) in the parallel-to-grain directionwere obtained Each test includes 10 samples e materialproperties of Douglas fir timber are listed in Table 1 emechanical properties of timber are influenced by manyfactors such as the growth region and humidity us thedispersion of the mechanical properties for the timber isacceptable e representative stress-strain relationships forthe timber are shown in Figure 1 e tensile behaviour is ina perfect elastic stage A bilinear relationship was adopted todescribe the compressive behaviour εcy εcu and εtu rep-resent the compressive yield strain compressive ultimatestrain and tensile ultimate strain respectively e moisturecontent range of the lumber is between 1300 and 1358with an average value of 1328 which is less than the NDSrecommended value 16 for dry service conditions emean density of timber is 528 kgm3

e phenol resorcinol formaldehyde adhesive (PRF) wasused for the lamination and the glue consumption was 250to 300 g per square meter e mechanical properties of theadhesive provided by the manufacturer are listed in Table 1

22 Specimens Preparation To investigate the loading ca-pacity and mechanical response of glued-laminated timberarches four timber arches were fabricated and testedPrevious studies [21] indicated that the ratio betweenbending moments and axial forces in the arch dependspredominantly on the loading conditions and rise-to-spanratio of the arch us the major design parameters of thespecimens include (1) the rise-to-span ratio and (2) theloading conditione radius and cross-sectional (rectangle)dimensions of all specimens were 3000mm and56mmtimes 140mm respectively

e fabrication procedure of glued-laminated timberarches includes grading finger joining gluing and bendingforming processes First the desired length of lamellae wasobtained through finger joining method and the lamellaewere bent by a work bench to develop the circular profileen the glulam arches were made of 9 lamellae gluedtogether and were bent on the work bench again epressure applied at lamination was maintained around1MPa during the 24-hour curing procedure Final thelaminated arches were cut into specimens with the requiredrise-span ratio It is worth noting that the 45 mm thicklamellae in the original design are hard to be bent into acircular arch profile erefore the thickness of lamellae wasthinned from 45mm to 155mm e radius and cross-sectional dimensions of all specimens were identical forfabrication the dimensions of the specimens are shown inFigure 2

In total 4 glulam arches were fabricated and tested especimens were labelled alphanumerically depending on therise-to-span ratio and loading condition ldquoCrdquo and ldquoQrdquorepresent mid-point loading and quarter-point loadingconditions respectively e numbers following ldquoRrdquo rep-resent the rise-to-span ratio of the arch For example ldquoR16-Crdquo denotes a timber-arch specimen under the mid-pointload with a rise-to-span ratio of 16 (Table 2)

2 Advances in Civil Engineering

3 Experimental Program

31 Experimental Setup e specimens were tested usinghydraulic jacks (Hailing Taizhou China) with a loadingcapacity of 100 kN e specimens were connected to thesupport through a hinge at the arch foot e horizontaldisplacement of the arch foot was limited by the reactionframe and tension bar connecting two supports e testsetups for the timber arches are shown in Figure 3 In thetests four pairs of lateral supports were set at L5 (L is thespan) 2L5 3L5 and 4L5 to prevent out-of-plane defor-mation during the loading process

32 Loading Procedure andMeasurement emeasurementsystems for the displacement and strain are shown in Fig-ure 2 e local displacement was measured using sixelectronic dial indicators ree electronic dial indicators(2 3 and 4) were respectively located at L4 L2 and3L4 to measure the vertical displacements e other twoelectronic dial indicators (1 and 5) were installed tomeasure the horizontal deformation of the specimens causedby the rotation of the arch feet e electronic dial indicator6 was set at the arch crown to capture the out-of-planedeformation Rosette strain gauges were installed on thesurfaces of sections at 0L (left support) L4 L2 3L4 and L(right support) to capture the strain state A total of eightstrain gauges along the arch axis were arranged at eachsection In all 40 strain gauges were applied to each spec-imen e strain data were collected by the TST3826 staticdata acquisition system

During the test a concentrated load was monotonicallyapplied to the specimens through a hydraulic jack emagnitude of the applied force was measured by a load cellA multistep loading procedure was performed during the

tests When the load was less than 70 of the ultimate load(Pult) as predicted according to GBT 50708-2012 the loadwas applied at a rate of 4 kN per step After the load reached70 Pult the load was increased at a rate of 2 kN per stepuntil the failure of specimen

4 Results and Discussions

41 Failure Characteristics Previous research [22] indicatedthat the unreinforced laminated members subjected tobending moment alone or in combination of axial com-pression and bending actions failed in tension mode with abrittle manner In this study all the laminated archesexhibited the tension failure mode except Q16-C as shownin Figure 4 e failure positions of each specimen werelocated at the cross section of loading area due to thebending moment of cross section Specifically the failurepositions of specimens were located in the mid-span sectionunder mid-span point load while in quarter-span sectionunder mid-point load

In general under the mid-point load conditions thewood fibres in the mid-span tension zone fractured whichresulted in the failure of the specimen In contrast underquarter load conditions the failure position of the specimens(except R16-Q) was the tension zone of the loading sectionFor specimen R16-C obvious plastic deformation wasobserved in the compression zone of the mid-span sectionas shown in Figure 4(a) Taking specimen R15-C as anexample the typic failure process was described as followsFirst when the compressive stress at the mid-span crosssection reached the compression strength obvious com-pressive plastic deformation was observedWith the increaseof the applied load the tensile stress at the mid-span crosssection reached the tensile strength and tension failure wasobserved at mid-span section en the applied loaddropped continually and obvious upward deformations atthe position of L4 and 3L4 were observed For the specimenR15-Q the cause of failure was the tension failure in thebottom layer at the loading position It should be noted thatfor specimen R16-Q tensile cracks in the bottom layerwhich extended into the middle layers resulted in the failureof the specimen as shown in Figure 4(c) is is due to amanufacturing defect of the drilling holes at the arch footsection which leads to a weakening of cross section

