Laterally Restrained Bamboo Concrete Composite Archunder Uniformly Distributed Loading

C. Korde, Ph.D.1; R. West, Ph.D.2; A. Gupta, Ph.D.3; and S. Puttagunta, Ph.D.4

Abstract: The arch, as a structural element, has been used since ancient times, originally in stone or timber, more recently in reinforcedconcrete or steel. However, the more modern materials involving steel and concrete are highly energy and carbon intensive. Hardwood timber,although renewable, takes between 30 and 50 years to grow when used structurally. But a highly sustainable tropical material, bamboo, awoody grass, requires only 4–5 years of growth before its considerable compressive and tensile strength can be used for developing structuralarches for load-bearing applications. This paper investigates the structural performance of bamboo-concrete (Bamcrete) composite parabolictied arches of span 4.5 m with a rise-to-span ratio of 0.2 under a uniformly distributed loading. An innovative technique of integrating twoslender bamboos of the Dendrocalamus strictus genera together to form a rigid joint, termed a Haritha-IITD Bamcrete (HIB) joint, isdescribed. The paper also discusses the test set-up for loading and monitoring the performance of the Bamcrete arch. Furthermore, a com-parison is made between the experimental results and computer modeling using STAAD software, where good correlation is obtained withinthe linear response range. The techniques involved in making a Bamcrete arch are so successful as to suggest strong potential exists forwidespread use as a sustainable and renewable structural load-bearing element. DOI: 10.1061/(ASCE)ST.1943-541X.0000945. © 2014American Society of Civil Engineers.

Author keywords: Bamboo; Concrete; Ferrocement; Uniformly distributed loading; Parabolic tied arch; Wood structures.

Introduction

The arch, as a structural element, has been used over the ages fordifferent spans. The beauty of the parabolic structural form of anarch is that the major acting forces are compressive under a uni-formly distributed loading condition. Also, the bending momentdiagram is parabolic and the thrust line is close to the locusof centroid, making it inherently stable. Hence, any material hav-ing good compressive strength can be used for making a para-bolic arch. The various materials successfully used for makingan arch include stone, timber, concrete, steel and various compo-sites. However, these materials, with the exception of timber, arehighly energy intensive, although even structural timber requiresa long time, of the order of 30–50 years, to grow to sufficientmaturity.

On the other hand, bamboo, a woody grass, requires only4–5 years (Hidalgo-Lopez 2003) of growing to reach its fullstructural strength. This gives an enormous time-saving in utiliz-ing what is, effectively, a rapidly regenerating renewable re-source for building construction. The compressive strength ofa structural bamboo culms in its natural form is found to varywith species and geographical location, for example, from30–50 MPa for 20 species in India (NBC 2005a), 12–50 MPa

for seven species in South America (Ghavami 2005) and35–115 MPa for two species in China (Yu et al. 2003). Thus,bamboo, as a green material, has good potential to be used inan arch form. One of the challenges confronting the engineeringcommunity is to make the best use of the particular mechanicalproperties of bamboo to come up with innovative structuralengineering solutions.

Extensive research has been undertaken in understandingthe behavior of masonry arches (Clemente et al. 1995; BriccoliBati et al. 2007), reinforced concrete arches (Zhang et al.2007; Marefat et al. 2004), steel arches (Pi and Trahair 1999;Wei-Xin et al. 2004) and composite arches (Mirmiran and Made1993; Clarke and Hancok 1995). For example, a study of ulti-mate load carrying capacity of an arch has been carried outon old bridge arch ribs (Zhang et al. 2007), tied arches (Wanget al. 2007) and masonry arches (Briccoli Bati et al. 2007),respectively.

In the past, the applications of bamboo-concrete compositeswere reported (Janssen 2000; Hidalgo-Lopez 2003; Ghavami2005; Sudhakar, unpublished report, 2006). Use of bamboo inan arch form in domes, structures, etc. (Hidalgo-Lopez 2003)and even a 52-m-long arch bridge (Stamm 2009) is reported. Also,an engineering evaluation of parabolic bamboo bow arches withwire ties and cross ties has been carried out which are used forconstruction of roof structures at Haritha Ecological Institute(SARMET 1999). The limitation of these arches, with cross ties,in resisting bending moments is resolved with an innovative formof a bamboo-concrete composite joint (Sudhakar et al. 2007),termed as a HIB joint. Further, an experimental evaluation ofbamboo-concrete composites (Bamcrete) arches under uniformlydistributed loading is also undertaken for short-term static andcreep loading (Korde et al. 2007). A program for systematic evalu-ation of the HIB tied arch technology was initiated at IIT Delhi in2006 and the technology developed is hence proposed to be termedas Haritha-IITD Bamcrete (HIB) Technology.

1Research Associate, Centre for Rural Development and Technology,Indian Institute of Technology, Delhi 110016, India (corresponding author).E-mail: chaarukorde27@gmail.com

2Associate Professor, Dept. of Civil, Structural and EnvironmentalEngineering, Trinity College, Dublin 2, Ireland.

3Professor, Dept. of Civil Engineering, Indian Institute of Technology,Delhi 110016, India.

4Founder, Haritha Ecological Institute, Andhra Pradesh 507115, India.Note. This manuscript was submitted on August 31, 2012; approved on

September 10, 2013; published online on April 7, 2014. Discussion periodopen until September 7, 2014; separate discussions must be submitted forindividual papers. This paper is part of the Journal of Structural Engineer-ing, © ASCE, ISSN 0733-9445/B4014005(11)/$25.00.

