L5Masonry - LV1 RESISTO method.pdf

Seismic Vulnerability Assessment for
Masonry Building – Resisto method
HBR – HISTORIC BUILDING REHABILITATION
Dr. Michele Palermo
Prof. Marco Savoia
STRUCTURAL STRENGTHENING AND REHABILITATION LM

SEISMIC VULNERABILITY ASSESSMENT
FOR MASONRY BUILDINGS – RE.SIS.TO. METHOD
– In cases of single building: assess its seismic vulnerability with a simplified mechanical
approach: evaluation of the ratio Capacity/Demand in terms of PGA:
this value will be adjusted through additional expert judgments (technician expertise), by
means of a qualitative approach based on observations of the building’s construction and
historical analysis.
– In cases of many buildings: compare their safety levels in order to define a priority list for
interventions.
Using an approach based on the compilation of GNDT form
(National Group for Earthquake Defense) together with a
simplified evaluation of shear strength of the building
MAIN OBJECTIVES
HYPOTHESES
fa,RESISTO<0.1
0.1<fa,RESISTO<1.0
1<fa,RESISTO
fa,RESISTO=0.185
D
C
RESISTO
,
a PGA
PGA
f 

According to level LV1 approach, for step 2
only simplified mechanical considerations are used (no numerical analysis, e.g. FEM).
MAIN PHASES OF THE METHOD
HYPOTHESES
The method is based on 4 phases:
1. Obtaining Technical information on the actual state of the building (Knowledge Path);
2. Evaluation of the peak ground acceleration that induces the attainment of the safe life
limit state SLV (PGAC = Seismic Capacity) and evaluation of the reference peak
ground acceleration of the site for the same limit state (PGAD = Seismic Demand),
which depends on an accepted probability of exceedance in a predefined reference
period (i.e. SLV corresponds to a Pexceedance=10% in VR years);
3. Evaluation of the ratio Capacity/Demand in terms of acceleration, to assess the safety
level of the building, similar to the (NTC 2018)
4. Re.Sis.To. Classification and correction of the results considering Local Vulnerabilities
D
C
RESISTO
,
a
PGA
PGA
f 
PGA
PGA
C
E
D
 

MAIN PHASES OF THE METHOD
HYPOTHESES
Phase 1a: Knowledge level of the building from documents
Phase 1b: On-Site Investigation
Phase 2a: Assessment of seismic demand
Phase 2b: Capacity assessment (quantitative computation)
computation of shear strength of walls
computation of external shear forces for Sa=1g at each level
identification of the critical level of the building
Phase 2c: Capacity assessment (qualitative computation)
masonry quality - coefficient Crid
Phase 2d: Estimate of the actual shear resistance of the building
Phase 2e: Peak ground acceleration leading to SLV
Phase 3: Re.Sis.To.®
Capacity-demand comparison and Re.Sis.To. Classification
Phase 4: Local Vulnerabilities and eventual update of of Re.Sis.To. Classification
1
2
3
4

PHASE 1A: KNOWLEDGE LEVEL OF THE BUILDING FROM DOCUMENTS
Before the on-site investigation, it is important to know (when available):
– Plans, sections, views for each building portion (better if digital)
– Technical reports on quality of materials, on-site tests, etc.;
– Any documents pertaining to the construction phases and transformation phases of
the buildings
– Any documents of interventions made on the building during its life
PHASE 1: Knowledge Path
Mantua, Italy:
the Ducale Palace
Structural unit– a portion of the building
which can be considered independent and
therefore can be analyzed independently
from other portions of the building itself

the buildings
Mantua, Italy: the Ducale Palace
Restoration
intervention occurred
in 1951:
‘removing and
replacing’ technique
(cuci-scuci in Italian)
Mantua, Italy:
the Ducale Palace

– Plans, sections, views for each building portion (better digital)
the buildings
The Bridal Chamber,
painted room
Mantua, Italy: the Ducale Palace
Restoration
intervention occurred
in 1951:
‘local rebuilding’
technique
(cuci-scuci in Italian)

the buildings
Old plan of the Uffizi palace in Firenze
Phase 1 Phase 2 Phase 3 Phase 4

PHASE 1B: ON-SITE INVESTIGATION
ACTIONS DURING ON-SITE SERVEY (see the following):
- Photographic survey;
- Verification of the positions and dimensions of resisting elements and comparison with
blueprints of the building, identify the openings, the structural and non structural elements
(load bearing walls and partition walls, masonry vaults and ceiling vaults), etc;
- Identification of floor’s types and their thicknesses, their connections with external walls,
etc;
- Analysis of the conservation status of the building.
- On-site survey and tests: can be performed only through permission of people (e.g.
“building manager”), who has knowledge of the building’s status, especially in cases of
important public buildings as schools, museums, etc;
- Investigation Team: Technical staff, manager and workmen for small demolition
interventions;
- Investigation duration: one day.

