Masonries Structures - Part II

7/26/2019 Masonries Structures - Part II

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6. Calculation of buildings with masonry walls6.1. General principles for calculation

(1) Masonry is a non-homogeneous, anisotropic material characterized by an inelastic behavioreven for low levels of stress. Development of a computational model that takes into account all

these features and at the same time can be easily applied to the current design is practically

impossible.(2) For the current building design for all load groups, determining the efforts and strains for all

parts/masonry construction elements will be done using a computational model, sufficiently

accurate, based on the following simplifying assumptions:a. masonry material is assumed to be homogeneous, isotropic with an elastic response until

the ultimate stage;

b. sectional characteristics of masonry walls are determined gross section (non-cracked/

unplastered);c. the results of calculations based on the assumptions a and b of the models with correction

factors affecting such as to obtain the best possible data consistent test results.

(3) The computation model both for the sectional efforts determination and for the walls designstrengths under all groups of loads, must be suitably represent the strength, stiffness and ductility

properties of the whole structural system.

6.2. Structural computation for vertical loads

6.2.1. The calculation model for vertical loads(1) To calculate under the action of vertical loads in all the design cases, the structural walls will

be considered like a cantilever with supported at the floor above the basement or on the top of the

foundations (buildings without basement).

(2) The design of structural masonry walls will be considered simultaneously with the vertical

loads the horizontal loads perpendicular to the wall considered from:a. the earthquake action for the walls;

b. the wind pressure to the outer walls of the superstructure;c. the earth pressure onto the basement outline walls;

d. lateral forces (push) transmitted from other parts of the structure (vaults, arches or roofs);

e. service loads (furniture or equipment on consoles, pushing people into crowded areas, etc.).

The design values of these charges will be taken from the technical regulations.(3) The calculation model for vertical and horizontal loads for all load groups must take into

account:

a. the application mode of the loads (eccentricities specified in 6.2.2.2.)b. bonds/supports of the wall on boundary;

c.

wall slenderness.

6.2.2. Calculation methods for vertical loads

6.2.2.1. Axial compression forces in the structural walls

(1) Axial compressive force in a horizontal computational section of a wall structure comprises:a. sum of charges from related areas of floors over the section;

b. the weight of the wall portion located above the section.


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(2) If the concrete slabs transmit loads in two directions, regardless of the erection technology, the

loads from the appropriate areas of each slab panel to the wall will be calculated for areas

determined by the bisectors of the angles between the sides of the slabs (l 1l2), uniformlydistributed along the length of the wall. For complex shaped walls T, L, I, with woven plane bricks

or concrete column belts at junctions or branches will be considered a uniform distribution of

compressive forces on the whole area of the wall (fig. 6.1a).(3) If the slabs download just in one direction, regardless of the material, it will be considered thatthe loads are transmitted to the walls that abut the main elements and areas adjacent transverse

walls (Fig. 6.1b) according to (4).

Figure 6.1 Vertical loads from slabs on the structural walls(a) Monolithic reinforced concrete slab

(b) Deck beams slab (RC beams, steel, wood)

(4) For the concentrated loads or distributed loads which are not applied to the entire wall, wall

distribution efforts will be made after lines inclined at 30 from the vertical as shown in Fig. 6.2a.

For hollow walls discharge path changes as shown in Figure 6.2b. Forces applied aroundcorners/intersections are transmitted to the transverse walls too as 6.2c.

(5) In the case of buildings with asymmetrical cantilevers with important distances between the

center of gravity of the vertical loads from floors and center of gravity of the horizontal section ofthe walls will take account of the additional efforts from the overall bending.


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Figure 6.2 Vertical load concentrated on structural walls

(a) Current Case (b) discharge diversion route in the vicinity of voids(c) Charging the transverse wall

6.2.2.2. Determining the eccentricities of vertical loads application(1) The loads from floors are transmitted to walls with eccentricities coming from:

a. composition design of the structure;

b. imperfections of execution;c. local character loads effects,

(2) For the calculation of wall strength, eccentricity effects are introduced by strength reductioncoefficients calculated by axial loads.

6.2.2.2.1. Eccentricity from the structure composition

(1) The eccentricity from the structure composition is calculated using:

= + + (6.1)Where notations are:

N1the load transmitted from the upper floor wall;

d1N1load eccentricity

N2loads brought by the floor/floors directly supported on the wall;

d2N2load eccentricities.(2) The bending moment (M) given by the eccentricity ei0of the height of the wall varies linearly.


