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1 Send Orders or Rerints to 14 The Oen Civil Engineering Journal, 2018, 12, The Oen Civil Engineering Journal Content list available at: DO: / RESEARCH ARTCE Creation o Siilarity Requireent with Field Equations in Steel Bearing Systes Ahet C. Altunışık *, Ebru Kalkan and Hasan Basri Başağa Deartent o Civil Engineering, Karadeniz Technical University, Trabzon, Turkey Received: Aril 9, 2018 Revised: May 5, 2018 Acceted: May 29, 2018 Abstract: ntroduction: This aer aied to deterine the structural behavior o steel bearing systes by creating siilarity conditions with ield equations. Scaling lays a crucial role in designing exerients aied at understanding the structural behavior o systes where exeriental studies are diicult to eror due to huge structures in the roession o engineering ield. Scaling can be erored by using diensional analysis or by noralizing dierential equations that describe the dynaics o the syste. a odel and rototye are diensionally siilar, it is ossible to estiate exeriental results ro odel to rototye. Methods: The use o scaled odels is coon on engineering alications because these odels allow conducting exeriental tests without the need o a hysical syste (i.e. rototye) to be constructed. Considering these advantages entioned in this study, it is ored a siilarity relation between rototye and scaled odels o dierent steel bearing systes is established. Siilarity relationshis between systes are created by ield equations. As an exale, colun and cantilever beas were selected and 1/2 and 1/4 scale rocedure was alied. Results and Conclusion: The results obtained by inite eleent odels in SAP2000 rogra or each syste were coared with analytical results. The analysis results were exained and it was deterined that scale actors are constant deending on scale tyes or dierent bearing systes. n addition, the inluence diagras o the systes were also exained and it was observed that the scale actor was ixed. Keywords: Diensional analysis, Prototye, d odel, Siilarity condition, Steel bearing syste. 1. NTRODUCTON Full-scale constructions have been designed and built on a sall-scale in order to carry out exeriental studies o the structures. Zhou et al. [1] have conducted exeriental studies by roducing scaled odels in order to investigate the cracks that occur due to earthquake otions in the arch da designed the earthquake acceleration which the ossibility o which is exected to increase by 10% in the coing 500 years. Jiang and Shu [2] investigated on the eects o gun voices around the ilitary area. For this urose, using scaled odels created in the laboratory environent with dierent acceleration records on the shake table, they exained the changes in dynaic characteristics. Oliveira and Faria [] aied to deterine daage levels or arch das in a study conducted using sall scaled odels. To this end, they built the 1/250 scaled odels o the Alqueva and Alto indoso Arch Da o 96 and 110 height, resectively in the laboratory. To study the earthquake behavior o a da with an arch height o 278 and a crest length o in China, a 1/00 scaled odel o the da was constructed in the laboratory environent, * Address corresondence to this author at the Deartent o Civil Engineering, Karadeniz Technical University, Trabzon, Turkey; Tel: +90 (462) , Fax: +90 (462) ; E-ails: ahetcan8284@hotail.co, ahetcan@ktu.edu.tr / Bentha Oen

