Homework Earthquake

2 DESCRIPTION OF THE STRUCTURE

The purpose of the following report is to carry out the seismic assessment of an existing building

located in Gerace, Province of Reggio Calabria.

2.1 Geometry

The building under investigation is a two-storey building, where the top floor is represented by

an inclined roof. The structure is partially collapsed, this statement can be observed in the follow-

ing plans. In particular, in the first floor plan the top-right room has no indication about the floor

structural typology nether the load resisting system of the floor.

Figure 2.1: First floor plan

Figure 2.2: Second floor plan 3

Figure 2.3: Roof Plan

Figure 2.4: Front view a

Figure 2.5: Front view b –

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Figure 2.6: Front view c

2.2 Materials

The concept of "masonry quality" holds significant importance, even at the regulatory level, when

analysing the structural behaviour of existing masonry constructions. However, there is limited

awareness about the various types and unique characteristics of masonry, stemming from differ-

ences in materials and construction techniques. To address this gap, it is deemed necessary to

establish a procedure for analysing and classifying these types based on their mechanical proper-

ties.

Central to this approach is the Masonry Quality Index (IQM), which serves as a benchmark for

evaluating the mechanical behaviour of specific masonry types. The IQM provides reliable nu-

merical indicators that can estimate several mechanical parameters, including:

• average compressive strength;

=

• average shear strength;

=

0

• average value of the modulus of elasticity.

E =

The Masonry Quality Index (IQM) is a key parameter used to assess the quality and mechanical

properties of specific types of masonry. It provides a numerical indication of the strength, stiff-

ness, and other characteristics of the masonry, enabling an evaluation of its structural behavior.

The IQM serves several important purposes:

• Structural Analysis: The IQM offers insights into the load-bearing capacity and resistance

of masonry, facilitating assessments of structural safety and the identification of any nec-

essary consolidation or improvement interventions.

• Classification of Masonry Types: The IQM allows for the classification of various ma-

sonry types based on their mechanical properties. This classification aids in understand-

ing the differences between masonry types and selecting the most suitable ones for spe-

cific applications or load conditions.

• Design and Retrofitting: The IQM supports the design of new masonry constructions by

guiding the selection of appropriate materials and dimensions to ensure safety and dura-

bility. It is also valuable for retrofitting existing buildings, as it helps assess masonry

quality and identify appropriate improvement measures. 5

• Regulations and Codes: The IQM can be referenced in building regulations and codes to

define structural safety criteria and requirements for the construction and consolidation

of masonry buildings.

The IQM provides essential insights for the analysis, design, and management of masonry con-

structions, especially for types not explicitly covered in existing regulations such as those detailed

in C8.5.I (Circolare Esplicativa).

To determine the IQM for different types of masonry, a procedure involving the evaluation of

seven characteristic parameters is used. This evaluation is based on the observation of individual

masonry panels and can result in three outcomes: parameter met (R), partially met (PR), or not

met (NR). Scores are assigned based on these judgments, which are then combined to calculate

the IQM for that masonry type.

When limited information about the materials is available, traditional methods are preferred to

define mechanical parameters, following regulatory guidelines. Additionally, several methods can

provide information about the mechanical characteristics of masonry, such as:

• On-site Tests: Tests like single and double flat jack tests or sonic tests can be performed.

Single flat jack tests assess the existing stress state in the test section, while double flat

jack tests, combined with strain gauges, determine Young's modulus and Poisson's ratio

by measuring deformations induced by on-site pressure. These tests can also help define

compressive strength if the in-situ pressure is sufficiently high.

• Sonic Tests: This non-invasive method determines parameters like E (Young's modulus),

ν

G (shear modulus), and (Poisson's ratio) by measuring the velocity of waves transmitted

through the material. Although masonry is highly non-homogeneous, sonic tomography

provides qualitative information on its integrity in both vertical and horizontal directions.

Overall, the Masonry Quality Index is a valuable tool for assessing the mechanical properties and

strength of masonry, contributing to the effective analysis, design, and management of masonry

structures.

2.3 Mechanical parameters

In the context of the mechanical characterization of the building in question, which is constructed

with irregular stone masonry, there is a lack of detailed documentation regarding the load history

of the structure or any global or local material adaptations or modifications. This results in a high

level of uncertainty in the material assessment without specific analyses. Consequently, a

knowledge level of LC1 is assumed, which is the lowest according to the regulations. Knowledge

levels necessitate the application of a reduction coefficient (FC) to the mechanical parameters that

characterize the materials composing the structure. For an LC1 knowledge level, the correspond-

ing confidence factor is FC = 1.35.