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Figure 6.3 Eccentricity from the structure composition

6.2.2.2.2. Eccentricity from the imperfections of execution (accidental)

(1) Accidental eccentricity is taken into account by the greater of:

a. = 1.0 (6.2a)b. = 1.0 (6.2b)

Where notations are: t - wall thickness; het- level height.

6.2.2.2.3. Eccentricity of horizontal forces perpendicular to the plane(1) The eccentricity derived from the maximum bending momentMhm(i)given by horizontal forces

perpendicular to the plane, determined by par. 6.4. is calculated by the relationship

= + (6.3)Where notations are: N1 - load transmitted by the upper wall; N2 - the amount of the slabs

reactions that are supported on the verify wall.

6.3. Structural masonry walls calculation due to horizontal forces.(1) For the design of structural and nonstructural walls and framed masonry walls shall be taken

into account:

a. force in the plane of the wall ;b. forces perpendicular to the plane (out of plane) of the wall;

c.

forces from the imposed deformations by structure to masonry framed wallsIf the building type is auditorium/warehouse" for the roof structure will take into account the

vertical component of the seismic action as provided in P 100-1.(2) Safety for the wind in the structural walls plane for fundamental grouping of charges will be

made only in cases where the total seismic force determined according to P 100-1 is less than the

total lateral force given by wind action.(3) Wind loads shall be taken into account in all cases for:

a. calculation of the bending moments from the perpendicular action to the facade;


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b. roofs computation

(4) In case of seismic design will take into account the provisions of P100-1 and following

provisions.

6.3.1. The calculation model for horizontal forces.

(1) For all groups of loads, the superstructure of the building will be modeled by vertical structuralassemblies disposed on the main lines, consisting of full or hollow walls, connected by horizontalfloor slabs (slabs and spandrels).

(2) The embedding section for the entire assembly of structural walls to calculate the horizontal

force (in relation to the number of levels defined nniv) will take:a. higher level of pedestals for buildings without basement;

b. to the floor above the basement, though walled buildings (Honeycomb system) and rare -

walled buildings (cellular system) who have provided additional basement walls as

recommended in 5.4.3 (5) - Fig. 5.5 ;c. above the foundations for buildings with rare walls, if they provided additional basement

walls as recommended in 5.4.3. (5).

(3) The geometrical characteristics of the involved structural walls withstanding to horizontalforces (wind, seismic) will be established by considering, in the case of composite sections (L, T,

I) of equal active length to the wall thickness of the flange with the addition of each side of the

web, the smallest of the values

a. 6 t, where "t" is the thickness of the flange wall;b. distance until the edge of the transverse wall (to the first opening).

Figure 6.4. The width of the active flange

(4) The structure model must as accurately summarizing the following:a. general composition structure :

i. assembly geometry and all horizontal and vertical sub-assemblies ;

ii. links between structural subassemblies and links between components of eachsubset ;

iii. relevant mechanical properties of materials;

b. weight distribution on levels, plan and building height ;

c.

stiffness characteristics of the elements and damping capacity.(5) Structural regular buildings, type 1 of Table 5.1, to be calculated with two 2D models, each

consist of all the structural walls on one of the main directions. Each plane model is a flexible

system with one dynamic degree of freedom at each level (in terms of translational movement ofthe walls).

In buildings where the walls are not disposed in two orthogonal directions the seismic forces will

be applied in the directions of the wall system.


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(6) The calculation with plane models can be used for walls masonry buildings that do not meet

the criteria for regularity in plan but satisfy additional conditions P100-1, art.8.4.2.10.

(7) The buildings do not have a regular structural plan and elevation, type 2 of Table 5.1, will bemodeled as an elastic system with three degrees of freedom (two horizontal translations and one

rotation about the vertical axis) for each level.

6.3.2. Calculation method for horizontal seismic forces(1) For the design of the current buildings due to seismic calculation will be linear static calculation

methods according to Table 4.1 of the P 100-1.(2) For the design of buildings with architectural-structural embodiments that do not fully comply

with the recommendations in Chapter 5 and in all cases provided in chapter 8 P 100-1, use a static

nonlinear processes that take into account the expected post elastic behavior of structural masonry

walls.(3) Using the nonlinear dynamic analysis procedures is not justified for the design of buildings

with masonry structural walls.

6.3.2.1. Calculation of horizontal seismic forces for the whole building

(1) Behavior factors q for masonry structures will be taken into account depending on the type of

masonry and construction group regularly in table 8.7 of P 100-1. It will take into account

overstrength factors (u/1) the conditions of P 100-1, chapter 8.

