tính toán kết cấu liên hợp theo tiêu chuẩn eurocode 4Kết cấu liên hợp thép bê tông được hình thành bởi sự liên kết giữa hai thành phần thép và bê tông cốt thép thông qua các hình thức liên kết chịu cắt. Sự kết hợp hai thành phần này thành một kết cấu ứng xử đồng nhất giúp tận dụng được những ưu điểm và hạn chế nhiều nhược điểm của từng thành phần khi làm việc độc lập. Trong một kết cấu dầm liên hợp được minh họa trong , phần dầm thép sẽ chịu kéo và phần bê tôngchịu nén. Điều này mang lại hiệu quả sử dụng vật liệu tốt nhất vì bê tôngrất hữu hiệu trong chịu nén và thép có khả năng chịu kéo tốt. Các liên kếtchịu cắt phải đủ độ bền và độ cứng để hạn chế sự trượt và tách rời giữahai thành phần thép, bê tông để chúng làm việc đồng thời trong kết cấuliên hợp. Trong chương này, thuật ngữ kết cấu liên hợp thép bê tông sẽđược gọi ngắn gọn là kết cấu liên hợp.Để tránh nhầm lẫn, trong chương này, như kí hiệu trong Hình 5.1, têngọi “thép thanh” được dùng để đề cập đến các thanh cốt thép trongbản bê tông; các tên gọikhái niệm “thép kết cấu”, “dầm thép”, “thànhphần thép”, “cấu kiện thép” được sử dụng cho phần dầm thép (định hình,tổ hợp).Mục đích là cung cấp cho độc giả những khái niệm cơ bản nhất về kết cấu liên hợp, trong đó tập trung phân tích ứng xử của các cấu kiện cơ bản. Phần tính toán cũng chỉ đề cập đến một số cấu kiện cơ bản như sàn, dầm đơn giản, cột dựa trên tiêu chuẩn Châu Âu (Eurocode).
Dujmović / Androić / Lukačević Composite Structures according to Eurocode Composite Structures according to Eurocode Worked Examples Darko Dujmović Boris Androić Ivan Lukačević Univ Prof Dr.-Ing Darko Dujmović Department of Structural Engineering Faculty of Civil Engineering University of Zagreb Kaciceva 26 10000 Zagreb Croatia Univ Prof Dr.-Ing Boris Androić I.A Projektiranje Structural Engineering Ltd I Barutanski breg 10000 Zagreb Croatia Dr.-Ing Ivan Lukačević Department of Structural Engineering Faculty of Civil Engineering University of Zagreb Kaciceva 26 10000 Zagreb Croatia Cover: DEXIA Banque Internationale du Luxembourg, Complexe Administratif Esch-Belval, Luxembourg © Vasconi Architectes, Paris, France This book was published originally “Primjeri proračuna spregnutih konstrukcija prema Eurocode 4” in 2014 by I A Projektiranje, Zagreb, Croatia Translation: Univ Prof Dr.-Ing Darko Dujmović, Univ Prof Dr.-Ing Boris Androić, Dr.-Ing Ivan Lukačević Library of Congress Card No.: applied for British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at © 2015 Wilhelm Ernst & Sohn, Verlag für Architektur und technische Wissenschaften GmbH & Co KG, Rotherstraße 21, 10245 Berlin, Germany All rights reserved (including those of translation into other languages) No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers Registered names, trademarks, etc used in this book, even when not specifically marked as such, are not to be considered unprotected by law Coverdesign: Sophie Bleifuß, Berlin, Germany Production management: pp030 – Produktionsbüro Heike Praetor, Berlin, Germany Printing + Binding: Strauss GmbH, Mörlenbach, Germany Printed in the Federal Republic of Germany Printed on acid-free paper Print ISBN: 978-3-433-03107-0 ePDF ISBN: 978-3-433-60491-5 oBook ISBN: 978-3-433-60490-8 V Chapters A Creep and shrinkage B Composite beams 45 C Composite columns 397 D Composite slabs 671 E Fatigue 825 F Types of composite joints 879 Literature 887 VII List of examples A Creep and shrinkage Example Cross-section Page b hc A1 h0 A2 b 15 b b hc A3 b b 27 VIII List of examples B Composite beams Example Cross-section b1 b0 Static system and actions Page b2 B1 L1 L3 L2 47 b g k qk hc B2 53 L b gk q k hc B3 67 L b gk qk hc B4 