Alman standartları (DIN 1045) Amerikan standartları (ACI) Türk standartları (TS 500) Eurocode-2'de narinlik ve burkulma hesabı - Temel, Seyhan (Fen Bilimleri Enstitüsü, 1997)
Taşıyıcı sistemlerde burkulma, özellikle narin kolonlarda etkili olmaktadır. Narinlik ise, kolonun boyu ve atalet momenti, dolayısıyla kolon kesitleri ile ilgilidir. Eksenel basınçla birlikte eğilmeye çalışan narin elemanların boyutlandırılması ve donatılmasında ikinci mertebe etkiler dikkate alınmalıdır. Narinlik ikinci mertebe etkileri meydana getiren faktörlerden biri olup, düğüm noktalarına bağlanan kolon- kirişlere ve taşıyıcı sistemin özelliğine bağlıdır. Burkulma tahkikinde uygun metodun seçilmesi, herşeyden önce taşıyıcı sistemin cinsi ve basınç elemanlarının narinliklerine bağlıdır. Öncelikle sistemin yanal öteleme yapıp, yapmadığı tespit edilmeli, buna bağlı olarak burkulma tahkikinin gerekliliği kontrol edilmelidir. Narinlik hesaplarında narinliğin belirli sınırları içinde, Türk ve Amerikan Standartlarında Moment Büyütme Metodu kullanılmaktadır. Büyütülmüş momentin çok küçük olması halinde, minimum eksantrisite değerleri kullanılarak hesap yapılır. Alman Standartlarında ise, hesaplamalar doğrudan eksantrisite değerleriyle yapılmaktadır. Sistemin tamamı içinse, servis yükleri 1.75 değeri ile artırılıp, II. Mertebe Teorisine göre burkulma kontrolü yapılmaktadır.

In this study, it is seen how to do consider the slenderness on the strength of the column in DIN 1045, ACI, TS 500 and EC. 2. And some solutions are given in these standards. Buckling is interested in the slenderness of the compression members. The slenderness effect is the ratio of the effective length to the radius of gyration. In other words, the slenderness effect of a compression member is interested in the dimensions of the crossection. When the dimensions decrease and the length of the column increases, the slenderness of the column increases. The deformation of the compression members is very important in design. This deformations are computed as the second-order theory. In determining the form of the buckling, firstly the quality of material, and the quantity of the reinforcement must be determined. And then the suitability of these acceptances must be checked after the design. In the buckling design, first of all, it is known that the system is braced or unbraced. In DIN 1045, the effects of the crossection are computed with the first-order theory. These accountant for the short columns. For slender columns, second-order moment which is happened because of the deformations, reduces the axial loads capacity of the crossection. The second-order moment must be taken into the account. For very slender compression members, as the second-order moments which is happened from the external loads increase quickly, the system falls down before reaches to the condition of the falling down In slender compression members, the folio wings affect the capacity of loads. - the spread of the moment on the column. - the quality of the concrete - the quality of the reinforcement. - the quantity of the reinforcement. XV - effective length of the column. - the shape of the crossection and the dimensions. In DIN 1045, the elasticity theory is used in design. And the nomogrammes are used for calculating the effective lengths. Before the accountant, it is checked that the system in braced or unbraced. This study provides for an approximate design method based on a moment magnifier principle. After study of the normal range of variables in column design, limits of applicability were set which eliminate from consideration as slender columns a large percentage of columns in braced frames and susbtantial numbers of columns in unbraced frames. The moment magnification method calls attention to the basic phenomenon in slender compression members and allows an evaluation of the addiational moment requirements in restraining, a superior and safer design results. ACI Building Code, encouraged the use of second-order frame analyses or PA analyses which include the effects of sway deflections on the axial loads and moments in a frame. For sway frames or lightly braced frames, economies can be achieved by the use of second-order analyses. The following considerations are regarded as minimum for an adequate frame analyses for the design of compression members; - Realistic moment-curvature or moment-end rotation relationships should be used to provide accurate values of deflections and secondary moments. Since column design and stability considerations are considered at the ultimate limit state, the stiffnesses used in an elastic analysis should be representative of this state. - The effect of foundation rotations on the lateral deformations should be considered. - It is necessary to consider the effect of axial loads on the stiffness and carry -over factors for very slender columns. - In frames subject to sustained lateral loads as in the case of buildings resisting a horizontal reaction from an arch or unbalanced horizontal earth forces, and in frames in which unbalanced dead loads give rise to differential shortening of the two sides of a building resulting in lateral deflections, the effects of creep should be considered. - The maximum moment in the compression members should be determined considering the effects on the lateral deflections the frame and the deflections of the compression members itself. XVI The use of a second-order analysis will include the effects of the frame deflections. Generally, such an analysis will give the moments only at the ends of the column. For slender columns, the maximum moment may occur between the ends of the column. The possibility of this occurring increases as the deflected shape of the column approaches single curvature bending. TS 500 and ACI Code describe an approximate slenderness effect design procedure based on the moment magnifier concept. The moments computed by an ordinary frame analysis are multiplied by a moment magnifier which is a function of factored axial load and the critical buckling load for the column. Both TS 500 and ACI code require the use of effective length factors in computing slenderness effects. And effective length "k.l" is used in the computation of slenderness effect. The effective length is a function of the relative stiffness at each end of the compression member and studies have indicated that the effects of widely varying beam and column reinforcement percentages and beam cracking should be considered in determining the relative end stiffness. Using a value of 0,5 Ig for flexural members (to account for the effect of cracking and reinforcement on relative stiffness) and Ig for compression members when computing the relative stiffnesses will usually result in reasonable member sizes for columns with slenderness less than sixty. Because of the difference in behavior between a braced and an unbraced frame, it is necessary to have one set of effective length factors for