T Shape memory alloys (SMAs) are functional materials that feature shape memory effects and super- elasticity. These features have made SMAs efficient materials for reinforcement and improvement of the stability of a structure. The present study investigated the effect of local post-tensioning with SMAs to improve the load-carrying capacity of tapered steel industrial sheds. For this purpose, ABAQUS software was used to predict the flexural strength and load-bearing capacity of the alloys. The effects of the diameter and the post-tension force applied to the SMA tendons were investigated. The results showed that external post-tensioning using SMA tendons is an effective way to increase the load- carrying capacity of industrial sheds. In the maximum load capacity of the frame for the steel and SMA tendons increased by 36 and 60%, respectively. The performance of the sheds was improved by local post-tensioning, which can reduce the weight of the

Theoretical Analysis on the Behavior of Reinforced Industrial Shed Structures with Shape Memory Alloys

Examples are shown for analytical solution of engineering structures. The basic procedures for statically indeterminate systems are the force method and the deformation method. The calculation leads to a linear system of equations. The coefficients of the systems are in many cases tridiagonal or one-pair matrices. The solving of this kind of problems is based on a theorem, which states that the inverse of each tridiagonal matrix is a one-pair matrix and vice versa. This enables us to find an analytical solution in numerous particular problems. Examples are taken from theory of reinforced concrete and from different girder and cable-stayed structures.

Forces in load bearing structures suitable to be treated by tridiagonal and one-pair matrices

There are many problems of free cantilevered prestressed concrete to be solved by more 
convenient methods. One of these is the determination of the internal forces during 
the assembly and post-tensioning of the cantilevers. This question is also called the 
determination of the elastic shortening loss in already anchored tendons. 
A system of equations for the tendon forces as unknowns using the force method 
for the states of the construction of the cantilevers is written. The analytical solution 
of this equation is enabled by the recognition that the coefficient matrix of the system 
is a one-pair matrix modified by a diagonal matrix. Using the statement according to 
which the inverse matrix of a one-pair matrix is a symmetric tridiagonal matrix and vice 
versa the elements of the inverse of the one-.pair matrix in the coefficient matrix can be 
produced. The task finally can be reduced to the inversion of the symmetric tridiagonal 
matrix modified by a diagonal matrix. This further problem can be solved by means of 
one-pair matrices formed by quantities gained by a recursive algorithm. 
The importance of the result consists in the fact that the internal forces of a free 
cantilevered structure in an arbitrary stage of construction can be written in case of any 
parameters (changing cross-section, length of segments, number of tendons, etc.)

Forces in prestressed concrete bridges constructed by free cantilevering

SUMMARY The paper deals with the determination of forces in cable-stayed bridges by the deformation method and the force method. Using methods of linear algebra, it gives an analytical solution for determination of the internal forces in such structures.

/pdf/analytical-solution-of-basic-equations-of-theory-of-1do82hhuec.pdf

Analytical solution of basic equations of theory of structures for cable-stayed bridges

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Forces in prestressed concrete bridges constructed by free cantilevering

Analytical solution of basic equations of theory of structures for cable-stayed bridges

Forces in load bearing structures suitable to be treated by tridiagonal and one-pair matrices