Solution of lift-off problem of beams on pasternak type subgrade by using SAP2000

The aim of the engineering studies is to be able to produce both secure and economical solution to faced problems. It may be negligible that the solution is economical in an engineering project to be carried out in the public interest or where security is important. The way to ensure safety is through the choice of the closest account method to the actual behavior. Hand made calculations are time consuming. In early 1900's engineers were improving basic assumptions for taking the approximate results. Recent technological developments provide us to compute huge problems in seconds. High performance computers use some technics such as finite elements, finite difference, central difference and calculate complex problems. Even if there are still many used assumptions, regarding these possibilities, it is easy to model actual behaviour of materials and geometries. In today's civil engineering, the subgrade is represented by vertical seperate Winkler springs that are defined to start and end points of joints below the foundation elements. This is the first mechanical model for foundation bases (1867). This practical approach is not a mistake but rather lacking. The subgrade, which is idealized with vertical springs perpendicular to the foundation, does not reflect the actual soil behavior. These linear springs deflect proportioned with the load above. Apart from sand and gravel soil, due to cohesion between the vertical fibers of the soil, shear stresses occur and the soil deformation becomes continuous. There has been some other soil behaviour models to take this effect into account. Filolenko- Borodich (1940), Pasternak (1954) and Vlasov (1966) are wellknown two-parameter soil models. In this study, in addition to Winkler vertical springs, the second parameter of the soil representing these shear stresses has been used. Pasternak soil model is the most appropriate approach for this work. Basically it is the assumption that there is a non-shorten shear layer which is perpendicular to linear vertical springs. This shear layer only deforms under the effects of shear stresses. This approach seems there is an in-plane tension force at the fictituous shear layer in both directions. The subject covered in the research is based on the principle of solving the nonlinear contact problem between the beam and subgrade by sucesive approximation method. The length of the soil region where the contact with the foundation beam is cut off, the internal forces and displacements of the foundation beam are investigated for tensionless Pasternak foundation beam. It has been studied how different soil parameters affect the results of external loads, beam length and beam bending stiffness. It has been used CSI SAP2000 structural analysis program for calculations. Finite element method has been used. The element that simulates Pasternak foundation beam has been developed. Two dimensional (x-z plane) problems have been solved. The research consists of four parts. In the first part, the cause and the emergence of the problem and the situations in which the problem is encountered in practice have been explained. History of problem and solution approaches are illustrated. Moreover, the soil model to be taken into account has been introduced. Basically, there are two soil constants which are C and CT. The one is typical vertical Winkler spring (kN/m2) and the other is shear constant (kN). Beam bending rigidity, EI (kNm2) and these two constants ensure loads come from structure. While developing the load and deformation equations of these constants, the stiffness matrix and matematical expression of the beam on two-parameter Pasternak soil has been given. Similarity between tension force on bars at second order theory and Pasternak soil shear constant has been illustrated. Other soil models have been provided and similar works which are related to the subject have been given. The reference works to be used in the calculation have been introduced. In the second part, the solution method of the problem has been explained. In SAP2000 software, two-parameter Pasternak soil modelling has been shown. The characteristics of two parameter foundation have been described, It is possible to model two-parameter foundation by assigning P-delta force to all foundation and soil elements. Then the shear transfer can be provided. Vertical spring coefficient of soil, shear parameter and beam bending stiffness are superimposed to show internal forces of beam. SAP2000 does not give the exact internal forces that comes from two parameter soil. Spring forces option represent only winkler springs. To comprehend the reactions come from two-parameter soil hand made calculations has been done. Joint displacements have been multiplied with soil stifness matrices that has been proved at chapter-1. Then the reaction froces have been obtained. Positive shear forces at any point of the beam shows that lift-off from soil occures. The system is re-solved by cutting off the relationship between the springs and the shear parameter assignments of the beam. The application continued until it reached the exact contact point at two consequent step. Numerical examples are given in the third chapter. In order to verify the reliability of calculation method, problems existing in the literature are solved. Convergence tests have been carried on. Six numerical examples are solved and illustrated. Three of these examples have been taken from Ma, Butterford and Cliffton's article (2009). Other two examples are at Celep and Demir's article (2007). Behavior of foundation beam under the influence of point load and span load is investigated. Three of these examples, the point load effect in the opposite direction of gravity, causes lift-off. The other three examples show the calculation of the foundation beams separated from the edge by the effect of the point loads in the gravity direction. Shear forces, moments, lift-off lengths and joint displacements have been shown for each step. Furthermore, results of inclusion and neglect of shear deformations in each example are shown. The work done in the last section has been concluded. Existing structural analysis program results and solutions given by literature have been compared. Results have been listed. Keywords: Pasternak, Two parameter foundation, Lift-off, SAP2000