Presentation Master Zidarii -Curs Sem Baran Irina

7/29/2019 Presentation Master Zidarii -Curs Sem Baran Irina

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Masonry structures


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The buildings with structural walls made of brickwork are:

Dwellings for 1-2 families (with ground floor or ground

floor and one floor ( called also cheap dwellings); Dwellings with small commercial units at the ground floor

level;

Dwellings for rich people: palaces Stirbey, Ghica,

Cantacuzino; Public buildings with small dimensions for administration,

education, culture;

Monumental public buildings (Court Law);

Industrial buildings of small dimensions.


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Stirbey Palace -1835


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Ghica Palace -1822


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Cantacuzino Palace - 1903


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Cladirea CEC -1900


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Court Law - 1895


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Categories of masonry buildings

1. Buildings with load bearing walls made of

simple brickwork and floors of:

- massive vaults made of brickwork;

- metallic profiles and brickwork small

vaults;

- wooden beams;

- reinforced concrete; - prefabricated elements of small sizes.


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Categories of masonry buildings

2. Buildings with load bearing walls of brickwork

and reinforced concrete girdle and coreswith floors made of:

monolith reinforced concrete;

prefabricated elements of small dimensions;

prefabricated elements of big dimensions (

half panels, panels).


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From the plan disposing of walls, there were used 2

systems:

buildings with dense walls, placed at the rooms limit,called honeycomb system;

buildings with rare walls, placed at the apartments limit,called cellular system.


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The technical and economical advantages are important:

they ensure the structures solving for buildings with differentfunctions, shapes and proportions in plan and elevation;the walls resistance is used that in the architectural plan have

partition and closing functions for unloading the mechanical actions;

the structural walls have an important stiffness, which ensure theprotection of the unstructural elements during the seismic actionwithout additional measures/costs;

the walls thickness imposed by the fulfillment of the thermal andacoustic insulation requirements are in many cases enough to fulfillthe stability and resistance requirements and usually there are not

necessary an increasing of thickness for structural proposes;there are used cheap materials and there are not necessary higherqualified workers.


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In Romania, in 1992, it has been registered the following categories ofbuilding materials:

M1 buildings made of reinforced concrete: with structural walls orframes of reinforced concrete and floors of reinforced concrete;

M2 buildings with brickwork, stone structural walls with reinforced

concrete floors;M3 buildings with brickwork, stone structural walls with wooden

floors;

M4 buildings made of wood;M5 buildings made of trellis or adobe materials;M6 buildings made of unknown materials.


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Table 1. Dwellings with masonry structure in towns

Material

Total dwellings in

Romania

Dwellings in

buildings with P,

P+1E

Dwellings in buildings

P+2E

Total 4.000.000(100%) 1.100.000 (27.5%) 2.900.000 (72.5%)

M2 900.000 (22.5%) 230.000 (6.0%) 670.000 (16.5%)

M3 500.000 (12.5%) 480 (12.0%) 20.000 (0.5%)


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Table 2. Dwellings in buildings with P, P+1E

Material

Total


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Table 3. Dwellings in buildings P+2P

Material Total


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Objectives of the Eurocodes is the harmonization of technical rules for

the design of building and civil engineering works.


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Main advantages:

harmonization of building standards in Europe standardization of the basic requirements

and of the design concept for the different types of construction

equalization of the safety levels in respect of:

the different combinations of actions the different types of buildings and building elements

higher allowable stresses in some cases

more flexibility in the design practice


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The preliminary architectural and structural design of buildings with structural masonry involves several steps:


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Limit states are states beyond which the structureno longer satisfies the design performance requirements.

Ultimate limit states are those associated with collapse,

or with other forms of structural failure, which may endanger the

safety of people.States prior to structural collapse which, for simplicity,

are considered in place of the collapse itself are also classified

and treated as ultimate limit states.

Ultimate limit states which may require consideration

include:

loss of equilibrium of the structure or any part of it,

considered as a rigid body,

failure by excessive deformation, rupture, or loss of stability ofthe structure or any part of it, including supports and

foundations.


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Serviceability limit states correspond to states

beyond which specified service criteria are no longer met.

Serviceability limit states which may require consideration

include:

deformations or deflections

which affect the appearance or effective use of the structure(including the malfunction of machines or services)

or cause damage to finishes or non-structural elements,

vibration which causes discomfort to people,

damage to the building or its contents,

or which limits its functional effectiveness.


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Fundamental requirements1. A structure shall be designed and constructed in such a way

that:

with acceptable probability, it will remain fit for the use forwhich it is required, having due regard to its intended life and its

cost, and with appropriate degrees of reliability, it will sustain all actionsand influences likely to occur during execution and use and have

adequate durability in relation to maintenance costs.


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2. A structure shall be designed in such a way that it will not be

damaged by events like explosions, impact or consequences of

human error, to an extent disproportionate to the original cause.


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The potential damage should be limited or avoided

by appropriate choice of one or more of the following:

avoiding, eliminating or reducing the hazards which thestructure is to sustain,

selecting a structural form which has low sensitivity to thehazards considered, selecting a structural form and design that can surviveadequately the accidental removal of an individual element,

tying the structure together.


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The above requirements shall be met

by the choice of suitable materials,by appropriate design and detailing,

andby specifying control procedures for production,construction and use, as relevant for the particular project.


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Structural regularity criteria

Very important is the achievement of a direct and cleartransmission of vertical and horizontal loads to the

foundations and to ensure a spatial co-operation between

the masonry walls on the two directions and the between

walls and slabs.


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Very important is the favourable effect of the regularity of

the structure.

- In plan it enables the elimination/reduction of theeffects of torsion of the ensemble.

-In elevation it ensures the uniformity of the resistance

requirements at different levels, eliminating the stresses

concentration that could results in the deviation of thenormal/direct route toward the foundations of vertical

and horizontal forces.

The buildings with a regular structure in plan andelevation have the advantages to be analyzed with

simple methods and models.


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Oscillations of buildings without symmetry

during the earthquake


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For buildings with complex shapes the centroids of slabs are

different from the stiffness of floors, and the whole ensemble will

undergo a general torsion. The most vulnerable points are the

inlet corners and the areas closed to them where the stresses are

concentrated whatever will be the seismic load direction.

Fig. critical zones for buildings with composed shapes


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In the case of buildings with structural masonry walls, irregularities in

plan come, generally from two major causes (or a combination of them)

arising from architectural conception of the building:

irregular / unsymmetrical layout of major holes in walls;

plan with pronounced unbalance form.

The existence of long walls without gaps (turbot) is inherent, especially

for "filling" buildings and introduces powerful effects of torsion.

Fig. Irregularity in plan coming from the plan conception


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Another cause of the producing the situation of "irregularity" in the plan

comes from the composition floors:

-floors with different compositions at a certain level rigid ( concrete floor)

completed with a floor with a low rigidity (made of wood);

- floors with large hollows (with the opening area greater than 50% of floor

area).

