# Bruchmechanischer Beitrag zur Biegezugfestigkeit von Mauerwerk

*Aachen / Mainz (2015, 2015)* [Dissertation / PhD Thesis]

*Page(s): XI, 301 S. : Ill., graph. Darst.*

Abstract

The flexural strength of masonry is the decisive building material characteristic value in the design of masonry members loaded orthogonal to the plane, i. e. basement walls under earth pressure, facing masonry under wind loads as well as infill masonry and non-loadbearing internal partition walls. In this paper, the load bearing behaviour at a uniaxial load transfer - parallel and perpendicular to the bed joints - is examined with numerical calculation methods as well as in building component tests, the stress states in the masonry are analysed and calculation approaches for the flexural strength are derived. The determined fracture mechanical characteristic values and the complete material laws of the masonry units and the bond joints form the essential basis for the examinations on masonry.The examined masonry unit materials show a significantly different behaviour under tensile stress which can be described as “brittle” (brick) up to “distinctly non-linear, ductile” (lightweight concrete) and which is reflected in the sensitivity to notches as well as in the determined stress-crack opening curves. Nevertheless, it proved possible to describe the examined size effect on the flexural tensile strength of the masonry unit by means of one functional correlation for all types of masonry units.The bond joints are described using a meso model in which the mortar and the interface masonry unit / masonry mortar are modelled in a smeared way. For the bond joints, the complete material laws are determined for different masonry unit / masonry mortar combinations under tensile as well as shear load at a simultaneous compressive load orthogonal to the joint. Especially the tensile load bearing behaviour is significantly influenced by the notch effect resulting from shrinkage effects as well as by the anchoring effect of the mortar bolts in perforated bricks. The experimental investigations prove a considerable influence of the type and quality of the workmanship on the bond strength. The material laws under shear stress can be directly determined with torsion tests on hollow cylinders applying a newly developed test method validated by means of numerical calculations. On solid cylinders, they can be determined applying a derived analytical approach. On the one hand, the numerical investigations on two-unit specimens with rectangular cross-sections illustrate the influence of the stiffness of the mortar joint on the shear stress distribution up to the first crack load. On the other hand, it can be noted that the cross-section is almost completely plastified at the maximum transferable torsional moment. So, for the examined mortars and cross-sectional geometries in the state of failure, the calculational approach of a fully plastified joint on the stress level of the shear strength (adhesion and friction) is reasonable.In order to calculate the load bearing behaviour of a wall under bending stress parallel to the bed joints, where the number of influencing factors is higher and the stress states are more complex due to the head joints as compared to a wall under bending stress perpendicular to the bed joints, a numerical model is developed and calibrated on wall tests. In general, the test and calculation results show a very good correlation. The analysis of the stress states in the masonry units and mortar joints in the numerical investigations and the experimental tests on the masonry walls with extensive deformation measurements make it possible to comprehend the failure mechanisms.With the developed numerical model, comprehensive parameter studies are conducted for the failure cases “unit” and “joint”. In doing so, the material laws of the masonry units and the mortar as well as the geometric properties of the masonry are varied. The influence of the head joint mortar as well as of a superimposed load perpendicular to the bed joint is examined. The investigations on unit failure illustrate that the stress distribution in the masonry unit and hence the flexural strength of the masonry are significantly influenced by the overlap and the unit width (masonry width) as well as by the post-failure behaviour of the unit materials after the first crack formation. The determined stress states in the bed joints are extremely complex and they can obviously not be described by analytical approaches. Therefore, for the determination of the maximum transferable moment in the bed joint, analogous to the torsion tests on two-unit specimens, first a completely plastified bed joint is assumed applying the shear bond strength and the percentage of friction depending on the superimposed load. However, it turns out that the softening behaviour depending on the overlap geometry and the material law must be taken into account for the correct determination of the torsional moment. By mortaring the head joint, the rotation point is displaced from the centre of the overlap area to the edge of the unit.The results of the numerical simulation calculations are analytically described in the form of calculation approaches considering the findings gained in the experimental investigations, partly making simplified assumptions to describe the complex stress states. In parts, simplified assumptions are used to describe the complex stress states. The comparison of the calculation to the test results shows a good correlation especially for the own investigations where the decisive input parameters for the calculation approaches are available. A satisfactory correlation could however also be achieved for previous test results. At a bending load perpendicular to the bed joints, normally a joint failure occurs. The material law of the bond joint under tensile stress which was determined on small-size specimens is decisive. The conducted wall tests illustrate the influence of the scatter of the material properties and of the workmanship on the flexural strength. In principle, the statistic approach of the “weakest-link” theory seems targeted, however, the own tests do not allow for a statistic evaluation due to the number of test specimens. Based on the own examinations it can however be seen that, in addition to the scatter of the material properties, the number of joints and, when indicated, the wall length, also the brittleness of the bond joint must be taken into account as decisive characteristic value in a statistic approach.Summing up, on the one hand, this paper provides essential findings with regard to the material laws of the masonry components “unit” and “mortar joint” as well as to their determination; on the other hand, it illustrates findings regarding the stress distributions in masonry under uniaxial bending load and the failure mechanisms considering the non-linear material behaviour.

## Authors

### Authors

Schmidt, Ulf

### Advisors

Brameshuber, Wolfgang

Jäger, Wolfram

Reinhardt, Hans-Wolf

### Identifier

- ISBN: 978-3-95886-025-4
- URN: urn:nbn:de:hbz:82-rwth-2015-015364
- REPORT NUMBER: RWTH-2015-01536