2 Creation o Siilarity Requireent The Oen Civil Engineering Journal, 2018, Volue including reservoir-ground interaction by Wang and i [4]. Wang and He [5] investigated the eects o cracks occurring in arch das with natural requencies along with exeriental studies conducted on large scaled odels. n the scoe o the study, a single curved arch da was designed at an arch height o 80 and crest length o 209. Wang and i [6] constructed the laboratory odel o the da by considering the da-oundation-reservoir interaction in order to exerientally study the earthquake behavior o Xiao Wan Arch Da which has the 292 height in China. There are any exeriental studies using scaled odels in laboratory environent [7-11]. Diensional analysis is used to deterine the relationshi between the rototye and the scaled odel. Buckingha Pi Theore is oten used in any theoretical studies to deterine this relationshi. Carinteri and Corrado [12] investigated structural behaviors such as cracking or racture o concrete and yielding or ruture o reinorced during the loading rocess in reinorced concrete and yielding or ruture during the loading rocess in reinorced concrete beas subjected to bending eect by eans o diensional analysis. Rau et al. [1] aied to irove the rules o scaling with resect to Buckingha Π Theore and the siilarity criteria. n the study, it is stated that scaled odels siilar to rototye can be created and uloaded. Balaguer and Claraonte [14], in the work resented, investigated iortance, advantages and the goals o diensional analysis in detail. t is correlated in between rototye and scaled odels that created with Buckingha Pi Theore. Ghosh [15] has dwelled on areas o usage o scaled odels and has stated general descritions. Balawi et al. [16] aied at exaining the scaling rules based on the theory o siilarity in lates and beas under low velocity iact and static loading. n this study, in order to ensure coliance with rototyes, the scaled actor is resented as the ratio o each change in the scaled odels. With established siilarities between systes, it is stated that various equations written or a syste aly to all systes, and that in any cases it is iossible to establish colete siilarity between odel and rototye. Steel bearing syste is studied by taking the scaling rinciles into consideration. n the scoe o the study, 1/2 and 1/4 scaled odels o steel colun and console rototyes were created. Dynaic characteristics and structural behavior between rototyes and odels were investigated. 2. SCANG, SMARTY AND DMENSONA ANAYSS Scaling is the size reduction o large eleents or systes and the size o sall eleents or systes by exanding the in a certain ratio. The ai o the scaling is to acilitate the work by aking the hard and tie-consuing systes saller and siler to test. Exaining and testing o large structures (rototye) as ulti-story buildings, das and airorts is a very exensive, tie-consuing and diicult-to-control rocess. For this reason, it is very easy and convenient to do the study on the sall odels created by scaling the rototye. Owing to the siilarity between the rototye and the odel, the results obtained ro the sall odel will be evaluated so that the behavior o the rototye can be redicted. The ai o siilarity analysis is to reveal the relation between large and exensive systes by using inoration obtained ro exerients o sall odels. There are soe siilarity laws that are used to accolish this. Equality or relativity o variables written or a syste is valid or all systes. Each variable in a odel is roortional to the corresonding variable in the rototye. Analytical and exeriental studies are carried out to solve a roble. The solution o the roble is investigated irstly analytically. Then exeriental easureents are ade to check the accuracy o the results. The ost suitable scales are used according to the diensions o the systes in laboratory studies. There are two ways to relate the rototye with the scaled odel. Siilarity conditions, i there is a atheatical odel o the syste, are derived ro the related ield equations, or i the atheatical odel o syste is not valid, by eans o diensional analysis. n diensional analysis, all araeters and variables that aect the behavior o the syste have to be known. The equation created by diensional analysis is the diensionless roduct o syste araeters and variables. Thus the siilarity condition can be created by the obtained equation. Exeriental studies, which are an iortant ste in coaring and coniring correctness o results, require careul exaination o exeriental data. The ain urose o exeriental studies is to obtain axiu inoration with the least exerientation. n line with this urose, diensional analysis is used. Diensional analysis is a ethod used to reduce the nuber and colexity o exeriental variables aecting a hysical henoenon considered. The generalization o eirical orulas and diagras obtained ro exeriental studies is very iortant in ters o alications in which the syste with dierent diensions is used. One o the ain uroses o diensional analysis is to establish exeriental studies that will rovide this generalization. n an exeriental study, there ay be diensionless quantities that deine the relationshi between a large nuber o araeters aecting a studying. For this urose, diensional analysis is a ethod which has an eect on the interretation o results with ewer araeters,

3 16 The Oen Civil Engineering Journal, 2018, Volue 12 Altunışık et al. and also rovides ease o oeration Creation a Siilarity Forula With the Aid o Matheatical Models With the ield equations o the bearing systes, the characteristic roerties and structural behaviors o the systes can be calculated. The requency o systes varies in roortion to the stiness. The stiness values o soe bearing systes are given in Table 1. Table 1. Stiness exressions o soe bearing systes. Bearing Systes Rigidity (k) 48E k Sile Bea Cantilever Bea Cantilever Bea E k EA k k 24E h T k 12E h k Frae 12E h 15E kt h k 12E h k Where, and E are Moent o nertia and lexural rigidity, resectively. E h Frae