Fig. Irregularities resulted from the floors composition


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Separation of building in sections.

The segmentation buildings with complex compositions depends on the shape and

proportions in plan of the whole built ensemble.

Fig. Possible segmentation for complex buildings


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Fig. Possible segmentation of buildings with a plan in Ushape

Fig. Possible segmentation of buildings with interior enclosures and in the Tshape with different proportions


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Principles for masonry structure

for areas where the seismic acceleration ag0.20g it isrecommended to chose a regular structure in plan and in

vertical direction;

it is better a geometrical and mechanical symmetry(resulted from the disposing in plan of the structural

walls);


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the floor area will be maintained constant at all the

levels; are excepted some area reductions from a level to

another of 10-15% with the condition that the route of

unloading to the foundation do not be interrupted;

the buildings must have a spatial structure made by:- vertical elements: the structural walls disposed on

orthogonal directions;

- horizontal elements: the floors which are rigid

diaphragms in horizontal plan.


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The spatial character of the masonry structure is obtained

by:

A. The connection between the structural walls on the two

main directions, at corners, intersections is achieved by:

Bonding of the masonry; Concrete cores in the case of confined masonry;

Bonding of the masonry from the exterior layers and

the concrete continuity and reinforcement from the

core in the case of masonry with reinforced core.


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B. The connection between floors and structural walls is

achieved depending on the masonry type:

For simple masonry: with wall beams of reinforced

concrete on all the walls;

For confined masonry: by including and anchorage of the

reinforcement in concrete core in the walls beams at eachfloor level;

For the masonry with reinforced core: by including and

anchorage of bars from the median layer in the wall beams

at each floor level.


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The stiffness structure will be approximately the same on

the two main directions; the difference between them must

not exceed 25%.

The resistance and stiffness of building will be constant on

all the height of the building. It is admitted that the

reduction of resistance and stiffness must not exceed 20%and the reduction is achieved by:

walls density;

walls thickness;compressive strength of the masonry.


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The masonry buildings are considered to be with

structural regularity in plan if:

1.The shape in plan satisfies the following criteria:it is approximately symmetric related to the maindirections;

is compact, with regular outlines and with a reducednumber of inlet corners;the possible recesses/prominences in comparison withthe current outline of the slab do not exceed, each of

them, the greatest value from: 10% from the slab area

or 1/5 from the dimension of that side.


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2. The plan distribution of the structural walls does not

lead to important dissymmetry of the lateral stiffness, of

the strength capacity and/or of the permanent loads

related to the main directions of the building;


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3. The stiffness in horizontal plan is sufficiently large

so that it is ensured the compatibility of the lateral

displacements of the structural walls under the

effect of horizontal forces


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4. At the ground floor level, on each main direction of thebuilding, the distance between the mass centre (CG) and

the stiffness centre (CR) does not exceed 0.1L where L is

the building dimension on the direction perpendicular on the

calculus direction.


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Figure 1. Conditions for structural regularity in plan


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The disposing in plan of the structural walls

The disposing in plan will be as much uniform as possible

to avoid the unfavourable effects of the ensemble torsion.

To ensure the strength and stiffness to torsion it isrecommended that the structural walls with big stiffness will

be placed as much closer to the building outline.

It is recommended that the sum of the net areas of the

masonry walls on the two directions to be approximately

equal.

It is recommended that the transversal structural walls

from the end of the sections will be as much as possiblewithout holes.


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The holes in the structural wallsThe dimensions and placement of holes in the walls will

have in view the following requirements:

functional;

facades appearance;structural.


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The structural requirements refer to:

avoiding the reduction of the strength and stiffness of

walls;

getting of some net masonry areas approximately equal

on the two directions;

fulfillment of the requirements of strength and ductility forthe vertical complete walls and horizontal ( coupling

beams, lintels) between holes.


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The ratio between the areas in plan of the holes and the

areas of complete walls will be limited depending on:

seismic acceleration of the placement (ag);

level number (nniv);

wall position in the building.


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The holes for windows and doors will be placed on the same

vertical direction on all levels. It is accepted the alternative

disposition if it is complied the distances that will allowed the

loads transmission through a system truss beam

The minimum length (lmin) of the adjacent mullion to


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holes will be limited, depending on the height of the holes

(hgol) or the wall thickness (t):For unreinforced masonry (ZNA):

marginal mullion :

lmin = 0.6hgol1.20m

intermediary mullionlmin = 0.5hgol 1.00m

For confined masonry (ZC or ZC+AR);marginal mullion

lmin = 0.5hgol1.00m

intermediary mullion

lmin = 0.4hgol 0.80m

For masonry with reinforced core (ZIA) lmin = 3t


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Disposing in plan of holes in masonry walls


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In the case of masonry with the row height 200mm, the height of the wall

between the reinforced beam walls will be an entire multiple of the row height.

Modulation of masonry related the elements dimensions for masonry


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The thickness of the structural walls

The thickness of the structural walls will be

estimated in order to satisfy the following

requirements:

structural ensurance;thermal insulation/energy saving;

acoustic insulation;

fire protection.


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The minimum thickness of the structural walls,whatever the material of the masonry, will be 240mm.

From the point of view of the structural ensurance,

whatever the calculus results, the ratio between the height

level (het) and the thickness (t) must fulfill the followingminimum conditions:

unreinforced masonry (ZNA) het/t 12;

confined masonry (ZC) and masonry with reinforced

core (ZIA) het/t 12

For walls subjected to axial compression,the slenderness coefficient hef/t 20 for ZC, ZC+AR,

ZIA

and hef/t 16 for ZNA


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The preliminary design of the horizontal structuralsubsystems

For the preliminary design of floors, it will be followed that

they will be conceived as rigid diaphragm in horizontal plan,

taken into account their role concerning the:the collection of inertia forces and their transmission to the

vertical elements of the structure ;


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the ensurance of cooperation between the vertical

elements for taking over the horizontal seismic forces :

the distribution of the level seismic force between thestructural walls proportionally to each translation rigidity;

re-transmission to the walls that have reserves of loads

capacity for additional loads that results after the walls

failure with insufficient resistance capacity;

the possibility to adopt some models for a simplified

calculus, having one or three freedom degrees


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The floors rigidity in horizontal plan depends on:

constructive composition of the floor;

dimensions and positions of big holes in floors.

The stiffness of floors in horizontal plan will be higher

than the lateral rigidity of the structural walls, so that the

floors deformability do not significantly influence the

seismic force distribution between the vertical structuralelements.


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Floors types

The floors for masonry buildings can be classified, from

the point of view of stiffness in horizontal plan in two

categories:

rigid floors in horizontal plan;

floors with unimportant rigidity in horizontal plan.


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When they are not weakened by important holes, the floorscould be considered rigid in horizontal plan when they have

the following constructive composition:

monolith reinforced concrete floor);

floors from panels or halfpanels prefabricated of reinforcedconcrete joint on the outline

floors made of prefabricated elements ,


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The following floors are considered to have insignificantrigidity in horizontal plan:

floors made of prefabricated elements like band type with

locks or connection bars at the end, without reinforcedoverlayer concrete or with unreinforced covering concrete

with a thickness 30mm;

floor made of prefabricated concrete elements with small

dimensions or of ceramic blocks, with reinforced covering

concrete;

wooden floors.

