Masonry structures

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.

Stirbey Palace -1835

Ghica Palace -1822

Cantacuzino Palace - 1903

Cladirea CEC -1900

Court Law - 1895

Categories of masonry buildings1. 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.

Categories of masonry buildings2. Buildings with load bearing walls of brickwork

and reinforced concrete girdle and cores with floors made of:

monolith reinforced concrete; prefabricated elements of small dimensions; prefabricated elements of big dimensions

( half panels, panels).

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.

The technical and economical advantages are important:

they ensure the structures solving for buildings with different functions, 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 the protection of the unstructural elements during the seismic action without additional measures/costs;

the walls thickness imposed by the fulfillment of the thermal and acoustic insulation requirements are in many cases enough to fulfill the 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 higher qualified workers.

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

M1 – buildings made of reinforced concrete: with structural walls or frames 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.

Table 1. Dwellings with masonry structure in towns

MaterialTotal 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%)

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

MaterialTotal <1944 1945-1960 1961-1980 1981-1991

Total 1.100.000 450.000 250.000 340.000 60.000

100% 41.0% 22.7% 30.9% 5.4%

M2 220.000 85.000 40.000 75.000 20.000

20.0% 7.7% 3.6% 6.8% 1.8%

M3 480.000 220.000 100.000 140.000 20.000

43.6% 20.0% 9.1% 12.7% 1.8%

Table 3. Dwellings in buildings ≥ P+2P

Material Total <1944 1945-1960 1961-1980 1981-1991

Total 2.900.000 190.000 120.000 1.450.000 1.140.000

100% 6.6% 4.1% 50.0% 39.3%

M2 670.000 120.000 90.000 350.000 110.000

23.1% 4.1% 3.1% 12.0% 3.8%

M3 18.000 15.000 1.100 1.300 600

0.6% 0.5% 0.03% 0.04% 0.02%

Objectives of the Eurocodes is the harmonization of technical rules for the design of building and civil engineering works.

Main advantages:– harmonization of building standards in Europe– standardization of the basic requirementsand 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

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

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 considerationinclude:– 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 of the structure or any part of it, including supports and foundations.

Serviceability limit states correspond to statesbeyond which specified service criteria are no longer met.

Serviceability limit states which may require considerationinclude:– deformations or deflectionswhich 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.

Fundamental requirements 1. A structure shall be designed and constructed in such a way that:• with acceptable probability, it will remain fit for the use for which it is required, having due regard to its intended life and its cost, and• with appropriate degrees of reliability, it will sustain all actions and influences likely to occur during execution and use and have adequate durability in relation to maintenance costs.

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.

The potential damage should be limited or avoidedby appropriate choice of one or more of the following:

• avoiding, eliminating or reducing the hazards which the structure is to sustain,• selecting a structural form which has low sensitivity to the hazards considered,• selecting a structural form and design that can survive adequately the accidental removal of an individual element,• tying the structure together.

The above requirements shall be met

•by the choice of suitable materials,•by appropriate design and detailing,and •by specifying control procedures for production, construction and use, as relevant for the particular project.

Structural regularity criteria

Very important is the achievement of a direct and clear transmission 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.

Very important is the favourable effect of the regularity of the structure.- In plan it enables the elimination/reduction of the effects 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 the normal/direct route toward the foundations of vertical and horizontal forces.

The buildings with a regular structure in plan and elevation have the advantages to be analyzed with simple methods and models.

Oscillations of buildings without symmetry during the earthquake

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

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

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

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

Fig. Possible segmentation of buildings with a plan in “U”shape

Fig. Possible segmentation of buildings with interior enclosures and in the “T”shape with different proportions

Principles for masonry structure

for areas where the seismic acceleration ag≥0.20g it is recommended 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);

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.

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.

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 each floor 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.

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.

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 main directions;•is compact, with regular outlines and with a reduced number of inlet corners;•the possible recesses/prominences in comparison with the 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.

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;

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

4. At the ground floor level, on each main direction of the building, 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.

Figure 1. Conditions for structural regularity in plan

The disposing in plan of the structural wallsThe 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 is recommended 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 possible without holes.

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.

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 for the vertical complete walls and horizontal ( coupling beams, lintels) between holes.

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.

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 holes will be limited, depending on the height of the holes (hgol) or the wall thickness (t):For unreinforced masonry (ZNA):marginal mullion :lmin = 0.6hgol≥1.20mintermediary mullionlmin = 0.5hgol ≥1.00m

For confined masonry (ZC or ZC+AR);marginal mullion lmin = 0.5hgol≥1.00mintermediary mullionlmin = 0.4hgol ≥0.80m

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

Disposing in plan of holes in masonry walls

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

The thickness of the structural wallsThe 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.