Referring to the Circolare Esplicativa per l’applicazione dell’aggiornamento delle "Norme Tec-

niche per le costruzioni 2018" - C8.5.3.1 - Tab. C8.5.I, the main mechanical parameters to be used

in the assessments were selected for irregular stone masonry, ensuring compliance with the min-

imum and maximum tolerances specified in the table provided below. –

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Figure 2.7: Suggested parameters for each material

Where:

• is the average compressive strength of masonry;

• is the average shear strength in the presence of normal stresses, evaluated according to

0

the regulations in §C8.7.1.3;

• is the average strength in the absence of normal stresses and evaluated according to

0

§C.8.7.1.3;

• is the average value of the normal modulus of elasticity of the masonry;

• is the average value of the tangential modulus of elasticity the masonry;

• is the average specific weight.

For each parameter, the following values were considered:

Table 2.1: Design mechanical parameters

Parameter Value UoM 2

1.5 N/ 2

0.02 N/

0 2

0 N/

0 2

750 N/ 2

250 N/

3

19 kN/

After identifying the building and conducting various investigations on the ground and founda-

tions, as stated in section 4.2 of the “Linee Guida per la valutazione e la riduzione del rischio

it is

sismico del patrimonio culturale con riferimento alle Norme Tecniche per le Costruzioni”

necessary to assume a confidence factor ( ) ranging from 1 to 1.35. This factor is used to grade

the reliability of the structural analysis model and the evaluation of the seismic safety index. 7

The corresponding confidence factor for LC1 is =1.35, so the parameters are obtained dividing

Table 2.1

the ones in by :

Table 2.2: Design mechanical parameters divided by 1.35

Parameter Value UoM 2

1.11 N/ 2

0.015 N/

0 2

0 N/

0 2

556 N/ 2

185 N/

3 LOAD ANALYSIS

3.1 Self weight 3

Self-weigh is considered equal to = 19 kN/ ; it is the only parameter which was not reduced.

3.2 Floor slab the Italian system “Solaio

The floor slab is characterized by a putrelle e tavelloni”, which is com-

γ (γ=

posed of steel beams IPE140 (height = 20 cm, interspace = 110 cm, = 12,9 kg/m ), bricks 5

l

3

kN/m and heigh= 0,2 m) and a layer of floor covering.

Table 3.1: Floor loads

g q

floor floor

2 2

[kN/m ] [kN/m ]

Brick 1,00 -

IPE140 0,013 -

Subfloor 2,3 -

Total floor 3,3 2,0

3.3 Roof

Since more precise informations about the roof details are not available, the following typical

scheme has been considered. Figure 3.1: Roof scheme –

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The weight of each single component is computed and multiply by the correspondent specific

weight.

The covering is not walkable, but it is necessary to consider the snow load, which is a static load

and depends on the local weather and exposure conditions. To determine this load, reference is

made to NTC 2018 § 3.4.2. Table 3.2: Roof loads

g q

roof roof

2 2

[kN/m ] [kN/m ]

roof tiles 0,45 -

terracotta 0,58 -

joists 0,1 -

beams 0,15 -

Roof 1,28 0,6

3.4 Barrel vaults the one of the walls, so γ = 17

Barrel vaults have wight of 40 cm and a specific weight lower than

3

kN/m has been taken into account. Table 3.3: Barrel vaults loads

g q

roof roof

2 2

[kN/m ] [kN/m ]

Vault 6,80 -

Subfloor 2,3 -

Vault 9,1 2,0

tot 9

4 SEISMIC ACTION

In the following chapter, the seismic action that the existing structure should withstand is defined.

The seismic action at the specific site is represented by an elastic response spectrum associated

with a return period of 475 years. This value has been determined based on various site-specific

parameters, including the intended use of the building, the limit states considered for the assess-

ments, the type of soil at the location, the topography of the area, and the characteristic seismic

risk level of the zone where the building is situated.

Ground motion is generally characterized by three translational components: two horizontal and

one vertical, which are considered independent from each other. These motion components can

be described using appropriate elastic response spectra. In this study, the investigation of the ver-

tical motion component has been neglected.

The elastic response spectrum for horizontal acceleration is expressed by a spectral shape referred

to a conventional damping of 5% and multiplied by the maximum horizontal acceleration value,

ag, at a rigid horizontal reference site. Both the spectral shape and ag vary depending on the Peak

Vertical Acceleration Ratio (PVR), which represents the probability of exceeding a certain value

within the refe