Usually the masonry buildings are designed with floors

rigid in horizontal plan.

Positioning of big holes in floors

Th iti f bi h l i fl ill b h th t


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The position of big holes in floors will be chosen so that

the stiffness and strength of the floors will not be reduced.

Positioning of big holes in the floors


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Underground walls

Usually , the underground walls will be placed under all the

structural walls from the ground floor. They will be made ofreinforced concrete.

The thickness of the underground walls will be

dimensioned in order to fulfill the resistance requirements

to:vertical loads;

seismic load;

ground pressure in the case of walls from the

underground outline.


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It is recommended that the underground stiffness will be

higher than the stiffness of the upper levels. There are some

measures:the number and dimensions of holes in underground walls

will be reduced as much as possible;

the holes for windows and doors will be placed in other

positions than those from the holes from the ground floor, so

that will be avoid some weak zones in walls. In the case

when this situation it is not possible, the dimensions of holes

will be smaller than those from the ground floor.

-In the case of walls in cellular system and areas with ag


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0.24g it is recommended to introduce some additionalwalls.

Additional walls for underground level in the case of rare walls


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The masonry buildings are considered tobe with structural regularity in elevationif:

1. The heights of the adjacent levels areequal or differ with no more than 20%;


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2. The structural walls have in plan the same

dimensions at all levels above the terrain or

differ in some limits:

- The length of one wall is not shorter than the

wall from the inferior level with 20%;

- The reduction of net area of the walls fromthe upper levels, for buildings with nniv 3

does not exceed 20 % from the area of the

masonry from the ground floor.


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3. The building does not have weak levels

(with a stiffness and/or strength capacity lower

than the superior levels).


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Figure 2. Buildings with weak levels (without structural regularity in elevation)

Th b ildi ith t t l ll l ifi d


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The buildings with structural masonry walls are classified

into regularity groups:

Regularity group of the

building

Regularity

Plan Elevation

Regular building 1 Yes Yes

2 No Yes

Irregular building 3 Yes No

4 No No


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One way to solve the problem is to separate the

building into sections. This happens when:

the length of the building exceeds the limits;

the plan shape has irregularities;the terrain has some irregularities concerning thestratification, content, etc.


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It is recommended that the ratio between the

main dimensions of the building sectionsresulted through fragmentation would be:

height/ breadth 1.5;

length/ breadth 4.0;for normal foundation terrain, the maximumlength of the section is 50.0m.


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The choice of the system for structural walls

The choice of the structural walls system will be

chosen so that the following requirements will befulfilled simultaneously:

functional: dimensions of free spaces, levelheight, type of circulation spaces;comfort;structural safety.


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The density of the structural walls, on each maindirection of the building, is defined by the

percentage of the total net area of the masonry

walls (Az, net) on that direction, related to the floorarea (Apl) on that level.


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Structure with dense walls (honeycomb system)

This kind of system is defined by the followinggeometric parameters:

level height is 3.2m;

distance between walls, on both main directions 5.00m;the cell area resulted from the walls on both twodirections 25.0m2.


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Figure3. Structures with dense walls (honeycomb system)

Structures with rare walls


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The structures with rare wall (cellular system) aredefined by the following geometric parameters:

level height 4.00m;

the maximum distances between walls, on both

main directions 9.00m;

cell area formed by the walls on both maindirections 75.0sm.

In this case, the structural walls are disposed,

usually, at the limit between the functional units,

which eliminates the weakness because of thecirculation gaps.


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Figure4. Structure with rare walls (cellular system)


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The choice of the masonry type

The masonry type is chosen depending on:

number of level above the soil level (nniv);structural regularity of building;group of the masonry elements;design seismic acceleration (ag).


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The buildings with structural brickwork walls could

be with the following types:

Simple masonry/ without reinforcement(ZNA);

Confined masonry (ZC);Confined masonry and reinforcement inhorizontal joints (ZC+AR);

Masonry with reinforced core (ZIA).


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Classification of the masonry walls:

Structural wall: wall designed to resist to vertical and horizontalforces that act mainly in its plan;

Stiffening wall: a wall perpendicular to another wall, with which itco-operates for unloading the vertical and horizontal forces and

contributes to the ensurance of its stability. There are also bracing

(strut) walls that take over the horizontal forces that are acting in

their plan.

Walls without a structural role: a wall that is not a part of thebuilding structure; this wall could be removed, and the building isnot affected.

Filling wall: a wall that is not a part of the main structure, but insome conditions it contributes to the lateral stiffness of the

building and to the seismic energy dissipation. The changing of this

kind of wall requires some adequate constructive measures.


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The constructive solution (with masonrystructural walls) is usually used for:

Buildings with a height up to P+4E:

dwellings, education buildings, healthcare buildings or some other types social-

cultural buildings that do not require

spaces too large; Hall type buildings with moderate sizes

(maximum spans 9.00-15.00m and

heights of 6.00-8.00m).


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The thickness of the structural walls are limited by theratio:

For the thickness t =25cm for het, max (ZNA) = 3,00mhet, max (ZC, ZIA) = 3,75m

For the thickness t = 30cm for het, max (ZNA) = 3,60mhet, max (ZC, ZIA) = 4,50m

Wall types


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Load-bearing wall:

A wall of plan area greater than 0,04 m2, primarily designed to

carry an imposed load in addition to its own weight.

Single-leaf wall:

A wall without a cavity or continuous vertical joint in its plane.Cavity wall:

A wall consisting of two parallel single-leaf walls,

effectively tied together with wall ties or bed joint reinforcement,

with either one or both leaves supporting vertical loads.

The space between the leaves is left as a continuous cavity or filled

or partially filled with non-load bearing thermal insulating material.

Double-leaf wall:

A wall consisting of two parallel leaves with the longitudinal joint

between (not exceeding 25 mm) filled solidly with mortar andsecurely tied together with wall ties so as to result in common

action under load.


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Grouted cavity wall:

A wall consisting of two parallel leaves, spaced at least 50 mm

apart, with the intervening cavity filled with concrete and securely

tied together with wall ties or bed joint reinforcement so as to

result in common action under load.

Faced Wall:

A wall with facing units bonded to backing units so as to result in

common action under load.Shell bedded wall:

A wall in which the masonry units are bedded on two general

purpose mortar strips at the outside edges of the bed face of the

units.


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Veneer wall:

A wall used as a facing but not bonded or contributing to the

strength of the backing wall or framed structure.

Shear wall:

A wall to resist lateral forces in its plane.

Stiffening wall:

A wall set perpendicular to another wall to give it support against

lateral forces or to resist buckling and so to provide stability to thebuilding.

Non-load bearing wall:

A wall not considered to resist forces such that it can be removed

without prejudicing the remaining integrity of the structure.