In order to complete the GNDT form (useful in the next phases), some basic information
about the actual status of the building is necessary :
– Connection Quality of masonry walls (at least two positions for each building
portion);
– Presence of lintels, ring beams, steel ties and rods (at each floor);
– Masonry Quality, including the quality of mortar joints and their thickness (at least
two positions for each building unit);
Connections between different walls
Mortar joint’s thickness and masonry texture

In the presence of reinforced concrete slabs, inspection of details with pachometer,
connections to the beams, presence of steel ties (for all the floors of the building);
Verification from digital blueprints (if available) of the building’s main dimensions (for each
part of the building);
Survey of the roof structure, highlighting the presence of thrusting roofs, false ceilings,
etc;
Presence of cracks and other degradation phenomena, trying to understand the main
motivations for their occurrence.
False ceiling
Crack pattern

Retaining Ring Beam
Heavy roof
PHASE 1B: INSPECTION EXAMPLES

The assessment of the seismic demand will be done with reference to the Italian Building Code
The main steps are:
PHASE 2A: ASSESSMENT OF SEISMIC DEMAND
PHASE 2: Demand and Capacity
Nominal life of the construction: VN (50y, 100y)
(Table 2.4.I – Italian Building Code)
Coefficient of usage: cU (class I – II – III - IV)
(Table 2.4.II – Italian Building Code)
𝑇𝑅 = −
𝑉𝑅
ln 1 − 𝑃𝑉𝑅
𝑉𝑅 = 𝑉𝑁 ∙ 𝑐𝑢 Reference period
e.g. SLV corresponds to a PVR = 10% in VR
In-situ geographic coordinates allows to evaluate
Considered limit state (SL)
Topographic Category: Ss, Cc
(Table 3.2.IV – Italian Building Code)
Ground Type: ST
(Table 3.2.II – Italian Building Code)
ag Peak ground acceleration on rigid and flat
reference soil;
F0 Dynamic amplification at the plateau
TC* corner period
considering the Local Amplification Effects
Return period
𝑎𝑔, 𝐹0, 𝑇𝑐
∗
𝑆𝑒(𝑇)
TO REMEMBER

Local Seismic Effect
appendix NTC
Excel file
SEISMIC HAZARD MAP ag TR
Elastic Response Spectrum for the
Pseudo-Acceleration horizontal component
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
0 1 2 3 4
NTC-suoloA
NTC-suolo B
NTC-suolo C
NTC-suolo D
NTC-suolo E
*
C
C
C
T
S
T
C
T
S
S
S




6
.
1
g
a
4
T
3
T
T
g
D
C
B



Litho-stratigraphic Amplification (SS CC)
Topographic Amplification (ST)
- ag Peak ground acceleration on a rigid
and flat reference soil;
- F0 Maximum value of the site
amplification factor
- TC* Period at end of the constant
acceleration region of the response
spectrum
Seismic Action
rigid soil, horizontal soil
TO REMEMBER
Peak Ground Acceleration

𝑃𝐺𝐴𝑑 = 𝑎𝑔 ⋅ 𝑆 = 𝑎𝑔 ⋅ 𝑆 𝑇 ⋅ 𝑆 𝑆
ST topographic amplification coefficient
SS stratigraphic amplification coefficient
PGAd
Reference:
NTC08 for the definition of the earthquake
spectrum according to Italian National Codes or
EC8 for the definition of the earthquake spectrum
according to European Codes
Maximum value
of the site
amplification
factor F0
Se= F0 x S x ag
TO REMEMBER

Ax
Ay
Earthquake directions:
PHASE 2B: CAPACITY ASSESSMENT (quantitative computation)
COMPUTATION OF SHEAR STRENGTH OF WALLS
Determine the resisting area (for in-plane shear strength) in both directions (x and y)
and the total weight for each level of the building.
To evaluate the resisting areas it is necessary to identify the portions of walls (structural
walls) which are continuos from bottom to top (for each storey)
X
Y
Atot=total floor area

