Yarım NPI başlıklı, dikdörtgen boşluklu, küt kaynaklı, yanal burkulması önlenmiş çelik kirişlerin davranışı ve taşıma gücü
The Behaviour and the ultimate strength of butt welded steel beams with half chords and rectangular openings, prevented against lateral buckling
- Tez No: 21784
- Danışmanlar: PROF. DR. TEVFİK SENO ARDA
- Tez Türü: Doktora
- Konular: İnşaat Mühendisliği, Civil Engineering
- Anahtar Kelimeler: Kirişler, Taşıma gücü, Yapı elemanları, Çelik yapılar, Çelik-metal, Beams, Bearing capacity, Building elements, Steel structures, Steel-metal
- Yıl: 1992
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: Belirtilmemiş.
Özet
ÖZET Gövdelerinde boşluklar bulunan yapı elemanları, uygu lamada sık olarak kullanılırlar. Genelde, ek bir işçilik gerektiri rlerse de, tesisatın giderek önem kazandığı çağ daş anlayışa uygun yapılarda, boşluklar neredeyse bir zo runluluktur. Bunun yanı sıra, eş alanlı bir dolu gövdeli elemana göre daha büyük dayanım ve daha küçük şekil de ğiştirme gibi olumlu nitelikler de gösterirler. Boşluklu yapı elemanlarında boşluklar: petek (altıgen ya da sekizgen), dikdörtgen, daire ve elips şeklinde ola bilmektedir. Bu çalışmada boşlukları dikdörtgen olan, NPI hadde profillerinden üretilmiş ve ara levhalara bir leşimi küt kaynaklı olan çelik elemanların kiriş göreviy le kullanılmaları, hem deneysel hem de teorik yönlerden ele alınmıştır. Deneysel araştırma kapsamında, toplam 12 merdiven kiriş Î.T.Ü. înşaat Fakültesi Yapı Laboratuva- rında denenmiştir. Epruvetler, göz adım uzunluklarına göre üç farklı grupta incelenmiştir. Deney düzeninde, iki uçlarından sabit mesnetli olan kirişlere, açıklıklarının ortasından tekil yük uygulanmak ta olup tüm kirişlerde aynıdır. Yanal burkulma, basınca çalışan üst başlığa kaba bulonlar yardımıyla monte edilen bir kafes düzenle önlenmiştir. Epruvetlerde gövde stabi- litesini sağlamak amacıyla yer yer konstrüktif düşey ri jidleştiriciler de kullanılmıştır. Deneylerde kullanılan P. yükü statik karakterli olup, sıfırdan başlayarak, belli artımlarla göçme mekanizması o- luşana kadar kademeli olarak uygulanmıştır. Bu yüklemele rin her kademesinde, hem max. sehimi veren yükün uygulama noktası hizasındaki düşey deplasmanlar, hem de kirişin çok sayıda noktasındaki birim uzama değerleri ölçülmüştür. Deney kirişlerinde çalışma içinde açıklanan“Plastik Kayma Kuvvetine Göre Hesap Yöntemi”ışığında boyutlandı- rılmış olan ara levhalar ve küt kaynaklı birleşimlerin ara bağlantılarında herhangi bir sorun çıkmamıştır. Çalışma kapsamında, ele alınan türden merdiven (dik dörtgen boşluklu) kirişlerin, yük altındaki davranışı elastik ve plastik hesap yöntemleriyle incelenmiş, deney sel sonuçlar daha önceden bilinen hesap yöntemleri ile kıyaslanarak bu yöntemlerin yaklaşıklık dereceleri sap tanmıştır. Ayrıca deneysel sonuçları çok daha iyi bir şekilde yansıtan, basit ve kolaylıkla uygulanabilir bir hesap yöntemi de çalışma içinde sunulmuştur. xvı ı
Özet (Çeviri)
SUMMARY THE BEHAVIOUR AND THE ULTIMATE STRENGTH OF BUTT WELDED STEEL BEAMS WITH HALF CHORDS AND RECTANGULAR OPENINGS, PREVENTED AGAINST LATERAL BUCKLING Structural elements including openings in their webs, are used in various applications abundantly. Despite the fact that they require an extra amount of workmanship, openings are almost a requirement in modern buildings where different installations have an ever-increasing importance. Additionally, due to the production techni ques, the increasing distance between the flanges results in an increase of moment of inertia; which in turn causes an increased strength and a lesser amount of deformation when compared with a solid web structural element of equ al cross-sectional area. The openings inside the structural elements can be of various shapes, such as hexagon, octagon, rectangle, ci rcle or ellipse. This research is devoted to the study of steel struc tural elements with rectangular openings »constructed from NPI rolled steel sections and joined by intermediate pla tes with butt welds. The usage of these structural ele ments as beams is examined both experimentally and theo- oretically. Beams used in the experiments were construc ted at Pendik Machinery Shop of STFA from the material donated by Ata Construction Company. NPI 200 rolled pro files were cut by oxygen torch into two, along a dividing line in the middle in the longitudinal direction. The tested beams were then constructed by welding intermedi ate plates of 200 mm heigth to these half NPI shaped chords in a way to form rectangular holes. The beams that were tested were all of the same depth since they were constructed from the same intermediate plates. A total of twelve beams with openings were tested, half of them ha ving a span of 4 m and the other half 5 m. The beams were tested in three groups with 40 cm, 50 cm and 60 cm opening step lengths. The