4 Creation o Siilarity Requireent The Oen Civil Engineering Journal, 2018, Volue The dislaceent relationshis, which are an exression o the structural behavior o the syste, are given in Table 2 or soe carrier systes. Table 2. Dislaceent exressions o soe bearing systes. Bearing Systes Dislaceent P E Cantilever Bea P 48E Sile Bea P 2EA Colun n the study carried out on the steel bearing systes, the sizes available in the steel tables are used because each diension o the steel roiles cannot be scaled in the desired area. A geoetric and ass scaled is alied as scaling tye. Frequency equations or bearing systes; For syetrical roiles ZE k ω k, ω, 2π (1) For non-syetrical roiles ZE k ω k,ω, y x x x, ω x, x 2π ZE k k,ω, x y y ω y, y ω y 2π (2) are exressed (Eqs. 1-2). Where, Z, E,,, and x-y are a coeicient, Modulus o Elasticity, the oent o inertia, the roile length, ass and the axis directions o the syste, resectively. When these exressions are written in the requency equation or rototye and odel, or rototye; ZE 1 1 2π () or odel;

5 18 The Oen Civil Engineering Journal, 2018, Volue 12 Altunışık et al. ZE 1 1 2π (4) Eqs. (-4) are obtained. With the alication o the siilarity condition between rototye and odel requency equations, ZE 1 1 ZE 2π ZE (5) Eq. (5) is obtained. Assuing that the ass is ket constant, the relation is =, (6) Eq. (6) is obtained. For dislaceent equations; F K.U F V. ZE k (7) Eq. (7) is obtained. Where, U, F, K, V,, E,, Z and are dislaceent, orce (ass o syste), rigidity, volue, density, Modulus o Elasticity, Moent o nertia, a coeicient and length, resectively. For rototye: 12E W U (8) For odel: W 12E U (9) (Eqs. 8-9) is obtained. With the alication o the siilarity condition U U between rototye and odel, (10) 1 Eq. (10) is obtained. With the alication o the scale actor in Eq. (10) S U W S U W (11) Eq. (11) is obtained. Assuing that the ass is ket constant, the relation is =, U U S (12)

6 Creation o Siilarity Requireent The Oen Civil Engineering Journal, 2018, Volue Eq. (12) is obtained. With the necessary siliications, equations o requency and dislaceent shows the ost general situation. These generalized equations that relect the relationshi between rototye and odel are alied to dierent systes.. OBTANNG OF DYNAMC CHARACTERSTCS AND STRUCTURA BEHAVOR.1. Finite Eleent Analysis Colun and cantilever beas are selected or alication o the scale eect in steel bearing systes. The act that roiles are actory-ade disallows the ro being reduced in ters o size in all diensions o syste in case o scaling. For this reason, the diensions in the steel tables are selected and rocessed. n the studies done in box and roiles, 1/2 and 1/4 scaled odels have been used. The roerties o roiles are resented in Table. Table. Data or roiles. Proiles Moent o nertia ( 4 ) Weight (kn) Mass (kns 2 /) Diension () ength () X Y PE E-6 2.1E-4 PE E E-6 PE E E-6 The unit length weights (G, kg/) or roiles are given in the steel tables. The weight o the selected roile is calculated by unit height. Since the weights o the unit height o the selected box roiles are not included in the tables, the weights o the selected roiles are calculated ro seciic orulas. Unit length weights or box roile (kg/); Kg / (O 4W )*W * c t t (1) calculated using Eq. (1) [17]. Where, O c and W t are outer diaeter and wall thickness, resectively (Fig. 1). or square section: o c = 4a or rectangular section: o c = 2a + 2b is obtained. Fig. (1). Square and rectangular box sections. 400x400x8 unit weight o box roile; Kg / (O 4W )*W * c t t Kg / (4*400 4*8)*8* Kg / kg / (14)

7 140 The Oen Civil Engineering Journal, 2018, Volue 12 Altunışık et al. Eq. (14) is solved. 2 long box roile weight, W * kg W *9.806E W kn (15) was calculated by (Eq. 15). By dividing the weight o the roile into gravity acceleration, kns / (16) Eq. (16) was calculated. The asses o the other box roiles were calculated and resented in Table 4. Table 4. Data or box roiles. Diension () Box Proiles ength () Weight (kn) Mass (kns 2 /) Moent o nertia ( 4 ) 400x400x E-4 400x400x8 200x200x E-5 200x200x4 100x100x E-6 100x100x2 The inite eleent odels o the selected roiles were created with the Sa2000 [18] rogra. The inite eleent odels or the systes are shown in Fig. (2). a) Box colun b) Box cantilever bea d) PN colun e) PN cantilever bea Fig. (2). Finite eleent odels o steel roiles..2. Matheatical Model Frequency and dislaceent values were obtained analytically by using atheatical odels o systes. The stes o calculation o the requency value obtained as a result o considering the rototye, 1/2 and 1/4 scaled odel o the colun that is box roile are resented as ollows: The rototye Data o the Colun Diensions E 2.1 E 8KN / E- 4 4