𝐴𝑦,𝑖 = ෍
𝑛=1
𝑁𝑀𝑦,𝑖
𝐴𝑦,𝑛,𝑖
𝐴𝑥,𝑖 = ෍
𝑛=1
𝑁𝑀𝑥,𝑖
𝐴𝑥,𝑛,𝑖
𝑞𝑖 =
𝐴𝑥,𝑖 + 𝐴𝑦,𝑖 ∙ ℎ𝑖
𝐴𝑡𝑜𝑡,𝑖
∙ 𝑝𝑚,𝑖 + 𝑝𝑠,𝑖
(Weight per unit surface for each floor)
𝑊𝑖 = 𝑞𝑖 ∙ 𝐴𝑡𝑜𝑡,𝑖
(Total weight for each floor)
Load analysis = permanent
+ accidental loads (seismic
combination)
(G1 + G2 + Q)
Determine the resisting area in both directions (x and y) and the total weight for each
level of the building.
𝐴𝑡𝑜𝑡,𝑖=total area of the i-th floor
𝑝𝑚,𝑖
𝑝𝑠,𝑖
wall density
Slab permanent + accidental loads (seismic combination)

Table C8.5.I from CircNtc18
Irregular stones and pebbles
Pseudo-rectangular/wedgeshaped elements with external walls
havingirregular thickness
Coursed random rubble masonry
Irregular masonry made of stones with low mechanical properties
(i.e. tuff, sandstone)
Regular masonry made of stones with low mechanical properties
(i.e. tuff, sandstone)
Squared stone masonry
Solid clay bricks and lime mortar
Masonry made of hollow bricks with cementitious mortar
(i.e doppio UNI with <= 40% hollows)
MASONRY TYPE
𝜏𝑟,𝑖 = design shear strength according to the NTC18
Select the MECHANICAL PARAMETERS of masonry
- 𝜏0 minimum value of the interval
- 𝐹𝐶=1.35
- 𝛾𝑀=2.0
- Coefficients from
the NTC18 TableC8a.2.2
𝜏𝑟 =
𝜏0
𝐹𝐶 ∙ 𝛾𝑀
∙ 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡𝑠
Define the shear strength of masonry material at each level of the building.

𝜎0,𝑖 =
σ𝑘=𝑖
𝑁
𝑊𝑘
𝐴𝑥,𝑖 + 𝐴𝑦,𝑖 𝑉𝑟,𝑖 = 𝐴𝑚𝑖𝑛,𝑖 ∙ 𝜏𝑟,𝑖 ∙ 1 +
𝜎0,𝑖
1.5 ∙ 𝜏𝑟,𝑖
(Turnsek – Cacovic 1970 capacity model)
Shear Resisting Force for each floor
𝜏𝑟,𝑖
𝐴𝑚𝑖𝑛,𝑖 Minimum area between 𝐴𝑥,𝑖 and 𝐴𝑦,𝑖;
𝜏𝑟,𝑖 Design shear strength according to the NTC;
σ0,𝑖 Compression stress due to the vertical loads;
N Number of levels of the building;
• because the shear strength is assumed
depending only on the area of the
resisting walls,
• because the vertical stress is evaluated as
mean value on all the resisting areas
then the verification can be performed only
along the weakest direction
Determine the shear resisting force at each level of the building.

Computation of the seismic shear forces at the various levels applying an equivalent
static forces distribution considering a spectral acceleration equal to one Sa=1g.
Sa=1g
𝐹𝑖 = 1𝑔 ∙
𝑊
𝑔
∙
𝑧𝑖∙𝑊𝑖
σ𝑗=1
𝑁
𝑧𝑗∙𝑊𝑗
= 1𝑔 𝑊𝑖
𝑧𝑖
𝑧𝑔
(External forces applied at each level of the building)
EQUIVALENT STATIC FORCE DISTRIBUTION (the same along both directions)
𝑊𝑖 = WEIGHT OF THE i-th FLOOR
𝑊 = TOTAL WEIGHT OF THE BUILDING
In order to identify the critical level (the weakest floor) of the building
COMPUTATION OF EXTERNAL SHEAR FORCES AT EACH LEVEL
𝑧𝐺
W Sa
𝑧𝐺 =
σ𝑗=1
𝑁
𝑧𝑗 ∙ 𝑊
𝑗
σ𝑗=1
𝑁
𝑊
𝑗

𝑉𝑠,𝑖 = ෍
𝑘=𝑖
𝑁
𝐹𝑘
The external shear force at the generic level (i) is equal to the sum of external forces
applied at the upper levels ( i  k  N ).
External shear force at each floor
𝑉𝑠,𝑖 i-th floor
Computation of the seismic shear forces at the various levels applying an equivalent
static forces distribution considering a spectral acceleration equal to one Sa=1g.
In order to identify the critical level (the weakest floor) of the building
COMPUTATION OF EXTERNAL SHEAR FORCES AT EACH LEVEL

