Analysis of Pimjointed Trusses (original) (raw)
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Truss structures constitute a special class of structures in which individual straight members are connected at joints. The members are assumed to be connected to the joints in a manner that permit rotation, and thereby it follows from equilibrium considerations, to be detailed in the following, that the individual structural members act as bars, i.e. structural members that can only carry an axial force in either tension or compression. Often the joints do not really permit free rotation, and the assumption of a truss structure then is an approximation. Even if this is the case the layout of a truss structure implies that it can carry its loads under the assumption that the individual members act as bars supporting only an axial force. This greatly simplifies the analysis of the forces in the structure by hand calculation and undoubtedly contributed to their popularity e.g. for bridges, towers, pavilions etc. up to the middle of the twentieth century. The layout of the structural members in the form of a truss structure also finds use with rigid or semi-rigid joints, e.g. space truss roofs, girders for suspension bridges, or steel offshore structures. The rigid joints introduce bending effects in the structural members, but these effects are easily included by use of numerically based computational methods.
A framework composed of members joined at their ends to form a rigid structure is called a truss. Bridges, roof supports, derricks, and other such structures are common examples of trusses. Structural members commonly used are I-beams, channels, angles, bars, and special shapes which are fastened together at their ends by welding, riveted connections, or large bolts or pins. When the members of the truss lie essentially in a single plane, the truss is called a plane truss.
The Static Analysis of the Truss
2016
In this paper the static analysis of the truss is investigated. The analytical and computational method of the roof structures are presented. At the beginning, the analytical method is used for determination of values of external supports, axial forces and principal stresses in truss. Then the computational method is used for the solution of the same problems. The roof structure is modeled by the finite element method, where the bar members are represented by the truss elements. The finite element model loaded by external forces, without and with self-weight of structure is computed. At the end, the analytical and computational buckling analysis for the trusses with maximal compressive axial force is performed. The comparison of results of analytical and computational method shows that all methods are accurate enough, but of course computational method is faster and more adaptive for any subsequent changes.
Joint Flexibility in Rectangular Hollow Section Trusses
1991
The normal practice in designing steel trusses is initially to consider them as being pin-jointed for preliminary sizing of the members. Subsequently the sections might then be checked for the combined effect of the axial and shear forces, and the bending moments that could be derived from a rigid joint analysis. In the case of trusses formed from Rectangular Hollow Sections (RHS), this method does not allow for the punch-in and pull-out effects of the struts and ties on the chords to which they are connected. In other words, the rigid joint assumption implies that full displacement and slope continuity exists between adjoining members. However, trusses welded from RHS members are neither rigid nor pinned, but have some intermediate flexibility between these two extreme cases.
Journal of Civil Engineering and Architecture, 2019
The paper presents results of calculations of forces in members of selected types of statically indeterminate trusses carried out by application of the two-stage method of computations of such structural systems. The method makes possible to do the simple and approximate calculations of the complex trusses in two stages, in each of which is calculated a statically determinate truss being an appropriate counterpart of the basic form of the statically indeterminate truss structure. Systems of the statically determinate trusses considered in the both stages are defined by cancelation of members, number of which is equal to the statically indeterminacy of the basic truss. In the paper are presented outcomes obtained in the two-stage method applied for two different shapes of trusses and carried out for various ways of removing of appropriate members from the basic trusses. The results are compared with outcomes gained due to application of suitable computer software for computation of the same types of trusses and for the same structural conditions.
Stability of trusses by graphic statics
Royal Society Open Science, 2021
This paper presents a graphical method for determining the linearized stiffness and stability of prestressed trusses consisting of rigid bars connected at pinned joints and which possess kinematic freedoms. Key to the construction are the rectangular areas which combine the reciprocal form and force diagrams in the unified Maxwell–Minkowski diagram. The area of each such rectangle is the product of the bar tension and the bar length, and this corresponds to the rotational stiffness of the bar that arises due to the axial force that it carries. The prestress stability of any kinematic freedom may then be assessed using a weighted sum of these areas. The method is generalized to describe the out-of-plane stability of two-dimensional trusses, and to describe three-dimensional trusses in general. The paper also gives a graphical representation of the ‘product forces’ that were introduced by Pellegrino and Calladine to describe the prestress stability of trusses.