8 Creation o Siilarity Requireent The Oen Civil Engineering Journal, 2018, Volue The solution stes taken considering the above entioned data are as ollows. With the hel o equation; k ω 12*1.2E8*.214E 1.2E kN / rad / s , Hz 2π (17) Eq. (17) was solved. 1/2 d Model Data o the Colun Diensions E 2.1E8KN / E The solution stes taken considering the above entioned data are as ollows. With the hel o equation; 12*1.2E8* 1.2E E 5 k kN / 1 ω rad / s Hz 2π (18) requency value was obtained (Eq. 18). When the obtained data were evaluated, the scale actor o the colun; was obtained Eq. (19). 1/4 d Model Data o the Colun Diensions E 2.1E8KN / E The solution stes taken considering the above entioned data are as ollows. With the hel o Eq. (1); 12*1.2E8*1.255E 1.2E E 6 k kN / 0.5 ω rad / s Hz 2π (19) (20) requency value was obtained (Eq. 20). When the obtained data were evaluated, the scale actor o the colun; (21)

9 142 The Oen Civil Engineering Journal, 2018, Volue 12 Altunışık et al. was obtained Eq. (21). The stes o calculation o the dislaceent values obtained as a result o considering the rototye, 1/2 and 1/4 scaled odel o the cantilever bea that is box roile are resented as ollows: The rototye Data o the Cantilever Bea Diensions , 2 Modulus o Elasticity E = 2.1E8KN / 2 Syste dislaceent P E Syste Weight P P kN Table 4 Moent o nertia.214e 4 The solution stes taken considering the above entioned data are as ollows. With the hel o dislaceent equation or cantilever bea; P E * 2 *2 2.1E8*.214E 214E (22) was obtained dislaceent value which is given in Eq. (22). P load according to bulk ass accetance is alied as syste weight. 1/2 d Model Data o Cantilever Bea Diensions , 1 Modulus o Elasticity E = 2.1E8KN / 2 P Syste dislaceent E Syste Weight P P kN 4 Table Moent o nertia 2.009E 5 The solution stes taken considering the above entioned data are as ollows. With the hel o dislaceent equation or cantilever bea; P E * *2.1E8* 1E8*2.009E (2) dislaceent value is obtained (Eq. 2). P load according to bulk ass accetance is alied as syste weight. When the obtained data are evaluated, the scaled actor o the cantilever bea; (24) was obtained (Eq. 24). The dislaceent values o the other systes are resented in next chater.

10 Creation o Siilarity Requireent The Oen Civil Engineering Journal, 2018, Volue Coarison o Results Obtained The requency values o the all bearing systes are resented in detail in Tables 5, 6, 7 and 8 or dierent scaling tyes o the results o inite eleent analysis and atheatical orula. Table 5. The requency values obtained ro the analytical and inite eleent analysis belonging to the box roile bearing systes or 1/2 scaled. Tyes Geoetric Geoetric and Mass Bearing Syste Eleents Box Proile Finite Eleent Analysis Results (Hz) Analytical Results (Hz) Prototye 1/2 d Model Prototye 1/2 d Model Colun Bea Colun Bea Table 6. The requency values obtained ro the analytical and inite eleent analysis belonging to the box roile bearing systes or 1/4scaled. Tyes Geoetric Geoetric and Mass Bearing Syste Eleents Box Proile Finite Eleent Analysis Results (Hz) Analytical Results (Hz) Prototye 1/4 d Model Prototye 1/4 d Model Colun Bea Colun Bea Table 7. The requency values obtained ro the analytical and inite eleent analysis belonging to the roile bearing systes or 1/2 scaled. Tyes Geoetric Geoetric and Mass Bearing Syste Eleents Colun Bea Colun Bea Proile Finite Eleent Analysis Results (Hz) Analytical Results (Hz) Prototye 1/2 d Model Prototye 1/2 d Model Table 8. The requency values obtained ro the analytical and inite eleent analysis belonging to the roile bearing systes or 1/4 scaled. Proile Tyes Bearing Syste Eleents Finite Eleent Analysis Results (Hz) Analytical Results (Hz) Prototye 1/4 d Model Prototye 1/4 d Model