completely braced frames and a second set for completely unbraced frames. In actual structure, however, there is rarely a completely braced or a completely unbraced frame. When the stability index for a story is not greater than 0,04, the second-order moments should not exceed 5 percent of the first-order moments and the structure can be considered to be braced. In many cases, it is possible to ascertain by inspection whether a story is braced or unbraced. And the other more approximate procedure can be used to determine ifa story is braced or unbraced. A compression member may be assumed braced, if located in a story in which the bracing elements have a total stiffness, resisting lateral movement of the story, at least six times the sum of the stiffnesses of all columns within the story. The moment magnification method is used in slenderness design. Moment magnifier amplifies the column moments to account for the effect of axial loads on these moments. The column cross-section is then designed for the axial load and the magnified moment. 8 is a function, of the ratio of the axial load in the column to the assumed critical load of the column, the ratio of column and moments, and the deflected shape of the columns. In the design of a moment resisting frame is effectively braced against side sway by shear walls or diagonally braced frames, the moment resulting from lateral loads becomes zero. Because, the drift of the frame is small under lateral loads. When shearwalls or diagonal bracing is tall and slender or flexible, this moment must be XVII considered. Because the moment resisting frame may not be effectively braced by the shearwalls or diagonal bracing. For moment resisting frames which are not braced by other elements, both the moment resulting from gravity loads and the moment resulting from lateral loads must be evaluated. In both cases, these moments are computed using a first-order frame analysis. The member stiffnesses used in the analysis should allow, at least approximately for cracking of the flexural members. In ACI Code, the application of gravity loads to an unbraced frame in an unsymmetrical pattern or to an unsymmetrical unbraced frame will result in some calculated sidesway of the frame. Unless this lateral deflection due to vertical loading is appreciable, the minor effects of this sway component can be neglected and the corresponding moments can be considered as nonsway moments and should be magnified by the braced frame magnifier. In TS 500 and ACI, provide for different methods of calculating 8 for the braced and unbraced cases. For the braced frame, the magnifier 8 uses effective length factors of 1.0 or less. While for the unbraced case they are greater than 1.0. Cm factors for braced frames can be from 0.4 to 1.0 while for unbraced frames 1.0 is used. Thus, critical loads are higher and magnification factors are smaller for the braced case. Basic stability theory indicates that moments which produce sway deflection should be magnified by a sway magnifier and moments which do not produce sway deflections should be magnified by a braced magnifier. In addition, it must be realized that the maximum magnified moments produced by the braced magnifier occur at different locations, i.e, somewhere along the column length but not necessarily at the column end. If the gravity moments are significantly larger than the lateral load moments and the braced magnifier İs large, the maximum moment for the gravity plus lateral load case can theoretically at some midheight region of the column. If the lateral load deflections involve a significant torsional displacement the moment magnification in the columns farthest from the center of twist may be underestimated by the moment magnifier procedure. In such cases a second-order analysis is recommended. Any slender column analysis must carefully consider the flexural restraint at the column ends as well as the restraint against lateral movement of the column ends. XVII] The behavior response of any eccentrically loaded unbraced column is generally considerably more complex than that of a similar but braced column. The secondary or PA moments of an eccentrically loaded unbraced column are made up of both the axial loads effect and the joint rotation effect. The various components of the actual lateral deflection indicate that joint rotations played a major role in the failure. In the slender columns, under the axial load effects, there are occurred different types of curvature. And, as the load increases the curvature changes. Because the and joints don't rotate freely and the center deflection increases rapidly points of inflection appear. The reduced effective length between inflection points becomes the critical length. The moment magnification method is based on an analysis of an elastic curve that increases amplitude. But it does not change in shape as axial load is applied at the column ends or at the joints of the frame. Although for concrete the deflected shape will change, this normally does not involve serious error. In a general frame, five important problems arise; - The effective EI of reinforced concrete is dependent on the magnitude and type of loadings as well as the materials and varies along the column length. - The creep of concrete occurs when load is sustained. And creep modifies the effective EI needed. - The effective length of column for the calculation of critical load may be either more or less than the length of the column. - The magnified moments must distinguish between sway-producing and nonsway- producing loadings. Column sway is limited to the story deflection. The maximum moment does not always occur at midheight. In the analysis of a given slender column with given restraint conditions, the pratical question is what is the axial load and moment capacity, under the amplified moment and eccentricity conditions. Any slender column analysis should begin with a check of the translational and rotational restraint conditions. And preliminary check for approximate slenderness. The effective length factor must be determined. The unsupported length is the clear distance between lateral supports. The radius of gyration is approximated as 0,30. h for rectangular members and 0,25. h for circular members. XIX If appreciable slenderness effects exist, the moment magnification procedure can be used. Slenderness is accounted for by magnifying the column and moments. If the factored column moments are very small or zero, the design of slender column must be based on the minimum eccentricity. It is not intended that the minimum eccentricity be applied about both axes simultaneously.
The slenderness effects and the buckling design in din1045-aci-ts500 and ec-2
Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Sosyal Bilimler Enstitüsü, 1997
Keywords: Burkulma; Karşılaştırmalı analiz; Standartlar; DIN 1045; EC 2; TS 500; Buckling; Comparative analysis; Standarts; DIN 1045; EC 2; TS 500