42 Load-DisplacementResponse e load (P) displacement(v) curves for all specimens are illustrated in Figure 5 emeasured displacements at 3 and 4 dial indicators wereselected to describe the v minus P curves for the mid-point and

Table 1 Material properties of timber and PRF

Materials ft (MPa) fc (MPa) E (MPa)

Douglas timberMean value 837 400 98043

Standard deviation 452 378 14296COVa 55 947 145

Epoxy resin Mean value 92 700 3320Note acoefficient of variation

εcu εcyεtu ε

σftu

fc

Figure 1 Stress-strain relationships of glulam timber

Advances in Civil Engineering 3

quarter-point loading conditions e v minus P curves can bedivided into two stages elastic and elastoplastic stages All ofthese v minus P curves are in linear relation at the elastic stagee v minus P curves exhibited a nonlinear relation with rapidincrease of displacement at the elastoplastic stage When theapplied load reached the ultimate value the specimens failedin a brittle manner

e curves of R16-Q and R15-Q enter the elastoplasticstage when the load reaches 12 kN However the curves ofR16-C and R15-C exhibit a nonlinear relationship whenthe load reaches 14 kNe ultimate load and correspondingdisplacement for the specimens under quarter-point loadconditions are lower than those for the specimens under amid-point load condition From Figure 5 it can be

conducted that the v minus P curves of all specimens have noobvious descending branches

e applied load and corresponding displacements at theelastic state and ultimate state and failure modes of allspecimen are illustrated in Table 3e elastic limit load (Pe)under themid-point load is 14 kN which is 117 times of that(12 kN) under quarter-point load While the ultimate load(Pult) under the mid-point load is 113ndash134 times of thatunder the quarter-point load It can be conducted that thespecimens under quarter-point load exhibited plastic be-havior earlier than the specimens under the mid-point loaddid e loading condition has a slight effect on the elasticlimit loads (Pe) but has a significant effect on the ultimateloads (Pult) e main reason is that all the specimens failed

Vect

or h

eigh

t

Central loadQuarter point load

1

23

4

5

6

Tension bar

Span

0 LL4 L2 3L4

Electronic dial indicatorsStrain gauges

(a)

56

140

Strain gauges

(b)

Figure 2 Schematic drawing of specimens (unit mm) (a) vertical view and (b) cross section

Table 2 Specimen details

Circleradius

Specimennumber

Height(m)

Span(m)

Rise-to-spanratio

Loadingconditions

Sectional dimension(mm) Moisture content ()

R 3m

R16-C 06 36 16 Mid-point load

56times140 1328R16-Q 06 36 16 Quarter-point

loadR15-C 085 42 15 Mid-point load

R15-Q 085 42 15 Quarter-pointload

Loading device Lateral supports

Dial indicator

Tension bar

(a)

Lateral supports

Tension barArch support Arch support

Strain gauges

(b)

Figure 3 Experimental setup (a) mid-point and (b) quarter-point loading conditions


in tension mode due to bending moments us the glulamarches under quarter load displayed larger moments thanthe arches under the mid-point load

All the specimens presented an obvious deflection at theloading section At the ultimate state the maximum de-formations are 3845ndash6759mm which is between 162 and198 of the span e obvious deformation and cracks wereobserved at the ultimate state for each specimen

Representative experimental vertical displacements un-der different load levels are given in Figure 6 e measuredvalues of 2 3 and 4 dial indicators were selected to

describe the vertical displacement distributions In the fig-ure the downward and upward displacements are givennegative and positive values respectively e results showthat the maximum deformation locates at the loading sec-tion e specimens under the mid-point load exhibitedsymmetric deformation In contrast the specimens underquarter-point load exhibited antisymmetric deformation

43 Load-Strain Relationships e relationships of appliedload and longitudinal strain of each specimen are illustratedin Figure 7 e measured values of strain gauges located inmid-span and 3L4 sections were selected to describe theload-strain relationships e compressive and tensilestrains are defined as negative and positive values respec-tively According to the limit strain analysis method thecross section fractured when the fibres in the tension regionreached their tensile ultimate strain and then the wholespecimen failed due to tension fracture

Under the mid-point load conditions the tensile andcompressive strains exhibited a linear distribution at theearly stage of loading and the strains were satisfied with theplane section assumption With the increase of loading thenonlinearity of compressive strain became more obviouse neutral axis began to shift toward the tension regionunder the mid-point load e offsets of R15-C and R16-Cwere approximately 08 and 2 cm respectively which isbetween h18 and h7 (h is the height of the cross section) asshown in Figures 7(a) and 7(c)e reasons can be explainedas follows According to the constitutive relation of materialsas shown in Figure 1 the compressive stress did not increaseanymore when the compressive strain came to compressiveyield strain (εcy) However the tensile limit strength (ftu)

40

35

30

25

20

15

10

5

00 10 20 30 40 50 60 70

Load

(kN

)

Displacement (mm)