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The simple masonry/without reinforcement

is a material capable to take important vertical loads;it is not able to take vertical and horizontal loads thatresults in tension unitary stresses;the breaking is fragile.


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Because of:

its low capacity to dissipate the seismic energy;low tensile and shear strength;

low ductilitythe use of this kind of structure is not recommended.


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Even though they are used when are fulfilled some

conditions:the height level 3.00m;the structural walls is of honeycomb type;the maximum number of levels over the fixing section(nniv) for buildings of masonry elements from group 1,2and the minimum value (p%), depending on the seismic

acceleration (ag) are:


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nniv Seismic acceleration (ag)

0.08g 0.12g; 0.16g 0.20g 0.24g; 0.28g;

0.32g

1 4% 4% 5% 6%

2 4% 6% NA NA

3 5% NA NA NA


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Measures:

It is used only for buildings with a small number of

levels;The building must have a structural regularity inplan and elevation;

The seismic load static equivalent is estimatedusing low values for the behaviour factor, in order to

limit the post elastic incursions;

The limitation of the relative length of the tensionzone under the effect of vertical and seismic loads.


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Masonry with reinforcement (ZC,ZC+AR, ZIA)

The reinforcement ensures:ductility;capacity to dissipate the seismic energy;limitation of excessive degradation of strength andstiffness;

maintaining in some limits the walls integrity after asevere seism.

The maximum levels number for buildings of confined masonry (ZC) and

confined and reinforced masonry (Z+AR) and with reinforced core (ZIA)

with clay units from group I and II is given below:


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with clay units from group I and II is given below:

nniv Design seismic acceleration ag

0.08g, 0.12g 0.16g, 0.20g 0.24g 0.28g, 0.32g

1 3% 4% 4% 4%

2 3% 4% 5% 6%3 4% 5% 6% NA

4 4% 6% NA NA

5 5% NA NA NA

In the case of buildings from ZNA, the attic is considered to be

level that is included in the levels number


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level that is included in the levels numberIn the case of reinforced masonry buildings (ZC< ZC+AR< ZIA),

the attic is not included in the levels number if the following

conditions are fulfilled:

the minimum constructive density of walls is increased with1%; the outline walls of masonry do not exceed the height of 1.25m; the partition walls are light ones; the wooden framework is designed that in the outline walls willnot result horizontal force;

the masonry walls from the attic is confined with concrete coresas a continuation of those from the lower ones;

at the upper level of the masonry walls of the attic, will berealized a wall beam.

If at least one of the before conditions is not fulfilled, the attic is

considered level.

The disposing of the concrete core and beam walls for the

confined masonry


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confined masonry.

In the case of confined masonry, the concrete core will be

placed in the following positions:

at the free ending of each wall;on both parts of each hole with the area 2.5m2 (like a door

hole);

at each exterior and inlet corner on the building outline;

on the wall length, so that the distance between the concretecores axis do not exceed:

- 4.0m in the case of cellular system;

- 5.0m in the case of honey comb system;

at the walls intersections, if the closer concrete core is placed

at a longer distance than 1.5m.


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Positions of reinforced concrete columns for a confined masonry

The concrete columns will be made on the whole building height.


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e co c e e co u s be ade o e o e bu d g e g

The beams walls will be placed in the following positions:at the level at each floor, whatever the building material of the

floor;

in an intermediary position, between floors at the buildings

with rare walls.

Technical conditions associated to the

resistance and stability requirement


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resistance and stability requirement

a. The favourable mechanism for the seismic energy

dissipation

The main feature of the masonry structures placed inseismic areas results from the requirement that the structure

has some specific proprieties, additional to those necessary

for buildings loaded only with gravitational loads:

Ductility of ensemble and local level;

Capacity of dissipation of seismic energy;

Moderate degradation of resistance and rigidity under theeffect of repeated alternating loads.

In the case of the masonry buildings, the favourable

mechanism for the seismic energy dissipation consists int lli th f th l ti d f ti


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gy pcontrolling the zones for the plastic deformation

development in the zones from the base of the stud, that is

defined as fixing section.

This could be achieved by the following measures:

The capable bending moments will be higher, in all the

sections, than the bending moment corresponding to the

fixing section plastification.

The resistance to the shear strength of the structural walls

will be higher, in all the sections, than the shear strength

associated to the resistance capacity to the compressiveeccentric force.

Measures in order to ensure the local ductility.

I th f th ll l d ith li i dl d


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In the case of the walls coupled with coupling girdles made

entirely of reinforced concrete, it may be assumed the

formation of the plastic joints in the girdles if:

the collapse from bending of the girdle precedes:

- stud collapse through eccentric

compression;

- girdle collapse through shear force.

girdle collapse through shear force precedes the girdle

(stud) support collapse through local crush of the masonry.


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b. The resistance condition

The resistance condition is fulfilled if in all the structuralelements, in the most stressed sections, the resistance

capacity is higher than the designed stresses, for all the

combination of loads.

c. The stability condition

The stability of the whole masonry building is


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The stability of the whole masonry building is

ensured if:

- the building placed on a sloped terrain does not

have a slide risk;- there is not a upsetting risk for the building

because of the horizontal forces;

- it is ensured the spatial rigidity of the building.

The local stability of the walls is ensured if:

- the walls are stiffened;

- the compressive efforts (stresses) are limitedtaking into account the flexion and eccentricities of

loads.

d. The stiffness condition


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The masonry buildings will have enough stiffness so

that:

the inelastic deformations of the structural elements,

under the designed earthquake forULS, will stay in

acceptable limits ( the resulted damages will be

reparable in acceptable technical and economic

conditions);

the damages from the designed earthquake will be

limited forSLS;it is avoided the collision of adjoining buildings.

c The ductility condition


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c. The ductility condition

The ductility condition is aiming mainly to:

the ensurance of a sufficient capacity for a plastic

rotation in the potential plastic sections, without the

important reduction of the resistance capacity;

the reduction, through constructive dimensioning, of the

probability to happen breakings with a fragile character

( for example the failure in steps by shear force ).

The designed values of the mechanical proprieties of

masonry

For all the loads types the reference values result from the


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For all the loads types, the reference values result from the

characteristic values divided by a partial safety coefficient for

the material M1differentiated depending on:

limit state for which is made the verification;

elements quality for the masonry and mortar;

quality of the execution.

The designed values resulted from the reference values

multiplied by a coefficient for the working conditions mz.Its value depends on:


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Its value depends on:

the limit state taken into account;

characteristics of the stress state of the element;the necessity to compensation of some simplification of

calculus methods.

The values of the working conditions coefficient mz are as follows

A For the verification for the ultimate limit state (ULS):


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A. For the verification for the ultimate limit state (ULS):

mz,ULS = 1.0 for all the cases, excepting the cases

mentioned below; mz,ULS = 0.85 for the elements with the cross area


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B. For the verification for serviceability limit state:

mz,SLS = 1.0 for all the cases, excepting the casesmentioned below;

mz,SLS = 2.0 for all the elements with usual plaster;

mz,SLS = 1.5 for elements with waterproofing plaster

working under the hydrostatic pressure;

mz,SLS = 1.2 for elements with decorative plaster and

higher quality finishings.

