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scelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only ICCREM 2018 Innovative Technology and Intelligent Construction Edited by Yaowu Wang; Yimin Zhu; Geoffrey Q. P. Shen; and Mohamed Al-Hussein Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. ICCREM 2018 INNOVATIVE TECHNOLOGY AND INTELLIGENT CONSTRUCTION PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON CONSTRUCTION AND REAL ESTATE MANAGEMENT 2018 August 9–10, 2018 Charleston, South Carolina SPONSORED BY Modernization of Management Committee of the China Construction Industry Association The Construction Institute of the American Society of Civil Engineers EDITORS Yaowu Wang Yimin Zhu Geoffrey Q. P. Shen Mohamed Al-Hussein Published by the American Society of Civil Engineers Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. Published by American Society of Civil Engineers 1801 Alexander Bell Drive Reston, Virginia, 20191-4382 www.asce.org/publications | ascelibrary.org Any statements expressed in these materials are those of the individual authors and do not necessarily represent the views of ASCE, which takes no responsibility for any statement made herein. No reference made in this publication to any specific method, product, process, or service constitutes or implies an endorsement, recommendation, or warranty thereof by ASCE. The materials are for general information only and do not represent a standard of ASCE, nor are they intended as a reference in purchase specifications, contracts, regulations, statutes, or any other legal document. ASCE makes no representation or warranty of any kind, whether express or implied, concerning the accuracy, completeness, suitability, or utility of any information, apparatus, product, or process discussed in this publication, and assumes no liability therefor. The information contained in these materials should not be used without first securing competent advice with respect to its suitability for any general or specific application. Anyone utilizing such information assumes all liability arising from such use, including but not limited to infringement of any patent or patents. ASCE and American Society of Civil Engineers—Registered in U.S. Patent and Trademark Office. Photocopies and permissions. Permission to photocopy or reproduce material from ASCE publications can be requested by sending an e-mail to [email protected] or by locating a title in ASCE's Civil Engineering Database (http://cedb.asce.org) or ASCE Library (http://ascelibrary.org) and using the “Permissions” link. Errata: Errata, if any, can be found at https://doi.org/10.1061/9780784481721 Copyright © 2018 by the American Society of Civil Engineers. All Rights Reserved. ISBN 978-0-7844-8172-1 (PDF) Manufactured in the United States of America. ICCREM 2018 iii Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. Preface We would like to welcome you to the 2018 International Conference on Construction and Real Estate Management (ICCREM 2018). Harbin Institute of Technology, Louisiana State University, Hong Kong Polytechnic University, University of Alberta, Luleå University of Technology, Heriot-Watt University, Marquette University, Karlsruhe Institute of Technology, Guangzhou University. The Conference is a continuation of the ICCREM series which have been held annually since 2003. The theme for this conference is “Innovation Technology and Intelligent Construction”. It especially highlights the importance of innovation technology for construction engineering and management. The conference proceedings include 138 peer-review papers covered fourteen important subjects. And all papers went through a two-step peer review process. The proceedings of the congress are divided into four parts:  Innovative Technology and Intelligent Construction  Sustainable Construction and Prefabrication Analysis of Real Estate and Construction Industry Construction Enterprises and Project Management   On behalf of the Construction Institute, the American Society of Civil Engineers and the 2018 ICCREM Organizing Committee, we welcome you and wish you leave with a wonderful experience and memory at ICCREM 2018. Professor Yaowu Wang Professor Yimin Zhu Harbin Institute of Technology Louisiana State University P. R. of China USA Acknowledgments Organized by Harbin Institute of Technology, P.R. China Louisiana State University, USA Hong Kong Polytechnic University, P.R. China University of Alberta, Canada Luleå University of Technology, Sweden © ASCE ICCREM 2018 iv