11 144 The Oen Civil Engineering Journal, 2018, Volue 12 Altunışık et al. (Table 8) contd... Tyes Geoetric Geoetric and Mass Bearing Syste Eleents Colun Bea Colun Bea Proile Finite Eleent Analysis Results (Hz) Analytical Results (Hz) Prototye 1/4 d Model Prototye 1/4 d Model As can be seen ro the results, the scale actors ( / ) between dierent systes with the sae scale are constant. The dislaceent values o the other bearing systes are resented in detail in Tables 9, 10, Table 11 and 12 or dierent scaling tyes o the results o inite eleent analysis and atheatical orula. As can be seen ro the results, the scale actor ( ) between dierent systes with the sae scale is constant. Table 9. The dislaceent values obtained ro the analytical and inite eleent analysis belonging to the box roile bearing systes or 1/2 scaled. Tyes Geoetric Geoetric and Mass Bearing Syste Eleents Box Proile Finite Eleent Analysis Results () Analytical Results () Prototye 1/2 d Model Prototye 1/2 d Model Colun Bea Colun Bea Table 10. The dislaceent values obtained ro the analytical and inite eleent analysis belonging to the box roile bearing systes or 1/4 scaled. Tyes Geoetric Geoetric and Mass Bearing Syste Eleents Box Proile Finite Eleent Analysis Results () Analytical Results () Prototye 1/4 d Model Prototye 1/4 d Model Colun Bea Colun Bea Table 11. The dislaceent values obtained ro the analytical and inite eleent analysis belonging to the roile bearing systes or 1/2 scaled. Tyes Geoetric Geoetric and Mass Bearing Syste Eleents Proile Finite Eleent Analysis Results () Analytical Results () Prototye 1/2 d Model Prototye 1/2 d Model Colun Bea Colun Bea

12 Creation o Siilarity Requireent The Oen Civil Engineering Journal, 2018, Volue Alication o Forulas Obtained by Fored Siilarity Calculation o the requency value o the 1/2 scaled odel by using the requency value o the rototye box cantilever bea is as ollows. written, =.214E- 4 4, = 2.009E- 5 4 (Table 4) and = 107,869hz Table 5 in Eq. (6), 2.009E E Hz (25) Eq. (25) is obtained. This result obtained with Eq. (25) agrees with the 1/2 geoetric scaled (constant ass) result resented or the box cantilever bea in Table 5. Table 12. The dislaceent values obtained ro the analytical and inite eleent analysis belonging to the roile bearing systes or 1/4 scaled. Tyes Geoetric Geoetric and Mass Bearing Syste Eleents Proile Finite Eleent Analysis Results () Analytical Results () Prototye 1/4 d Model Prototye 1/4 d Model Colun Bea Colun Bea Calculation o the dislaceent value o the 1/2 scaled odel by using the dislaceent value o the rototye box cantilever bea is as ollows. written =.214E - 4 4, = E Table 4 and = Table 8 in Eq. (12); S 1 S.214E E (26) Eq. (26) is obtained. This result obtained with Eq. (26) agrees with the 1/2 geoetric scaled (constant ass) result resented or the box cantilever bea in Table Eect o Change on nluence Diagras The inluence diagras under the weight o the syste at the colun and cantilever bea are exained in Figs. (-4). The relationshi between the rototye and odel with the ield equations used to obtain the section eects was observed. The inluence diagras o the inite eleent odels were exained and the existence o the relationshi was deterined.

13 146 The Oen Civil Engineering Journal, 2018, Volue 12 Altunışık et al. W Fig. (). oading status and axial orce or colun. W a) oading status b) Shear orce W W W a) oading status b) Shear orce c) Bending oent Fig. (4). oading status, shear orce and bending oent or cantilever bea. 8). The araeters aecting axial orce are syste weight and colun diensions change. The araeters aecting shear orce and bending oent are syste weight and bea length change. The inluence diagras obtained ro the inite eleent analysis are resented coaratively in Figs. (5, 6, 7 and N (kn) N (kn) N (kn) N (kn) N (kn) N (kn) Prototye 1/2 d 1/4 Prototye 1/2 d 1/4 d Fig. (5). Axial orce diagra or geoetric scale (variable ass). a) roile b) Box roile

