# 72782 - Mechanics of Historical Masonry Structures

## Academic Year 2023/2024

• from Sep 18, 2023 to Dec 18, 2023

## 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

1 Introduction to Structural Masonry

1.1 Advantages and disadvantages of 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

• Comprehensive teacher course Handout (freely available for the course students in book format);

• 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.

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

## 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;

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 mode for student in classroom and for those connected online.

The online teaching will be delivered using Microsoft Teams mainly. 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 activated 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

### SDGs

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