experiments were conducted at the Struc tural Laboratory of Civil Engineering Faculty. The intermediate plates and the butt welds were de signed in the light of“Plastic Design Procedure Accor ding to Shearing Force”method and, no problems were en countered relating this joining procedure used during the course of experiments. The Turkish Standards TS 3357 [46] XVI 11and TS 4561 C47J were also used for the design. The electrodes used for welding were of the Oerlikon- Overcord S rutile type; a standard welding electrode used in Turkey. The steel material used in the beams experimented is nominally St. 37. However, the tension test performed in accordance with The Turkish Standard TS 138 C41] yielded an experimental value of 2300 daN/cm for the yield stress; and this value was used for the calculations. The test frame was designed to apply a concentrated load at the midpoint of the span which were simply sup ported at both ends. Lateral buckling was prevented by a trussed equipment mounted on the top chord of the beam by unfitted bolts. Due to the loading location and testing conditions, this top chord lateral truss was not continu ous all along the beam. However, the beam was also late rally supported at its mid-span. The reason of this equ ipment againts the lateral buckling is that, these types of beams were used in practice, connected with the rein forced concrete slabs they support and therefore were not subjected to lateral displacement. In order to ascertain the structural stability of the experimented beams, verti cal constructive stiffeners were placed at the two sup ports, at the central point where the load was applied and at the two arbitrary locations between those points, closer to the supports. The load P applied to the beams is static in charac ter, and is applied in steps starting from zero up to the point where the failure mechanism was observed. At each step of loading, both the vertical deflection at the load application point where the maximum deflection occurred, and the strains at various points of the beam were measu red. The deflections were measured by mechanical compara tors with a sensitivity of 1/100 mm, and the strains were measured by strain-gauges. The deflections were measured up to the yielding point and then stopped for comparators' safety, and strains were measured up to their own yield po int or to the failure of the beam. The measured values are given in tabular form in this report. The evaluation of the experimental results began with an interpretation of the general behaviour of the beams. For this purpose, the load-strain CP-s ) diagrams of a beam with a sufficient number of gauges sticked all along the span were examined. This examination showed that, the tested beams with rectangular openings were acting under the loading, as the superposition of two different behaviours. On one hand, the designated beam shows the behaviour of a bending member, def lecting under the effect of a force-couple with a compression in the top flange and a tension in the bottom flange; and on the other hand due to the effect of the openings, also exhibits the be- behaviour of a shear panel between the added intermediate XIXplates. This last mentioned panel behaviour is especially observable between the central intermediate plate of the beam where the concentrated load was applied and the ne ighbouring intermediate plates. The ultimate and serviceability limit states of the experimented beams are examined in the following sub-chapters. As well known, the term“ultimate limit state ”defi nes the largest internal forces a structural element can endure, if the restrictions due to deformation are not ta ken into account. It is clear that a structural element can exhibit different ultimate limit states under various combinations of internal forces. Different ultimate loads can be calculated relating with the combinations of internal forces and their interaction. The theoretical ultimate loads of the tested beams have been calculated using different approaches and, been compared with the experimental ultimate loads. Thus, the correlation between the experimental and theoritical ul timate loads has been examined. i )The Mechanism Method and the Shear Panel Mechanism: From the examination of tested beams, it is observed that the shear panel mechanism is encountered in the two openings situated on both sides of the beam mid-span, by the formation of eight plastic hinges. Using the mechanism method, it is possible to calculate the ultimate load P IT by equating to each other the works of external and in ternal forces. The ultimate load of a beam with openings, can be calculated by the relation : 8 M IT where M is the plastic moment of the beam's chord and s is thep length of an opening. ii)The Panel Mechanism Including the M + N Interac tion