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Scope of Present Study

The present study reports on the preliminary experimental evalu-ation of three HIB arches (nominal specifications: 4.5-m span;0.2 rise to span ratio). The aim of the experimental evaluation isto evolve the following:1. A test setup that can take the above arches to ultimate failure

under uniformly distributed loading conditions;2. An understanding of the maneuverability of simple hydrauli-

cally based equipment for generating the complete load-deflection curves all the way up to ultimate failure for bamboostructures;

3. The cyclic load behavior of bamboo arches; and4. A model of a HIB arch with a typical bamboo.The study reported on here is the first of its kind of an innovative

structural form with bamboo. The test reported here is the first stageof a comprehensive test program of evaluating the performanceof Bamcrete arches under various forms of loading as follows: uni-formly distributed loading, left half distributed loading, right halfdistributed loading, center half distributed loading, crown pointloading and ultimate uniformly distributed loading.

Experimental Investigation

General

As shown in Fig. 1, the Dendrocalamus strictus genera of bam-boo have a naturally bent shape. This species of bamboo isslender, gradually changing from solid to hollow in diameter frombottom to top, respectively, with a tapering cross-section reduc-ing from base to top. Fig. 2 shows a schematic view of the bamboo-concrete composite parabolic tied arch. The two bamboos are

rigidly connected and separated at a required clear spacing s usinga ferrocement band of depth d and width w.

From Fig. 3 it can be seen that the horizontal thrust is very highfor the arch with a low rise to span ratio which reduces hyperboli-cally with reduction in rise to span ratio. Also, from field experi-ence, it is observed that, in cases of higher rise to span ratios, the

Fig. 1. Bamboo bush (Dendrocalamus strictus) (image byChaaruchandra Korde)

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Fig. 2. Bamcrete parabolic tied arch details: (a) elevation; (b) crosssectional details

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Axial Thrust

Fig. 3. Parabolic arch under uniformly distributed loading: (a) freebody diagram; (b) horizontal thrust versus rise to span ratio

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amount of flexure induced in the bamboo culm to bend it to therequired parabolic profile is much greater as compared to that ofrise to span ratios of, say, between 0.2–0.25. Hence, a rise to spanratio of 0.2 is taken for the fabrication of the arches in this work.Specimen arches A, B, and C are selected to have span a length, L,of 4.5 m, rise to span ratio of 0.2, clear spacing, s, of 75 mm, width,w, of 200 mm and depth, d, of 200 mm. These are achieved throughprefabrication on a workbench, Fig. 4(a). In practice, on releaseafter fabrication, the three arches A, B, and C are found to havea span of 4.4 m and rise to span ratios as 0.2, 0.19, and 0.22, re-spectively. The support conditions provided for the experimentaltest set up are pinned at one end and roller support at the other side.

Fabrication of Test Specimen

The Bamcrete arch is prepared using three culms of the Dendro-calamus strictus genera, this bamboo being thick at the base andtapering towards the top, is amenable to be bent into a parabolicarch profile. To develop the parabolic profile, a work bench is usedas shown in Fig. 4. Initially, the studs on the workbench are posi-tioned with measurements at the calculated parabola coordinates.The base of the bamboo is locked at one corner, as shown in Fig. 4,and a bamboo culm is then bent along the studs to generate therequired parabolic profile. The bamboo culm so bent, is lockedat the other corner with a stud so that it does not spring back. Thus,this gives the bamboo culm a parabolic profile as shown in Fig. 2(a)for the bottom bamboo of the Bamcrete arch segment. To integratethe top bamboo culm, a wooden block spacer is used to generate therequired spacing. These spacers are placed at regular intervalsabove the bottom bamboo on the workbench. Another bambooculm is then taken and guided in a similar manner onto the workbench along the wooden spacers. This bamboo is initially locked atboth ends and in between with studs so that it is fully engaged withthe spacers. Thus, two bamboo culms forms the required twin ver-tically separated parabolic profiles. Also the tapering in these bam-boo culms are placed alternate to each other, as shown in Fig. 4(b),to ensure a broadly similar average cross-sectional area along thecomposite arch.

There is extensive literature on the traditional practices of join-ing two bamboos together using bamboo slivers, ropes, interlock-ing and using wooden or bamboo dowel pins. Also, in moderntimes researchers have worked on joining bamboo together usingnails, nuts and bolts, bamboo board, gusset plates, wooden block

and glue with metal clamp, steel dowels for locking single culm andtwo culms together to the foundation, fiber-reinforced glue jointsand jute reinforced acrylic joints. The challenges before researchersin joining two bamboo culms come because bamboo is hollow anda unidirectional fiber matrix composite. Hence, it has relatively lowshear strength in the longitudinal direction along the fibers (com-pared to the transverse direction), as a consequence of which it hasa tendency to split when dowels or bolts are used and, in a worstscenario, when nailed.

Also, the bamboo cannot be firmly gripped, as this leads tocrushing of the material because of its hollowness. Further, as aconsequence of studies to determine the actual cause of failurein bamboo, it has long been realized that bamboo does not usuallyfail in compression, bending or shear but when a maximum tangen-tial tensile stresses is reached (Acre 1993). Owing to these limita-tions, a strong joint which can connect two bamboo together rigidlyin a cost-effective manner is far from reality. Also, for applicationsin structural engineering, a rigid joint may be required which is ableto space two bamboos at a given spacing apart to generate the re-quired second moment of area of cross-section. This will enable amore optimum use of even thin bamboo culms, like that of Den-drocalamus strictus, leading to an enhanced bending strength andstiffness of the cross section.