14kN

12kN

Elastoplastic stage

Elastic stage

R16-CR15-C

R16-QR15-Q

Figure 5 Load-displacement curves of glulam arch specimens

Compression region

Tensile region

Tension failure in bottom layer

(a)

Compressive plasticdeformation Tension failure in top layer

Tension failure in top layerLongitudinal cracksin the middle layer

(b)

Tensile cracks in bottom layerextended into middle layers

(c)


(d)

Figure 4 Failure modes of the specimen (a) Specimen R16-C (b) Specimen R15-C (c) Specimen R16-Q (d) Specimen R15-Q


was larger than the compressive strength (fc) the tensilestress continued to increase before the tensile strain reachingthe tensile ultimate strain (εtu) Based on the stress equi-librium condition the depth of the compression regionincreased and the neutral axis shifted downward Finallywhen the load reached Pult the compressive and tensilestrain exceeded their limit value

Under the quarter-point load conditions the shifting ofthe neutral axis toward the tension region was not ob-served as shown in Figures 7(b) and 7(d)e reason is thatthe member with larger bending moment resulted in amore rapid increase of tensile and compressive strain and adecrease of loading-carrying capacity e tensile strain ofspecimens subjected to a quarter-point load was higherthan that of specimens subjected to a mid-point load

It is worth noting that the compressive and tensilestrain of R16-Q were 3738 με and 5531 με respectivelywhen the load reached the ultimate load e specimen R16-Q was destroyed before the compressive and tensile stressreached its limit (εcu and εtu) is also indicates that thefailure mode of specimens R16-Q was not tension failureat 3L4 section erefore the strain distributions of the

loading cross section are significantly influenced by theload condition

5 Theoretical Analysis

51 Equivalent Beam-Column Method Based on theequivalent beam-column method [15] the arches underaxial compression and bending actions are regarded aseccentric columns en the internal forces of the corre-sponding cross section can be obtained by interaction for-mula Lastly the critical load of arches can be calculatedaccording to the relationship between the load and internalforce To simplify the calculation of loading capacity ofglulam arches we assume that

(1) ere is no slip between adjacent lamellae(2) Timber is an anisotropy material and the failure of

specimens is determined by the strength parallel tothe grain

(3) e initial defects such as inner stress due tobending of lamellae and geometric imperfectionswere ignored

30

15

0

ndash15

ndash30

ndash45

ndash60

Vert

ical

def

orm

atio

n (m

m)

0 L4 L2 3L4 LCoordinates of measuring points

P = 0kNP = 4kNP = 8kNP = 10kNP = 12kNP = 14kNP = 16kNP = 18kN


(a)

P = 18kNP = 20kNP = 22kNP = 24kNP = 26kNP = 28kNP = 303kN

30

15

0

ndash15

ndash30

ndash45

ndash60Ve

rtic

al d

efor

mat

ion

(mm

)



(b)

Figure 6 Experimental vertical displacement distributions (a) under mid-point and (b) quarter-point loads

Table 3 Experimental results

Specimen numberElastic limit state Ultimate capacity state

Failure modePe (kN) De (mm) Pult (kN) Dmax (mm)

R16-C 1400 1292 3750 4788 aR16-Q 1200 1304 2800 3845 cR15-C 1400 1104 3420 6759 aR15-Q 1200 1131 3030 4274 bNote Failure modes a tension failure at mid-span section b tension failure at quarter-span section (loading section) and c tearing failure at arch foot


By first-order analysis the relationship between theapplied load and the internal forces at the cross section canbe established Under mid-point load the internal forces ofthe mid-span section are

M Pl

16 (1)

N 5Pl

16f (2)

where P is the applied load l and f are the span and heightof arches respectively

Under quarter-point load the internal forces at quarter-span section are

M 21Pl

128 (3)

N 1

4f2 + l2

1113968 middot3Pf

2+15Pl2

32f1113888 1113889 (4)

16

14

12

10

8

6

4

2

0

ndash2

Sect

ion

heig

ht (c

m)

ndash8000 8000ndash6000 6000ndash4000 4000ndash2000 20000Longitudinal strain (με)

Neutral axis

εcu εtu

4kN14kN22kN30kN37kN

10kN18kN26kN345kN375kN

(a)

16

14

12

10

8

6

4

2

0

ndash2

Sect

ion

heig

ht (c

m)


Neutral axis

εcu εtu

4kN12kN18kN22kN26kN

8kN16kN20kN24kN28kN

(b)

16

14

12

10

8

6

4

2

0

ndash2

Sect

ion

heig

ht (c

m)


Neutral axis

εcu εtu

8kN16kN20kN24kN28kN318kN

4kN12kN18kN22kN26kN

342kN30kN

(c)

16

14

12

10

8

6

4

2

0

ndash2

Sect

ion

heig

ht (c

m)


Neutral axis

εcu εtu


5kN10kN16kN20kN24kN

303kN28kN

(d)

Figure 7 Section stress distributions of specimens (a) Specimen R16-C (b) Specimen R16-Q (c) Specimen R15-C (d) Specimen R15-Q


52 Discussions on the Load Bearing Capacity of GlulamArchIn current standards such as GBT 50708-2012 [16] and NDS[17] the design formula of glulam arches is based on the bi-linear interaction relationship between the axial force (N) andbending moment (M) at a specific cross section of the archese interaction formulas presented in the above standards wereadopted to estimate the loading capacity of glulam arches

e interaction formulae recommended in NDS [17] areas follows

N

Anfc1113888 1113889

2

+M

Wfm 1 minus NAnfcE( 11138571113858 1113859le 1 (5)

fcE 047E

l0h( 11138572 (6)