6.3.2.1.1. Equivalent static seismic forces method(1) For buildings with regularity in plan and elevation (type 1.1 in Table 5.1) calculate the base

shear force for the whole building will be the equivalent static seismic forces method described in

P 100-1.(2) Distribution of base shear force on the height of the building will be the relation (4.6) of P 100-

1 torque and overall effects will be calculated in accordance with Chapter 5 of the P 100-1.

6.3.2.1.2. Modal response spectrum analysis method

(1) For no regular buildings, type 2 in Table 5.1 for whole building seismic forces are calculated

using the method of "modal response spectra" described in P 100-1.(2) If the buildings have prominence on the top floor, its structure will be introduced in the general

model, even if it satisfies the conditions of P 100-1, chapter 8.

6.3.2.2. Calculation of sectional efforts in structural walls(1) Base seismic force will be distribute to structural walls in concordance with the model for

calculating.(2) In the case of walls with doors and / or windows openings, fully serviced horizontal masonry

will be considered only if the coupling beams are actually woven with piers join and relate to both

the floor and beam ties (belts) with reinforced concrete lintel in masonry (whether it is separatedfrom the floor belt).


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(3) If the conditions in (2), or if the coupling beams are RC entirely, may use a frame calculation

for determining the effects of vertical and seismic actions in piers and spandrels.

(4) If the conditions in (2) or (3) are not fulfil the walls shall be considered like independentcantilevers connected to the floor slabs (without bending stiffness) on each floor or only at the top

level.

(5) For buildings with rigid horizontally floors in situations from (3) and (4) the base seismic shearforce, calculated according to 6.3.2.1., shall be distributed to structural walls in proportion to therelative stiffness of each level.

(6) For buildings with insignificant rigid horizontal floors the base seismic shear force, calculated

according to 6.3.2.1., shall be distributed to structural walls in proportion to each correspondingmass.

(7) The base shear forces for structural walls determined by calculating with linear elastic method

can be redistributed among the walls in the same direction, provided that the overall balance is

satisfied and the shear force in any wall is not reduced / increased by more than 20 %.Redistribution is acceptable only for structures that - constitutive law of the masonry is linear-

rectangular with limited ductility (Figures 4.3b and 4.3c of the Code)

(8) In case of walls with composed section (I, T, L) vertical sliding force in the section betweenthe web and flange (Lv,et) is calculated for a level with the relationship:

,= (6.4)Where notations are: M = Minf- Msupwith:

-Minf- the bending moment in the design stage on the bottom section;-Msup- idem, in the section at the bottom of the upper floor;

Sz- area static moment of the flange according to the wall section CG;

Iz- moment of inertia of the section of the wall.

To calculate Sz and Iz is considered that the masonry wall is composed only from masonry

(neglecting confinement elements if any).

(9) The wall elastic stiffness is calculated as P 100-1, art.8.4.1.(10) The sectional efforts of masonry RC or steel framed walls will be determined according to

P100-1, art. 10.5.3.1.1.

(11) To determine the sectional efforts (N, M, and V) in the structural elements and to determine

its lateral displacements can be used any computer program based on recognized principles ofstructural mechanics.

6.3.2.3. Calculation of lateral displacements in the plane of the wall(1) Under the action of horizontal loads in the median plane, the deformations and the lateral

displacements of the structural masonry walls made of masonry, dependent of constitutive law-

:a. In the case of masonry with the law - linear-rectangular with parameters mu>m1 in

seismic calculation will consider the following types of displacements:

i. elastic deformations for specific deformations m1

ii. inelastic deformations for specific deformations m1


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6.4. Computation of the masonry walls perpendicular to the load(1) Loads categories perpendicular to the wall are given in 6.2.1. (2).

(2) Design values for each category of loads shall be taken of specific technical regulations:a. Earthquake loading action as P 100-1, chapter 8 and 10.

b. Loads from wind pressure data according to CR 1-1-4.

c.

Exploitation loads (pushing of people in crowded spaces) according to EN 1991-1-1/NA.d. Other exploitation charges (furniture or equipment / overhead supplies) according to thedesign theme and applicable technical regulations, but at least equal to the value of

ETAG003.

(3) The design values of the perpendicular load from:a. the earth pressure onto the basement outline walls;

b. lateral forces (push) transmitted from other parts of the structure (vaults, arches or roofs);

Will be determined from the calculation of the whole building.