By understanding the limitations of bamboo, an innovative andcost-effective method of joining two bamboos together rigidlywith a given spacing has been proposed and demonstrated(Sudhakar, unpublished report, 2006). The technology used inmaking the joint is of ferro-cementing and the joint is called aHaritha-IITD Bamcrete or an HIB joint. Here, a U-shaped stirrupof 6-mm diameter mild steel rod, hexagonal thin wires mesh andconcrete are used for integrating two bamboos together. The appli-cation of a HIB joint for the fabrication of a bamboo parabolic tiedarch is shown in Fig. 5. Here, in stage 1, at the location of the jointin the bamboo parabolic arch, a single hole is drilled in the innerand outer bamboos, and the U-shaped stirrup is protruded, as illus-trated in Fig. 5(b). The extended stirrup is lapped up at stages 2 and3. This location of the joint is scraped to make the surface of bam-boo roughened. Now, the scraped portion of bamboos in the bandregion is coated with a resin mixed with cement called Tapecrete.This material acts as a coating over the bamboo, thus giving aninteractive surface where the cement paste can generate a bond.However, although the bond generated will not be very strong,given the fact that the bamboo will undergo expansion/contractionand swelling/shrinkage over its life time, being a natural fiber, thecoating helps in restricting the moisture absorption during casting.

(a)

(b)

Fig. 4. Placing of bamboo for bamcrete arch: (a) workbench for bend-ing bamboo (image by Chaaruchandra Korde); (b) placement of twobamboo culms

(a) (b)

Fig. 5.HIB joint fabrication process: (a) stages of fabrication; (b) actualphoto (image by Sudhakar Puttagunta)

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Hence, this ensures a better bonding with the hexagonal thin wiremesh which is wrapped over the bamboo in the band region in stage4 – see Fig. 5(b).

The number and spacing of joints is decided from the experi-mental condition of testing the parabolic bamboo tied arch underuniformly distributed loading, using the test set up as shown inFig. 6. Now, the band region is placed into formwork, which en-sures enough cover to the stirrups, and is filled with concrete. In all,nine joints are made along the length of the arch as shown in Fig. 2.Thus an innovative rigid connection, the HIB joint, is establishedbetween two bamboos which are spaced a fixed distance apart, in abamboo parabolic tied arch.

Setup and Instrumentation

To load the arch in a uniformly distributed manner, a wiffle treeform of loading is applied using chains, beams and jack. Here, steelchains are hung from the center of eight segments of the arch, asshown in Fig. 6. To ensure a more uniform distribution and to averta concentrated loading on the bamboo segment, an inverted steelequal angle is placed over the top of each bamboo segment. Further,each chain is looped and hung from the center of the steel anglesabove the segments (see Fig. 6, section B-B). To the bottom end ofthe chains, four short steel beams are supported within the loop.The center points of these beams are marked and, over everytwo beams, one more steel beam is placed. Thus two more steelbeams are placed at the second level. Similarly, the center pointsof these beams are marked and one more steel beam is placed at thenext level, as illustrated.

The load is applied to the top beam about the center point byoperating the hydraulic jack incrementally in pull mode. The jack isfixed to the strong floor along the center line of the arch and wiffletree network. Thus, a uniform load distribution is achieved acrossthe arch when the jack pulls the center point of the girder at level 3in Fig. 6. To measure the applied load, a tension load cell is used inbetween the jack and the main beam. The deflection measurementsare taken at the crown point, roller support, and left and right quar-ter spans using digital dial gauges. The support conditions in theexperiment are a hinge and roller simple support at opposite ends.The arches are laterally restrained at near quarter span location us-ing a steel frame, as in Fig. 7. Initially, to ensure the uniform dis-tribution of the load under a wiffle tree network, four proving ringsare placed as shown in Fig. 7. The load is recorded at these provingrings and the readings obtained are similar, demonstrating that auniformly distributed loading has been achieved. Hence, in the sub-sequent experiments, the proving rings are removed and the finaltest set up is as shown in Fig. 6.

A cyclic loading sequence is performed up to 11 kN on arch Aand the load-deformation relationship obtained under cyclic load-ing is as shown in Fig. 8. From this figure, it can be observed thatthe arch undergoes a significant amount of energy loss. This isnoted to be resulting from the lateral deformations of the central1=3rd region of the arch owing to the lack of restraints. Hence,two additional bamboo culms are integrated with the steel framein a manner as shown in Fig. 7(a) to provide additional lateral re-straint. With this intervention, the reduction in the energy loss of

Jack

A

AB

B

Load Cell

Fig. 6. Bamcrete parabolic tied arch under UDL condition

Fig. 7. Experimental setup: (a) uniformly distributed loading condi-tion; (b) roller support; (c) hinge support (images by ChaaruchandraKorde)

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the system can be observed in the subsequent cycles as shownin Fig. 8.

Material Test

In the making of the arch, the two principal materials are bambooand concrete. Hence, their properties from literature along withonly a few material tests are conducted and reported hereunder.

Compression Test of Bamboo

Bamboo is a natural functionally graded material, so it tapers frombottom to top and varies from inner to outer. Also, the culm consistsof nodal (where there can be diaphragms internally) and inter-nodalsections. Hence, the six samples from one culm, with and withoutnodes, are assembled, one each from the bottom, middle and topregions. The samples prepared are ensured to have a test surface atright angles to the length of the specimen and they are tested underuniform compression rate, the results of which are shown in Table 1.