An blowast h (7)

W bh2

6 (8)

where N and M are the axial force and bending momentcalculated by equations (1)ndash(4) respectively An and W arethe area of cross-section and the sectional resistance mo-ment respectively calculated by equations (7) and (8) re-spectively b and h refer to the width and height of cross-section E is themodulus of elasticity l0 is the effective lengthof the compression member For hinge-supported arches l0is equal to arc-length fcE is the compressive criticalbuckling strength 1 minus (NAnfcE) is the moment amplifi-cation factor to consider the second-order effect Accordingto the compressive and tensile strength [23] the bendingstrength parallel to the grain fm is

fm fc3 ftfc( 1113857 minus 1

ftfc( 1113857 + 1 (9)

e interaction formula recommended in [16] is similarto equation (5) but the main difference is

fcE 0822Eminprime

l0h( 11138572 (10)

here Eminprime is modified modulus of elasticity Based on theLoad and Resistance Factor Design method in [18] Eminprime iscalculated as

Eminprime Ct middot CM middot KF middot φ middot Emin (11)

where Ct and CM are the temperature factor and wet servicefactor which are taken as 10 KF is the format conversionfactor 176 φ is the resistance factor and 085 Emin is thereference value of elastic modulus 5447MPa

e elastic load (Pe) under the mid-point load is higherthan that under quarter-point load According to equations(1)ndash(4) under the same applied load the bending moment atthe quarter-span section under quarter-point load is larger thanthat at the mid-span section under central-point loaderefore the elastic load (Pe) of specimens is higher for thecentral load position e experimental and theoretical resultsof loading capacity for all specimens are listed in Table 4 PC

U1

and PCU2 are the theoretical values of loading capacity calcu-

lated by the formula in [16 17] respectively e values ofmaterials properties were taken as the mean values in Table 1PT

U is the experimental value of test specimen e theoreticalvalues ofPC

U1 are 052 to 067 times ofPTU while thePC

U2 is 076to 098 times of PT

Ue results show that the design formula ofGBT 50708-2012 underestimates the loading capacity ofglulam arches under mid-point and quarter-point load theformula in NDS can predict the loading capacity more ac-curately e values of (PC

U2PTU) for specimens R15-C and

R1-5-Q are 09 and 076 respectively With the increase ofbending moment at the loading position the value of(PC

U2PTU) decreases gradually us the design formulas in

NDS can be used to evaluate the loading capacity of glulamarches with acceptable accuracy

e main reason is that the moment amplification factorin NDS is a variable that depended on the bending stress andmodulus of elasticity However the moment amplificationfactor in GBT 50708-2012 is a fixed value which is the lowerlimit value of that in NDS

6 Conclusions

is study investigates the in-plane loading capacity ofglued-laminated arches subjected to vertical concentratedloads A total of 4 specimens with different rise-to-spanratios and loading conditions were designed to study theirmechanical properties including structural response failuremodes and loading capacity Furthermore based onequivalent beam-column method the calculated method ofloading capacity was discussed e following conclusionscan be drawn

(1) e loading condition slightly affects the elastic limitloads but significantly affects the ultimate loads ofglulam arches e loading capacity of the archesunder the mid-point load is 113ndash134 times of thatunder quarter-point load e glulam arches undermid-point load display larger moment under ulti-mate load than the arches under quarter-point loaddo

(2) e load-displacement relationships for all theglulam arches have elastic and elastoplastic stagesand they contain no obvious descending branchesAll of the glued-laminated arch specimens mainlyfailed due to tension failure in a brittle manner especimens respectively presented symmetric andantisymmetric deformation under mid-point

Table 4 eoretical and experimental results of load bearingcapacity

Specimen numberLoading capacity (kN)

PCU1 PC

U2 PTU (PC

U1PTU) (PC

U2PTU)

R16-C 2518 3659 3750 067 098R16-Q 1822 2648 2800 065 095R15-C 2113 3072 3420 062 090R15-Q 1589 2309 3030 052 076


loading and quarter-point loading conditions At theultimate state obvious deflections were observed atthe loading section which is between 162 and 198of the span

(3) e strain distribution strongly depends on the loadcondition Under mid-point loading conditions theneutral axis shifting toward the tension region in thecross section at the loading position was observedand the maximum offsets of the neutral axis were 118and 17 of the cross section height However thisphenomenon did not appear in quarter-point loadingconditions

(4) Based on the interaction formula proposed in cur-rent standards for timber structures an equivalentbeam-column method was introduced to estimatethe loading capacity of laminated timber archessubjected to vertical concentrated loads e designformulas in NDS can be used to evaluate the loadingcapacity of glulam arches with acceptable accuracye moment amplification factor provided in NDSwas recommended to integrate the second-ordereffect

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is research was funded by the National Natural ScienceFoundation of China (Nos 51778069 51978081 and51578554) the Horizon 2020 Marie Skłodowska-Curie In-dividual Fellowship of European Commission (Grant no793787) the Hunan Provincial Innovation Foundation forPostgraduate China (No CX20190656) and the SpecialFunds for Scientific Research in Public Welfare Industries ofChina Forestry Administration (Grant no 201304504)

References

[1] H Yang D Ju W Liu andW Lu ldquoPrestressed glulam beamsreinforced with CFRP barsrdquo Construction and BuildingMaterials vol 109 pp 73ndash83 2016

[2] D Michael and P Dave ldquoEngineered timber and structuralform in sustainable designrdquo Construction Materials vol 168no 4 pp 161ndash172 2015