The values for the partial safety coefficient:


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M = 2.2 for the calculus at the ultimate limit state (ULS)

with the elements for masonry of class I and mortar forgeneral use (G) performant or of prescription, in normal

control conditions;

M = 2.5 for the calculus at the ultimate limit state (ULS)

with the elements for masonry of class II and mortar madein site conditions, and in normal control conditions;

M = 3.0 for the calculus at the ultimate state (ULS) with

the elements for every class and in low control conditions;

M = 1 for the calculus at serviceability limit state (SLS).

Normal control conditions mean that:

th k i d tl b i li d


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the works are supervised permanently by specialized

personnel;

the designer controls the works;the technical responsible of the owner verifies regularly

the works.

Low control conditions mean that:the works are not supervised permanently;

the designer rarely controls the works;

the technical responsible of the owner does not control the

materials quality and the works quality.

Selection of materials Masonry units

Types of elements for masonry


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Types of elements for masonry

clay masonry units;calcium silicate masonry units;

aggregate concrete masonry units ( with dense

aggregate or lightweight aggregate);

autoclaved aerated concrete masonry units;manufactured stone masonry units;

natural stone masonry units.


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Masonry units may be Category I or II:

category I units with a declared compressive strength

with a probability of failure to reach it not exceeding 5 %

category II lower confidence level than for I.


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Grouping is defined with limits on:

volume of all holes

volume of each hole

declared value of thickness of web and shellsdeclared value of combined thickness of web and shells.


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Depending on the geometrical characteristics, the masonry

elements could be in two groups:

Group I

clay masonry units 240x115x63;

clay masonry units with circular holes;

lightweight concrete units with holes volume 25%;

autoclaved aerated concrete masonry units.

Group II


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Group II

clay masonry units with rectangular holes

lightweight concrete units with holes volume between

25% and 50%;

ordinary concrete units with the volume holes between

25% and 50%.


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The masonry units with vertical holes could be used if there

are followed the conditions:

the holes volume is 50%;

the thickness of external web and shells te15mm;

the thickness of internal web and shells ti10mm;the vertical internal walls are continually realized on the

whole length element.

The grouping units depending on the exterior profile


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The grouping units depending on the exterior profile

of the element:

Depending on the exterior profile of the sides elements,the masonry units could be classified as follows:

elements with plane sides;

elements with place for mortar;elements with place for mortar and additional prints for

mortar;

elements with shapes


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Masonry:

An assemblage of masonry units laid in a specifiedpattern and joined together with mortar.

Reinforced masonry:

Masonry in which bars or mesh, usually of steel, areembedded in mortar or concrete so that all the materials

act together in resisting forces.

Prestressed masonry:Masonry in which internal compressive stresses have been


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y p

intentionally induced by tensioned reinforcement.

Confined masonry:

Masonry built rigidly between reinforced concrete or

reinforced masonry structural columns and beams on all four

sides (not designed to perform as a bending resistant frame).

Masonry bond:

Disposition of units in masonry in a regular pattern to achieve

common action.

The mechanical properties of the masonry elements

The compressive strength of masonry units

The compressive strength of masonry units, to be used


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p g y ,

in design, shall be the normalized mean compressive

strength, fb.In the case when the compressive strength is assessed in

accordance with specific standards and is declared by the

producer as mean resistance, this value will be converted in

normalized compressive strength , in order to take intoaccount the high and width of the masonry elements, by

multiplication with a factor.

Transformation factor and fb values for clay and concrete elements

Masonry element

fact

or

fmed(N/mm2)


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or 10 7.5

Clay bricks 240x115x63mm 0.81 8.1 6.1

Clay bricks with vertical holes 240x115x88mm

290x240x138mm

0.92 9.2 6.9

Clay bricks with vertical holes 240x115x138mm 1.12 11.2 8.4

Clay bricks with vertical holes 290x140x88mm 0.87 8.7 6.5

Clay bricks with vertical holes 290x140x138mm

290x240x188mm

Blocks with holes of ordinary and light concrete

290x240x188mm

1.07 10.7 8.0

MortarsClassification


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Depending on the way of realization, the mortars could be:factory made masonry mortar;

site made mortars.

Depending on the composition definition, the mortars couldbe:

designed mortars (declared performances);

prescribed mortars (declared proportions plus compressive

strength declared using publicly available references).

Compressive strength of mortars

The masonry mortars are classified depending the

mean compressive strength, expressed by the letterMfollowed by the compressive strength value expressed

2


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in N/mm2 (for example: M5 mortar with the mean

unitary strength fm

= 5N/mm2).The masonry mortars

must have fm > 1N/mm2.

Building type

Structural walls Unstructural walls

Elements Mortar Elements Mortar

Lastingbuildings

All the

importance

class

fmed>10 M10 f med>10 M5

fmed 10 M5 f med 10 M2.5

Temporary

buildings

M2.5 M1

Compressive strength of masonry

Characteristic compressive strength of masonryWhen there are not data concerning the loads, the

characteristic compressive resistance fk realized with general


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characteristic compressive resistance fk realized with general

use mortar (G) for normal loads on the horizontal joints, will be

estimated depending on the compressive strength of themasonry units and of the mortar:

where:K constant coefficient depending on the masonry element type

and of the mortar type;

fb normalized compressive strength of the masonry element,

on the perpendicular direction on the horizontal joints, in N/mm2;

fm mean compressive strength of mortar in N/mm2.

Values of the K coefficient


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Masonry element type

Coeff. K

Full clay bricks 0.50

Clay bricks with vertical holes 0.45

Blocks of ordinary and light concrete 0.50Small blocks of autoclaved aerated concrete 0.50

This formula may be used if there followed the followingrequests:


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the element strength for the masonry is fb75N/mm2;

the mortar resistance fm 20N/mm2 and fm 2fb;

the variation coefficient of the resistance of the masonry

elements is 25%;

all the joints are full of mortar;the masonry thickness is equal with the breadth or the length

of the element, so that there is no mortar joint parallel with the

wall face; in the case when there is a joint parallel with wall face

the value is reduced with 20%.


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Typical wall bonds relative to longitudinal joints

The unitary designed compressive strength of masonry


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where:

-mz is the working condition coefficient

-fk characteristic compressive strength of masonry-M partial factor for material

Shear strength of masonry in horizontal joint

The characteristic initial shear strength in horizontal

joint (fvk0)


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vk0

Elements for masonry

Mean strength of mortar fm (N/mm2)

M10 M5, M2.5 M1

Clay elements 0.30 0.20 0.10Ordinary and light concrete 0.20 0.15 0.10

Autoclaved aerated concrete - 0.15 0.10

The characteristic shear strength of masonry, fvk, realized


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g y, ,

with mortar for general use of masonry (G) , with all the

joints full of mortar, will be chosen equal with smallest valuefrom:

For elements for masonry from group I

fvk =fvk0 + 0.4d

fvk =(0.034fb + 0.14 d)

For elements for masonry from group II


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y g p

fvk = fvko + 0.4 d

fvk =0.9(0.034 fb + 0.14 d)

where:

fvk0 unitary characteristic initial strength to shear strength

d perpendicular compressive unitary stress on the shearplan in the masonry wall;

fb normalized compressive strength of masonry elements.