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 following minimum 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

The preliminary design of the horizontal structural subsystemsFor 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 ;

the ensurance of cooperation between the vertical elements for taking over the horizontal seismic forces :the distribution of the level seismic force between the structural 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

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 structural elements.

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.

When they are not weakened by important holes, the floors could be considered “rigid in horizontal plan” when they have the following constructive composition:monolith reinforced concrete floor);floors from panels or halfpanels prefabricated of reinforced concrete joint on the outline floors made of prefabricated elements ,

The following floors are considered to have insignificant rigidity in horizontal plan:

floors made of prefabricated elements like band type with locks or connection bars at the end, without reinforced overlayer 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 floorsThe 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

Underground wallsUsually , the underground walls will be placed under all the structural walls from the ground floor. They will be made of reinforced 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.

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≥ 0.24g it is recommended to introduce some additional walls.

Additional walls for underground level in the case of rare walls

The masonry buildings are considered to be with structural regularity in elevation

if:

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

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 from the upper levels, for buildings with nniv ≥ 3 does not exceed 20 % from the area of the masonry from the ground floor.

3. The building does not have “weak” levels (with a stiffness and/or strength capacity lower than the superior levels).

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

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

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 the stratification, content, etc.

It is recommended that the ratio between the main dimensions of the building sections resulted through fragmentation would be:

•height/ breadth ≤ 1.5;•length/ breadth ≤ 4.0;•for normal foundation terrain, the maximum length of the section is 50.0m.

The choice of the system for structural wallsThe choice of the structural walls system will be chosen so that the following requirements will be fulfilled simultaneously:•functional: dimensions of free spaces, level height, type of circulation spaces;•comfort;•structural safety.

The density of the structural walls, on each main direction 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 floor area (Apl) on that level.

pl

netz

AA

p ,100(%)

Structure with dense walls (honeycomb system)

This kind of system is defined by the following geometric parameters:•level height is ≤ 3.2m;•distance between walls, on both main directions ≤ 5.00m;•the cell area resulted from the walls on both two directions ≤ 25.0m2.

Figure3. Structures with dense walls (honeycomb system)

Structures with rare wallsThe structures with rare wall (cellular system) are

defined 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 main

directions ≤ 75.0sm.

In this case, the structural walls are disposed, usually, at the limit between the functional units, which eliminates the weakness because of the circulation gaps.

Figure4. Structure with rare walls (cellular system)

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).

The buildings with structural brickwork walls could be with the following types:

•Simple masonry/ without reinforcement (ZNA);•Confined masonry (ZC);•Confined masonry and reinforcement in horizontal joints (ZC+AR);•Masonry with reinforced core (ZIA).

Classification of the masonry walls:

•Structural wall: wall designed to resist to vertical and horizontal forces that act mainly in its plan;•Stiffening wall: a wall perpendicular to another wall, with which it co-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 the building structure; this wall could be removed, and the building is not affected.•Filling wall: a wall that is not a part of the main structure, but in some 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.

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

Buildings with a height up to P+4E: dwellings, education buildings, health care 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).

The thickness of the structural walls are limited by the ratio:For the thickness t =25cm for het, max (ZNA) = 3,00m

het, max (ZC, ZIA) = 3,75m

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

4,50m

Wall typesLoad-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 filledor partially filled with non-load bearing thermal insulating material.Double-leaf wall:A wall consisting of two parallel leaves with the longitudinal jointbetween (not exceeding 25 mm) filled solidly with mortar and securely tied together with wall ties so as to result in common action under load.

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.

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 the building.Non-load bearing wall:A wall not considered to resist forces such that it can be removedwithout prejudicing the remaining integrity of the structure.

The simple masonry/without reinforcement

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

Because of:

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

the use of this kind of structure is not recommended.

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 1,2 and the minimum value (p%), depending on the seismic acceleration (ag) are:

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 NA3 ≥5% NA NA NA

Measures:•It is used only for buildings with a small number of levels;•The building must have a structural regularity in plan and elevation;•The seismic load static equivalent is estimated using low values for the behaviour factor, in order to limit the post elastic incursions;•The limitation of the relative length of the tension zone under the effect of vertical and seismic loads.

Masonry with reinforcement (ZC,ZC+AR, ZIA)The reinforcement ensures:•ductility;•capacity to dissipate the seismic energy;•limitation of excessive degradation of strength and stiffness;•maintaining in some limits the walls integrity after a severe 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:

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% NA4 ≥4% ≥6% NA NA5 ≥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

In 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 will not result horizontal force;•the masonry walls from the attic is confined with concrete cores as a continuation of those from the lower ones;•at the upper level of the masonry walls of the attic, will be realized 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.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 concrete cores 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.

Positions of reinforced concrete columns for a confined masonry

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

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 “

requirementa. The favourable mechanism for the seismic energy dissipationThe main feature of the masonry structures placed in seismic 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 the effect of repeated alternating loads.