Heriot-Watt University, UK Marquette University, USA Karlsruhe Institute of Technology, Germany Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. Guangzhou University, P.R. China Executive Editors Yue Cao Zhuyue Li Xuewen Gong Jia Ding Xianwei Meng Mengping Xie Jiaqing Chen Tianqi Zhang Yushan Wang Chong Feng Xiangkun Qi Jingjing Yang Xiaoting Li Yu Hua Wenting Chen Xiaowen Sun Hang Shang Shiwei Chen Tongyao Feng Conference website: http://www.iccrem.com/ Email: [email protected] Conference Committee Committee Chairs Prof. Yaowu Wang, Harbin Institute of Technology, P.R. China Prof. Geoffrey Q.P. Shen, Hong Kong Polytechnic University, P.R. China Conference Executive Chair Prof. Yimin Zhu, Louisiana State University, USA Conference Co-Chairs Prof. Mohamed Al-Hussein, University of Alberta, Canada Director Katerina Lachinova, Construction Institute of ASCE.(ASCE members), USA Prof. Thomas Olofsson, Luleå University of Technology, Sweden Prof. Ming Sun, Heriot Watt University, UK Prof. Yong Bai, Marquette University, USA Prof. Kunibert Lennerts, Karlsruhe Institute of Technology, German Prof. Xiaolong Xue, Guangzhou University, P.R. China © ASCE ICCREM 2018 Organizing Committee and Secretariat General Secretariat Asso. Prof Qingpeng Man, Harbin Institute of Technology, P.R. China Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. Deputy General Secretariat Asso. Prof. Hongtao Yang, East China University of Science and Technology, P.R. China Asso. Prof. Xiaodong Li, Tsinghua University, P.R. China Asso. Prof. Chengshuang Sun, Beijing University of Civil Engineering and Architecture, P.R. China Committee Members Dr. Yuna Wang, Harbin Institute of Technology, P.R. China Dr. Tao Yu, Harbin Institute of Technology, P.R. China Mr. Yongyue Liu, Harbin Institute of Technology, P.R. China Mr. Zixin Han, Harbin Institute of Technology, P.R. China Mr. Zhenzong Zhou, Harbin Institute of Technology, P.R. China © ASCE v ICCREM 2018 vi Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. Contents On-Site Safety Uncertainties Assessment of Construction Based on Cloud Model and Fuzzy Sets Theory................................................................................................... 1 Yongyue Liu, Yaowu Wang, Zhihe Yang, and Tao Yu USA Professionals’ Perception of Key BIM Maturity Indicators ......................................... 13 Yunfeng Chen, Dylan John, and Robert F. Cox Research on a Technical Framework in Smart Construction Based on Big Data ................................................................................................................................... 26 Zixin Han and Yaowu Wang Bibliometric Review of Artificial Intelligence (AI) in Construction Engineering and Management ................................................................................................ 32 Chao Xiao, Yang Liu, and Amin Akhnoukh BIM Implementation in Public Sector of Pakistan Construction Industry .......................... 42 Babar Ali, Hafiz Zahoor, Khwaja M. Mazher, and Ahsen Maqsoom Construction of Information Management Model of Engineering Project Based on BIM Technology ...................................................................................................... 52 Yu Hua and Yaowu Wang Qualitatively Exploring the Impact of BIM on Construction Performance ......................... 60 Yunfeng Chen, Dylan John, and Robert F. Cox A Novel IoT-Cloud-BIM Based Intelligent Information Management System in Building Industrialization ...................................................................................... 72 Chao Han and Haowen Ye Integration of Building Information Modeling (BIM) and Prefabrication for Lean Construction ............................................................................................................. 78 Manisha Goyal and Zhili Gao Additive Manufacturing: A Revolutionized Power for Construction Industrialization ...................................................................................................................... 85 Qiancheng Wang, Shujia Zhang, Dongyang Wei, and Zijian Ding Life Cycle Carbon Emissions of Industrialized Buildings Based on BIM ............................ 95 Zhiye Huang and Yanyan Fan A Critical Review on BIM Research Process and Future Trends at Home and Abroad ............................................................................................................................ 104 Jiaqing Chen and Qingpeng Man © ASCE ICCREM 2018 Effect of BIM Technology on Green Buildings .................................................................... 