The unitary characteristic shear strength in horizontal joint fvk for elements of clay

masonry from group I:

fbN/m

m2

Morta

r

Unitary compressive stress d (N/mm2)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

10 0 M10 0 340 0 368 0 382 0 396 0 410 0 424 0 438 0 452 0 466 0 480


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10.0 M10 0.340 0.368 0.382 0.396 0.410 0.424 0.438 0.452 0.466 0.480

M5/2.5 0.240 0.280 0.320 0.360 0.400

M1 0.140 0.180 0.220 0.260 0.300 0.340 0.380 0.420 0.460

7.5 M10 0.269 0.283 0.297 0.311 0.325 0.339 0.353 0.367 0.381 0.395

M5/2.5 0.240 0.280

M1 0.140 0.180 0.220 0.260 0.300

5.0 M5/2.6 0.184 0.198 0.212 0.226 0.240 0.254 0.268 0.282 0.296 0.310

M1 0.140 0.180

The unitary characteristic shear strength in horizontal joint fvk for elements of

clay masonry from group II:

fbN/mm2

Mortar

Unitary compressive stress d (N/mm2)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0


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10.0 M10 0.319 0.332 0.345 0.358 0.371 0.384 0.397 0.410 0.423 0.436

M5/2.5 0.240 0.280 0.320

M1 0.140 0.180 0.220 0.260 0.300 0.340 0.380

7.5 M10 0.243 0.256 0.269 0.282 0.295 0.308 0.321 0.334 0.347 0.360

M5/2.5 0.240

M1 0.140 0.180 0.220 0.260

5.0 M5/2.6 0.166 0.179 0.192 0.205 0.218 0.231 0.244 0.257 0.270 0.283

M1 0.140

For the marked values, the characteristic value is given by the strength in horizontal

joints, and in the others by normalized strength of the element

The designed unitary shear strength in horizontal joint


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The unitary tension strength from bending

perpendicular on the masonry plan

In the case of bending produced by perpendicular forces


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In the case of bending, produced by perpendicular forces

on the masonry plan, it will be taken into account the

strength corresponding to the following failure cases:

the bending strength in a failure plan parallel with the

horizontal joints, fx1;the bending strength in a failure plan perpendicular on

the horizontal joints, fx2 .


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Flexural strength. a. Plan of failure parallel to bed joints; b. Plan of failure

perpendicular to bed joints

The unitary characteristic strength for bending perpendicular on the

masonry plan

Element

Mean strength of the mortar


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Element

typeM10, M5 M2.5

fxk1 fxk2 fxk1 fxk2

Clay

masonry

units

0.240 0.480 0.180 0.360

Autoclaved

aeratedconcrete

0.080 0.160 0.065 0.130

The designed unitary tension strength from bending perpendicular on

the masonry plan


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Calculus of buildings with structural masonry

walls

General calculus principles

To design the usual buildings with masonry structure, the

l l d l i b d th f ll i i lif i


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calculus model is based on the following simplifying

assumptions:

masonry is a material supposed homogeneous, isotropic

and with an elastic answer till the ultimate stage;

the sectional characteristic of masonry walls is assessedfor the gross section (unfissured);

the results get by models based on the upper mentioned

are affected by correction factors, so that will be obtained abetter concordance with results from tests.

The model must take into account simultaneously the

following specific aspects:


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the complex character of the constitutive law - that isusually non-linear;

the particularities of the law - depends on the element

proportions and the masonry type (simple/reinforced);

the strength and stiffness degradation is caused by therepeated incursion in the plastic range;

the particularities of the dissipation phenomenon

depends on the masonry type.

Calculus of structures to vertical loads

1. Calculus model for vertical loads

The structural walls are vertical elements that take


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The structural walls are vertical elements that take

over the gravitational loads brought by floors andtransmitted to the foundation.

The structural walls are considered cantilevers fixed

- at the underground floor level (in the case ofbuildings with underground) and

- at the superior level of foundations (in the case of

buildings without underground).

The walls can be loaded simultaneously withvertical loads and horizontal ones that are actingperpendicular on the wall plan:

loads from earthquake for the walls types;


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loads from earthquake for the walls types;

loads from wind for the exterior walls; loads from ground pressure for the outline walls

from the underground level;

forces caused by horizontal forces producedarches, vaults or wooden frames;

loads from operating (furniture or equipments

suspended).

The calculus model must take into account :


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the particularities of the vertical loads;

eccentricities of bending moments produced

by horizontal loads;

wall slenderness.

2. Calculus method for vertical loads

Determination of axial compressive strength in

structural walls


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structural walls

The compressive strength in a section is made of:

loads from afferent areas of floors placed under the

calculus section level;

own weight of the wall part placed over the calculussection.

In the case of floors that transmit loads on two directions, the

walls takeover the loads from areas get by the bisecting lines.

These loads are considered uniformly distributed on the walllength. In the case of walls with holes, it is added from the

breadth of hole that border the wall.


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In the case of walls with complex shape, T,L, I, it is

considered that through the masonry bonding or by

concrete columns from the intersections or ramification it isrealized an uniform distribution of compression strength on

the whole area of wall.


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For concentrated loads or for loads distributed only on

certain areas it is admitted that the stresses repartition is

made after inclined lines at 30.In the case of walls withholes, the route is changed.


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In practice, the design of loadbearing walls and columns is

reduced to the determination of the value of the


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reduced to the determination of the value of the

characteristic compressive strength of the masonry (fk) andthe thickness of the unit required to support the design

loads.

Once fk is calculated, suitable types of masonry/mortarcombinations can be determined from tables, charts or

equations.

The basic principle of the design can be expressed as

design vertical loading design vertical load


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design vertical loading design vertical load

resistance

in which:

- the term on the left-hand side is determined from theknown applied loading and

- the term on the right is a function of fk, the slenderness

ratio and the eccentricity of loading.

If it were possible to apply pure axial loading to walls or

columns then the type of failure which could occur would be


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dependent on the slenderness ratio = the ratio of the effectiveheight to the effective thickness.

For short columns, where the slenderness ratio is low,

failure would result from compression of the material, whereasfor long thin columns and higher values of slenderness ratio,

failure would occur from lateral instability.

It is virtually impossible to apply an axial load to a wall or

column since this would require a perfect unit with no


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column since this would require a perfect unit with no

fabrication errors. The vertical load will, in general, beeccentric to the central axis and this will produce a bending

moment.