[3] M Cepelka and K A Malo ldquoMoment resisting on-site spliceof large glulam elements by use of mechanically coupled longthreaded rodsrdquo Engineering Structures vol 163 pp 347ndash3572018

[4] A W Ostrycharczyk and K A Malo ldquoParametric study oneffects of load position on the stress distribution in networkarch timber bridges with light timber decks on transversecrossbeamsrdquo Engineering Structures vol 163 pp 112ndash1212018

[5] J Murnieks D Serdjuks and K Buka-Vaivade ldquoLoad-car-rying capacity increase of arch-type timber roofrdquo in Pro-ceedings of the 12th International Scientific and PracticalConference vol 1 pp 175ndash179 Rezekne Latvia June 2019

[6] R Crocetti J M Branco and J F Barros ldquoTimber archbridges with V-shaped hangersrdquo Structural Engineering In-ternational vol 29 no 2 pp 261ndash267 2019

[7] U Rodman M Saje I Planinc et al ldquoe lateral buckling oftimber archesrdquo International Journal of Structural Stabilityand Dynamics vol 13 no 8 2013

[8] E Zhu and H Zhou ldquoCreep buckling of glulam archesrdquoJournal of Shenyang Jianzhu University (Natural Science)vol 25 no 4 pp 640ndash655 2009 in Chinese

[9] B Kasal and R Blass ldquoExperimental and analytical investi-gation of crack development in composite reinforced lami-nated archrdquo Materials and Structures vol 46 no 1-2pp 173ndash180 2013

[10] J Jonsson ldquoLoad carrying capacity of curved glulam beamsreinforced with self-tapping screwsrdquo Holz als Roh- undWerkstoff vol 63 no 5 pp 342ndash346 2005

[11] A Kukule and K Rocens ldquoReduction of wood consumptionfor glulam arch by its strengtheningrdquoin Proceedings oftheInternational Conference on Innovative Materials Struc-turesand Technologies Riga Latvia vol 12 pp 69ndash76 2014

[12] N Olsson ldquoReliability and optimization of timber archesrdquoMasterrsquos thesis Lulea University of Technology Lulea Swe-den 1997

[13] A Kannar Z Karacsonyi K Andor and L Csoka ldquoAnalysisof glued-laminated timber structure during five years ofoutdoor operationrdquo Construction and Building Materialsvol 205 pp 31ndash38 2019

[14] D Rammer and P Line ldquoLateral testing of glued laminatedtimber tudor archrdquo in Proceedings of the 2016 World Con-ference on Timber Engineering Vienna Austria August 2016

[15] J Wei Q Wu B Chen and T-L Wang ldquoEquivalent beam-columnmethod to estimate in-plane critical loads of parabolicfixed steel archesrdquo Journal of Bridge Engineering vol 14 no 5pp 346ndash354 2009

[16] GBT 50708-2012 Standard for Test Methods of TimberStructures China Architecture amp Building Press BeijingChina 2012

[17] American Wood Council National Design Specification forWood Construction American Wood Council (ACI) Lees-burg VA USA 2018

[18] BS EN 1995-1-12004+A22014 Eurocode 5 Design of TimberStructures Part 1-1 GeneralmdashCommon Rules and Rules forBuildings European Committee for Standardization (CEN)Brussels Belgium 2014

[19] GB 50005-2017 Standard for Design Timber Structures ChinaArchitecture amp Building Press Beijing China 2017

[20] GBT 50329-2012 Standard for Test Methods of TimberStructure China Architecture amp Building Press BeijingChina 2012

[21] R C Spoorenberg H H Snijder and J C D HoenderkampldquoA theoretical method for calculating the collapse load of steelcircular archesrdquo Engineering Structures vol 38 pp 89ndash1032011

[22] H Yang W Liu W Lu S Zhu and Q Geng ldquoFlexuralbehavior of FRP and steel reinforced glulam beams experi-mental and theoretical evaluationrdquo Construction and BuildingMaterials vol 106 pp 550ndash563 2016

[23] S Huang ldquoA brief description of the design formula of timbermembers under compression and lateral loads in Chinesecoderdquo Journal of Building Structures vol 20 no 3 pp 50ndash571999 in Chinese


Research ArticleExperimental Study on Loading Capacity of Glued-LaminatedTimber Arches Subjected to Vertical Concentrated Loads

Jiale Zhou1 Chuanxi Li1 Lu Ke 1 Jun He12 and Zhifeng Wang 3

1Key Laboratory of Bridge Engineering Safety Control by Department of EducationChangsha University of Science and Technology Changsha 410114 China2Institute for Infrastructure and Environment Heriot-Watt University Edinburgh Currie EH14 4AS UK3Department of Civil Engineering and Mechanics Central South University of Forestry and Technology Changsha 41004 China

Correspondence should be addressed to Lu Ke clkelustucsusteducn and Zhifeng Wang 13607431423163com

Received 27 December 2019 Revised 2 May 2020 Accepted 4 May 2020 Published 22 May 2020