The ratio between the shear strength and the shear external force evaluated for Sa=1g
indicates the shear capacity of that floor of the building, in terms of maximum acceleration
(reported to 1g) that can be withstood at that level.
The minimum value of the ratio indicates the weakest level of the building
and allows for the calculation of the resistance of the whole building in terms of maximum
spectral acceleration corresponding to SLV limit state: 𝑆𝑎,𝑐
∗
IDENTIFY THE CRITICAL LEVEL OF THE BUILDING
𝑽𝒔,𝒊 = ෍
𝒌=𝒊
𝑵
𝑭𝒌
𝑽𝒓,𝒊 = 𝑨𝒎𝒊𝒏,𝒊 ∙ 𝝉𝒓,𝒊 ∙ 𝟏 +
𝝈𝟎,𝒊
𝟏. 𝟓 ∙ 𝝉𝒓,𝒊

min(
𝑉
𝑟
𝑉
𝑠
)
Level N° PT P1 P2 P3
Vr [kN] 462 559 587 486
Vs [kN] 9607 6158 4446 2285
Vr/Vs [g] 0.048 0.091 0.132 0.213
𝐸𝑋𝐴𝑀𝑃𝐿𝐸
𝑆𝑎 = 1g
𝑆𝑎,𝑐
∗ /1g
building resistance
IDENTIFY THE CRITICAL LEVEL OF THE BUILDING
To be compared with the one
corresponding to the building in that
particular site
min(
𝑆𝑎,𝑐
∗
1𝑔
)
𝑤𝑒𝑎𝑘𝑒𝑠𝑡 𝑙𝑒𝑣𝑒𝑙
𝑆𝑎,𝑐
∗
=
𝑉
𝑟
𝑊
remember

PHASE 2C: CAPACITY ASSESSMENT (qualitative computation)
MASONRY QUALITY - COEFFICIENT Crid
𝑆𝑎 = 𝑆𝑎,𝑐
∗
The adjustment of the conventional capacity to a more realistic value is obtained using the
coefficient Crid, evaluated through 10 parameters of the GNDT forms of seismic vulnerability.
The resistance of the building (capacity) can be defined in terms of:
resistant shear force Vr or in terms of spectral acceleration Sa /1g
BUT this value of capacity (e.g. shear force or spectral acceleration) is a
conventional value, because it does not take into account all the others
characteristics of the construction evaluated through the survey
𝑉
𝑟
𝑆𝑎,𝑐 = 𝐶𝑟𝑖𝑑 ∙ 𝑆𝑎,𝑐
∗
𝑉𝑟,𝑟𝑖𝑑 = 𝐶𝑟𝑖𝑑 ∙ 𝑉
𝑟
𝑆𝑎,𝑐
∗ =
𝑉
𝑟
𝑊

GNDT II level form for building with masonry elements:
– 10 parameters are required
– For each parameter, 4 vulnerability classes
(A, B, C and D) and 4 values of the quality of
information (E-high, M-medium, B-low, A-absent)
– A score for each class (see table next slide);
– Different weight coefficients.
Parameter n.3 is not considered, because the shear
resistance of the building is calculated explicitly.

– 10 parameters are required
(A, B, C and D) and 4 values of the quality of
information (E-high, M-medium, B-low, A-absent)
– A score for each class (see the table below);
Parameter n.3 is not considered, because the shear
resistance of the building is calculated explicitly.
A B C D
1 Typology and organization of the resisting system 0 5 20 45 1.50
2 Quality of the resisting system 0 5 20 45 0.25
4 Building location and foundation 0 5 20 45 0.75
5 Horizontal structural elements 0 5 20 45 VAR
6 Plan configuration 0 5 20 45 0.50
7 Configuration in elevation 0 5 20 45 VAR
8 Maximum distance between masonry walls 0 5 20 45 0.25
9 Roof 0 5 20 45 VAR
10 Non structural elements 0 5 20 45 0.25
11 State of conservation of the building 0 5 20 45 1.00
Score
weight
Parameter
N.
(0.5-1.25)
(0.5-1.50)
(0.5 OR 1.0)

– 10 parameters are required (Parameter n.3 is not considered, because the shear resistance of the building
is calculated explicitly.
(A, B, C and D) and 4 values of the quality of information (E-high, M-medium, B-low, A-absent)
– A score for each class (see table next slide);
vulnerability
class
quality of
information
extra
information

𝒘𝟏 = 𝟏. 𝟓
𝑝1 =
0 (𝑐𝑙𝑎𝑠𝑠 𝐴)
5 (𝑐𝑙𝑎𝑠𝑠 𝐵)
20 (𝑐𝑙𝑎𝑠𝑠 𝐶)
45 (𝑐𝑙𝑎𝑠𝑠 𝐷)
It quantifies the degree of box behavior:
• Presence and effectiveness of connections between orthogonal walls
• Presence and effectiveness of chains
T.B.N Quality of masonry is not taken into account here
1) TYPOLOGY AND ORGANIZATION
OF THE RESISTING SYSTEM
PHASE 2C: CAPACITY ASSESSMENT
Masonry Class
A, B, C and D
Quality of Information
E-high, M-medium, B-low, A-absent
TYPOLOGY AND
ORGANIZATION
OF THE
RESISTING
SYSTEM