In the case of the masonry buildings, the favourable mechanism for the seismic energy dissipation consists in controlling 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 compressive eccentric force. Measures in order to ensure the local ductility.

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.

b. The resistance condition

The resistance condition is fulfilled if in all the structural elements, 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 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 limited

taking into account the flexion and eccentricities of loads.

d. The stiffness condition

The masonry buildings will have enough stiffness so that:

the inelastic deformations of the structural elements, under the designed earthquake for ULS, 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 for SLS;it is avoided the collision of adjoining buildings.

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 characteristic values divided by a partial safety coefficient for the material γM≥1differentiated depending on:

limit state for which is made the verification;elements quality for the masonry and mortar;quality of the execution.

M

zkzd

ff

The designed values resulted from the reference values multiplied by a coefficient for the working conditions mz. 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.

zdzzd fmf

The values of the working conditions coefficient mz are as follows:

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 <0.30m2;

mz,ULS = 0.85 – for masonry with cement mortar (without lime addition) for the compressive strength

mz,ULS = 0.75 – the same, for the tension resistance from bending, shear stress along the horizontal joint and the main tension stress

mz,ULS = 1.25 – for testing the elements strength during the execution.

B. For the verification for serviceability limit state:

mz,SLS = 1.0 – for all the cases, excepting the cases mentioned 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:

γM = 2.2 for the calculus at the ultimate limit state (ULS) with the elements for masonry of class I and mortar for general use (G) – performant or of prescription, in normal control conditions;γM = 2.5 for the calculus at the ultimate limit state (ULS) with the elements for masonry of class II and mortar made in site conditions, and in normal control conditions;γM = 3.0 for the calculus at the ultimate state (ULS) with the elements for every class and in low control conditions;γM = 1 for the calculus at serviceability limit state (SLS).

Normal control conditions mean that: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 unitsTypes 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.

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.

Grouping is defined with limits on:

volume of all holesvolume of each holedeclared value of thickness of web and shellsdeclared value of combined thickness of web and shells.

Depending on the geometrical characteristics, the masonry elements could be in two groups:

Group Iclay masonry units 240x115x63;clay masonry units with circular holes;lightweight concrete units with holes volume ≤25%;autoclaved aerated concrete masonry units.

Group II

clay masonry units with rectangular holeslightweight concrete units with holes volume between 25% and 50%;ordinary concrete units with the volume holes between 25% and 50%.

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 te≥15mm;the thickness of internal web and shells ti≥10mm;the vertical internal walls are continually realized on the whole length element.

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

Masonry:An assemblage of masonry units laid in a specified pattern and joined together with mortar.

Reinforced masonry:Masonry in which bars or mesh, usually of steel, are embedded in mortar or concrete so that all the materials act together in resisting forces.

Prestressed masonry:Masonry in which internal compressive stresses have been 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 achievecommon action.

The mechanical properties of the masonry elementsThe compressive strength of masonry units

The compressive strength of masonry units, to be used 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 into account the high and width of the masonry elements, by multiplication with a δ factor.

Transformation factor and fb values for clay and concrete elements

Masonry elementδ factor

fmed (N/mm2)

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

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

Depending on the composition definition, the mortars could be:designed mortars (declared performances);prescribed mortars (declared proportions plus compressive strength declared using publicly available references).

Compressive strength of mortarsThe masonry mortars are classified depending the

mean compressive strength, expressed by the letter M followed by the compressive strength value expressed in N/mm2 (for example: M5 mortar with the mean unitary strength fm = 5N/mm2).The masonry mortars must have fm > 1N/mm2.

Building typeStructural walls Unstructural walls

Elements Mortar Elements Mortar

Lasting buildingsAll the importance class

fmed>10 M10 fmed>10 M5

fmed≤ 10 M5 fmed≤ 10 M2.5

Temporary buildings

M2.5 M1

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

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 the masonry units and of the mortar:

30.070.0mbk fKff

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

Masonry element typeCoeff. K

Full clay bricks 0.50Clay bricks with vertical holes 0.45Blocks of ordinary and light concrete 0.50Small blocks of autoclaved aerated concrete 0.50

This formula may be used if there followed the following requests:

the element strength for the masonry is fb≤75N/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%.