Assessment of eccentricities of vertical loads

The eccentricities are coming from many sources:

a. constructive structure, that may involve deviation of

vertical loads flow from one level to another;


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b. imperfections from execution, structure geometry,homogeneity of materials, relative positions of elements;

c. effects of some local loads, of lower intensity than the

dead and seismic loads.

The effects of these eccentricities are additional bending

moments that act perpendicular on the maximum

resistance/rigidity plan.

These effects are introduced by reducing coefficients ofthe resistance capacity estimated as for ideal axial loads.

a. Eccentricities resulted from structure

composition

The eccentricities coming from the structurecomposition are produced in areas where is produced the

vertical forces transfer from a level to another and is the

result of:


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result of:

eccentrically superposition on vertical direction of walls

from the adjacent floors;

eccentrically support of slabs on the walls;

support on walls of some slabs with different loads and

spans.

The resulted bending moments resulted from the

mentioned eccentricities varies linear on the wall heightbetween the maximum value at the upper side of the wall,

and zero to the inferior side of it.

where:

N1 load from the wall of the


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Eccentricities from the structure composition

1

superior level;d1 eccentricity with which is

applied the load N1;

N2- loads from slab/slabs that

are directly supported by the wall;

d2 eccentricities with whichare applied the loads N2

b. Eccentricities from the execution imperfections

(accidental eccentricity)

The accidental eccentricities of vertical loads (ea) may becaused by the following execution imperfections:

relative displacement of the median plans of walls from the

two adjacent levels;


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deviations from the nominal value of the walls thickness;deviations from the vertical position of the wall;

lack of homogeneity of materials.

The accidental eccentricity is introduced with the greatestvalue between the values:

where: t wall thicknesshet floor height.

Table 1. The value of the calculus eccentricities ea

Height of the

floor (m)

Wall thickness (cm)

25,0 30,0 37,5 45,0


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3,00 1,00 1,25 1,50

3,20 1,07

3,40 1,13

3,60 1,20

3,80 1,27

4,00 1,33

c. Eccentricities from the bending moments

produced by horizontal forces perpendicular on the

wall planThe eccentricities of vertical force corresponding to

moments Mhm(i) is given by:


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where:

ph is the uniformly distributed load

N1 load transmitted by the superior wall;N2 the reactions sum of slabs that are supported by the wall.

3. Calculus of masonry structures to horizontal loads

The wind action is taken into account only for:


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calculus of eccentricities of vertical force resulted frombending moments when the wind action is perpendicular on

the faade;

calculus of the pitched roofs;

verification of strength and rigidity of facades of glass of big

dimensions.

Calculus model for horizontal seismic load

The fixed section of the structural walls for the horizontal

forces will be taken:


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at the higher level of socle, in the case of buildings without

basement;

at the slab over basement, for buildings with dens walls

(honey comb system) or for the rare walls (cellular system)

when there are additional walls in the basement

over the foundation level with rare walls, if there are not

additional walls in the basement.

The lateral stiffness of a masonry wall depends on:


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geometry of the wall;

static conditions at the extremities: double fixed , or

cantilever;

deformability proprieties of the brickwork: elasticity modulus(longitudinal and transversal).

For the active walls on each direction of the building, as

participant to overload the seismic load, it is necessary to

delimitate the length of the active flange equal with thewall thickness and on each side is added the smallest

value from:

In compressed area:


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- htot/5 where htot is the total height of the structural wall;- of the distance between the structural walls that are

connected with a transversal wall;

- the distance to the end of the transversal wall on each

side of the core;

- from the free height of the wall (h).

In tensioned area:

- from the free height of the wall (h);-distance to the end of the transversal wall on each side of

the core.


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The holes in flange with maximum dimension h/4 may be neglected ,

and holes with dimensions > h/4 will be considered margins of flange.

The structural model must emphasize the elements:

the general composition of the structure:


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- the ensemble geometry and of each under ensemble;-the connection between the structural under ensemble

and the connection between the components of each

under ensemble;

distribution of the level mass, in plan and in the height;

stiffening characteristics and the damping capacity.

The multistoried buildings, with reinforced concrete slabs


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rigid in their plan, are modeled as elastic system with threefreedom degrees (two horizontal translations and one

rotation around the vertical axis) for each level.

In the case of buildings with structural regularity, the calculus

is made taking into account two plan models, each of them


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being made of all the structural walls on one main direction.In this case, for buildings with rigid slabs in horizontal plan,

each plan model is an elastic dynamic system with one

freedom degree for each level. It is considered that the

seismic force acts successively and independently on each

main direction, and the seismic answers are not superposed.

For buildings without structural regularity, the calculus


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model will take into account the spatial character of theseismic action and of the structure answer.

The rigidity of the structural elements must be

estimated taking into account the deformability from

bending and from shear. It is used the elastic rigidity of


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the unfissured masonry.

The rigidity from bending and shear of the fissured

masonry will be equal with half of the elastic rigidity of

the unfissured masonry.

For the simple masonry, the effect of the coupling beams

ill t b id d


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will not be considered.They will be constructively reinforced, so that the failure of

the coupling beam from bending will precede:

the failure of the beam from shear strength;

the failure of the support from the local crushing of themasonry.

The rigidity of the structural elements must be estimated

t ki i t t th d f bilit f b di d f


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taking into account the deformability from bending and fromshear. It is used the elastic rigidity of the unfissured masonry.

The rigidity from bending and shear of the fissured

masonry will be equal with half of the elastic rigidity of theunfissured masonry.

Calculus method for horizontal loads

Usually it is admitted the linear elastic behaviour of the

material.

The unlinear static calculus method follows, according to

th i i f l t l l d th l ti f th l di


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the increasing of lateral loads, the evolution of the loadingtill their successively exit from working state.

The ultimate carrying capacity of the structure is

considered as being get when the plastic joint of mullions is

produced, and they take over at least 15% from the seismicload .

The use of the unlinear static calculus method is not

justified for buildings with structural masonry walls.

Calculus of horizontal seismic force for the

building ensemble

Forbuildings with structural regularity, the calculus of the

seismic force is calculated with the method of lateral forces

associated to the f ndamental ibration mode In this method


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associated to the fundamental vibration mode. In this method,the dynamic character of the seismic load is simply represented

by static force (equivalent static method).

For buildings without structural regularity, the seismic

forces for the building ensemble will be determined with the

method of modal calculus with answer spectrum.

where:Fb = basic shear strength corresponding to the fundamental

mode;

Sd(T1)= ordinate of the answer spectrum corresponding to the


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Sd(T1)= ordinate of the answer spectrum corresponding to thefundamental period T1;

T1 = fundamental period of vibration

m = total mass of the building as the sum of the levels

masses; = correction factor that takes into account the contribution

of the fundamental mode by the effective modal mass

associated to it, with values:

= 0.85 if T1Tc and the building has more than 2 levels = 1.0 for other situations

For the calculus of seismic forces, it will be taken into

account the over resistance coefficients (u/1), that have in

view the resistance reserves coming from many sources:


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view the resistance reserves coming from many sources:

redundance of the structural system (plastic joints from the

mullion base are not produced simultaneously),

over resistance of the reinforcement,

favourable effects of some constructive measures.

