Reply to the Discussion by H. Jiang and B. Fu of “Confined masonry walls subjected to combined axial loads and out-of-plane uniform pressures” 1Appears in the Canadian Journal of Civil Engineering, 39(11): 1238–1239 [doi: 10.1139.l2012-105

Abstract

Both horizontal and vertical in-plane displacements of confining elements of masonry walls are reported to show that arching action mechanism is a two-direction mechanism. The spring-strut model is a simplified model that only considers equilibrium of forces in the main arching action direction. For the case of the walls studied, with a wall aspect ratio of about 0.75, the main direction is the vertical one. The two-direction arching mechanism is included in the model only for the calculation of the in-plane stiffness (K) of the confining elements. The stiffness (K) is an “equivalent” stiffness represented by a single spring located at the top of the wall. This in-plane stiffness is calculated modeling the four confining elements as a frame. After the formation of the wall final cracking pattern, arching action forces are transfered from the wall segments to the confining elements in two directions. For this reason, the frame is loaded with two triangular and two trapezoidal load distributions. Maximum value of these loads is represented by FT. The frame is also loaded with the corresponding axial load (P), if any. Boundary conditions considered are consisted with those used during testing. A structural analysis of the frame is carried out to determine the total in-plane vertical displacements at different points in the top confining element. Nine equally spaced points are used along this element. For wall specimen S-1, these vertical displacements are upwards; for this reason, an individual stiffness is calculated at each point dividing the force FT by the corresponding in-plane vertical displacement. The average value is defined as the “equivalent” in-plane stiffness (K). For specimens S-2 and S-3 the vertical in-plane displacements are downward; for this reason, the stiffness K is calculated assuming that the confining elements are very rigid and therefore vertical in-plane displacements are neglected. In this case, the stiffness K is calculated as the compressive force that causes crushing of the masonry divided by the corresponding axial deformation of the wall segments. The in-plane stiffness (K) of the confining elements, as presented in this work, depends on cross section properties, material properties, boundary conditions, and axial load. For the walls studied, gross cross sections were equal, modulus of elasticity varied among walls, boundary conditions were equal, and axial load changed from wall to wall. For these reasons, changes in the in-plane stiffness are related not only to the modulus of elasticity of concrete but also to the axial load. The experimental results and analytical models sections are consistent with this matter. The authors believe that the discussers misunderstood those sections. For the walls studied, cracking maximum pressure depends on boundary conditions, flexural tensile strength of masonry perpendicular to bed joints, out-of-plane load pattern (uniform pressure), and axial load. All these variables are included in the analytical models developed in the work. The authors did not consider it necessary to explain, for example, that cracking pressure increases as axial load or tensile strength increases.