Typical wall bonds relative to longitudinal joints

The unitary designed compressive strength of masonry

M

kzd

fmf

where:-mz is the working condition coefficient-fk characteristic compressive strength of masonry-γM partial factor for material

Shear strength of masonry in horizontal joint

The characteristic initial shear strength in horizontal joint (fvk0)

Elements for masonryMean 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 0.10Autoclaved aerated concrete - 0.15 0.10

The characteristic shear strength of masonry, fvk, realized with mortar for general use of masonry (G) , with all the joints full of mortar, will be chosen equal with smallest value from:

For elements for masonry from group I

fvk =fvk0 + 0.4σdfvk =(0.034fb + 0.14 σd)

For elements for masonry from group IIfvk = fvko + 0.4 σdfvk =0.9(0.034 fb + 0.14 σd)

where:fvk0 – unitary characteristic initial strength to shear strength σd – perpendicular compressive unitary stress on the shear plan 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:

fb

N/mm2

Mortar

Unitary compressive stress σd (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

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:

fb

N/mm2

Mortar

Unitary compressive stress σd (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 0.319 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 0.140For 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

M

vkzvd

fmf

The unitary tension strength from bending perpendicular on the masonry plan

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 .

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 type

Mean strength of the mortar

M10, M5 M2.5

fxk1 fxk2 fxk1 fxk2

Clay masonry units

0.240 0.480 0.180 0.360

Autoclaved aerated concrete

0.080 0.160 0.065 0.130

M

xkzxd

fmf

1

1

M

xkzxd

fmf

2

2

The designed unitary tension strength from bending perpendicular on the masonry plan

Calculus of buildings with structural masonry walls

General calculus principlesTo design the usual buildings with masonry structure, the 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 assessed for the gross section (unfissured);the results get by models based on the upper mentioned are affected by correction factors, so that will be obtained a better concordance with results from tests.

The model must take into account simultaneously the following specific aspects:

the complex character of the constitutive law σ-ε that is usually non-linear;the particularities of the law σ-ε depends on the element proportions and the masonry type (simple/reinforced);the strength and stiffness degradation is caused by the repeated 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

over the gravitational loads brought by floors and transmitted to the foundation.

The structural walls are considered cantilevers fixed - at the underground floor level (in the case of

buildings with underground) and - at the superior level of foundations (in the case of

buildings without underground).

The walls can be loaded simultaneously with vertical loads and horizontal ones that are acting perpendicular on the wall plan:

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 produced

arches, vaults or wooden frames; loads from operating (furniture or equipments

suspended).

The calculus model must take into account :

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 wallsThe 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 calculus section.

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 wall length. In the case of walls with holes, it is added ½ from the breadth of hole that border the wall.

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 is realized an uniform distribution of compression strength on the whole area of wall.

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 with holes, the route is changed.

In practice, the design of loadbearing walls and columns is reduced to the determination of the value of the characteristic compressive strength of the masonry (fk) and the thickness of the unit required to support the design loads. Once fk is calculated, suitable types of masonry/mortar combinations can be determined from tables, charts or equations.

The basic principle of the design can be expressed as

design vertical loading ≤ design vertical load resistance

in which:-the term on the left-hand side is determined from the

known 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 dependent on the slenderness ratio = the ratio of the effective height to the effective thickness.

For short columns, where the slenderness ratio is low, failure would result from compression of the material, whereas for 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 fabrication errors. The vertical load will, in general, be eccentric 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;

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 of the resistance capacity estimated as for “ideal” axial loads.

a. Eccentricities resulted from structure composition

The eccentricities coming from the structure composition are produced in areas where is produced the vertical forces transfer from a level to another and is the 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 height between the maximum value at the upper side of the wall, and zero to the inferior side of it.

Eccentricities from the structure composition

21

22110 NN

dNdNei

where:N1 – load from the wall of the

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 which

are applied the loads N2

cmtea 0.130

cmh

e eta 0.1

300

b. Eccentricities from the execution imperfections (accidental eccentricity)The accidental eccentricities of vertical loads (ea) may be caused by the following execution imperfections:relative displacement of the median plans of walls from the two adjacent levels;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 greatest value between the values:

where: t – wall thickness het – 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

≤ 3,00 1,00 1,25 1,503,20 1,073,40 1,133,60 1,203,80 1,274,00 1,33

21

)()( NN

Me ihm

ihm

12

2eth

hmhihp

MM

c. Eccentricities from the bending moments produced by horizontal forces perpendicular on the wall plan

The eccentricities of vertical force corresponding to moments Mhm(i) is given by:

where:

ph is the uniformly distributed loadN1 – 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:

calculus of eccentricities of vertical force resulted from bending moments when the wind action is perpendicular on the façade;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:

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 basementover the foundation level with rare walls, if there are not additional walls in the basement.

The lateral stiffness of a masonry wall depends on:

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 the wall thickness and on each side is added the smallest value from:In compressed area:- htot/5 where htot is the total height of the structural wall;- ½ 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;- ½ from the free height of the wall (h).In tensioned area:-¾ from the free height of the wall (h);-distance to the end of the transversal wall on each side of the core.

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:- 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 rigid in their plan, are modeled as elastic system with three freedom 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 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 model will take into account the spatial character of the seismic 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 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 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 the masonry.

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 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.