111 L b gk qk hc hp B5 151 L b gk q k hc hp B6 L1 L2 177 876 E vL (kN/m) Fatigue vL,Rd 422 vL,Ed for maximum sagging bending moment 301 296 257 vL,Ed for maximum hogging bending moment Number of troughs 12 11 17 B L (m) A 13 7,8 4,0 4,4 1,6 12 17 10,0 18 Equivalent number of single studs Figure E2.12 Arrangement of stud connectors in one 10 m span According to clause 6.8.1(3), EN 1994-1-1, the maximum longitudinal shear force per connector should not exceed to 0,75·PRd for the characteristic combination of actions For the characteristic combination, the shear flow from non-cyclic variable action is increased from 54,7 kN/m to 54,7/ͺ1 = 54,7/0,7 = 78,1 kN/m Thus, the increase is 23,4 kN/m The value of shear flow for the characteristic combination is PEk = 130,9 + 23,4 = 154,3 kN/m Accordingly, the ratio of PEk to PRd is: PEk / PRd = 154,3 / (5·51,3) = 0,60 The obtained value is below the limit, 0,75, given in clause 6.8.1(3), EN 1994-1-1 The shear stress range can be calculated as: ͇Ͷ E = shear flow for cyclic loading (number of studs per unit length)·(d · Ͳ / 4) The shear stress range is: Example E2 ͇Ͷ E = 877 54700 = 38,6 N/mm2 5·192 · Ͳ / In the expression (6.50), EN 1994-1-1, ࠾ͶC is the reference value at 2·106 cycles with ࠾ͶC equal to 90 N/mm2 According to clause 6.8.3(4), EN 1994-1-1, for studs in lightweight concrete with the density class 1.8, the reference value ࠾ͶC at 2·106 cycles is: ͇Ͷ C = ͩE ·͇Ͷ C = ( ͳ / 2200)2 ·͇Ͷ C = (1,8 / 2,2)2 ·90 = 60 N/mm2 The design cyclic loading consists of a single load cycle repeated NE times The damage equivalent factor ͭv used in clause 6.8.6.2, EN 1994-1-1 on shear connection is calculated using the Palmgren–Miner rule, as follows The load cycle causes a shear stress range ࠾Ͷ in a stud connector and the slope of the fatigue strength curve m = Then, the following expression can be given: (͇Ͷ E )8 N E = (͇Ͷ E ,2 )8 · N C with NC = 2·106 cycles Hence: ͇Ͷ E ,2 / ͇Ͷ E = ͭv = ( N E / N C )1/8 From above expression, the equivalent constant range of shear stress ࠾ͶE,2 for 2·106 cycles is given by: ͇Ͷ E ,2 = ͇Ͷ E ( N E / N C )1/8 With NE = NEd = 2·2,5·106 = 5·106, the equivalent constant range of shear stress is: ͇Ͷ E ,2 = 38,6·[5·106 / (2·106 )]1/8 = 43,3 N/mm2 For ͥMf,s = 1,0, the design fatigue strength ࠾ͶC = 60 N/mm2 For the verification of shear connection, the following condition must be satisfied: ͇Ͷ E ,2 ࡌ ͇Ͷ C Check: ͇Ͷ E ,2 ࡌ ͇Ͷ C 878 E Fatigue 43,3 N/mm2 < 60 N/mm2 the shear connection is verified 10 Commentary Fatigue verification is mainly needed for bridges, but this example demonstrates the application for buildings with composite floors on which a forklift is travelling Generally, fatigue problems are treated in EN 1993-1-9 in great detail In EN 1993-1-9, the unified European rules for fatigue verifications are given Fatigue in reinforcement and concrete is covered in EN 1992-1-1 For a building, fatigue of concrete is unlikely to influence design Fatigue failure of a shear stud connector is covered by EN 1994-1-1 In the analysis of the fatigue limit state the following effects should not be neglected: ࢎ primary and secondary effects due to shrinkage and creep of concrete flange, ࢎ effects of construction type, ࢎ effects due to temperature For building structures, fatigue verification is not required except for specific cases These specific cases are given in clauses of the particular EN as follows: ࢎ ࢎ ࢎ for concrete, clauses 6.8.1 (1) and 6.8.1 (2), EN 1992-1-1 Fatigue verification should be carried out for crane rails, bridges subjected to high traffic loads, i.e for structures and structural components that are subjected to cyclic loading In