Academic Editor Jorge Branco

Copyright copy 2020 Jiale Zhou et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Glued-laminated timber arches are widely used in gymnasiums bridges and roof trusses However studies on their mechanicalbehaviours and design methods are still insufficient is paper investigates the in-plane loading capacity of circular glued-laminated timber arches made of Douglas fir Experiments were conducted on four timber-archmodels with different rise-to-spanratios under concentrated loads at mid-span and quarter-point locations e structural responses failure modes and loadingcapacity of the timber arch specimens were obtained e results show that the timber arches presented symmetric and anti-symmetric deformation under mid-point and quarter-point loading conditions respectively e downward shifting of theneutral axis of the cross section was observed under mid-point loading condition which contributes to higher loading capacitycompared to that under quarter-point loading condition e loading condition significantly affects the ultimate loads and thestrain distribution in the cross section Based on the design formula in current standards for timber structures an equivalentbeam-columnmethod was introduced to estimate the loading capacity of the laminated timber arches under vertical concentratedloads e moment amplification factor in the formula was compared and discussed and the value provided in the NationalDesign Specification for Wood Construction was recommended with acceptable accuracy

1 Introduction

Glued-laminated (glulam) timber which is made of gluedlayers of solid sawn lumber (timber lamellae) has numerousadvantages such as high strength-to-weight ratio excellentsustainability of sources and superior designability [1] eglued-laminated timber arches (glulam arches) have beenwidely used in many large-span structures such as gymnasi-ums bridges and roof trusses [2ndash6] However the failuremechanism of glulam arches subject to external loads has notbeen sufficiently studied many problems are still not wellunderstood It is of importance to understand the failuremechanism and design method for glulam arches underconcentrated loads e loading capacity of glulam arches isinfluenced by many factors such as the rise-to-span ratiolateral supports [7] creep of timber material [8] and rein-forcement measures [5 9ndash11]

Regarding the research on glulam arches Rodman et al[7] investigated the stability of glulam arches subjected tovertical distributed loads finding that the rise-to-span ratiosignificantly affects the lateral buckling capacity of glulamarches e lateral deformation is no longer crucial whensufficient lateral supports were provided Zhu and Zhou [8]analyzed the influence of creep of the timber material on theloading capacity of glulam arches under full-span uniformloads through theoretical analysis they revealed that thecreep is the crucial factor affecting the loading capacityOlsson [12] analyzed the influence of the load distributionon the internal forces in the glulam arches e results showthat the internal force distribution of glulam arches issensitive to the load distribution Kannar et al [13] analyzedthe global bending and shear strength of timber structuresfinding that the use of thinner lamella enables producingmore homogeneous glulam structures Ostrycharczyk and

HindawiAdvances in Civil EngineeringVolume 2020 Article ID 7987414 9 pageshttpsdoiorg10115520207987414



























εcu εcyεtu ε

σftu

fc







Vect

or h

eigh

t


1

23

4

5

6

Tension bar

Span

0 LL4 L2 3L4


(a)

56

140

Strain gauges

(b)



Circleradius

Specimennumber

Height(m)

Span(m)

Rise-to-spanratio

Loadingconditions


R 3m






Dial indicator

Tension bar

(a)

Lateral supports


Strain gauges

(b)









40

35

30

25

20

15

10

5

00 10 20 30 40 50 60 70

Load

(kN

)

Displacement (mm)

14kN

12kN

Elastoplastic stage

Elastic stage

R16-CR15-C

R16-QR15-Q


Compression region

Tensile region


(a)



(b)


(c)


(d)












30

15

0

ndash15

ndash30

ndash45

ndash60

Vert

ical

def

orm

atio

n (m

m)




(a)


30

15

0

ndash15

ndash30

ndash45

ndash60Ve

rtic

al d

efor

mat

ion

(mm

)



(b)








M Pl

16 (1)

N 5Pl

16f (2)



M 21Pl

128 (3)

N 1

4f2 + l2

1113968 middot3Pf

2+15Pl2

32f1113888 1113889 (4)

16

14

12

10

8

6

4

2

0

ndash2

Sect

ion

heig

ht (c

m)


Neutral axis

εcu εtu

4kN14kN22kN30kN37kN


(a)

16

14

12

10

8

6

4

2

0

ndash2

Sect

ion

heig

ht (c

m)


Neutral axis

εcu εtu

4kN12kN18kN22kN26kN

8kN16kN20kN24kN28kN

(b)

16

14

12

10

8

6

4

2

0

ndash2

Sect

ion

heig

ht (c

m)


Neutral axis

εcu εtu


4kN12kN18kN22kN26kN

342kN30kN

(c)

16

14

12

10

8

6

4

2

0

ndash2

Sect

ion

heig

ht (c

m)


Neutral axis

εcu εtu


5kN10kN16kN20kN24kN

303kN28kN

(d)





N

Anfc1113888 1113889

2

+M


fcE 047E

l0h( 11138572 (6)

An blowast h (7)

W bh2

6 (8)



ftfc( 1113857 + 1 (9)


fcE 0822Eminprime

l0h( 11138572 (10)





U1












6 Conclusions






PCU1 PC

U2 PTU (PC

U1PTU) (PC

U2PTU)

R16-C 2518 3659 3750 067 098R16-Q 1822 2648 2800 065 095R15-C 2113 3072 3420 062 090R15-Q 1589 2309 3030 052 076







Acknowledgments


References



















































εcu εcyεtu ε

σftu

fc







Vect

or h

eigh

t


1

23

4

5

6

Tension bar

Span

0 LL4 L2 3L4


(a)

56

140

Strain gauges

(b)



Circleradius

Specimennumber

Height(m)

Span(m)

Rise-to-spanratio

Loadingconditions


R 3m






Dial indicator

Tension bar

(a)

Lateral supports


Strain gauges

(b)









40

35

30

25

20

15

10

5

00 10 20 30 40 50 60 70

Load

(kN

)