Calculus method for horizontal loadsUsually it is admitted the linear elastic behaviour of the

material.The unlinear static calculus method follows, according to

the increasing of lateral loads, the evolution of the loading till 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 seismic load .

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

For buildings with structural regularity, the calculus of the seismic force is calculated with the method of lateral forces 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”.

mTSF db )( 11where:Fb = basic shear strength corresponding to the fundamental

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

fundamental period T1;T1 = fundamental period of vibrationm = total mass of the building as the sum of the levels

masses;λ = correction factor that takes into account the contribution

of the fundamental mode by the effective modal mass associated to it, with values:

λ = 0.85 if T1≤Tc and the building has more than 2 levels λ = 1.0 for other situations

For the calculus of seismic forces, it will be taken into account the over resistance coefficients (αu/α1), that have in 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) are established as a function of masonry type, regularity class and the over resistance factor (αu/α1) where:

•αu 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;•α1 represents the horizontal seismic force for which, if the effects of other actions remain constant, the first structural element gets the ultimate resistance (bending with centric compression or to shear strength).

For buildings with nniv≥2, the values αu/α1 as follows:

-masonry with elements from group 1 and 2: unreinforced masonry αu/α1=1.10 reinforced masonry αu/α1 = 1.25

-masonry with elements from group 2S: reinforced and unreinforced masonry αu/α1 = 1.00

Regularity Behaviour factor q for masonry typePlan Elev

ationZNA ZC ZC+AR ZIA

Yes Yes 2.00 αu/α1 2.50 αu/α1 3.00 αu/α1 3.50 αu/α1

No Yes 2.00 αu/α1 2.50 αu/α1 3.00 αu/α1 3.50 αu/α1

Yes No 1.75 αu/α1 2.00 αu/α1 2.50 αu/α1 3.00 αu/α1

No No 1.50 αu/α1 1.75 αu/α1 2.00 αu/α1 2.50 αu/α1

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.

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%.

i

ietv I

SML ,

supinf MMM

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:

Minf = bending moment in the section from the base of the floor for which is calculated the sliping forceMsup = 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

d

cdech f

fn

75.0

Calculus of deformations and lateral displacements in the wall plan

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

1. for unreinforced masonry (ZNA):geometric characteristics of the unfissured section;½ from the elasticity modulus of short period (Ez);½ from the transversal elasticity modulus.

2. for confined masonry (ZC) and with reinforced core (ZIA):geometric characteristics of unfissured section;½ from the equivalent longitudinal elasticity modulus, of short duration (EZC (ZIA));½ 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 slab, and lateral, on the stiffening walls (perpendicular on the considered wall plan).

In the case of underground walls, for the bending moment calculus 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 calculated by help of elastic plates theory.

In the case of walls with holes, for the bending moments calculus, the walls will be divided in half panels which may be calculated using the rules for full panels.

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 accepted that the bending moments in the slabs direction and those in the middle of the floor height are equal and are estimated with:

12

2eth

hmhihp

MM

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

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 exploitinghorizontal loads acting in median plan of the slab.

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

multistoried buildings with rare walls (cellular system);buildings of hall type, for the roof slab;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 a continue beam, supported by structural walls.

In the case of slabs with complicated shapes, with big holes 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 considered linear 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:

)61(minmax/ Ld

LS

p RGniv 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 wall mullions:

R

Rdinivi V

VSF

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.

For buildings with structural regularity, with all slabs 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;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:- supporting way at the slab level;- lateral supporting way;- holes effects on the supporting conditions.

The peculiar conditions for loads application refers to:- application eccentricities resulted from the constructive structure;- eccentricities resulted from execution imperfections;- effects of loads of long duration.

The resistance and rigidity proprieties refer to:- constitutive law of the masonry σ-ε;- rheological proprieties of masonry;- compatibility of specific ultimate deformations of masonry and concrete (in the case of ZC, ZC+AR, ZIA).

The designed resistance of structural walls is determined for:internal forces caused by forces acting in the median plan of the wall:

centric force (NRd);bending moment (MRd);shear strength (VRd);vertical sliping force in walls with composed sections (VLhd).

internal forces caused by forces acting perpendicular on the median plan of the wall;bending moment in parallel plan with the horizontal joints (MRxd1);bending moment in a perpendicular plan on the horizontal joints (MRxd2).

Calculus hypothesisThe assessment of internal forces and deformation in masonry elements is based on the following hypothesis:

plane section hypothesis;the tension strength of masonry on perpendicular direction on horizontal joint is zero.the relation between internal forces and specific deformation is rectangular for the ultimate limit state (ULS);the relation between internal forces and specific deformation is triangular for service limit state (SLS).

Geometric characteristics of the horizontal section of the wall

The dimensions of the transversal section of the walls are net dimensions, meaning without plaster.

The walls with holes with maximum dimensions ≤0.2lw could be considered as full walls, if the hole is placed in the middle third of the level height, and the full masonry to the wall end is with less 20% greater than the minimum values given above.