International Journal of Space Structures, 2016
This article extends the overview relating graphic statics and reciprocal diagrams to linear algebra-based matrix structural analysis. Focus is placed on infinitesimal mechanisms, both in-plane (linkage) and out-of-plane (polyhedral Airy stress functions). Each self-stress in the original diagram corresponds to an out-of-plane polyhedral mechanism. Decomposition into sub-polyhedra leads to a basis set of reciprocal figures which may then be linearly combined. This leads to an intuitively appealing approach to the identification of states of self-stress for use in structural design and to a natural ‘structural algebra’ for use in structural optimisation. A 90° rotation of the sub-reciprocal generated by any sub-polyhedron leads to the displacement diagram of an in-plane mechanism. Any self-stress in the original thus corresponds to an in-plane mechanism of the reciprocal, summarised by the equation s = M* (where s is the number of states of self-stress in one figure, and M* is the number of in-plane mechanisms, including rigid body rotation, in the other). Since states of self-stress correspond to out-of-plane polyhedral mechanisms, this leads to a form of ‘conservation of mechanisms’ under reciprocity. It is also shown how external forces may be treated via a triple-layer Airy stress function, consisting of a structural layer, a load layer and a layer formed by coordinate vectors of the structural perimeter.
System behaviour of wood truss assemblies
Progress in Structural Engineering and Materials, 2005
Wood truss assemblies are widely used in light frame construction all over the world. Although the volume of literature on single trusses and joints is relatively huge, the system behaviour of truss assemblies has received only limited attention. The main approach to take into account the system behaviour of an assembly is to use a system factor in the design of single trusses. However, technical advances now make it possible to analyse and design these complex assemblies as systems using three-dimensional structural analysis programs, thereby including the system effect directly. This paper presents an overview of previous research on system behaviour of truss assemblies and recommends a system design approach to designing truss assemblies.
New Simple Method of Calculation of Statically Indeterminate Trusses
2014
The paper presents a very simple method, which in two stages enables to calculate the plane statically indeterminate truss by the application of one of methods used for the force calculation in the statically determinate trusses [1]. The results are obtained in a very simple and quick way. Although the force values are approximated but they are relatively very close to those, which are determined by the exact methods. The point of the two-staged calculation process of the statically indeterminate trusses is to determine schemes of two independent and simple statically determined trusses, which after superposition of their patterns will give in the result a pattern of the initial, more complex form of the statically indeterminate truss. Each of the simple truss has to be of the same clear span, the load forces have to be of the half values and they have to be applied to the same nodes like in truss of the initial structural configuration. For example in the first stage, see Fig. 1, f...
A Two-Stage Method for an Approximate Calculation of Statically Indeterminate Trusses
Journal of Civil Engineering and Architecture, 2014
The paper presents the principles of a method, which in two simple stages makes possible to carry out the statically calculation of values of forces acting in the flat static indeterminate trusses. In each stage, it is considered the static determinate truss, scheme of which is obtained after remove the suitable number of members from the basic static indeterminate truss. The both intermediate statically determinate trusses are of the same clear span and they are loaded by forces of half values applied to the corresponding truss nodes. The method applies one of the typical procedures of calculation of the statically determinate trusses and then it is applied in an appropriate way the rule of superposition for obtaining the final values of forces acting in particular members of the basic truss. The values of forces calculated in this way are of a very close approximation to the force values determined in the special and complex ways being considered as the exact calculation methods. The proposed method can be useful mostly but not only for the initial structural design of such systems. The simplicity of the two-stage method justifies an assumption that it can be relatively easy and worthy to adjust to the requirements of the computer aided technology of statically calculation of the complex forms of trusses.