these cases, verification is carried out separately for concrete and reinforcement for structural steel, clause 4(4)B, EN 1993-1-1 There are several cases where fatigue should be considered: where members support cranes, vibrating machinery or rolling loads, and where members are subjected to wind-induced vibrations or crowd-induced oscillations for composite structures, clause 6.8.1 (4), EN 1994-1-1 This clause gives guidance for types of building where fatigue assessment may be required According to clause 4(4)B, EN 1993-1-1, this includes buildings where members support cranes, vibrating machinery or rolling loads, and where members are subjected to wind-induced vibrations or crowd-induced oscillations In accordance with clause 6.8.1, EN 1992-1-1, this includes reinforcing steel and concrete components which are subjected to large numbers of repetitive loading cycles 879 F Types of composite joints 881 F1 Beam to beam joints Figure F1.1 illustrates four types of secondary beam to primary beam pinned joints End plate Bolted web cleats Bolts Bolts Stiffener Fin plate Shear plate Gap Gap Figure F1.1 Types of secondary to primary beam pinned joints In cases where speed of erection is an important consideration, the joint shown in Figure F1.2 can be used In this case, the secondary beam is connected to the primary beam by means of the single extended end plate which is welded onto the cleat The cleat is welded onto the top flange of the primary beam The extended end plate is slotted and welded onto the cleat, so the transmission of tensile force from the secondary to the primary beam is ensured Composite Structures according to Eurocode Worked Examples First Edition Darko Dujmović, Boris Androić, Ivan Lukačević © 2015 Ernst & Sohn GmbH & Co KG Published 2015 by Ernst & Sohn GmbH & Co KG 882 F Cleat Types of composite joints Cleat detail a a Zp Vz l1 D l2 Zp = Vz(l1 + l2)/l2 End plate Figure F1.2 Secondary to primary beam pinned joint Two variants of continuous beam to beam joints are shown in Figure F1.3 Continuity is achieved by means of cover plates welded onto the top flanges of the secondary beams and contact plates Alternatively, the continuity can also be ensured by steel reinforcement in the concrete slab Cover plate Cover plate Stiffener Fin plate Tuck weld Contact plate Shear plate Contact plate Figure F1.3 Types of secondary to primary beam rigid joints (continuous) 883 F2 Beam to column joints Pinned joints of composite beams to steel or composite columns are often used in multi-storey buildings Pinned joints are normally assumed to give vertical support and to be able to rotate without damage Figure F2.1 illustrates a pinned joint of a composite beam to a steel column with angle cleats Double web cleats Gap (s ࡌ 10 mm) Figure F2.1 Composite beam to steel column pinned joint with angle cleats The composite joint of partially encased composite beam to steel column is shown in Figure F2.2 Welded web cleat Concrete encasement Figure F2.2 Partially encased composite beam to steel column pinned joint with welded web cleat The joint shown in Figure F2.2 is a very economic joint A seating cleat may be used to help erection The web cleat is welded to the steel column in the workshop Composite Structures according to Eurocode Worked Examples First Edition Darko Dujmović, Boris Androić, Ivan Lukačević © 2015 Ernst & Sohn GmbH & Co KG Published 2015 by Ernst & Sohn GmbH & Co KG 884 F Types of composite joints Figure F2.3 illustrates the type of shear plate connection This type of joint is particularly suitable where beam shear is high and/or speed of erection is an important consideration The specific