Showing papers on "Tangent stiffness matrix published in 1970"

Analyses of repair and maintenance of a masonry wall

Abstract: For the masonry walls, we use low tensile strength and fracture energy. The nonlinear uniaxial compressive behaviour is defined by initial Young's modulus E, crushing point and ultimate point in the stress-strain plane. In multiaxial compressive stress condition, the crushing and ultimate points may be enhanced, relating to the projection on the multiaxial failure envelope in principal stress axes. Unloading from a compressive state is parallel to the initial Young's modulus. Cracking occurs when one tensile principal stress tends to overcome the tensile strength. A crack plane develops at right angle to the previous principal direction and is conserved its orientation for the whole loading process. Subsequent crack planes could be only orthogonal to the first and between them. After cracking, the stiffness matrix at the integration point is modified according to fracture or aggregate interlock theories. The local tangent stiffness matrix is referred to: 1) principal stress directions before tensile failure, 2) cracks coordinate system after tensile failure. The convergence tolerances on unbalanced load and energy are imposed within 0.1%. Initially, masonry panels were obtained by the wall and were tested in situ in compression, splitting and shear tests. These three experimental tests were compared with analogous numerical analyses in order to obtain all the mechanical characteristics for the wall analysis. Cyclic tests on a stone wall of irregular size for a building placed in l'Aquila were performed. These tests were compared with analogous analyses, both to design the tests and to obtain new mechanical features of the material. The damaged wall were strengthened with various steel reinforcements, and then analyzed with new load conditions.