14 Creation o Siilarity Requireent The Oen Civil Engineering Journal, 2018, Volue N (kn) N (kn) N (kn) N (kn) N (kn) N (kn) Prototye 1/2 d 1/4 Prototye 1/2 d 1/4 d Fig. (6). Axial orce diagra or geoetric scale (constant ass). a) roile b) Box roile Prototye 1/2 d 1/4 a) roile Fig. (7). nluence diagra or geoetric scale (variable ass). Prototye 1/2 d 1/4 b) Box roile Prototye 1/2 d 1/4 a) roile Prototye 1/2 d 1/4 Fig. (8). nluence diagra or geoetric scale (constant ass). b) Box roile

15 148 The Oen Civil Engineering Journal, 2018, Volue 12 Altunışık et al. When the diagras were exained, it was observed that changes were due to the scale tye and scale ratio between the rototye and the odel. CONCUSON This study aied to deterine the characteristics roerties and structural behaviors o steel bearing systes by establishing siilarity relationshi between rototye and scaled odels. Colun and cantilever beas were selected or alication o the scale eect in steel bearing systes. The diensions in the steel tables were selected and rocessed. n the studies carried out on box and roiles, 1/2 and 1/4 scaled odels were used. The inite eleent odels o the selected roiles are created with the Sa2000 [18] rogra. Frequency and dislaceent values were obtained analytically by using atheatical odels o systes. The requency values o the all bearing systes are resented in detail or dierent scaling tyes o the results o inite eleent analysis and atheatical orula. As can be seen ro the results, the scale actors (and) between dierent systes with the sae scale are constant. Also, the inluence diagras obtained ro the inite eleent analysis or dierent scaling tyes are resented coaratively. When the diagras were exained, it was observed that changes were due to the scale tye and scale ratio between the rototye and the odel. For exale, shear orce is constant in geoetric scale or box cantilever bea and bending oent changed with the changing o bea san. t was observed in this study that the characteristic roerties and structural behaviors o the systes can be obtained establishing a siilarity relation, by establishing sall scaled odels. CONSENT FOR PUBCATON Not alicable. CONFCT OF NTEREST The authors declare no conlict o interest, inancial or otherwise. ACKNOWEDGEMENTS Declared none.. REFERENCES [1] J. Zhou, G. in, T. Zhu, A.D. Jeerson, and F.W. Willias, "Exeriental investigation into seisic ailure o high arch das", J. Struct. Eng., vol. 126, , [htt://dx.doi.org/ /(asce) (2000)126:8(926)] [2] D. Jiang, and D.W. Shu, "Prediction o eak acceleration o one degree o reedo structures by scaling law", J. Struct. Eng., vol. 11, no. 4, , [htt://dx.doi.org/ /(asce) (2005)11:4(582)] [] S. Oliveira, and R. Faria, "Nuerical siulation o collase scenarios in reduced scale tests o arch das", Eng. Struct., vol. 28, , [htt://dx.doi.org/ /j.engstruct ] [4] H. Wang, and D. i, "Exeriental study o dynaic daage o an arch da", Earthquake Eng. Struct. Dyna., vol. 6, , [htt://dx.doi.org/ /eqe.67] [5] B.S. Wang, and Z.C. He, "Crack detection o arch da using statistical neural network based on the reductions o natural requencies", J. Sound Vibrat., vol. 02, , [htt://dx.doi.org/ /j.jsv ] [6] H. Wang, and D. i, "Exeriental study o seisic overloading o large arch da", Earthquake Eng. Struct. Dyna., vol. 5, , [htt://dx.doi.org/ /eqe.517] [7] M. Rau, V. Prabhu Raja, and P. R. Thyla, "Establishent o structural siilitude or elastic odels and validation o scaling laws", KSCE J. Civ. Eng., vol. 17, no. 1, , 201. [htt://dx.doi.org/ /s x] [8] P.. Datin, and D.O. Prevatt, "Using instruented sall-scale odels to study structural load aths in wood-raed buildings", Eng. Struct., vol. 54, , 201. [htt://dx.doi.org/ /j.engstruct ] [9] F. Haeez, and F. Alaskari, "Exeriental investigation o the scaling laws in laterally indented ilaent wound tubes suorted with v shaed cradles", Coos. Struct., vol. 126, , [htt://dx.doi.org/ /j.costruct ]

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