Class A/B: Constructions built following a seismic
design, regular, with rigid floors, reinforced concrete
ring-beams at each floor, well-connected vertical
structural elements, concrete or steel lintels, steel
chains in vaults and arches;
Class C: Mean quality of the connections between
vertical structural elements, rigid floors, concrete
ring-beams, inefficient steel chains;
Class D: Absence of ring-beams and steel ties, no
connections between vertical structural elements,
flexible floors.
1) TYPOLOGY AND ORGANIZATION
OF THE RESISTING SYSTEM

𝒘𝟏 = 𝟎. 𝟐𝟓
𝑝2 =
The parameters influencing the quality of the resisting system are:
• the type and homogeneity of material (quality of bricks/blocks and mortar);
• the texture typology (regularity, shape of the blocks and their dimensions throughout
the walls);
• transversal connections between wall-leaves (“diatoni”).
2) QUALITY OF THE RESISTING
SYSTEM
Typology of Masonry:
A (two leaves with a poor internal core)
…
L (Solid clay bricks and lime mortar)
…
Z
Masonry Class
A, B, C or D
Quality of Information
E-high, M-medium, B-low, A-absent

21 different masonry typologies are listed in the manual from A to Z (see first lecture)
Class A/B: Masonry with homogeneous/ slightly non homogeneous elements, with a good
texture and good-quality mortar (by surface scratching);
Class C: Irregular masonry, with a medium-quality texture, medium-quality mortar (by surface
scratching);
Class D: Masonry with presence of rounded elements or with consistent voids, insufficient
transversal connections (“diatoni”), poor-quality mortar (by surface scratching).
SYSTEM
Texture quality:
Ao organized
Ad disorganized
Masonry Typology (34)
Masonry Class
Masonry Class
Mortar quality:
Mb good quality
Mc poor quality

D B
C
A
SYSTEM

𝒘𝟒 = 𝟎. 𝟕𝟓
𝑝4 =
Synthetic evaluation of the influence of the soil on the structure and the foundations, in
particular:
• The consistency and slope of the soil;
• The presence of foundations at different levels;
• The unbalanced pressures of the embankments.
4) BUILDING LOCATION AND
FOUNDATIONS

Class A: Buildings on bedrock or on non-
thrusting loose soil, with slopes smaller than
10% and Δh=0;
Class B: Buildings on bedrock or on non-
30% and Δh<1m;
Class C: Buildings on non-thrusting or
50% and/or Δh<1m;
Class D: Buildings on non-thrusting or
thrusting loose soil, with slopes greater than
50% and/or Δh>1m.
4) BUILDING LOCATION AND
FOUNDATIONS
Δh is the difference between the
foundation levels

𝒘𝟓 =
𝟎. 𝟓
𝜶𝟎
≤ 𝟏
𝑝5 =
Evaluation of the structural behavior of the horizontal structural elements and in
particular:
• The in-plane stiffness and strength of the floors;
• The connections between the floor and the vertical resisting elements.
5) HORIZONTAL STRUCTURAL
ELEMENTS
𝛼0 =
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑙𝑜𝑜𝑟𝑠 𝑤𝑖𝑡ℎ 𝑎 𝑠𝑐𝑜𝑟𝑒 < 5 (𝑖. 𝑒. < 𝐵)
𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑙𝑜𝑜𝑟𝑠
Good connections

Class A: every kind of floors satisfying the following
three conditions: 1) in-plane rigid floor; 2) good
connections between floors and vertical elements; 3)
absence of floors at different levels
RC slabs, precast or cast-on-site RC slabs with
hollow blocks, corrugated metal sheets and
concrete, timber slabs with double layered planking,
consolidated vaults with steel ties; presence of
connections between structural elements (ring-
beams, connections between timber beams and
between timber beams and masonry walls, …)
Class B: Similar to Class A but with floors at different
levels;
A
ELEMENTS

Class C: every kind of floors having in-plane
flexible floor, but with good connections between
floors and vertical elements.
Precast or cast-on-site, non-reinforced concrete
slabs with hollow blocks (Varese, c.a.p. or SAP),
vaulted ceilings (“solaio a voltine”), timber slabs
(simple or double-frame beams), masonry vaults;
C
ELEMENTS
Class D: Flexible floors, as for Class C, with bad
connections between floors and vertical elements.
Absence of ring beams, limited support length at
the end of the beams.
Particular attention should be given when dealing
with heavy floors built on vertical elements
characterized by poor-quality masonry.
D