6.4.1. Models and calculation methods for perpendicular loading

(1) In order to calculate the moments from the perpendicular loads to the plane, for all groups ofloads, the walls are modeled according to boundary supports, such as:

a. Simply supported beam when the walls leaning on two sides, up and down on the floors

(with free vertical sides) ;

b. Anisotropic elastic plates leaned up and down on that floor slab and side stiffening walls(perpendicular to the plane of the wall considered).

(2) For masonry panels without doors or windows openings, the design bending moments caused

by forces perpendicular to the wall (MSxd1iMSxd2) will be calculated taking into account:a. fixing conditions on the sides of the brick panel;

b. composition of the wall in section;

c. masonry anisotropy expressed by tensile strength ratio of bending perpendicular to the

wall ( = fxk1/fxk2)(3) Fixing the sides of the walls will be achieved by:

a. link with intermediate floors or roof;

b. weave with perpendicular walls;(4) The modeling of the boundary supports for the masonry panels will be considered as follows:

a. complete continuity :

i. vertical side - when the wall is tissue with a transverse wall which has at least thesame thickness, and vertical load forces ;

ii. on the horizontal, for the current floor when the wall abuts a RC slab ;

b. partial continuity :

i. when the wall is tissue with a transverse wall which has less thickness (but no morethan 50%) or with a wall without vertical load forces or less thickness;

ii.

on the horizontal, for the current floor when the wall abuts a RC slab wit

insignificant stiffness

c. simple bearing (support):i. on the horizontal, if the floor is not supported on the wall (the wall is erected after

slab formwork removal) or on the capillary breaking layer

ii. to the last level, when special constructive measures are not provided for bindingRC slab with the masonry wall;


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(5) In the case of double pane walls with an interior hollow (eg ventilated facades, facades filler

panels), it is considered complete continuity even if only one layer is continuous tissue to support,

provided the wall to have connections between layers. In all other cases will be considered partialcontinuity.

(6) In the case of underground walls, to calculate the pressure of the earth, the wall will be

considered to be articulated or embedded in the foundation, depending on the adopted designresolution, and the partial continuity of the basement floor.(7) For the walls supported only at the top and bottom (free on the sides - near the door openings,

for example), the break plane being parallel to the alignment joints (Fig. 4.2a), and the bending

moment will be determined by the relation

= (6.5)The notations are as follows:

= 0.125 (1/8) simple supports for both ends (the maximum bending moment in the

mid- height of the wall);

= 0.083 (1/12) for the case supports with complete continuity at both ends (maximum

moment is supports);

WEdis the design load perpendicular to the wall uniform distributed;hwis the clear height of the wall.

(8) For walls supported on three or four sides, bending moments will be determined as follows:

a. To a plane parallel to the joints breaking alignment in the direction fxk1 (Fig. 4.2a), the

bending moment per unit length of the wall is calculated by the formula:

= (6.6a)b. For the plan breaking joints perpendicular alignment in the direction fxk2 (Fig. 4.2b.)

bending moment per unit height of the wall is calculated using:

= (6.6b)The notations are as follows:

is a coefficient that takes into account thei. masonry anisotropy (strength ratio = fxd1/fxd2 fxk1/fxk2);

ii. fixing conditions on the sides of the wall;iii. the ratio between the height and length of the wall ;

lwis the length of the wall between supports;

WEdDesign is the side loading per unit area;

Figure 6.5 Notation for calculating moments MEd2and MEd1


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(9) The constant values for the ratio used for this code is given in table 6.1.

Values in the table are valid only if the following conditions are met:

a. masonry is made with all vertical joints filled with mortarb. Wall thickness is 350 mm.

(10) For masonry with vertical joints of tongue and groove and fxd2, fxd1 strengths will be

declared from shape profiles.(11) If, for a particular type of masonry fxd1/fxd2strengths ratio determined by testing differentvalues in Table 6.1, the bending moments will be calculated according to Appendix E to SR EN

01.01.1996.

(12 ) For panels with thickness > 350 mm bending moments shall be calculated using the theoryof breaking lines for anisotropic elastic plates (with different elastic moduli of the two directions).

(13) For the calculation of bending moments, in panels with openings these will be divided into

fragments that can be calculated with the rules of full panels (Fig. 6.6).

Figure 6.6. Models for calculating the forces perpendicular to hollow walls

coefficient values for the calculation of bending moments normal to the plane of the wall

Table 6.1.