113 Wenbo Zheng and Jianguo Chen Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. Study on the Post Evaluation of Construction Science and Technology Research Project Performance Based on Fuzzy Synthetic Evaluation ............................... 118 Yunpin Hu, Tianyun Zhong, Zhongguo Tang, and Chongbo Gao A Review of the Application of BIM in the Assembly Construction ................................... 125 Tianqi Zhang and Qingpeng Man Research on Lean Construction System in the Background of Construction Industrialization .................................................................................................................... 132 Lixia Chen, Jun Chen, and Jianxin Zhang BIM Application Research of Assembly Building Design: Take ALLPLAN as an Example........................................................................................................................ 138 Jun Xie, Difei Jiang, Zhentai Bao, and Pin Zhou Application of BIM Technology in the Refined Management of Construction Cost ................................................................................................................. 148 Qiangnian Li, Jingzhong Zhao, and Haohao Zhang Building Industrialization Oriented Profit Allocation in Supply Chains Using Weighted Shapley Value ............................................................................................. 156 Xiyue Jin and Xiaolin Yang Research on the Development of 3D Printing Construction Industry Based on Diamond Model ................................................................................................................ 164 Jingkuang Liu and Guokai Li Policy Trends and Policy Analysis for the Industrialization of the Construction Industry: A Review ......................................................................................... 177 Xiaoting Li, Yuna Wang, Yunpeng Geng, and Qian Wang Evaluation of Construction Industrialization Policy Based on PMC Index Model ..................................................................................................................................... 192 Yuanxin Zhang, Yali Jin, and Xiaolong Xue Research on Sharing and Construction of Multi-Subject Smart Community Based on Game Theory ......................................................................................................... 202 Lijun Wan and Qi Li Research on the Integrity Control of Engineering Consulting Enterprises with Interconnection BIM in the Context of New Era ......................................................... 209 Yan Song and Deyi Chen Study on the Durability of Modified Recycled Concrete in Cold Region ........................... 215 Shuqing Lv and Lin Tian © ASCE vii ICCREM 2018 Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. Study on Multi-Objective Project Planning and Scheduling Model with Competitive Collaboration under Resource Constraints .................................................... 223 Chong Zhu, Yun Kan, Zhenqiang Bao, Weizhong Wang, and Zhaoyue Zhang City Scale’s Effects on Income of Urban Residents in Different Industries: Based on the Empirical Evidence of CHIP2009 ................................................................... 231 Yanju Liang and Zhiguo Gao Effect of Aggregate Proportion on Properties of Modified Recycled Concrete in Cold Region ....................................................................................................................... 238 Lin Tian “Internet +” Speed Up for the Wisdom Sites ....................................................................... 243 Qiangnian Li and Yuan Zeng Customer Requirement Analysis of Engineering Project Safety Management Intelligent System .................................................................................................................. 252 Jun Hu, Jun Fang, Ruixian Qiu, and Yuexia Wu Application of BIM Technology in Prefabricated Building ................................................. 263 Min Luo and Deyi Chen Mapping Global Research on the Construction Industrialization ...................................... 271 Ting Luo, Xiaolong Xue, Yongtao Tan, Yuna Wang, and Zebin Zhao Application of Building Information Modeling (BIM) Technology in Information Management of Steel Structure Materials ...................................................... 