C
A
A
A
A
C
ELEMENTS

𝒘𝟔 = 𝟎. 𝟓
𝑝6 =
0 (𝑐𝑙𝑎𝑠𝑠𝑒 𝐴)
5 (𝑐𝑙𝑎𝑠𝑠𝑒 𝐵)
25 (𝑐𝑙𝑎𝑠𝑠𝑒 𝐶)
45 (𝑐𝑙𝑎𝑠𝑠𝑒 𝐷)
This parameter takes into account the plan configuration and so also the regularity of
the building. A regular configuration is associated to a better seismic behavior of the
construction.
The parameters β1 and β2 needs to be defined (see next slide).
6) PLAN CONFIGURATION

Class A: Buildings with β1≥80 and β2≤10;
Class B: Buildings with 60≤β1≤80 and 10<β2≤20;
Class C: Buildings with 40≤β1<60 and 20<β2≤30;
Class D: Buildings with β1<40 and β2>30.
ATTENTION: The worst condition determines
the definition of the class.
𝛽1 =
𝑎
𝐿
𝑥100 𝛽2 =
𝑏
𝐿
𝑥100

D
C
B
A

𝒘𝟕 = 𝟎, 𝟓𝟎 𝒊𝒇 𝒑𝒐𝒓𝒕𝒊𝒄𝒐𝒔 𝒂𝒓𝒆 𝒑𝒓𝒆𝒔𝒆𝒏𝒕 𝒂𝒕 𝒈𝒓𝒐𝒖𝒏𝒅 𝒇𝒍𝒐𝒐𝒓, 𝒐𝒕𝒉𝒆𝒓𝒘𝒊𝒔𝒆 𝟏. 𝟎𝟎
𝑝7 =
It takes into account the regularity in elevation of the building. For masonry buildings,
irregularities in elevation are mainly associated with the presence of porticos or towers
with a significant mass. It is possible to substitute the ratio in terms of mass with the
ratio in terms of covered surfaces.
With very poor materials (worse than the ones reported for Parameter n° 2), the
buildings in class A/B become C and the buildings in class C become D.
7) CONFIGURATION IN ELEVATION

𝒘𝟕 = 𝟎, 𝟓𝟎 𝒊𝒇 𝒑𝒐𝒓𝒕𝒊𝒄𝒐𝒔 𝒂𝒓𝒆 𝒑𝒓𝒆𝒔𝒆𝒏𝒕 𝒂𝒕
𝒈𝒓𝒐𝒖𝒏𝒅 𝒇𝒍𝒐𝒐𝒓, 𝒐𝒕𝒉𝒆𝒓𝒘𝒊𝒔𝒆 𝟏. 𝟎𝟎
𝑝7 =
It takes into account the regularity in elevation of the building. For masonry buildings,
irregularities in elevation are mainly associated with the presence of porticos or towers
with a significant mass. It is possible to substitute the ratio in terms of mass with the
ratio in terms of covered surfaces.
With very poor materials (worse than the ones reported for Parameter n° 2), the
buildings in class A/B become C and the buildings in class C become D.

Class A: Buildings with a uniform or
decreasing distribution of the mass(es) or
the resisting elements in elevation.
Differences in the plans between floors
should be less than 10%;
Class B: Buildings with areas of their
porticos less than 10% of the total floor
area, and differences in the plans between
floors less than 20%. Towers with height
smaller than 10% of the total height of the
building

Class C: Buildings having the areas of their
porticos less than 20% of the total floor area
and/or differences in the plans between
floors less than 20%. Towers with height
being less than 40% of the total height of the
building;
Class D: Buildings having the areas of their
porticos greater than 20% of the total floor
area. Towers with a height greater than 40%
of the total height of the building

𝑤8 = 0,25
𝑝8 =
It takes into account the presence of transversal walls
and their role as a potential efficient constraint of each
considered wall. The classes are defined as a function
of the distance between transversal walls and the
thickness of the considered wall.
8) MAXIMUM DISTANCE BETWEEN
MASONRY WALLS

Class A: Buildings with R < 15
Class B: Buildings with R = 15 – 18
Class C: Buildings with R = 18 – 25
Class D: Buildings with R > 25
MASONRY WALLS
R = Ratio between the distance of the transversal walls
and the thickness of the considered wall
l
s