in the Chord Cross Sections : A more accurate way of determining the beam ultimate load by the way of this method, is to use M which inclu des the axial force and shearing force effects, in the formation of plastic hinges in beam chords, instead of M. As a first step, the M + N interaction diagram is the line p obtained. The next stepu is the determination of M M = f XXand its point of intersection with the interaction diag ram. Since the interaction diagram exhibits two diffe rent curves according whether the chord axial force is tensile or compressive the M value which forms the plas tic hinge is obtained by using two different values, M and M ui u2 The ultimate load of a beam with an opening length s can be calculated by the following relation 4 CM ui M ) u2 2T The values obtained by this method of calculation, show the best correlation with the experimental results. iii ) The Panel Mechanism Including M + N + Q Inte raction in the Chord Cross Sections : In addition to the axial force and bending moment ef fects on the beam chords, there exists also the shearing account by accordance force. The shearing force Q, is taken into a reduction in the chord web thickness, in with TS4561 C47] and; the M + N interaction diagram of the chord cross section is drawn with this virtual reduction. The second step consists of the determination of the line M = f M N N and its point of intersection with the interaction diag ram. By an analogy to the previous relation, the ultimate load of a beam with an opening length s can be calcula ted as 4 CM + M ) ^ Ui U2 3T iv) The Simlified Method, Using Directly Couple Acting on the Beam Chords -. the Force- In this method, the shearing force and the bending moment actions in chords are neclegted and only the chord axial force, which is obtained by dividing the beam ben ding moment M to the beam moment arm h,is taken into ac count. For a beam with a chord area a and a span L, ultimate load can the relation A, a yield stress be calculated by 4 Ah b s İM <y XXIv) Method Based on the Plastic Modulus of the Beam : In this method the first step is determination of the factored mean plastic modulus of the beam. This plastic modulus of the beam can be given as 1^ S Z = L-. ZJ + - 2L- Z o r t d o s s where Z is plastic modulus of a section with an opening, Z is plastic modulus of its full section, 1 is the length of intermediate plate, s is the length of the ope ning and s is the opening step length. In this fifth method, the ultimate load of a beam with openings, can be calculated by the following relation P 2M 4 Z a o r t a where L is the span of the beam, a is the yield stress. To obtain the experimental/theoretical ultimate capa city ratios, the experimental ultimate loads of the twelve tests were divided by the theoretical ultimate loads which were determined by the five different methods men tioned above. The characteristic ratios, with a 5% proba bility of error bound, were calculated for each theoreti cal method, by statistical evaluation. These evaluations revealed that the best correlation between experimental and theoretical results was reached by the theoretical ultimate load P which is 1.02, is closest to unity. 2T J This indicates that the theoretical results calcula ted by the panel mechanism method including the M + N interaction, best reflects the experimental results? Theu second best prediction was achieved, by a characteristic ratio of 1.05, by P, the method which additionally in cluded the shearing force effect. The traditional P theoretical ultimate load which 1 T only take the bending moment into account, is much be low the acceptable range, with its characteristic ratio of 0.30. The other two methods which give.P and P and which relate the theoretical ultimate load to beam bending in a simple way achieve relatively better results, with characteristic ratios of 0.76 and 0.73 res pectively. This last comparison means that, it is possib le to obtain accurate results, by multiplying the results of P method, which is the simplest, by a factor of 0.76; at least for preliminary design calculations. The general evaluation of these comparisons indicates that the recommended procedure of calculation, when accuracy is required, is the usage of mechanism method xxxiinvolving M + N interaction, i. e, P method. The calcu lation method to be prefered when rapid results are needed, is the method of resolving moment into force-coup le, or P method. 1M On the other hand, attempts to obtain the ultimate load of beams with openings, by elastic methods were also investigated. Vierendeel beam and castellated beam elastic solutions were used for this purpose. In these elastic calculations, the stress was first taken being equal to the proportionality limit stress (80% of the yield stress =0.8c ) and later, the same stress was taken equal to the allowable stresses which mean 0. Sa for the loading case 1 and 1.15x0.6 a = 0. 