The behaviour factors for masonry structures (q) areestablished as a function of masonry type, regularity class

and the over resistance factor (u/1) where:

t 90% f th h i t l i i f f


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u represents 90% from the horizontal seismic force for

which, if the effects of the other actions remain constant, the

structure gets the maximum value of the capable lateral force;

1 represents the horizontal seismic force for which, if theeffects of other actions remain constant, the first structural

element gets the ultimate resistance (bending with centric

compression or to shear strength).

For buildings with nniv2, the values u/1 as follows:

masonry with elements from group 1 and 2:


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-masonry with elements from group 1 and 2:unreinforced masonry u/1=1.10

reinforced masonry u/1 = 1.25

-masonry with elements from group 2S: reinforced andunreinforced masonry u/1 = 1.00

Regularity Behaviour factor q for masonry type

Plan Elev

ation

ZNA ZC ZC+AR ZIA

Yes Yes 2.00 u/1 2.50 u/1 3.00 u/1 3.50 u/1

N Y 2 00 / 2 50 / 3 00 / 3 50 /


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No Yes 2.00 u/1 2.50 u/1 3.00 u/1 3.50 u/1

Yes No 1.75 u/1 2.00 u/1 2.50 u/1 3.00 u/1

No No 1.50 u/1 1.75 u/1 2.00 u/1 2.50 u/1

For the structures with one level, the q values are reduced with 15%.

Calculus of stresses in structural walls

For buildings with stiffened slabs in horizontal plan, the

seismic force is distributed to the structural walls

proportional with the lateral stiffness of each wall


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proportional with the lateral stiffness of each wall.

For buildings with slabs with unsignificant stiffness, the

seismic force is distributed to the structural walls

proportional with the mass of each wall.

The basic shear strengths for structural walls estimated through an

elastic linear calculus may be distributed between the walls on the same

direction, with the condition that the global balance is ensured and that

the shear strength in every wall is not reduced/increased with more than

20%.

When the walls have a composed section (I,T,L), the vertical sliping

strength in the section between the core and the flange (Lv,et) is

calculated for a floor with the relation:

where:


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Minf = bending moment in the section from the base of the floor for

which is calculated the sliping force

Msup = the same , in the section from the base of the upper floor.Si = static moment of the ideal section of flange to the mass centre of

the ideal section of the wall;

Ii = moment of inertia of ideal section of wall.

The geometric characteristics of the ideal section

(Si and Ii) is determined using the equivalent coefficient nech


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Calculus of deformations and lateral displacements in

the wall plan

For the calculus of deformations and lateral displacements of masonrywalls under seismic load, it will be used:

1. for unreinforced masonry (ZNA):

geometric characteristics of the unfissured section;

from the elasticity modulus of short period (Ez);


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y p ( ); from the transversal elasticity modulus.

2. for confined masonry (ZC) and with reinforced core (ZIA):

geometric characteristics of unfissured section; from the equivalent longitudinal elasticity modulus, of short duration

(EZC (ZIA));

from the equivalent transversal elasticity modulus (GZC (ZIA)).

Calculus models for perpendicular loads on the wall plan

For the calculus of bending moments under the effect of

perpendicular loads on the their plan, the walls are

considered to be elastic slabs fixed up and down, on the floor


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co s de ed to be e ast c s abs ed up a d do , o t e ooslab, and lateral, on the stiffening walls (perpendicular on the

considered wall plan).

In the case of underground walls, for the bending momentcalculus given by the ground pressure, the wall will be

considered fixed or plastic hingh at the foundation level and

elastically fixed at the floor level over the underground level.

Calculus methods for perpendicular loads on the

wall plan

For wall without holes, the bending moments produced

by perpendicular forces on the wall plan may be


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by perpendicular forces on the wall plan may be

calculated by help of elastic plates theory.

In the case of walls with holes, for the bendingmoments calculus, the walls will be divided in half panels

which may be calculated using the rules for full panels.


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Calculus models to perpendicular forces for walls with holes

As simplification, the bending moments may be

assessed neglecting the effect of lateral supports, as for a

vertical continue band in the slabs direction. It is acceptedthat the bending moments in the slabs direction and those

in the middle of the floor height are equal and are

estimated with:


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Mhi= bending moment in the slabs rightMhm= bending moment at the middle of the floor height.

ph is the uniformly distributed force from the wind action, or is the

mean force on the floor height, in the case of seismic loads


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The simplified model for the perpendicular loads on the wall plan for multistoried

buildings

The slabs calculus

The slabs are dimensioned for:

vertical loads, died and from exploiting


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horizontal loads acting in median plan of the slab.

The verification of slabs resistance and stiffening is necessaryfor the following categories:

multistoried buildings with rare walls (cellular system);

buildings of hall type, for the roof slab;


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buildings with big holes in slabs;

buildings with prefabricated slabs (to verify the joints

capacity).

For buildings with dense walls (honey comb system) this

verification is not necessary.

Calculus model

For buildings with simple shapes in plan, (rectangular)

the internal forces (shear strength and bending moment)produced by horizontal forces the slab will be considered as


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produced by horizontal forces, the slab will be considered as

a continue beam, supported by structural walls.

In the case of slabs with complicated shapes, with bigholes and with big concentrated loads, it will be adopted

models and methods that will emphasize their behaviour.

Calculus method

The total force for a slab is equal with the seismic

force applied at that level. This force may be consideredlinear distributed on the slab length, the resultant passing

through the rigidity centre of the structure from that level.

In this hypothesis, the extreme values will be:


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Sniv seismic force applied on the slab leveldRG between the mass centre (G) and rigidity centre (R)

L building dimension perpendicular on the calculus direction

The reaction from the supporting section of the slab

on a structural wall is proportional with the sum of the

resistance capacity to shear strength of all the wallmullions:


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where VR resistance capacity to shear strength of building on

the calculus direction.

The bending moment and the shear strength in slab is determined

from the conditions of static balance under the effect of loads p and

reactions Fi.


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For buildings with structural regularity, with all slabsidentical and where the seismic force is linear distributed


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identical and where the seismic force is linear distributed

on the height, the verification will be made only for the

last level, where Sniv has a maximum value.

Calculus of the masonry walls strength

The calculus model will take into consideration :

wall geometry;

supporting conditions of the wall;

peculiar conditions for loads application;

i t d d f bilit i ti f


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resistance and deformability proprieties of masonry;

execution conditions.

The geometry wall concerns to:- the shape of the transversal section;

- ratio between height and thickness;

- presence of weak zones ( slots, recesses).

The supporting conditions refers to:


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The supporting conditions refers to:

- supporting way at the slab level;

- lateral supporting way;

- holes effects on the supporting conditions.

The peculiar conditi

Presentation Master Zidarii -Curs Sem Baran Irina

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