C
A
A
C
D
B
MASONRY WALLS

𝑤9 = 0.5 + 𝛼1 + 𝛼2 𝑤𝑖𝑡ℎ
𝑝9 =
The factors influencing the seismic behavior of the building are the typology and weight
of the roof. In particular the additional elements to be considered are:
- the classification of thrusting or non-thrusting roof;
- the presence of a ring beam connecting the roof to the vertical walls;
- the presence of steel ties;
- the value of permanent loads;
- the support length.
9) ROOF
𝛼1 = 0.25 𝑖𝑓 ℎ𝑒𝑎𝑣𝑦 𝑟𝑜𝑜𝑓 𝑜𝑟 𝑤𝑖𝑡ℎ 𝑟. 𝑐. , 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 = 0
𝛼2 = 0.25 𝑖𝑓 𝑡ℎ𝑒 𝑟𝑎𝑡𝑖𝑜 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑎𝑛𝑑 𝑠𝑢𝑝𝑝𝑜𝑟𝑡𝑖𝑛𝑔 𝑙𝑒𝑛𝑔𝑡ℎ 𝑖𝑠 > 2, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 = 0

𝑤9 = 0.5 + 𝛼1 + 𝛼2 𝑤𝑖𝑡ℎ
- the support length.
9) ROOF
𝛼1 = 0.25 𝑖𝑓 ℎ𝑒𝑎𝑣𝑦 𝑟𝑜𝑜𝑓 𝑜𝑟 𝑤𝑖𝑡ℎ 𝑟. 𝑐. , 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 = 0
𝛼2 = 0.25 𝑖𝑓 𝑡ℎ𝑒 𝑟𝑎𝑡𝑖𝑜 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑎𝑛𝑑 𝑠𝑢𝑝𝑝𝑜𝑟𝑡𝑖𝑛𝑔 𝑙𝑒𝑛𝑔𝑡ℎ 𝑖𝑠 > 2, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 = 0

Class A: Rigid, non-thrusting roof with ring-
beams and/or steel or timber ties.
9) ROOF

Class B: Rigid, non-thrusting roof, without ring-beams and without steel or timber ties
as well as roof without efficient connections. Rigid, low-thrusting roof with ring-beams
and /or ties.
9) ROOF

Class C: Non-thrusting, brittle roof, without efficient connections and without a top slab.
Rigid, low-thrusting roof, not well connected. Rigid, thrusting roof with ring-beams
and/or ties.
9) ROOF

Class D: Rigid, thrusting roof without ring-beams and/or ties. Heavy roof positioned
over poor-quality masonry walls.
9) ROOF

𝒘𝟏𝟎 = 𝟎. 𝟐𝟓
𝑝10 =
It takes into account the presence of elements that can injure to people or damage
elements, such as cornices or window frames, etc.
They should be identified in the vulnerability assessment of the building even if they
are “secondary elements”.
10) NON STRUCTURAL ELEMENTS

Class A/B: Buildings without attachments, cornices,
etc.. Well-connected false ceilings and chimneys,
and/or balconies well-connected to the structure;
Class C: Buildings with window fixtures which are
not well connected, and/or having false ceilings
covering large surfaces yet not well connected;
Class D: Buildings with chimneys close to the
perimeter of the roof but not well connected,
dangerous additions and/or balconies without efficient
connections, as well as heavy false ceilings.
10) NON STRUCTURAL ELEMENTS

𝒘𝟏𝟏 = 𝟏. 𝟎𝟎
𝑝11 =
The classes are defined according to the state of the building’s conservation, taking into
account the degree and extent of damages throughout the structures as well as the width of
the cracks.
Class A: Buildings in good condition without damages;
Class B: Buildings with hairline cracks and non-distributed damages;
Class C: Buildings with mid-level damages (e.g. crack width around 2-3 mm);
Class D: Buildings with significant damage and out-of-plumb walls
11) CONSERVATION STATE OF THE
BUILDING

𝐶𝑟𝑖𝑑 = 0.6 (worst case)
𝐶𝑟𝑖𝑑 = 1.0 (better case)
α is a calibration coefficient
𝐾𝑖 𝐷 = 𝑝𝑖 𝐷 ∙ 𝑤𝑖 𝐾𝑤𝑜𝑟𝑠𝑡 = ෍
𝑖=1
10
𝐾𝑖 𝐷
𝐶𝑟𝑖𝑑 = ෑ
𝑖=1
10
1 − 𝛼 ∙
𝐾𝑖
𝐾𝑤𝑜𝑟𝑠𝑡
Limit lower value - Determine the lower value of shear resistance considering the
worst value (D) for each parameter
PHASE 2D: CAPACITY ASSESSMENT
EVALUATION OF THE ACTUAL SHEAR RESISTANCE OF THE BUILDING
for masonry structures α is assumed = 0.5
This is the value which guarantees that the minimum value of 𝐶𝑟𝑖𝑑 is equal to 0.6