The holes in flange with maximum dimension ≤ h//4 may be neglected, and those >h/4 could be considered as margins of the flange.

Unitary strength of masonry, concrete and reinforcement

M

kzd

fmf

where: γM = 1.50 for structural walls and nonstructural

from the importance class IγM =1.0 for all the elements what ever the

importance class.

Compression strength of unreinforced masonry with burned clay elements

The centric compression strength for an element is determined with:

dmiRd AfN )(Φi(m) – coefficient for the strength reduction because of the

effect of the element slenderness and of the eccentricities of loads in extreme sections (Φi) and respectively in the section from 2/3 from the element height measured from the base (Φm);

A – area of the transversal section of the element;fd – compression strength

For masonry walls with rectangular section, the equation became:

dmiRd tfN )()1( where

t – wall thickness NRd(1) – designed strength of the rectangular wall on 1m.

tei

i 21

teeee ahiii 05.00

The assessment of the coefficient of resistance reduction Φi

The coefficient of strength reduction in sections from the wall extremities (Φi)- up and down- depends on the eccentricity of the loads applying and will determined:

where t – wall thickness; ei – eccentricity related to the wall plan, in the section from the

wall extremity, calculated with:

e0i – eccentricity caused by all the loads over the calculus levelehi – eccentricity caused by forces applied perpendicular on the wall plan;ea – accidental eccentricity

kmmk eee

ahmim eeee 032

te

he mefk 002.0

The assessment of the coefficient of strength reduction Φm

For the masonry elements with clay units, with all the joints filled, the reduction coefficient will be taken from the table 6.1. depending on the ratio hef/t and emk/t where emk is the calculus eccentricity in the central area of the wall ( at 2/3het measured from the wall base) is given by:

where:

and

where:ek - eccentricity caused by curgere

lenta Φ∞ - coefficient of curgere lenta

Assessment of the effective height of the wall (hef)

The effective height of the wall is established depending on the panel dimensions and the connection conditions with the adjacent elements (slabs and perpendicular wall).

In order to be considered lateral supports, the elements that are ending the wall must have a rigidity comparable with that of the wall which they stiffening.

A masonry wall is considered to be stiffened if it is tied by bonding with a masonry wall perpendicular on it that fulfils the following conditions:

- the length of the stiffening wall is ≥1/5 from the floor height;

- the stiffening wall thickness is ≥ ½ from the wall thickness which is stiffened;

- in the case of a wall with holes in the stiffened wall vicinity, its length must fulfill the conditions from the figure:

The wall stiffening with transversal walls

In the case of the wall of 240mm, the stiffened walls of 120mm are considered only stiffened element and are not considered active walls for the seismic load.

The stiffening of a wall may be ensured by the help of some masonry columns ( pilaster) with thickness ≤3t and the distances between their axis d≤20t , t is the thickness of the wall which is stiffened.

The real thickness of the wall with pilasters is:

tt wcalc

Walls strengthening with masonry pilasters

The effective height of the masonry wall is calculated:

hh nef where:ρn (n=2..4) - coefficient that takes into account the

supporting conditions and the number of sides of the wall;h – free height of the wall;lw – length of the horizontal section of the wall.

The coefficients ρn:

wall supported on a reinforced concrete or wood on both sides ρ2 = 0.75

wall supported on a reinforced concrete or wood on one side ρ2 = 1.00

23

16

12

wlh

hlw5,13

23316

12

wlh

hlw23

23

31

1

wlh

23

1

1

wlh

The coefficients ρ3 (for the stiffened wall on a vertical side) and ρ4 (stiffened wall on two vertical sides) are determined from the table 6.3 as function of free height of the wall.

Values ρ2 Values ρ3 Values ρ4

h≤3,5lw h>3,5lw h≤lw h>lw

0,75

1,00

Compression strength of walls made of reinforced masonry – ZC, ZC+AR, ZIA

d

cdech f

fn

75,0

cdf

df

The walls strength will be estimated by transforming the mixed section in a ideal section of masonry using the equivalent coefficient nech

where:

= compression strength of concrete from concrete core

m=0,75 coefficient of working conditions

= compression strength of masonryThe calculus is made as in the case of simple masonry walls.

Local compression strength of walls under the concentrated loads effect

For a wall made of simple masonry , the local compression strength because of concentrated loads is calculated with:

dbclRd fAN , where:

max)1.15.1)(30.01(0.1 ef

bl

AA

Ha

where:

β = increasing coefficient for concentrated loads;al = distance from the end of the wall till the closed limit of the area on which is transmitted the load;Ab = the area on which is transmitted the load;H = the wall height from the base till the level where the load is applied;Aef = loaded area;Aef = tLef where t

AL b

ef2.2

is the effective length for taking over of the load measured from the middle of the wall resulted from the unloading the vertical load to an angle of 60º with the horizontal line.