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6.5. Slab computation

(1) The slab floors for masonry walls buildings be designed to:a. Vertical load in all load groups;

b. Horizontal seismic load acting on the center plane of the floor.(2) The design of RC slabs to vertical loads shall be made according to EN 1992-1-1.

(3) Design of wooden floors for vertical loads will be as technical regulations, in working

(4) The design of reinforced concrete slabs for horizontal seismic load aims to ensure resilienceand rigidity needed for the floor to be considered rigid horizontal diaphragm and ensuring

retransmission effort between the structural walls.

6.5.1. The calculation model

(1) In buildings with simple shapes in plan (approximately rectangular), the calculation of sectionalefforts due to horizontal seismic forces will be made in accordance with 6.5.2 considering the floorlike a continuous beam, supported on the structural walls.

(2) Designing slabs with complicate composition and/or structures with irregularities on vertical

or in the plan will use models and calculation methods able to reveal their behavior to vertical

loads and earthquake.(3) Designing mixed slabs made of cast or precast concrete beams reinforced / prestressed and

ceramic bodies or concrete filling, with proper reinforce finishing, will be made only on the basis

of the provisions of specific technical regulations in force.

6.5.2. The calculation method(1) In the requirements of 6.5.1 (1) the total force calculation for a slab is equal to the seismic forceapplied to that level. In a simplified way, this force shall be deemed distributed linearly along the

length of the floor, the result of passing through the center of stiffness of the structure at that level.

In this case, the extreme values of the forcepmax/minacting on the floor will be calculated using:

/= 1 6

(6. 7)


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Where notations are:

Sniv- seismic design force applied to the respectively floor;

dRGthe distance between the center of gravity of the floor (CG ) and the center of rigidity of thestructure (CR) ;

L - size of the building perpendicular to calculation direction .

(2) Reaction of the supported section of the slab on a structural wall (Fi) is simplify calculated,with (6.8) considering that it is proportional to the sum of all shear strength of wall piers (VRdi)

= (6.8)Where VRis the shear strength of the building in the direction of computing.

(3) In the assumptions (1) and (2) the bending moment M and shear force T will be determinedfrom the slab equilibrium conditions under the influence of the loadpand reaction forcesFi.

Figure 6.7. Calculation of sectional design efforts in slabs due to horizontal loads(a) the loading slab plan (b) Sectional efforts in the slab

(4) In buildings with structural regularity in elevation, the checking is done only at the top level,where Snivhas the maximum value.

6.6. Calculation of the design strength of the wall in masonry

6.6.1. Calculation Conditions

6.6.1.1. Calculation model.(1) The calculation for determining the design strength for masonry walls due to effects of all load

groups must take into account:

a. geometry of the wall;b. boundary conditions on the contour of the wall;


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c. conditions for implementing the load;

d. strength and deformability properties of masonry;

e. probable execution conditions;(2) The design strength for structural walls will lead to:

a. the sectional efforts produced by the forces acting on the median plane of the wall:

i.

axial force (NRd);ii. bending moment (MRd);iii. shear (VRd);

iv. vertical sliding force for composed sections walls (VLhd);

b. efforts sectional produced by forces acting perpendicular to the median plane of the wall:i. bending moment in the plane parallel to the horizontal beds (MRxd1);

ii. bending moment in the plane perpendicular to the horizontal beds (MRxd2);

6.6.1.2. Assumptions for calculation(1) The design strength of the masonry walls are determined in relation to the ultimate limit state

(ULS), and special cases mentioned in the text, in relation to the serviceability limit state (SLS).

(2) The conditions referred to in 6.1.(2) calculation of the strength and deformations forunreinforced masonry walls will be made based on the following assumptions:

a. assuming the Bernoulli hypothesis of plane sections;

b. tensile strength of masonry perpendicular to the horizontal beds is zero;

c. the distribution of stresses in the compression zone of the wall is simply considered,constant or linear by:

i. stress type;

ii. masonry constitutive law form;iii.

limit state calculation;

6.6.1.3. Geometrical characteristics of the horizontal section of the wall(1) Cross-sectional dimensions of structural masonry walls used for calculating dimensions are

"net" (Wall unplastered) satisfying:

a. the minimum length and thickness of the P 100-1, chapter 8;

b. conditions of maximum length blocks are in 6.3.1 . (3);(2) Thickness of masonry panels framed in frames and non-structural walls will be determined by

calculating the strength requests according to P100-1, chapter 10 and other essential requirements.