Displacement (mm)

14kN

12kN

Elastoplastic stage

Elastic stage

R16-CR15-C

R16-QR15-Q


Compression region

Tensile region


(a)



(b)


(c)


(d)












30

15

0

ndash15

ndash30

ndash45

ndash60

Vert

ical

def

orm

atio

n (m

m)




(a)


30

15

0

ndash15

ndash30

ndash45

ndash60Ve

rtic

al d

efor

mat

ion

(mm

)



(b)








M Pl

16 (1)

N 5Pl

16f (2)



M 21Pl

128 (3)

N 1

4f2 + l2

1113968 middot3Pf

2+15Pl2

32f1113888 1113889 (4)

16

14

12

10

8

6

4

2

0

ndash2

Sect

ion

heig

ht (c

m)


Neutral axis

εcu εtu

4kN14kN22kN30kN37kN


(a)

16

14

12

10

8

6

4

2

0

ndash2

Sect

ion

heig

ht (c

m)


Neutral axis

εcu εtu

4kN12kN18kN22kN26kN

8kN16kN20kN24kN28kN

(b)

16

14

12

10

8

6

4

2

0

ndash2

Sect

ion

heig

ht (c

m)


Neutral axis

εcu εtu


4kN12kN18kN22kN26kN

342kN30kN

(c)

16

14

12

10

8

6

4

2

0

ndash2

Sect

ion

heig

ht (c

m)


Neutral axis

εcu εtu


5kN10kN16kN20kN24kN

303kN28kN

(d)





N

Anfc1113888 1113889

2

+M


fcE 047E

l0h( 11138572 (6)

An blowast h (7)

W bh2

6 (8)



ftfc( 1113857 + 1 (9)


fcE 0822Eminprime

l0h( 11138572 (10)





U1












6 Conclusions






PCU1 PC

U2 PTU (PC

U1PTU) (PC

U2PTU)

R16-C 2518 3659 3750 067 098R16-Q 1822 2648 2800 065 095R15-C 2113 3072 3420 062 090R15-Q 1589 2309 3030 052 076







Acknowledgments


References





























Vect

or h

eigh

t


1

23

4

5

6

Tension bar

Span

0 LL4 L2 3L4


(a)

56

140

Strain gauges

(b)



Circleradius

Specimennumber

Height(m)

Span(m)

Rise-to-spanratio

Loadingconditions


R 3m






Dial indicator

Tension bar

(a)

Lateral supports


Strain gauges

(b)









40

35

30

25

20

15

10

5

00 10 20 30 40 50 60 70

Load

(kN

)

Displacement (mm)

14kN

12kN

Elastoplastic stage

Elastic stage

R16-CR15-C

R16-QR15-Q


Compression region

Tensile region


(a)



(b)


(c)


(d)












30

15

0

ndash15

ndash30

ndash45

ndash60

Vert

ical

def

orm

atio

n (m

m)




(a)


30

15

0

ndash15

ndash30

ndash45

ndash60Ve

rtic

al d

efor

mat

ion

(mm

)



(b)








M Pl

16 (1)

N 5Pl

16f (2)



M 21Pl

128 (3)

N 1

4f2 + l2

1113968 middot3Pf

2+15Pl2

32f1113888 1113889 (4)

16

14

12

10

8

6

4

2

0

ndash2

Sect

ion

heig

ht (c

m)


Neutral axis

εcu εtu

4kN14kN22kN30kN37kN


(a)

16

14

12

10

8

6

4

2

0

ndash2

Sect

ion

heig

ht (c

m)


Neutral axis

εcu εtu

4kN12kN18kN22kN26kN

8kN16kN20kN24kN28kN

(b)

16

14

12

10

8

6

4

2

0

ndash2

Sect

ion

heig

ht (c

m)


Neutral axis

εcu εtu


4kN12kN18kN22kN26kN

342kN30kN

(c)

16

14

12

10

8

6

4

2

0

ndash2

Sect

ion

heig

ht (c

m)


Neutral axis

εcu εtu


5kN10kN16kN20kN24kN

303kN28kN

(d)





N

Anfc1113888 1113889

2

+M


fcE 047E

l0h( 11138572 (6)

An blowast h (7)

W bh2

6 (8)



ftfc( 1113857 + 1 (9)


fcE 0822Eminprime

l0h( 11138572 (10)





U1












6 Conclusions






PCU1 PC

U2 PTU (PC

U1PTU) (PC

U2PTU)

R16-C 2518 3659 3750 067 098R16-Q 1822 2648 2800 065 095R15-C 2113 3072 3420 062 090R15-Q 1589 2309 3030 052 076







Acknowledgments


References































40

35

30

25

20

15

10

5

00 10 20 30 40 50 60 70

Load

(kN

)

Displacement (mm)

14kN

12kN

Elastoplastic stage

Elastic stage

R16-CR15-C

R16-QR15-Q


Compression region

Tensile region


(a)



(b)


(c)


(d)












30

15

0

ndash15

ndash30

ndash45

ndash60

Vert

ical

def

orm

atio

n (m

m)




(a)


30

15

0

ndash15

ndash30

ndash45

ndash60Ve

rtic

al d

efor

mat

ion

(mm

)



(b)








M Pl

16 (1)

N 5Pl

16f (2)



M 21Pl

128 (3)

N 1

4f2 + l2

1113968 middot3Pf

2+15Pl2

32f1113888 1113889 (4)

16

14

12

10

8

6

4

2

0

ndash2

Sect

ion

heig

ht (c

m)