69 a for the loading case 2. The factors of safety of those procedures were obtained by dividing the experimental ultimate loads to those va lues. Since all of those factors of safety yielded very high values, for even the proportionality limit, the elas tic methods can be qualified as not economical. In addition to the ultimate limit states of the tested beams, their serviceability limit states were also investigated from the point of view of displacements. The term“serviceability limit states”refers to the limitations induced by the maximum amount of deformation permitted on any structural element independently from its ultimate limit state. For a beam this limitation is the value of the deflection which should not be exceeded. This limiting value is dependent on the span of the beam and is expressed as a percent of this span. In this in vestigation, these limits for the deflection has been ta ken equal to : L/300 in accordance with TS648 C493, and also to L/333 for ordinary loads and to L/250 for exces sive loads in accordance with Eurocode 3 CS03. In the a- bove ratios, L is the beam span. The measurement related with the deflections made in the experiments, have been compared with the values cal culated theoretically with various approaches. The amount of accuracy of these theoretical approaches were thus de termined. The methods of theoretical calculation are : i ) The solution of Vierendeel beams with matrix-dis placement method, with the aid of a computer, ii) The simple beam simulation, assuming the beam with openings has only two chords as cross section, iii) Method including the shear def ormations, using as the moment of inertia of the beam the factored average of solid and hollow parts. The experimental and theoretical loads that lead to the same serviceability limit state have been calculated for the three different serviceability limits with each of these three methods. Then, the ratios of theoretical xxiiiand experimental values thus obtained for the twelve tes ted beams were examined and, characteristic ratios corres ponding to a S% probability of error were determined. This statistical evaluation has indicated that the avera ge characteristic ratios are : 0.60 for Vierendeel beam assumption, 0.37 for simple beam allowance and 0.48 for the method which includes the shear deformations. Those coeff icients, relating the theoretical to the experimental results for serviceability limit states, are smaller in 4m beams since the shear panel mechanism is more effecti ve when compared with the 5m beams. When these three methods mentioned above are critici zed from the point of view of their representation of ex perimental data, it can be said that none of them leads to the serviceability limits exactly. When the theoreti cal methods are graded according to their exactness of prediction of the results, the following listing can be made : Vierendeel beam assumption, method involving the shear def ormation, the simplified beam solution neglecting the shear deformation. However it is essential that such a calculation should be made rapidly in practical usage. Additionally, simple methods of calculation do decrease the probability of error. From this point of thought, the simple beam bending method can be qualified good for usage, with the obligation to multiply its result with the characteristic factors, both for the serviceability limit states and for the ultimate limit states. The ratios f /f, obtained by dividing the experi mental values of deflection to the theoretical deflec tions calculated by the three methods mentioned above for each value of loading, have been shown in tables and di agrams. An examination of those diagrams, which show a bet ter view of the trend, reveal the fact that the f./f ra tio keeps on almost constant value from the begin ning of the experiments till the approach of their end. Towards the end of the test, the ratio values are offset from the constant due to the shear panel mechanism invol ved. However, the cases when the ratios are offset from the constant value are beyond the serviceability limits of the beam. This enables the designer to use one of the theoretical results, by multiplying it with a constant factor. On the other hand, the ratio of P obtained by dividing the experimental ultimate limit state by a factor of safety equal to 1.7 as in Turkish Standard, to the loads which take the serviceability limit. states as the basis and are calculated in accordance with the dif ferent methods are examined. This observation shov/s clearly that, for the types of tested beams, the ultimate limit state is more important when compared with the ser viceability limit state. XXIV
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