Tension Test of Bamboo

A test (Ahmad and Kamke 2005) on the bamboo slivers is con-ducted on Dendrocalamus strictus, where each culm is divided intofour locations, namely, lower bottom as L1, upper bottom as L2,lower top as L3 and upper top as L4. Here, more than 50 inter-nodaltensile test samples are prepared as per ASTMD 143-95 i.e., width,thickness, and length as 12, 3, and 120 mm, respectively, from L1and L2 zones; In addition, 30 nodal samples are prepared from L1.The middle section of the specimen is necked down to 5 mm;wooden plates are glued to the ends to prevent splitting and to pro-mote failure at the neck during the test. The test is conducted at arate of deformation of 2.54 mm=min with specimens precondi-tioned at 20°C and 65% relative humidity. The mean ultimate ten-sile strengths (with standard deviations) for intermodal samples

were 156.1 MPa (37.7 MPa) and 185.3 MPa (41.8 MPa), for L1and L2, respectively. In comparison, the nodal sample strengthof L1 was 106.2 MPa (26.8 MPa), considerably lower. Themean tensile modulus of elasticity (E) of L1 and L2 respectivelyfor inter-nodal samples were 16,779 MPa (6952 MPa) and12,723 MPa (4496 MPa), respectively, while for nodal samplesit was 17,771 MPa (5354 MPa). It is noticeably that, not unex-pectedly, the variability is high, bamboo being a naturally grownmaterial.

Compression Test of Concrete

The concrete used in the band region is of a relatively high strength.The objective of using such a concrete is to ensure that no failureoccurs in the concrete, so that the failure mode in the experiment isconfined to the bamboo. The strength of concrete is tested usingthree number 150 mm concrete cubes cured for 28 days, givingan average compressive strength of 42.0 MPa.

HIB Arch Test

To determine the ultimate strength of Bamcrete arches, three arches(A, B, and C) are tested under uniformly distributed loading. Thesepreliminary tests had the objective of determining the performanceof the test set-up and understanding the complete structural behav-ior of a Bamcrete arch. Arch A is loaded to determine the ultimateload-carrying capacity; Arch B and Arch C are used to study thecyclic load behavior. In the course of this study, deformations atfour locations, namely the crown, left and right quarter pointsand roller deformations are noted. The total dead load resultingfrom the steel beam and girders is approximately 2 kN which needsto be included in load capacity as it is significant. Also, the arch isinitially loaded with an additional load of 1 kN for a few cycles ofloading and unloading to check the test setup. Further, this load isalways maintained to ensure that there is no slacking in the loadapparatus or bamboo joints.

Arch A

The stiffness of the arch during its initial cycles (Fig. 8) and ulti-mate loading cycle (Fig. 9) are 2.0 kN=mm and 1.33 kN=mm,respectively. This reduction in stiffness is accounted for by earlysecondary effects that occurred owing to unrestricted lateral defor-mations, resulting prior to the laterally restraining of the arch.Because a number of trials of different load patterns (i.e., UDL,LHDL, RHDL, CHDL, and CrPL) are undertaken on the archduring this unrestricted phase, the excessive lateral deformations

Table 1. Compressive Strength of Bamboo

Number SampleArea(mm2)

Maximumload (kN)

Maximumstress (N=mm2)

1 Bottom 1,724 77.3 452 Bottom nodal 2,293 88.26 393 Middle 1,318 35.48 274 Middle nodal 1,345 37.22 285 Top 637 18.79 306 Top nodal 766 21.59 28

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Fig. 9. Ultimate failure loading on HIB arch A: (a) failure of arch A (image by Chaaruchandra Korde); (b) ultimate load versus crown deformation

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resulted in a minor failure at the node of the top bamboo segment atband 7. Though this failure caused the arch to deform from itsparabolic profile, the deviation was not prominent and furtherload could be applied to the arch A to determine its ultimate capac-ity. Thus, when tested to its ultimate loading, arch A sufferedsignificant distortion in the top segment between bands 6 and 7(counted from the left) at a node near band 7, whereupon the archwas unloaded.

In Fig. 9(b), the first cycle has a clear initiation of failure beyond20 kN. The load-deflection curve took a dip and then increased andthen dipped again, with a negative slope. The phenomenon of de-crease in load with increase in deflection is observed in two inter-vals at around 20 kN load, which was captured by the manualoperation of the hydraulic pump. After the second failure occurred,as indicated by the second negative slope segment, it was decidedto deliberately reduce the load by operating a relief valve, until theload reduced to the starting value of 1 kN, with a permanent set of5 mm at the crown.

A second cycle on the same arch is again initially linear withalmost the original stiffness, showing that the two regions of failurein the first test had hardly any permanent effect on the elastic stiff-ness of the arch. In the second cycle, the load was deliberately lim-ited to 12.5 kN and the decreasing load part of the curve wasgenerated by bringing the load down to about 7 kN.

The third cycle is initiated from 7 kN to generate the load-deflection curve until complete failure. It is significant to note thateven the third cycle shows linearity up to nearly 16 kN. Further, the

ultimate load is about 19.5 kN, where the absolute deflection isapproximately 20 mm. The deflection was subsequently takenup to 35 mm for a drop in the load of only 4 kN, while theaverage slope over the additional 15-mm deflection was closeto −0.25 kN=mm. This indicated the considerable resilience andresidual load carrying capacity of the structure.

The load-deflection curve over this additional 15 mm of deflec-tion has several significant regions where segments have nearly zeroslopes, resulting in a negative step downwards. It appears as if, afterevery failure at any place along the arch, the structural reconfiguresitself to resist the residual load. It may be noted that after every pointthat is manually recorded, an intervention by way of a small pump-ing, for a very brief period, is all that is necessary to cause an increasein deflection. Typically as soon as the hydraulic pump is operated,the deflection begins to increase and the increase continues even afterthe pumping action stops, albeit with a progressively reduced rate.The ultimate failure occurs under a 34-mm crown deformation be-tween band 6 and 7 from the left [see Fig. 9(a)].

