# 72782 - Mechanics of Historical Masonry Structures

### SDGs

This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.

## Learning outcomes

The goal of the course is to provide the students with the fundamentals for the analysis of historical masonry structures. In particular, the course treats the theoretical aspects, the numerical tools and the experimental techniques for an effective structural diagnosis of histrorical structures aimed at preservation and rehabilitation. Structures from different periods of histrory are analyzed.

## Course contents

MODULE 1

1 Introduction to Structural Masonry

1.2 Morphology of historical masonry

1.3 Masonry Stonework

1.4 Brickwork

1.5 Stress distribution (percolation of stress)

1.6 Some consideration about damage and units arrangement

2 Masonry mechanical behavior and performances

2.1 Masonry mechanical properties

2.2 Compressive strength based on elastic theories

2.3 Local-global failure of masonry

2.4 Masonry Quality Index

3 The rigid no-tension model

3.1 The unit resistant Masonry Cell

3.2 Consideration on realistic admissible domain

4 The masonry continuum

4.1 Compatibility conditions

4.2 Photo-elasticity and masonry

4.3 Displacements field and kinematic compatibility conditions

4.4 The boundary of the cracked body

5 Equilibrium and compatibility

5.1 Principle of virtual work (PVW)

5.3 Mechanism state

5.4 Collapse state

5.5 The static theorem

5.6 The kinematic theorem

5.7 Uniqueness of the collapse multiplier

5.8 Example - application of kinematic theorem

6 Masonry arches: the concept of thrust and limit analysis

6.1 Introduction

6.2 Bearing capacity of the arch

6.2.1 Limit analysis of the arch

6.3 Minimum and maximum Thrust

6.4 Use of the limit analysis to estimate the pressure curve

6.5 Extreme lines of thrust, joints and associated mechanisms

6.6 Self equilibrated systems

6.7 Internal equilibrium of the arch

7 Vaulted systems

7.1 Introduction

7.2 Elastic solution: membrane state in cylindrical vaults

7.3 Transition from the uncracked to the cracked state. The no tension

model applied to barrel vaults

7.4 Cross vaults

8 Domes

8.1 Introduction

8.2 The implemented Static approach

8.3 Membrane state in domes

8.4 From membrane state to cracked state

8.5 Some Other Funiculars

8.6 The dome of S. Pietro in Rome

9 Piers

9.1 Eccentricity and masonry piers

9.2 Yokel approach for piers

9.3 Photo elastic experimental tests on prismatic rectangular dry-stone pillars

10 Walls

10.1 Kinematic analysis

11 Introduction to fracture mechanics

11.1 Historical perspective

11.2 Effect of material properties on fracture

11.3 Linear Elastic Fracture Mechanics

11.4 Brittle and cohesive materials

MODULE 2

Applied analysis of theoretical topics developed within Module 1 of a cultural Heritage structure (case histories such as churches) with special regards to:

• structural comparison with a similar monument;
• first aid intervention after possible seismic injures;
• monitoring project for structural safety;
• reduction of vulnerability with composite materials.

Basics of relevant approaches for Structural Conservation of Historical Constructions:

1. Composite materials FRP or FRCM inhibiting collapse mechanisms
2. First Aid post sisma contrasting masonry block tectonic movements

• Comprehensive teacher course Handout (Book version freely available for students);

• Statics of Historic Masonry Constructions, M. Como, Springer, 2013.

• The Stone Skeleton, J. Heyman, Cambridge University Press, 1995.

• Historic Construction and Conservation: Materials, Systems and Damage, P. Roca, P. Lourenco, A Gaetani, Routledge; 1st ed. 2019.

• Structural brickwork, A.W.Hendry, MacMillan, 1981.

• The Construction of Gothic Cathedrals, J. Fitchen, The Univ. Chicago Press, 1961.

• Fracture and Size Effect (in concrete and other quasi-brittle materials), Z.P. Bazant and J. Planas, CRC Press, 1998

## Teaching methods

The course content will be entirely covered by the lectures.

The course includes some invited keynote lectures, which will help cover the practical aspects of the lectures.

The instructors will supervise students during all activities.

## Assessment methods

A full comprehensive final (written and oral) exam will be used to assess students’ knowledge and understanding of the topics covered in the course. A final project will be presented by the student

The final exam will be organized as follows:

WRITTEN TEST (delivered using the EOL system):

• 30 random question about theoretical aspects developed during Module 1;
• 1 exercise to solve about kinematic analysis of masonry structures (a wall, an arch or a wall with openings);

ORAL TEST/COLLOQUIUM

•  colloquium of 5-20 minutes about a particular theoretical aspect;
PROJECT
• A project related to the study of particular historical buildings will be assigned during the lectures delivered within Module 2: Gothic churches of San Petronio or San Francesco in Bologna; Garisenda or Asinelli towers.
Students will present their project at the end of the course (slides in pptx). The assessment of the presentation will be part of the final grade.

SELF EVALUATION EXAM (Mock exam test)

Before the end of the course, a self-evaluation test will be delivered for some of the course topics.

This self-evaluation test proposes 30 random questions among some of the all possible exam questions related to theoretical aspects. The time provided is forty minutes (that is the same time we will provide for the final exam). In the self evaluation exam the students can attempt the test as many times as he/she wants. Then, the solution is provided as soon as the answer is submitted.

## Teaching tools

The course will be delivered in blended modality: half of the course in class and half of the lectures online.

The online teaching will be delivered using mainly Microsoft Teams. The software Zoom will be also used for specific activities.

The instructor will use PDF slides to be annotated during the lecture using a tablet device. Clean and annotated slides will be provided to the students.

Recording of the lectures will be turned on by the instructor at the beginning of the lecture.

During the lectures the teacher will use small models and videos to better clarify some concepts.

In the absence of obstacles (i.e. social distancing or covid19 emergency), the course includes the organization of guided tours on the field to local cultural heritage historical structures.

## Office hours

See the website of Giovanni Castellazzi