Neutral axis

εcu εtu

4kN14kN22kN30kN37kN


(a)

16

14

12

10

8

6

4

2

0

ndash2

Sect

ion

heig

ht (c

m)


Neutral axis

εcu εtu

4kN12kN18kN22kN26kN

8kN16kN20kN24kN28kN

(b)

16

14

12

10

8

6

4

2

0

ndash2

Sect

ion

heig

ht (c

m)


Neutral axis

εcu εtu


4kN12kN18kN22kN26kN

342kN30kN

(c)

16

14

12

10

8

6

4

2

0

ndash2

Sect

ion

heig

ht (c

m)


Neutral axis

εcu εtu


5kN10kN16kN20kN24kN

303kN28kN

(d)





N

Anfc1113888 1113889

2

+M


fcE 047E

l0h( 11138572 (6)

An blowast h (7)

W bh2

6 (8)



ftfc( 1113857 + 1 (9)


fcE 0822Eminprime

l0h( 11138572 (10)





U1












6 Conclusions






PCU1 PC

U2 PTU (PC

U1PTU) (PC

U2PTU)

R16-C 2518 3659 3750 067 098R16-Q 1822 2648 2800 065 095R15-C 2113 3072 3420 062 090R15-Q 1589 2309 3030 052 076







Acknowledgments


References


































30

15

0

ndash15

ndash30

ndash45

ndash60

Vert

ical

def

orm

atio

n (m

m)




(a)


30

15

0

ndash15

ndash30

ndash45

ndash60Ve

rtic

al d

efor

mat

ion

(mm

)



(b)








M Pl

16 (1)

N 5Pl

16f (2)



M 21Pl

128 (3)

N 1

4f2 + l2

1113968 middot3Pf

2+15Pl2

32f1113888 1113889 (4)

16

14

12

10

8

6

4

2

0

ndash2

Sect

ion

heig

ht (c

m)


Neutral axis

εcu εtu

4kN14kN22kN30kN37kN


(a)

16

14

12

10

8

6

4

2

0

ndash2

Sect

ion

heig

ht (c

m)


Neutral axis

εcu εtu

4kN12kN18kN22kN26kN

8kN16kN20kN24kN28kN

(b)

16

14

12

10

8

6

4

2

0

ndash2

Sect

ion

heig

ht (c

m)


Neutral axis

εcu εtu


4kN12kN18kN22kN26kN

342kN30kN

(c)

16

14

12

10

8

6

4

2

0

ndash2

Sect

ion

heig

ht (c

m)


Neutral axis

εcu εtu


5kN10kN16kN20kN24kN

303kN28kN

(d)





N

Anfc1113888 1113889

2

+M


fcE 047E

l0h( 11138572 (6)

An blowast h (7)

W bh2

6 (8)



ftfc( 1113857 + 1 (9)


fcE 0822Eminprime

l0h( 11138572 (10)





U1












6 Conclusions






PCU1 PC

U2 PTU (PC

U1PTU) (PC

U2PTU)

R16-C 2518 3659 3750 067 098R16-Q 1822 2648 2800 065 095R15-C 2113 3072 3420 062 090R15-Q 1589 2309 3030 052 076







Acknowledgments


References


























M Pl

16 (1)

N 5Pl

16f (2)



M 21Pl

128 (3)

N 1

4f2 + l2

1113968 middot3Pf

2+15Pl2

32f1113888 1113889 (4)

16

14

12

10

8

6

4

2

0

ndash2

Sect

ion

heig

ht (c

m)


Neutral axis

εcu εtu

4kN14kN22kN30kN37kN


(a)

16

14

12

10

8

6

4

2

0

ndash2

Sect

ion

heig

ht (c

m)


Neutral axis

εcu εtu

4kN12kN18kN22kN26kN

8kN16kN20kN24kN28kN

(b)

16

14

12

10

8

6

4

2

0

ndash2

Sect

ion

heig

ht (c

m)


Neutral axis

εcu εtu


4kN12kN18kN22kN26kN

342kN30kN

(c)

16

14

12

10

8

6

4

2

0

ndash2

Sect

ion

heig

ht (c

m)


Neutral axis

εcu εtu


5kN10kN16kN20kN24kN

303kN28kN

(d)





N

Anfc1113888 1113889

2

+M


fcE 047E

l0h( 11138572 (6)

An blowast h (7)

W bh2

6 (8)



ftfc( 1113857 + 1 (9)


fcE 0822Eminprime

l0h( 11138572 (10)





U1












6 Conclusions






PCU1 PC

U2 PTU (PC

U1PTU) (PC

U2PTU)

R16-C 2518 3659 3750 067 098R16-Q 1822 2648 2800 065 095R15-C 2113 3072 3420 062 090R15-Q 1589 2309 3030 052 076







Acknowledgments


References



























N

Anfc1113888 1113889

2

+M


fcE 047E

l0h( 11138572 (6)

An blowast h (7)

W bh2

6 (8)



ftfc( 1113857 + 1 (9)


fcE 0822Eminprime

l0h( 11138572 (10)





U1












6 Conclusions






PCU1 PC

U2 PTU (PC

U1PTU) (PC

U2PTU)

R16-C 2518 3659 3750 067 098R16-Q 1822 2648 2800 065 095R15-C 2113 3072 3420 062 090R15-Q 1589 2309 3030 052 076







Acknowledgments


References






























Acknowledgments


References

























experimental study on loading capacity of glued-laminated

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