278 Qiangnian Li, Hui Zhang, and Lei Zhang © ASCE viii ICCREM 2018 1 On-Site Safety Uncertainties Assessment of Construction Based on Cloud Model and Fuzzy Sets Theory Yongyue Liu1 ; Yaowu Wang2 ; Zhihe Yang3; and Tao Yu, Ph.D.4 Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. 1 Ph.D. Candidate, Dept. of Construction Management, School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China (corresponding author). E-mail: [email protected] 2 Professor, Dept. of Construction Management, Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education, Key Lab of Smart Prevention and Mitigation of Civil Engineering, Disasters of the Ministry of Industry and Information Technology, Harbin Institute of Technology, Harbin 150090, China. E-mail: [email protected] 3 Ph.D. Candidate, Dept. of Construction Management, School of Management, Harbin Institute of Technology, Harbin 150001, China. E-mail: [email protected] 4 Dept. of Construction Management, School of Management, Harbin Institute of Technology, Harbin 150001, China. E-mail: [email protected] ABSTRACT Safety uncertainties widely exist in every phase of construction projects, especially during the on-site building stage. To identify different kinds of on-site safety uncertainties, a four-level analytic hierarchy process (AHP) model is proposed based on China’s current construction industry standards. Then analyze the influence and frequency of level-4th (L4) factors, synthesized cloud model (SCM) is applied to sampling calculation program, with which both randomness and fuzziness can be jointly considered. Finally, a multi-factor assessment method (MAM) under fuzzy sets theory is used to assess level-3rd (L3), level-2nd (L2), and level-1st (L1) factors of on-site safety system. Such methodology not only avoids the limitation of filling in huge numbers of written documents, but also can realize the dynamic adjustment of system factors, and may significantly decrease the difficulty of on-site safety management and safety inspection. In addition, practical advices are put forward to avoid some limitations of standard. INTRODUCTION More often than not, uncertainties are inherent in every condition of building engineering projects (Tam et al. 2004). During different construction stages, these projects may consist of various safety uncertainties, most of which will contribute to unacceptable hazards, such as threaten to people health, failure of mechanical equipment and damage to environment. Also in the same construction stage, safety uncertainties may exist in different dimensions, like on-site, off-site and coordination (Arashpour et al. 2017). According to statistical analysis of safety accidents in China (Acebes et al. 2014), including but not limited to falls, contact with electricity, injured by falling/swinging objects, hit by rolling/sliding/flying object, contact with machinery/equipment moving parts, fire or explosion (Pinto 2014), large scale of which occurred in on-site dimension. In order to control the on-site built activities and reduce potential accidents, both government and contractors have spared no efforts to inspect regularly or irregularly on safety conditions, which may require more and more investment in human and material resources. The classical method of identifying the ranks of on-site safety conditions of projects in China is to fill-out a safety inspection score summary table that contains nearly 10 sub-tables, from which more than 500 factors must be carefully taken into inspectors’ considerations and © ASCE Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. ICCREM 2018 given score to every one of them (MOHURD 2011). However, such method has limitations to execution. (1) it is inspector’s subjective idea or experience to decide how much score should be given to each factor. This may lead to diametrically opposed conclusion of the sub-tables or even the summary table. (2) it is hard to measure the influence of one factor variation to the whole system and the interaction and integrity of uncertainties were emerged in cumbersome score accounting. (3) the heavily fill-out assignments of classical table documents will hinder from factors’ dynamic adjustment for different projects. (4) it is mainstream of safety uncertainty inspection to establish a set of procedures in the era of widespread application of artificial intelligence, which can take fuzziness of human cognition and randomness of events into consideration together, equivalent or better than to the current standard and easy to adjust dynamically with computer. To bridge this gap, this paper: (1) establishes a four-level model based on current national standards and