detail of the junction between the shear plate and the end plate ensures that the connection integrity is maintained End plate A Gap Shear plate Detail A Vd Column Vd End plate Gap Shear plate Upper end plate Beam Contact surface Shear plate Figure F2.3 Beam to column pinned joint Moment connections are those that are assumed to give vertical support, provide a degree of restraint against rotation and develop some moment capacity Generally, joints are classified by stiffness (rigid, nominally pinned or semi-rigid) and by strength (full-strength, nominally pinned or partial-strength) Further, clause 5.1, EN 1993-1-8 defines the links between the types of global analysis and the types of models used for joints In this way, it is possible to determine whether the resistance of the joint, its stiffness or both properties are relevant to the analysis Figure F2.4 illustrates the beam to column end plate joint For frames where the depth of construction is limited and where stiffness rather than resistance governs design, the semi-rigid joints shown in Figure F2.4 are a very economical solution Example F2 885 Figure F2.4 Beam to column joint with bolted end plates Appropriate structural details ensure that the forces transmitted from a beam through the beam-column connection are distributed between the steel and concrete parts of the composite columns Typical structural details are shown in Figure F2.5 a) Through-plate passed through slots and welded to each face of CHS or RHS column b) Welded fin plate Figure F2.5 Typical structural details c) Support 887 Literature [1] Amadio, C.; Fragiacomo, M.; Macorini, L.: Evaluation of the deflection of steel-concrete composite beams at serviceability limit state, Journal of Constructional Steel Research, 73, 95–104, 2012 [2] AndroiÉ, B.; ỴauševiÉ, M.; DujmoviÉ, D; Džeba, I.; Markulak, D.; Peroš, B.: Steel and composite bridges, IA Projektiranje, Zagreb, 2006 (in Croatian) [3] AndroiÉ, B.; 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Number (2006) 23-30 [10] Davaine, L.; Imberty, F.; Raoulsetra, J.: Eurocodes and - Application to steel-concrete composite road bridges, SETRA, 2007 [11] De Oliveira, W.L.A.; Beck, A.T.; El Debs, A.L.H.C.: Safety evaluation of circular concrete-filled steel columns designed according to Brazilian building code NBR 8800:2008, IBRACON Structures and Materials Journal, Vol 1, No 3, 212-2236, 2008 [12] Deutsches Institut für Normung (DIN): DIN 18800-5, Teil 5: Verbundtragwerke aus Stahl und Beton-Bemessung und Konstruktion, Berlin, 2007 [13] DujmoviÉ, D.; AndroiÉ, B.: Innovative systems of composite structures, Presjek, Ïasopis za detalje u arhitekturi (2011) , 1; 136-148 (in Croatian) Composite Structures according to Eurocode Worked Examples First Edition Darko Dujmović, Boris Androić, Ivan Lukačević © 2015 Ernst & Sohn GmbH & Co KG Published 2015 by Ernst & Sohn GmbH & Co KG 888 Literature [14] Ellobody, E.; Young, B.: Numerical simulation of concrete encased steel composite columns, 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Lukačević Composite Structures according to Eurocode Composite Structures according to Eurocode Worked Examples Darko Dujmović Boris Androić Ivan Lukačević Univ Prof Dr.-Ing Darko Dujmović Department... spregnutih konstrukcija prema Eurocode 4” in 2014 by I A Projektiranje, Zagreb, Croatia Translation: Univ Prof Dr.-Ing Darko Dujmović, Univ Prof Dr.-Ing Boris Androić, Dr.-Ing Ivan Lukačević Library... Wilhelm Ernst & Sohn, Verlag für Architektur und technische Wissenschaften GmbH & Co KG, Rotherstraße 21, 10245 Berlin, Germany All rights reserved (including those of translation into other languages)