Arch B and C

The testing of arches B and C under cyclic loading has given newinsight into the behavior of the Bamcrete arch, as shown inFigs. 10–13. Broadly, four distinct phenomena are observed:1. A continuous shift of deformation under cyclic loading

[Figs. 10(a and b) for arch B and Figs. 11(a and b) forarch C],

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2. Linear nonelastic flexibility in bamboo [Figs. 10(b) and11(b)],

3. A progressive increase in the stiffness of the arches withincreasing cycles (Fig. 12 for arch B) and

4. Asymmetric deformation patterns for arches B and C undersymmetric loading.

These can be understood by the following possible reasoning:

Continuous Shift of Cycles under Cyclic LoadingAs may be observed from Figs. 10 and 11, in every succeedingcycle, there is an offset in deflection. As the load increases, the cellwalls are subjected to gradually increasing longitudinal compres-sive load and as a result, they deform and rearrange into a new con-figuration to resist the load. Some of the sclerenchyma sheath fibersin the inner part of the bamboo culm buckle in longitudinal com-pression (Obataya et al. 2007). The cell wall rearrangement and/or the fiber sheath buckling may be irreversibly nonelastic, causinga small offset at the end of each cycle. Additionally, the steel dow-els that pass through the bamboo across its diameter may causepermanent bearing deformation which may also contribute to thisoffset.

Linear Nonelastic Flexibility in BambooIt is observed that though the behavior of arches A, B, and C isinitially linear under increasing load in any given cycle, it is not

purely elastic in the sense that when load is subsequently graduallydecreased, even before significant nonlinearity sets in, the unload-ing curve does not identically retrace along the loading curve, re-sulting in a small off-set in every cycle. This feature is similar tolinear nonelastic flexibility of bamboo as studied in publishedbending experiments on bamboo (Obataya et al. 2007).

Progressive Increase in Stiffness of the Arch with IncreasingCyclesDuring the testing of arch A, it may be observed that the stiffness ofthe arch progressively increase after every cycle. However, becausearch A had already undergone a series of loading combinationswhen this was observed, testing of a fresh one, such as arch B,was studied to capture this phenomenon over about 20 cycles. ArchB is loaded under UDL conditions and, in all, the responses to 22progressive cycles of loading are recorded. The stiffness of the archunder each cycle is plotted against the cycle number in Fig. 12.Cycles 1 to 12 are undertaken on day 1 and another 10 cycleson day 2. It is observed that the stiffness of the arch progressivelyincreases. It was observed that while the stiffness progressively in-creased during 12 cycles of day 1, the 13th cycle, on day 2, afterovernight relaxation, has a substantially lower stiffness. However,in subsequent cycles the trend of day 1 seems to have continued allthe way up to a stiffness of 2.9 kN=mm. It would have possiblybeen more instructive to have continued with the cyclic loadingon subsequent days on two counts: (a) to quantify the overnightrelaxation effect, and (b) to see if the stiffness on repeated diurnaltesting approached a plateau; however, because of time constraints,this was not done.

Asymmetric Deformation Pattern for Arches B and C underSymmetric LoadingThe measured load–deformation plots presenting the behavior atcrown and quarter points is as shown in Figs. 13(a and b) for archesB and C, respectively. It is observed that though the arch is loadedunder symmetrically distributed loading through the efficient wiffletree network, the arches deform in a distinctly asymmetric manner.Similar peculiar asymmetric deformation is reported to be related tomodified slenderness and stiffness ratios (Bradford et al. 2007) for aparabolic arch. The modified slenderness ratio (λ) and stiffness ra-tio (α) for a particular parabolic arch define a parameter given by½λ=ð1þ αÞð1=2Þ� referred to as the Bradford’s buckling ratio (BBR).If its value lies between 7.33 and 9.83, then the overall deformationis reported to be either symmetric or asymmetric while if it exceeds9.83, deformation is definitely asymmetric. The bamboo arches

3.5

y = 0.032x + 2.269

3

2

2.5

1

1.5

0

0.5

Stif

fnes

s pe

r cy

cle

(kN

/mm

)

0 5 10 15 20 25Number of Cycles

Fig. 12. Behavior of stiffness of arch with increasing number of cyclesfor HIB arch B

0

Roller L L/4 Crown R L/4 Hinge

Loacation along arch

No Load

-2

1 kN

3 kN

5 kN

-4

D

7 kN

9.4 kN

-6

Dis

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m)

11 kN

13 kN

-8 15 kN

Location along the arch

0Roller L L/4 Crown R L/4 Hinge

No Load

-2 1 kN

2 kN

4 kN

-6

-4

Def

lect

ion

(mm

)

6 kN

8 kN

-8

10 kN

12 kN

13 kN

-10(a) (b)

Fig. 13. Comparative load deformation behavior along the arch for HIB arch B & C: (a) HIB arch B; (b) HIB arch C

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under study here fall in the asymmetric deformation even undersymmetric UDL because the typical value for the BBR is 12.

Arch C is loaded with 2 kN as the initial load of the test setupattributable to the self-weight of the steel girders in the loading sys-tem. Hence, the actual load carried by the above arch is 15 kN intotal and the average compressive stress resulting from axial thrustis nearly 10 MPa, equal to the allowable stress, a limiting criteriafor use of bamboo ofDendrocalamus strictus genera (NBC 2005b).Also, it can be observed that the experimental response of the struc-ture is linear for every increment of load. Fig. 11 shows the elasticbehavior of the load versus crown deformation. As the behavior ofthe arch is linear, a linear-elastic model can be used to predict thebehavior of Bamcrete parabolic tied arches. Also, the structural de-formations at 10 MPa stress (under a 15 kN Load) is 8 mm at thecrown which is considerably lower than the allowed deflection ofspan/240 (¼18.75 mm) in wooden joists and beams (NBC 2005c).

The vertical stiffness of the arch is 1.4 kN=mm. Furthermore,the horizontal deformation observed at 13 kN load increment is4.5 mm; hence, the stiffness of the arch against horizontal defor-mation is 2.9 kN=mm. The deformation pattern observed under theuniformly distributed loading of the Bamcrete arch is antisymmet-ric. There is neither a crack nor any failure, during or after the cyclicload test.

