Joint displacements and forces university of asia pacific. Stiffness methods for systematic analysis of structures. Structural analysis 9 stiffness method part i stiffness method solutions. View direct stiffness method from mechanical meng 5544 at hawassa university. Usually, the basis of structural analysis, texts are very bulky and mainly focus on the theoretical description, which hinders the learning process through household work and research, leading to a better mastery of the material. Pdf geometrically nonlinear structural analysis by. The two quantities are related by a stiffness matrix.
We suppose the geometry of the assembled system is defined with respect to a global fiamet and use a superscript o to. It is important to understand how the method works. The loads p 1 and p 2 are point loads, while p 1 and p 2 are distributed element loads. Chapter 6 truss analysis using stiffness method objectives. Number the displacement coordinates and reaction coordinates in your frame. Talitruss analysis using the stiffness methodusing the.
Also write the boundary conditions eal constant 500 kipft. Developing the finite element equations for a system of springs using the direct stiffness approach. Displacement and force methods clearly explains the two fundamental methods of structural analysis. Like the portal frame example, the free body diagrams in figure 7. In this class, we will later apply the same concepts to the analysis of 2d trusses, beams and frames. Stiffness method of structural analysis the constructor. In this video i solve the unknown displacements and reaction forces of a frame element using the stiffness method and ms excel. Geometrically nonlinear structural analysis by direct stiffness method. The basic ideas remain the same, though some assumptions are released. It is a matrix method that makes use of the members stiffness relations for computing member forces and displacements in structures. It also shows how these methods are applied, particularly to trusses, beams, and rigid frames. Matrix structural analysis the stiffness method matrix structural analyses solve practical problems of trusses, beams, and frames. The element stiffness matrix for a beam element is given by 12. Both mentioned methods need high computational effort in solving the problems of infinite nonlinearities, such as frame analysis.
Reduced stiffness method for nonlinear analysis of. Analysis of continuous beams, arches, trusses, and frames is considered in detail. Other topics covered include influence lines, nonprismatic members, composite structures, secondary stress analysis, and limits of linear and static structural analysis. Stiffness method example 1 structural analysis youtube. The number of equations involved is equal to the degree of static indeterminacy of the structure. Note that in addition to the usual bending terms, we will also have to account for axial effects. The computer version is based on the following assumptions.
Fundamentals of the stiffness method the stiffness method. Chapter 11 is devoted to matrix stiffness method which is realized in the modern engineering software. The present book offers a set of distinguishing features in comparison with other books. Ke element stiffness matrix in global coordinates kg global structural stiffness matrix 1. We also consider that it can only move in the xdirection. October 10, 2016 a4 analysis of a statically indeterminate bar using the stiffness method the vertical displacement dc of point c, is taken as the unknown quantity.
Toward the end of the book, the displacement method reappears along with the moment distribution and slopedeflection methods in the context of beam and rigid frame analysis. Within the assumptions, the stiffness method for beam and frame structures is exact. The analysis of a rigid plane frame can be accomplished by applying stiffness matrix. Q kd q k d k d k u k 11 12 q k d k d u u k 21 22 member forces where. The stiffness method is currently the most common matrix structural analysis technique because it is amenable to computer programming. As one of the methods of structural analysis, the direct stiffness method, also known as the matrix stiffness method, is particularly suited for computerautomated analysis of complex structures including the statically indeterminate type. Advanced methods of structural analysis civil engineering. On the other hand, for linear systems with a low degree of statical indeterminacy, the flexibility method has the advantage of being computationally less intensive. The redundant forces are treated as basic unknowns. A chapter is devoted to present an alternate view of stiffness method as a variational approach. The computer version of the stiffness matrix is a generalization of the classical version leading towards the computer applications and the finite element method. The first step for frame analysis is to determine if the structure is structurally sound. Usually, the physical meaning of all matrix procedures.
Is a disp method of analysis can be used to analyse both statically determinate and. To accomplish this step assume that point c is moved downward by the distance dc. D f k 11 12 1 21 22 2 12 n n nn nn kk k kk k k kk k. Modeling assumptions state the modeling assumptions underlying this analysis, i. Stiffness method for frame structures for frame problems with possibly inclined beam elements, the stiffness method can be used to solve the problem by transforming element stiffness matrices from the local to global coordinates. For the love of physics walter lewin may 16, 2011 duration. Structural analysis examples civil engineering community. Ce474 additional stiffness problems purdue university. The triangular construction above the bridge is used for the free cantilever method freivorbau. Simplified method for nonlinear dynamic analysis of shear. Augmenting the direct stiffness method and performing the analysis in matlab in order to perform the analysis, please find the local stiffness matrix for a truss in your class notes. The stiffness method of analysis is the basis of all commercial structural analysis programs. The focus of this tutorial is development of these equations that only take into account bending deformations, i.