βmax =1.25 if 2a1/H = 0

βmax =1.50 if 2a1/H ≥ 0

For 0.0 <2a1/H≤1.0 the values will be get by linear interpolation between the values βmax mentioned before.

The eccentricity of the concentrated load, compared with the median plan of the wall, will not exceed ¼ from the wall thickness.

Design strength to axial load and bending in median plan of the masonry walls

General conditions for calculus

The general hypotheses are:

hypothesis of plan sections;in the case of reinforced masonry (ZC and ZIA) the concrete works together with the masonry till the ultimate state; the ultimate deformations (εub) of the concrete could not exceed those for the masonry (εuz);the tension strength of masonry is neglected;in the ultimate state, the unitary stresses in the compressed area of the masonry is considered to be uniformly distributed; the same is for concrete;

d

sdzc f

NA

8.0

zcSdRd yNM

Walls of masonry without reinforcement

The design strength for bending (MRd) will be estimated as follows:1. It is estimated the area of the compressed zone

2. It is calculated the distance yzc from the centroid of the wall till the mass centre of the compressed area3. It is calculated the design strength to bending (MRd)

tfN

xd

SdRd 8.0

)(2 RdwSd

Rd xlN

M

When the wall is rectangular with a length lw and a thickness t , the relations became:

The depth of the compressed zone

The bending moment

In the case of a rectangular wall with the length lw , the upper relation become :

EdwRd NlM 2.0

Fig. The calculus of the design strength to bending action with axial force for the masonry without reinforcement

tfN

xdmi

SdRd

)(8.0

m

When the axial force is eccentrically to the wall plan, the depth compressed zone will be calculated:

where

is the coefficient for the strength reduction

In the case of masonry walls without reinforcement at which the bending in the wall plan is produced by the seismic force, the design strength to bending action associated to axial force (NEd) will be determined as for non-seismic loads, but with the limitation of area on which are developed tension stresses by the condition:

sczc ry 2.1

Where:rzc = distance from the mass centre of the horizontal section till the limit of the central core being placed at the same part as the compressed fiber.

Walls with confined masonry with or without reinforcement in horizontal joints

The hypothesis for the calculus for design strength to bending (MRd) associated to axial force from seismic loads are:

Are neglected:

the strength to unitary stresses of tension of concrete in the concrete core from the extremity subjected to tension;the mortar strength from the horizontal joints;the concrete section and the reinforcement from the intermediate concrete core;

Are taken into account the contribution of the vertical confined elements:the section of the concrete core from the compressed extremity;the reinforcement of the both concrete core from the extremities.

In the ultimate state, the deformation state, in the “balance” situation is the following:at the compressed extremity there are registered the maximum values of specific deformations of masonry/concrete;in the reinforcement from the concrete core at the tensioned extremity is registered the curgere strength of steel.

The compression stresses block in masonry and/or concrete is rectangular and is developed on a depth of 0.80x, where ”x” is the distance from the neutral axis till the most compressed fiber.

Figure The calculus of the design strength to bending with axial force for confined masonry

In the case of elements from group 2 and 2S for which εuz<εub :

For the extremities without flanges of wall, the specific deformation of masonry, at the limit with the concrete core, will not be greater than the maxim specific deformation, and the maxim specific deformation in the concrete will not exceed εc =-3.0‰

For the extremities with flanges, the maximum specific deformation of concrete (εub) will not be greater than the maximum specific deformation of masonry.

Figure The ultimate specific deformations at confined masonry walls

If it is not necessary an exact calculus, the design strength at bending (MRd) associated to the design axial force (NEd), for a confined masonry wall of anyhow shape, may be estimated by summation the design strength to bending of the ideal section of simple masonry MRd(zna,i) with the design strength to bending corresponding to the concrete core from the extremities MRd (As).

)(),( AsMiznaMM RdRdRd

The design strength to bending of the ideal section of the simple masonry is calculated in the following assumptions:It is valid the plane sections hypothesis;The area of reinforced concrete of the compressed cores may be replaced by an equivalent area of masonry; the equivalence coefficient nech is equal with the ratio between the basic value of the design strength for compression of the concrete from the cores (fcd*) reduced with the working conditions coefficient m = 0.75 and the design strength for compression of the masonry (fd):

d

cdech f

fn

75.0

The compressive stresses block has a rectangular shape, with a maximum value equal with 0.80fd;

Maximum depth of the compression area will be x≤xmax=0.30lw where lw is the wall length

With these assumptions results:The ideal section area for the compressed masonry :

d

Edzci f

NA

8.0

The bending moment of the ideal section of masonry:

zciEdRd yNiznaM ),(Where yzci is the distance from the mass centre of the wall till the mass centre of the compressed zone of the ideal section of masonry.