In summary, it appears that, typically, the overall stiffness of theBamcrete arches is in the range of 1.1 kN=mm to 3.0 kN=mm; thestiffness of arch Avaries from 2.5 kN=mm (Fig. 8) to 1.12 kN=mm(Fig. 9); arch B varies from 2.3 kN=mm to 3.0 kN=mm (Fig. 13)and arch C varies from 1.85 kN=mm to 2 kN=mm (Fig. 11), in theorder of increasing cycles. Because arch A had undergone multiplecombinations of loading cycles and a defect was also observed inthe last cycle of ultimate failure loading (Fig. 9), the broad range,as per performance of arches B and C, can be considered as1.85–3.0 kN=mm. Also, the overall crown deformations under a

15 kN load are 12, 6, and 9 mm in arches A, B, and C, respectively,which are all within the allowed deflection of L/240. Further, thereis neither a crack in the concrete joint nor any failure in the bambooculm observed during or at the end of the cyclic load tests on archesB and C.

Comparison with Software Model

The experimental results are modeled using linear elastic modelingsoftware STAAD.Pro (Fig. 14). To compare the experimental re-sults with software models, the following assumptions are made:• Loading applied is in the plane of the arch under two patterns:

(1) 16-point distributed loading (PDL), Fig. 14(a), and (2) Uni-formly distributed loading (UDL).

• The rise to span ratio for the modeled arch is taken as an averageof arches B and C at 0.205.

• The arch is modeled for both uniform and varying cross sectionof bamboo culms, Fig. 14(b). An average effective diameter isconsidered for a uniform cross-section, whereas a uniformlyvarying outer and inner diameter is considered for varyingcross-section of the hollow pipe. The effect of nodes in the bam-boo is not considered.

• Geometric data was collected for typical generic bamboo culms,from the same location (Terigram, Delhi) as arches A to C, asshown in Table 2. The average outer and inner diameter of thethree nonnodal specimens is used for creating a piece-wise lin-ear approximation to estimate the gradual variation of outer andinner diameter across the entire length of the culm to create atypical bamboo for modeling purposes.

• Each bamboo in the modeled arch is divided into 33 number2-noded beam element segments. Here, the 1st, 17th, and33rd segments represent the actual values of top, middle andbottom of the culm respectively.

• Concrete bands are modeled using 4-noded plate elements andsteel dowels are modeled as 2-noded beam elements with rigidjoints, as shown in Fig. 15.

• The modulus of elasticity is assumed constant for all bambooelements and its value is taken as 15 GPa.

• Bamboo curvature at both arch levels represent a perfectparabola

• Supports are modeled as a hinge and roller.• The whole structural model in all consists of 117 beam elements

and nine plate elements.Figs. 15(a and b) show a comparison of the deformation

patterns between experimental and modeling results for thearches. It is observed that in modeling deformations under theUDL loading the deflected profile has a smaller number ofundulations, but with a more pronounced flat portion in thecentral half of the arch. The undulations are attributable tothe concentrated 16 PDL condition and the rigid bands formingthe three dips on either half of the arch. The flat zone is as per theexpected deformation pattern for a uniform distribution over aparabolic arch.

There is a small asymmetry of deformation pattern of themodeling result (for varying C/s of bamboo along the length)which remains unaffected with the reversal of the supportconditions. It may be attributable to taper in the bamboo crosssection. However, the asymmetry of the measured deformationsof arches B and C is much more pronounced and may be aresult of the phenomenon associated with Bradford’s theorybecause the buckling ratio is 12.14 for these arches. A detaileddiscussion of the asymmetry is beyond the scope of the cur-rent study.

Fig. 14. Software modeling details: (a) nodes, support conditions, andloading; (b) modeling of steel dowel and concrete band of HIB jointwith varying bamboo culm

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Estimating the effective cross-sectional area, Aeff , from axial ri-gidity requires the value of Young’s Modulus which is taken as15 GPa (NBC 2005a). However, from Table 3, it may be observedthat the estimated effective area is lower than the typical 738 mm2

(the average area for middle non-nodal section for typical bamboo).This has two possible explanations: (1) the Young’s Modulus islower than 15 GPa, and/or (2) the tie bamboo has one or more im-perfections in shape over its length. As the tension increases, thesebends tend to straighten out and the effective length of the tie in-creases. This can possibly explain the lower effective axial rigiditydeduced from the extension of the horizontal tie.

The modeled arch of 4.5-m span and 0.205 rise to span ratio,when loaded under both UDL and 16 PDL conditions to a total loadof 12 kN gives crown deformation and tie extension at the rollersupport as 3.3–4.6 mm and 2.82–3.15 mm, respectively. Thus thestiffness of the arch and tie vary between 2.6–3.6 kN=mm and

3.8–4.2kN=mm, respectively. The maximum external fiber stress,as obtained in the modeling, for bamboo under the combined effectof direct and bending stresses in compression and tension are15.0 MPa and 8.0 MPa, respectively. The maximum Von Missstress observed in the band region is 6.4 MPa. Also, it is interestingto note that the steel dowels undergo zero stress in the model.