𝟎. 𝟔 < 𝐶𝑟𝑖𝑑< 1
Actual shear resistant force is calculated considering the actual values for each
parameter.
𝑆𝑎,𝑐 = 𝐶𝑟𝑖𝑑 ∙ 𝑆𝑎,𝑐
∗
PHASE 2D: CAPACITY ASSESSMENT
EVALUATION OF THE ACTUAL SHEAR RESISTANCE OF THE BUILDING
𝑉𝑟,𝑟𝑖𝑑 = 𝐶𝑟𝑖𝑑 ∙ 𝑉
𝑟
Or in terms of spectral acceleration: 𝑆𝑎,𝑐 =
𝑉𝑟,𝑟𝑖𝑑
𝑊

𝑃𝐺𝐴𝑐 =
𝑆𝑎,𝑐
𝛼𝑃𝑀 ∙ 𝛼𝐴𝐷 ∙ 𝛼𝐷𝑇 ∙
1
𝛼𝐷𝑈𝐶
Given the pseudo-acceleration, 𝑆𝑎,𝑐, the peak ground acceleration of collapse, 𝑃𝐺𝐴𝑐,
is obtained as:
PHASE 2E: CAPACITY ASSESSMENT
PEAK GROUND ACCELERATION OF COLLAPSE
𝛼𝑃𝑀 = ቐ
0.80
1.00 (one level)
(more levels)
Modal partecipation
𝛼𝐴𝐷 = 2.50 (estimated, the period is not calculated )
Spectral amplification
𝛼𝐷𝑇 = 0,8 (for masonry buildings)
𝛼𝐷𝑈𝐶 = 1.00 ÷ 2.00
Behavior factor
Dissipative phenomena
𝑆𝑒 = 𝑆𝑎𝑔
𝐹0
𝜂
𝐹0
𝜂, q
M*

PHASE 2E: CAPACITY ASSESSMENT
PEAK GROUND ACCELERATION OF COLLAPSE
𝑃𝐺𝐴𝑐 =
𝑆𝑎,𝑐
𝛼𝑃𝑀 ∙ 𝛼𝐴𝐷 ∙ 𝛼𝐷𝑇 ∙
1
𝛼𝐷𝑈𝐶
Given the pseudo-acceleration, 𝑆𝑎,𝑐, the peak ground acceleration of collapse, 𝑃𝐺𝐴𝑐
is obtained as:
𝑺𝒂,𝒄
𝛼𝐴𝐷 ≅ 𝐹0
𝑷𝑮𝑨𝒄
𝑖𝑛 𝑡ℎ𝑒 𝑝𝑙𝑎𝑡𝑒𝑎𝑢 𝑆𝑒 = 𝑆𝑎𝑔
𝐹0
𝜂
𝑆𝑎𝑔 = 𝑆𝑒
𝜂
𝐹0
𝜂 =
1
𝑞
𝛼𝐷𝑈𝐶
𝛼𝐷𝑇
= 𝑞
(Dolce et al. 2004)

Comparison between LV1 Re.sis.to results and non linear FEM analyses
• Mean error equal to 11.5%
0
20
40
60
80
100
120
A007 A007 A007 Z010 Z015 Z001 Z013 Z013 Z013 Z016 Z012
PGAc/PGAd
[%]
Comparison RE.SIS.TO.® - Push Over FEM analyses
RE.SIS.TO. Push Over
VERIFICATION OF RESULTS FOR MASONRY BUILDING
PHASE 3: Safety Assessment

PHASE 3: Re.Sis.To.®
CAPACITY-DEMAND COMPARISON AND RE.SIS.TO. CLASSIFICATION
PGAc/ PGAd Resistance Class
0% - 25% V
25% - 50% IV
50% - 75% III
75% - 100% II
> 100% I
Ratio
𝑃𝐺𝐴𝑐
𝑃𝐺𝐴𝑑

Ratio
𝑃𝐺𝐴𝑐
𝑃𝐺𝐴𝑑
PGAc/ PGAd Resistance Class
0% - 25% V
25% - 50% IV
50% - 75% III
75% - 100% II
> 100% I
Local Vulnerabilities
Checked during the inspection
+
one possible
decrease in class
Conservation state of the building,
Particular vulnerabilities

Analysis of the stability of these
elements
Strengthening interventions on
this kind of masonry wall
Presence of vulnerable masonry
elements sustaining the roof
Presence of false ceilings
Safety stairs partially connected with
the structure
Evaluate the possibility of
separating the stairs from the
structure
Local vulnerabilities - Examples

L5Masonry - LV1 RESISTO method.pdf

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