The design strength for bending given by the reinforcement in concrete cores MRd (As) is calculated:

ydsssRd fAlAM )(

where:ls = distance between the mass centre of the two concrete core from

the extremities;As = the smallest area from the two concrete cores;fyd = the calculus strength of the reinforcement from the concrete

cores.

Masonry walls with reinforced core

Assumptions:

Plane sections hypothesis;The masonry, concrete and the reinforcement have a ductile behaviour defined by the curves “σ-ε”;The parallel layer of masonry and concrete work together till the ultimate stage;

The compression stresses block in the ultimate state is rectangular with a depth xconv=0.80x where x is the distance from the most compressed fiber till the neutral axis of the horizontal section of the wall;

The specific deformations in the ultimate state of masonry and concrete are equal εub=εuz=-3.0‰ if there are used masonry elements from the group 1;

The reinforcement in the mean layer is uniformly distributed along the wall.

In this case the design strength for bending (MRd) associated to design axial force (NEd) is calculated by summing the design strength for bending of the ideal section of the masonry without reinforcement with the design strength of the reinforcement from the mean layer

)(),()( asRdiznaRdRd MMZIAM

The equivalent thickness of the ideal section of the masonry without reinforcement is:

mechzech tntt 2

where:•tz is the layers thickness of the external masonry•tm the thickness of the mean layer of mortar/concrete

(grout)•nech equivalent coefficient

The design strength of reinforcement, MRd(as) is

ydwssRd flaaM 24.0)(

Figure The design strength for bending with axial force for masonry with reinforced core

The design strength to shear force of the structural walls of masonry

1. AssumptionsIt is considered that the shear unitary stresses given

by the design shear strength are uniformly distributed on the length of the compressed zone of the wall. The length of the compressed zone results from the design stresses (bending moment, axial force) resulted from the loading group.

In the case of the walls in the shape of I, L, T, the design strength to shear stresses is equal to the design strength to shear force of the core (rectangular section)

2. Walls without reinforcement

The design strength to shear force VRd of walls without reinforcement will be calculated with:

cvdRd tlfV where:•fvd – design unitary strength to shear of the wall;•t –thickness of the core ;•lc – length of the compressed zone of the core.

The unitary compression stress (σd) used for the unitary strength (fvd) will be calculated considering that the vertical load from the loads group, NSd or NEd, is uniformly distributed on the compressed zone of the wall.

In the case of walls with a composed section (L,T,I), in the compressed zone for which is determined σd there are included also the flanges with the dimensions settled as mentioned above.

3. Walls with confined masonryThe design strength to shear force, VRd, is get by summing the design strength to shear force of the masonry without reinforcement (VRd1), and the design strength to shear force get because of the reinforcement from the concrete core from the compressed extremity of the wall (VRd2)

21 RdRdRd VVV

VRd1 will be determined as above.

For the shear force from the seismic action, VRd1, will be determined in the same way, but it will be reduced by multiplying it with a sub unitary coefficient settled by P-100. VRd2 will be calculated with:

ydascRd fAV 2.02

Where:Aasc – area of reinforcement from the concrete core from

the compressed core;fyd – design strength of the reinforcement from the

compressed concrete core.

4. Walls of confined masonry and reinforcement in horizontal joints (ZC+AR)

321 RdRdRdRd VVVV

The design strength to shear force is calculated:

VRd1 and VRd2 has the same significance as above.VRd3 is the design strength of the reinforcement from the horizontal joints is calculated, in the case of walls with total height (htot≥ wall length lw)

ysdsw

wRd fs

AlV 8.03

where:lw = length of the wall;Asw = aria of the reinforcement from the horizontal joint;s = distance on the vertical direction between two successive rows of reinforcement; fysd = design strength of the reinforcement from the horizontal joints.

When htot < lw then lw will be replaced by htot .

5. Walls with reinforced core

The design strength at shear force will be determined by:

RdaRdbRdzRd VVVV

where:VRdz is the design strength to shear force of the masonry;VRdb is the design strength to shear force of the mean layer of concreteVRda is the design strength to shear force of the horizontal reinforcement from the mean layer

zcvdRdz tlfV fvd is the design strength at shear of masonrylc is the length of compressed zonetz is the total thickness of the two layer of the masonry.

6. The design strength at vertical sliding associated with bending

The design strength to vertical sliding force at the connection between the core and flange of a wall with a composed section (I,L,T) and in the vertical weakened areas is calculated on the floor height assuming that the shear unitary stresses are uniformly distributed on the floor height.

M

vkLetLhd

fthV

0

whereVLhd – design strength at sliding on the floor heighthet - floor heighttL – wall thickness in the section where is calculated the strength;fvk0 – the characteristic strength at shear of wall under the compression

stress equal with zero;γM - safety coefficient