Table 2. Details of Typical Bamboo Cross Section

Sample name Average (U.O.D) Average (U.I.D) Average (D.O.D) Average (D.I.D)

Individual Overall average

AreaA.O.D A.I.D A.O.D A.I.D

DS-TG-T-1 27.05 10.94 25.22 10.74 26.13 10.99 26.10 9.82 458.85DS-TG-T-1n 25.07 8.01 26.91 9.53 25.99 8.60 26.50 8.94 488.45DS-TG-M-1 32.53 0 33.93 0 33.23 0 31.04 4.83 737.87DS-TG-M-1n 34.39 0 33.43 0 33.91 0 31.58 5.02 763.11DS-TG-B-1 38.33 0 38.06 0 38.19 0 36.23 0 1030.64DS-TG-B-1n 41.41 0 38.50 0 39.95 0 37.89 0 1127.09DS-TG-T-2 24.29 10.35 26.07 10.87 25.18 10.38 — — —DS-TG-T-2n 26.70 9.16 27.15 10.57 26.92 10.28 — — —DS-TG-M-2 30.55 6.73 30.61 6.80 30.58 7.87 — — —DS-TG-M-2n 30.77 8.34 29.26 7.47 30.01 7.73 — — —DS-TG-B-2 36.22 0 39.20 0 37.71 0 — — —DS-TG-B-2n 36.95 0 36.12 0 36.53 0 — — —DS-TG-T-3 26.92 8.08 27.04 8.16 26.98 8.10 — — —DS-TG-T-3n 25.89 38.86 27.27 8.50 26.58 7.94 — — —DS-TG-M-3 29.07 6.72 29.55 6.73 29.31 6.64 — — —DS-TG-M-3n 30.36 6.98 31.30 8.10 30.83 7.35 — — —DS-TG-B-3 32.28 0 33.32 0 32.80 0 — — —DS-TG-B-3n 37.05 0 37.33 0 37.19 0 — — —

Note: U.O.D. = upper outer diameter; U.I.D. = upper inner diameter; D.O.D. = downward outer diameter; D.I.D. = downward inner diameter; A.O.D. =average outer diameter; A.I.D. = average inner diameter.

Fig. 15. Comparative deformation pattern at 12 kN load for arches B and C, and model: (a) 16-point distributed loading; (b) uniformly distributedloading

Table 3. Effective Cross Sectional Area of a Bamboo Tie in Tied Arch

Arch

Measured Deduced

Totalload

Rise tospan ratio

Horizontalextension

Tietension

Effectiveaxialrigidity

Effectivec=s area

kN — mm kN kN mm2

B 12 0.19 4 7.894 8,881 592C 12 0.22 5 6.818 6,136 409

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Considering the gross approximations used in modeling, theagreement can be considered reasonable such that the predictionsof behavior are possible, notwithstanding the large variability inalmost every parameter that is significant in the bamboo culmsas produced in nature. However, the computer modeling does givestrength to the potential practical benefit of using the green HIBarch technology in real structures.

Conclusions

This paper reports on the first of its kind short-term experimentaltesting and modeling of a typical Bamcrete arch. It shows that thetechnology of integrating two or more bamboo culms together us-ing the novel HIB joint behaves as a rigid joint and is amenable toengineering predictions.

The structural behavior up to the 15 MPa compressive stress inthe arches is found to be linear under each increasing cycle of load-ing. In spite of the gross assumptions made in the modeling for anonhomogenous material like bamboo; it makes the structuralbehavior predictable using the FEM modeling software. Basedon the experimental observations and the software analysis, itcan be concluded that:1. Bamcrete parabolic tied arches behave as linear nonelastic

flexible structures to a compressive stress limit of 10 MPa(a limiting criterion as per NBC 2005c for Dendorocalamusstrictus) for a given rise to span ratio in the range 0.19–0.22.

2. The slenderness and stiffness ratios along with geometryvariations across the length seem to govern the structuraldeformation pattern for the bamboo arch, where the amountof contribution of each element requires a more detailedstudy.

3. The stiffness of the arch with respect to the crown varies from1.3-3 kN=mm under uniformly distributed loading and alsoshows progressive improvement with increasing cycles. Thereproducibility of the phenomenon of enhancement of stiffnessneeds to be further validated.

4. The HIB joints provide enough rigidity of connection to inte-grate two bamboos together at the required spacing. Also, thejoint is effective in rigidly connecting the tie to the main arch,as no cracks were observed on the band indicating that therewas no slippage at the joints. Hence it can be concluded thatthe joint is a strong and effective means of developing a rigidbond between two bamboos spaced a small distance apart.However, a more systematic and extensive study is requiredto establish it.

5. The experimental set up developed for testing the arch is ef-fective in applying a uniformly distributed load and in arrest-ing lateral deformation leading to pure in-plane load testing ofthe arches.

6. It is possible to predict well the behavior of HIB arches in thelinear range using linear elastic software models.

Even though the current 4.5-m span arches reported in here usetwo culms for the arch and one culm for the tie, 8-year-old 7.3-mspan arches supported an A-frame using four culms in the arch seg-ment, two in the tie and two for the A-frame, have been in goodworking conditions in practice in a 11 × 7.3 m shed (Sudhakar, un-published report, 2006). Further engineering analysis and designmay be able to extend the HIB technology to spans up to 10 mor more. This enables engineered interventions of a given numberof bamboo culms to achieve a higher moment of area of cross-section as compared to that obtained by bundling, even with smallerdiameter and more solid bamboo species, such as Dendrocalamusstrictus. This is of particular interest to India where this species

makes up to over 45% of the entire bamboo resources and is widelyavailable across the country.

The experimental study reported here is a pilot study for bam-boo tied arches under short-term loading conditions. It shows thatbamboo has potential as a modern green engineering material formaking tied arches in load bearing applications. This paper alsoproposes an innovative way of using bamboo joints as a sustainablebuilding material with very limited utilization of more energy-intensive material such as steel and concrete, the optimization ofwhich requires a further study.