AHP. Comparing with current experts qualitative assessment model (Pinto 2014), the four-level model contains a larger number of factors (>500), which will have a strong practical significance. (2) analyzes the influence and frequency calculation of L4 factors. Taking whether to minus of a L4 factor and how much score should be reduced of that factor as two independent probability events. For those L4 factors whose minus score must be a numerical value, one Bernoulli distribution and Normal distributions (B-N-SCM) will be enough; for those L4 factors whose minus score belong to a consecutive numerical range, one Bernoulli distribution and two Normal distributions (B-2N-SCM) will be adopted. With the help of Forward Cloud Generator Algorithm (Zhang et al. 2015), random sampling programs are developed, from which we can find out the influence degree to L2factors dynamically when L4 factors are changing. (3) MAM is used to clarify the ranks of on-site safety system. This method takes L3 factors as the aspects of L2factor to judge the most possible scoring range, and takes L2factors as the aspects of L1 to rank the whole safety uncertainty system. METHODOLOGY Review of standard for construction safety inspection: Standard for construction safety inspection (JGJ59-2011) was published by MOHURD (2011) during the year of 2011 for measuring and controlling the safety situation of any building engineering projects in China, as a second edition to replace JGJ59-99, which was no longer suitable to the new era of continuous developing technologies and changing situations. With accumulation of comprehensive practical engineering experience under the standard of these years, there are empirical evidences to prove that likely accident scenarios were significantly decreased. According to the standard, a typical building engineering construction on-site safety inspection was divided into 10 parts in the safety inspection score summary table (see MOHURD 2011 table A). Each part was described as a sub-table, such as Safety Management score checking sub-table (see MOHURD 2011 table B.1). There are 19 subtables can be found in the standard. The whole inspection standard can be considered as the clarification of safety uncertainties and be analogous to a four-level event tree suitable for AHP method (see Figure 1).In the model, there are four levels can be divided column by column from the left to right. More detailed parts can be obtained from the Standard if needed. To fully understand the identify model assessment process and the relationships of different levels or factors, main accounting rules are described as Table 1. Synthesized cloud model (SCM): Defined as the integration of different distributions to the digital characteristics of cloud model (CM) in this paper, SCM is used to safety uncertainties analyze between L4 factors and L3 item. © ASCE 2 Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. ICCREM 2018 3 Figure 1. Safety uncertainties identify model (partial). CM was first invented by Li et al. (1995), and has been used to eliminate both randomness and fuzziness in event probability and human cognition (Meng et al. 2008; Li et al. 2009; Hu et al. 2008). Supposing there are some methods to make a reflection between a qualitative concept C and some quantitative numbers in U . Let an arbitrary number x ⊆ U , then x will be considered as a random realization of C , and a corresponding certainty degree function y ⊆ [0,1] will be called a cloud drop. A typical CM can be characterized with three digital indexes, namely Ex, En, He (Zhang et al. 2015). As Normal CM plays a prominent role in application because of its universality and stability (Li et al. 2009; Zhang et al. 2015), then Equation 1 can be regarded as a normal cloud and ( x, y ) in Equation 1 will be a random cloud © ASCE ICCREM 2018 4 drop. Also, x in Equation 1 may be described as x ~ CM ( Ex, En, He) for short. x ~ N ( Ex, En ); En ~ ∋ En, He ( ; y < exp Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. 