Sequentially linear analysis with equivalent frame method to simulate unreinforced masonry structures

Abstract

This research investigates how the equivalent frame method in combination with a sequentially linear analysis can be used to model the behaviour of a façade of an unreinforced masonry structure, subjected to a lateral pushover load. The experimental data of the two-story building experiment at the University of Pavia is used.
Two different types of models are made, a continuum model and a beam model, with each two different modeling approaches, the three-zoned approach for the piers and spandrels and a uniform model. The three-zoned approach uses the bed joint tensile strength at the ends of the piers and spandrels, and the maximum tensile strength at the center of those element to simulate rocking and shear failure respectively. The most important results are:
The three-zoned approach in combination with a continuum model was able to describe the failure mechanism of the façade and perform the analysis stable, with a maximum tensile strength adjusted to f_tu=0.08 MPa. Shear failure in the piers was dominant. As a lateral push-over load was used and not a cyclic load as in the experiment, the maximum load of the structure was for most displacements somewhat higher than in the experiment, but the maximum load was 150 kN in both cases. The displacement of 22 mm in the experiment was not reached, but a displacement of 10 mm.
The beam model analysis aborted early as a result of a reduction of the initial load factor. It was found that the fixed crack approach in combination with high shear forces in the structure resulted in a fixed crack coordinate system that was rotated from the beam axis. Principal stresses could exceed the strength of the material and wrong integration points were damaged reducing their strength severely. At this stage a maximum displacement of 5 mm is reached while the force is 165 kN, higher than in the experiment. The structure responds very brittle.
Shear stresses in the beam element model exceeded the strength of the material. Adding shear interfaces in an SLA will result in a more correct failure pattern.
For the beam model, a sensitivity check was done for the mesh size, fracture energy, number of saw-teeth and number of integration points. All values were accurate enough.
A relation exists between an initial load factor reduction and the opening of a crack in the corresponding integration point that damages at an initial load factor reduction.
In conclusion, the results of this thesis confirm the potential of the SLA to accurately approximate the behaviour of an URM structure as it was possible to run a stable analysis with accurate results for the continuum model. The beam model gave similar results in terms of forces and bending moments compared with an incremental iterative approach, but the analysis was aborted early. New developments like a rotating crack approach and shear interfaces will result in a more stable analysis as the right failure behaviour will be followed resulting in a more accurate load-displacement relation.