Acknowledgments

This research was supported by the National Agricultural Innova-tion Project (NAIP), Indian Council of Agricultural Research(ICAR) through its subproject entitled Bamboo as a Green Engi-neering Material in Rural Housing and Agricultural Structures forSustainable Economic Growth code number NAIP/ Comp–4/C-2009/ 2008-2009. The authors would like to acknowledge thesupport provided by Heavy Structures Laboratory, Departmentof Civil Engineering, IIT Delhi for undertaking the experiments.Also, the authors acknowledge the support of Prof. Supratic Gupta,Dept. of Civil Engineering, IIT Delhi during initial experimentationand providing mix design for concrete. Further, the authors wouldalso acknowledge M/s Bamboo Technocraft for providing the fab-rication support.

References

Acre, O. (1993). “Fundamentals of design of bamboo structures.” Ph.D.thesis, Eindhoven Univ. of Technology, Eindhoven, The Netherlands.

Ahmad, M., and Kamke, F. A. (2005). “Analysis of Calcutta bamboo forstructural composite materials: Physical and mechanical properties.”J. Wood Sci. Technol., 39, 448–459.

Bradford, M., Wang, T., Yong-Lin, P., and Gilbert, R. (2007). “In-Planestability of parabolic arches with horizontal spring supports. I:Theory.” J. Struct. Eng., 10.1061/(ASCE)0733-9445(2007)133:8(1130),1130–1137.

Briccoli Bati, S., Rovero, L., and Tonietti, U. (2007). “Strengtheningmasonry arches with composite materials.” Compos. Constr. J.,11(1), 33–41.

Clarke, M., and Hancok, G. (1995). “Tests and non-linear analysis of small-scale stressed-arch frames.” J. Struct. Eng., 10.1061/(ASCE)0733-9445(1995)121:2(187), 187–200.

Clemente, P., Occhiuzzi, A., and Raithel, A. (1995). “Limit behavior ofstone arch bridges.” J. Struct. Eng., 10.1061/(ASCE)0733-9445(1995)121:7(1045), 1045–1050.

Ghavami, K. (2005). “Bamboo as reinforcement in structural concreteelements.” Cement Concr. Compos., 27, 637–649.

Hidalgo-Lopez, O. (2003). Bamboo–the gift of gods. D’VINNI LTDA,Bogota, Colombia, 206–216, 217–242, 264–283, 370–382, 391–394,412–418, 318–326.

Janssen, J. (2000). “Designing and building with bamboo.” INBAR Tech-nical Rep. No. 20, 130–133.

Korde, C., Agrawal, A., Gupta, S., and Sudhakar, P. (2007). “Experimentalverification of bamboo concrete composite bow beam with ferro cementband.” 1st Int. Conf. of Modern Bamboo Structures, Taylor & FrancisGroup, London, 247–252.

Marefat, M., Ghahremani-Gargary, E., and Ataei, S. (2004). “Load test ofa plain concrete arch railway bridge of 20-m span.” Construct. BuildMater., 18, 661–667.

Mirmiran, A., and Made, M. (1993). “Inelastic buckling of pre-stressedsandwich or homogeneous arches.” J. Struct. Eng., 10.1061/(ASCE)0733-9445(1993)119:9(2733), 2733–2743.

National Building Code (NBC). (2005a). Section 3B: Bamboo, Part: 6:Structural design, Bureau of Indian Standards, New Delhi, 8.

© ASCE B4014005-10 J. Struct. Eng.

J. Struct. Eng.

Dow

nloa

ded

from

asc

elib

rary

.org

by

Indi

an I

nstit

ute

of T

echn

olog

y, D

elhi

on

07/1

1/14

. Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

National Building Code (NBC). (2005b). Section 3B: Bamboo, Part 6:Structural design, Bureau of Indian Standards, New Delhi, 9.

National Building Code (NBC). (2005c). Section 3A: Timber Part 6: Struc-tural design, Bureau of Indian Standards, New Delhi, 24.

Obataya, E., Kitin, P., and Yamauchi, H. (2007). “Bending char-acteristics of bamboo (Phyllostachys pubescens) with respect to itsfiber-foam composite structure.” J. Wood Sci. Technol., 41(5),385–400.

Pi, Y. L., and Trahair, N. (1999). “In-plane buckling and design of steelarches.” J. Struct. Eng., 10.1061/(ASCE)0733-9445(1999)125:11(1291),1291–1298.

Society for Advancement of Renewable Materials and Energy Technolo-gies (SARMET). (1999). “Building with bamboo arch roof at HaritaEcological Institute, India.” Review Rep. and recommendations fordesign up-gradation, Int. Network for Bamboo and Rattan (INBAR),Beijing.

Stamm, J. (2009). “Seven concepts to build a bamboo bridge.” Proc., 8thWorld Bamboo Congress, Thailand, 10, 70–100.

Sudhakar, P., Gupta, S., Korde, C., Bhalla, S., and Satya, S. (2007).“Conceptual development of bamboo concrete composite structuresin a typical tribal belt, India.” 1st Int. Conf. of Modern BambooStructures, Taylor & Francis Group, London, 247–252.

Wang, T., Bradford, M., Yong-Lin, P., and Gilbert, R. (2007). “In-planestability of parabolic arches with horizontal spring supports. II: Experi-ments.” J. Struct. Eng., 1130–1137.

Wei-Xin, R., Zhao, T., and Harik, I. (2004). “Experimental and analyticalmodal analysis of steel arch bridge.” J. Struct. Eng., 1022–1031.

Yu, W., Chung, K., and Chan, S. (2003). “Column buckling of structuralbamboo.” Eng. Struct., 25(6), 755–768.

Zhang, J., Li, C., Xu, F., and Yu, X. (2007). “Test and analysis for ultimateload-carrying capacity of existing reinforced concrete arch ribs.”J. Bridge Eng., 10.1061/(ASCE)1084-0702(2007)12:1(4), 4–12.

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