2 2 , ( x , Ex )2 2 En2 (1) As to the safety uncertainties identify model, the L4 factors (as deduction rules in MOHURD 2011 table B.1)to a L3 item (as items in MOHURD 2011 table B.1) can be defined as a vector. Let D as a deducted score vector described as Equation 2. D < {a1 , a2 ,Κ , am | b1, b2 ,Κ , bn } (2) Where ai : i th minus score of m value-deducted factors; b j : j th minus score of n rangededucted factors. Table 1. Main Accounting Rules of Safety Uncertainties Identify Model. Total Main accounting rules quantities L1 1 (on (1) A typical building engineering project safety behalf of uncertainties system will be divided into three qualitative summary ranks: Excellent (≥80), Qualified (70~80), Unqualified table) (<70). (2) The total score of perfect summary table or sub-tables are all 100. Aggregation score of sub-tables will be converted to 10, 15 or 5 (MOHURD 2011 table A). If a sub-table get 0 score, rank of summary table will be Unqualified. L2 About 10 (1) L1 may not contain ten L2 factors all the same because factors of the uniqueness of a project. If there are missing sub(on behalf tables, the rest tables will be proportional expensed to 100. of about 10 subtables) L3 About 100 (1) All the L3 factors belong to two types, namely assuring factors items and general items. The former play a critical role to (on behalf affect human health, mechanical equipment and of about environment, while the latter are not. 100 items (2) If in a sub-table, one assuring item get 0 score or total in 10 sub- acquired score of assuring items less than 40 score, tables) aggregation score of this sub-table will be 0. L4 About 500 (1) There are two types of deduction in L4 factors, one factors type is that deduction must be a numerical value, while the (on behalf other is the deduction belong to a consecutive numerical of about range. 500 (2) Total deduction score in a set of L4 factors will be no deduction more than the required score of a L3 item, or the acquired rules in score of that L3 item will be 0. 100 items) Taking No.1 item in MOHURD 2011 table B.1 for instance: this L3 item named safety responsibility system that contains 11 L4 factors, in which are 7 accurate value deducted factors © ASCE Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved. ICCREM 2018 5 and 4 consecutive range deducted factors, such vector will be described as D < {a1 , a2 ,Κ, a7 | b1 , b2 ,Κ, b4 } . Aiming to analyze the fuzziness of safety inspectors and measure the influence of single factor to the whole system, refer to the nature of CM, make the following hypotheses, namely: H1: All the L4 factors are independent random variables. H2: They are two independent probability events of whether to minus (random variable W ) of a L4 factor and how much score should be reduced (random variable H ) of that factor. H3: To the value-deducted L4 factors, there is only one fuzziness dimension: W obey Bernoulli distribution but not sure for p . Refer to Wang et al. (2017) and “3 En criterion” (Zhang et al. 2015), let p obey the Normal distribution as Equation 4 and 5. The H is an accurate number in MOHURD 2011 table B.1. W 9 Bernoulli( p ), 0 ′ p ′ 1 (3) 2 p 9 N ( p, ρ ) (4) (1 , p ) / 3,1 , p ; p ρ< (5) p / 3,1 , p ″ p H4: To the range-deducted L4 factors, there are two fuzziness dimensions: not sure for p in W and fuzzy with H . Let the score which should be deducted obey the Normal CM as Equation 6. As the deducted range boundary is [Vmin ,Vmax ] in MOHURD 2011 table B.1, then Ex, En, He will be calculated as Equation 7-9. H 9 CM ( Ex, En, He) (6) V ∗V Ex < min max (7) 2 ζ | n (Vmax , Vmin ) 2 (8) 6 n2 ∗ 1 He < En / n, n = 3 (9) Corresponding to the dimensions of D vector, p vector and ρ vector can be defined as Equation 10 and Equation 11. Follow the steps of Table 2, ai can be calculated from H3, b j can be calculated from H4. p < ζ p1 , p2 ,Κ, pm p1 , p2 ,Κ, pn | (10) En < ρ < ζρ 1, ρ 2 ,Κ,ρ m ρ1 ,ρ 2 ,Κ, ρ n | (11) MAM under fuzzy sets theory: MAM is used to assess safety uncertainties between L3 and L2 (or L2 and L1). Assuming there are t L3 items ( Fi ) in a L2 table ( F set) as Equation 12. Considering the eleven intervals of acquired score as E set in Equation 13, the possibilities of every interval in E to F set represented by R matrix in Equation 14 .The weight of each Fi can be denoted as W vector in Equation 15, as the normalization of the required score values in MOHURD 2011 table B.1 for instance. According to fuzzy sets theory, the union and Intersection calculate rules can be applied to get fuzzy sets Z in Equation 16 with max-min composition of fuzzy relational equations (Zadeh 1965). (12) F < ζF1 , F2 ,Κ , Ft | E < ζ( ,⁄ ,0],(0,1],Κ , (9,10]| © ASCE (13) ICCREM 2018 6 Downloaded from ascelibrary.org by RMIT UNIVERSITY LIBRARY on 01/03/19. Copyright ASCE. For personal use only; all rights reserved.  R1   r1,1  R  r 2,1 R <  2 <  Λ Λ   r  Rt   t ,1 r1,2 Κ r1,11  r2,2 Κ r2,11   Λ Ν Λ   rt ,2 Κ rt ,11  W < ΖW1 ,W2 ,Κ,Wt ∴ Z - Xem thêm -

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