CC BY
32
YflK 642. 072.2.042
DISTRIBUTIONAL CAPACITY OF SIMPLY SUPPORTED SPAN STRUCTURES MADE UP OF UNIFIED ELEMENTS
V.P. Kozhushko, Professor, Candidate of Engineering Science, O.V. Pervashova, senior lecturer; T.E. Lonovenko, student,
KhNAHU
Abstract. Basic principles of live loading analysis for diaphragmless span structures using the method of V.P. Kozhushko have been formulated. The assessment of the distributional capacity of a span structure consisting of eight prestressed rein-forced-concrete beam elements in the transverse direction of a span structure have been performed. The transverse mounting coefficients in the cross-sections 1/2, 1/4, 1/20, 1/40 and on the supports have been determined. Graphs of the transverse mounting coefficient as a function of the span length have been plotted.
Key words: mode of deformation, diaphragmless span structure, the lever method, the eccentric compression method, the elastic support method, the orthotropic slab method, the Winkler foundation, distributional capacity, transverse mounting coefficient.
Introduction
The analysis of a span structure is aimed at determining the mode of deformation of its elements. The assessment of the mode of deformation under live loadings is particularly difficult. A variety of techniques is available to determine the mode of deformation of span elements. Simple methods include the lever method, the eccentric compression method, and the elastic support method (the method of V.A. Rossiysky) [7]. Other methods, such as the beam grid method developed by B.P. Nazarenko [6], the ortho-tropic slab method, the energy methods of L.V. Semenets and N.P. Lukin [5, 8], and the methods devepoled by B.E. Ulytsky and A.V. Alex-androv are classified as complex methods.
Of these, the methods of B.E. Ulytsky and A.V. Alexandrov are considered to be the most accurate ones. The elastic support method and the energy methods also ensure sufficient precision, but they do not allow such factors as creep, plasticity, complex stress condition, and other nonlinear processes to be taken into account.
In this respect, the method developed by V.P. Kozhushko, according to which a span structure is idealized as a plate on the Winkler foundation,
offers more advantages because it allows a span structure of any type (in fact with a great number of beam elements) to be considered at both the elastic and inelastic stages, as well as regular and nonregular systems [2, 3]. That is why we have used this method as the most relevant for examining the behaviour of diaphragmless span structures.
Assessment Results
In order to evaluate the validity and effectiveness of the V. P. Kozhushko method, we have assessed a span structure 11,5 meter long comprising eight main beam elements using the V. P. Kozhushko method, the N. P. Lukin method, and the elastic support method. The results were presented as graphs showing the stress effect lines onto the main beam elements, which are identical in form.
The values of the maximum moments determined by these methods were found to vary within 0,03 - 0,9 %, and the values of dead loading effects were found to vary within 0,9-1,2 %. Hence, all the three methods are good enough for the analysis of the 3D behavior of the span structure under consideration. The V.P. Kozhushko method, however, offers more benefits because it allows the mode of deformation in
any cross-section through the length of a span structure to be determined.
A span distributional capacity is supposed to vary through the length of a span structure. According to the majority of available sources, the distributional capacity in the middle part should be determined by any method, and the distributional capacity in the cross sections on the tops of the supports should be determined by the lever method.
The distributional capacity can be expressed in terms of the transverse mounting coefficient. Then the transverse mounting coefficient has a constant value in the middle part of a span structure, the maximum value on the support structures, and varies according to the linear law at the ends of a span structure.
This distribution over the length is rather conditional. A.V. Semenets considered the distributional capacity to be invariable in the direction of the span length [8], which cannot be true. In
our opinion, it is more important to determine the transverse mounting coefficient in different cross sections and plot graphs representing the transverse mounting coefficient as a function of the span length.
In our research we have studied a 16,67 m. simply supported span structure of 122 - 63 Design Code [1]. We used for our analysis the unique on-site deflection measurements in the cross-sections 1/2, 1/4, 1/20, 1/40 and in the cross-sections on the supports available at the Department of Bridges at our university. The assessment results are presented in Figures 1, 2.
As seen from the graphs, the values of the transverse mounting coefficient vary through the span structure length. Consequently, the span structure distributional capacity varies in the direction of the span structure length. These results have been confirmed by experimental data. (Fig.
3).
Fig.1. The transverse mounting coefficient variation in the direction of the span structure length for beams 1, 2
Fig. 2. The transverse mounting coefficient variation in the direction of the span structure length for beams 3, 4
Fig. 3. The transverse mounting coefficient variation in the direction of the span structure length
Conclusion
1. The method developed by V. P. Koshushko provided us with a better understanding of 3D behavior of reinforced-concrete simply supported span structures and allowed us to study them in more detail than we could have done using other methods.
2. Our analysis showed that though the transverse mounting coefficient varies through the length of a span structure, this variation is not very significant. Consequently, for practical applications, the transverse mounting coefficient within the span length can be assumed constant. The transverse mounting coefficient on the supports should be determined by the lever method.
3. Our experiments also showed that the transverse mounting coefficient determined by the lever method does not always take on the maximum value in all beam elements.
4. Additional theoretical and experimental data are required to determine the distributional capacity of span structures of other types.
References
1. ДБН В. 2.3-14: 2006. Мости та труби.
Правила проектування. - К.: МБА та ЖКГ, 2006. - 359 с.
2. Кожушко В.П. Расчет пролетных строений
балочных мостов разрезной системы // Сопротивление материалов и теория
сооружений. - К.: Бущвельник. - 1980. -Вып. 36. - С.118 - 122.
3. Кожушко В.П. Расчет неразрезных балоч-
ных мостов регулярной и нерегулярной систем на временную нагрузку // Известия вузов. Строительство и архитектура. - 1982. - №5. - С. 118 - 121.
4. Кожушко В.П. До розрахунку балочно-
консольних прогшних будов на тимчасове навантаження // Автомобшьш дороги i дорожне бущвництво. - К.: Бущвельник. - 1985. - Вип. 37. - С. 56 -60.
5. Лукин Н.П. Пространственный расчет без-
диафрагменных мостов энергетическим методом // Сопротивление материалов и теория сооружений. - К.: Бущвельник. -1968. - Вып.6. - С. 112 - 123.
6. Назаренко Б.П. Железобетонные мосты. -
Изд. 2-е, доп. и перераб. - М.: Высш. шк., 1970. - 432 с.
7. Российский В.А., Назаренко Б.П., Сло-
винский Н.А. Примеры проектирования сборных железобетонных мостов: Учебное пособие. - М.: Высш. шк., 1970. -520 с.
8. Семенец Л. В. Пространственные расчеты
плитных мостов: Учебное пособие. - К.: Вища. шк. Головне вид-во, 1976. - 164 с.
Рецензент: В.В. Филиппов, профессор, д.т.н., ХНАДУ.
Статья поступила в редакцию 11 июня 2007 г.