Structural analysis 9 direct stiffness method part 11. View notes structural analysis 9 direct stiffness method part 11 from cven 90049 at university of melbourne. Download free sample and get upto 48% off on mrprental. The fixed end re actions were derived by force method as well as secondary forces for member stiffness matrix. The direct stiffness method the state of the structural system is defined by a matrix of displacements generalized displacements. Direct stiffness method as one of the methods of structural analysis, the.
In these methods, more computational effort is needed compared to those with physical reduction. Focus of this chapter will be development of stiffness equations that only take into account bending deformations, i. Structural analysis, is a science that studies the strength, stiffness, stability, durability and safety in the works. The treatment of flexibility and direct stiffness method is limited to introduction of elementary concepts. Examples in structural analysis in searchworks catalog. Of course, as before, step 0 and step 1 consist of known values, either caused by external forces or the previous storey for step 0 or the column axial forces that were solved using the cantilever method assumptions. Sway frame secondorder analysis shall be used iterations on a 1storder elastic analysis is usually adequate sructure that meets certain conditions, enables a 1storder analysis without any iteration process to be used either by. Linear springs have simple forcedeformation characteristics. Introduction we consider a system comprised of mnmembers which are connected at j joints. Nonsway frame firstorder analysis may always be used. Structural analysisstiffness method 9 5 6 j 4 2 3 i 1figure 1. Bridging the gap between what is traditionally taught in textbooks and what is actually practiced in engineering firms, introduction to structural analysis. For these reasons, the matrix stiffness method is the method of choice for use in general purpose structural analysis software packages. In this method, the stiffness of linear parts of structures is condensed at joints interconnected with nonlinear parts.
In this paper, only the new formulations implemented into the existing computer code vector5 guner and vecchio 2008 are presented. Frame analysis may be approached by a variety of methods. Assembly of stiffness matrix and load vector of a truss assemble the global stiffness matrix and write the global load vector of the truss shown below. Freedom codes of a member in a global coordinate system. Matrix structural analysis department of civil and environmental engineering duke university henri p. We represent a structural member by a spring which has a node or connection at each end. Transfer matrix method, plastic analysis by stiffness method and substructure method are included as additional topics of interest. Matrix structural analysis of plane frames using scilab. Direct stiffness method direct stiffness method as. The main framework of the analysis method is described in guner and vecchio 2010, 2011. The axial forces ra and rb in the upper and lower parts of the bar can be expressed in terms of dc.
Create the stiffness matrix of the structure using the method of example 2 write the kinetic and potential energy expressions for the springs and create the stiffness matrix for the structure using the energy method. The local stiffness matrix for a spring is that of a truss however with entries equal to the spring stiffness k. Chapter 2 introduction to the stiffness displacement. In the stiffness method of analysis, we write equilibrium equationsin. Plane frame, member vector of primary forces member vector of primary local forces is corresponding to the fixedfixed end endend re rreereaction action due to external load. Onedimensional spring systems have simple geometry. The external factors acting on the system are given by a force generalized force matrix. The stiffness displacement method we can express u as a function of the nodal displacements uiby evaluating u at each node and solving for a1 and a2. A practical look at frame analysis, stability and leaning. Application for beam analysis the beam can be related to the displacements using the structure stiffness equation. Take values of p of opposite sign as you getting,or simply multiply it by 1 thats it. In a planar frame, every node has three coordinates.
The stiffness method is tackled in almost all textbooks dealing with structure theories. The dsm is the method used in the computer analysis of structures and is the precursor to the more general finite element method. Direct stiffness method for frame analysis a planar frame is a structural system that satisfies the following requirements. Matrix stiffness method in objectivec for structural analysis. For the derivation of the element matrix follow the link below. F1 k x1 f2 f1 k x1 using the method of superposition, the two sets of equations can be combined. A secondorder inelastic analysis, while perhaps the most comprehensive, is also the most complex. This second edition of examples in structural analysis uses a stepbystep approach and provides an extensive collection of fully worked and graded examples for a wide variety of structural analysis problems.