(3) The walls with maximum openings size of 0.2 lwwill be considered in computations withoutopenings (solid) walls, where the opening is located in the middle third of the height level and if

the piers of masonry wall is at least 20 % higher than the minimum P100-1 data.

(4) The openings in the flanges with the maximum h/4 will be neglected and voids with size > h/4

will be considered the flange edges.(5) Confined masonry walls (ZC) and reinforced core masonry (ZIA) geometrical characteristics

of the horizontal section will be calculated as follows:

a. For burnt clay masonry elements in Group 1 which specifies the maximum allowable

deflection is mu3,5,, the area will turn into concrete masonry equivalent area by

multiplying by the ratio n between the concrete design compressive strength (fcd) and

masonry design compressive strength of (fd) .

= (6.9)


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Under these conditions, the characteristics section 'ideal' wall will be calculated by the

following relations:

i. The ideal areaAi= Azid+ (n-1) Abeton (6.10a)ii. The ideal moment of inertiaIi= Izid+ nIbeton (6.10b)

b. Burnt clay masonry elements of group 2 and 2S and AAC (BCA) and any other masonry

which specifies maximum permissible deformation is mu=2 horizontal sectional area forcalculation will be identical to the effective area of the wall (which include concreteelements).

6.6.2. Axial design compressive strength of structural walls

(1) The design strength to axial compression for structural masonry walls are determined for alldesign situations.

(2) For masonry walls, unreinforced or reinforced, stressed to axial compression, regardless of the

type for masonry and mortar, masonry maximum specific deformation (shortening) will be

max= 2.

6.6.2.1. Axial compressive strength of unreinforced masonry walls (ZNA)(1) The design strength to axial compression of any ZNA wall section, will be determined by the

relation

NRd= i(m)Afd (6.11)Where notations are:

i(m)- strength reduction constant taking into account the effects of wall slenderness andeccentricity of application of the load;

A- cross sectional area of the wall;

fd- design compressive strength of masonry.

(2) In the case of masonry walls with rectangular cross section, the design axial compressive

strength for unit length of the wall NRd(l) is calculated by the relationshipNRd(l)= i(m)tfd (6.11a)

Where tis the thickness of the wall.

6.6.2.1.1. Determination of strength reduction coefficients i and m

(1) The strength reduction constant in the walls edges (i) - above and below - will be determinedby the relationship:

= 1 2 (6.12)Where notations are:

t- Thickness of the wall;

ei- for calculating the eccentricity in relation to the median plane of the wall, the checkingsection which is calculated by the formula:

= 0.05 (6.13)With notations:

ei0- vertical loads eccentricity determined by the relation (6.1);

ehi- eccentricity due to the perpendicular force to the plane of the wall determined by the

relation (6.3);

ea- accidental eccentricity determined by the relations ( 6.2a ) or ( 6.2b )


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(2) For masonry made with all kinds of elements and mortar, with all bed joints filled with mortar,

reduction constant in the strength of the middle section of the wall height will be taken mvalues

corresponding to the maximum het/tdata P 100-1, art. 8.5.2.

m coefficient values to reduce the compressive strength

Table 6.2.Slenderness

ratio

(het/t)max

Masonrytype

Relative eccentricity em/t

0.05 0.10 0.15 0.20 0.25 0.30

12 ZNA 0.80 0.70 0.59 0.49 0.38 0.28

15 ZC, ZIA 0.75 0.64 0.53 0.42 0.32 0.22

emis the computational eccentricity calculated in the center region of the wall with the formula:

= (6.14)Where notations are:

hetfloor height;

ehmeccentricity due to the effect of the horizontal loads, in the middle section of theheight of the wall, calculated with (6.3).

6.6.2.2. Axial compressive strength of confined masonry walls (ZC) and reinforced core

masonry (ZIA)

(1) The axial compressive strength of confined masonry walls and reinforced core masonry will

be calculated according to 6.6.2.1 converting mixed section in an ideal section of masonry asspecified in 6.6.1.3. (4)

(2) The contribution of the piers reinforcements in the middle (core) layer (ZIA) on taking

compressive force will be ignored.

6.6.2.3. Local compressive strength under concentrated load effect

(1) For a ZNA wall with masonry elements in Group 1 local design compression strength underconcentrated loads shall be determined by the relationship:

NRd,cl=Abfd (6.15)

is an increasing constant for concentrated loads;

1.00 = 1 0.30 (1.51.1 ) (6.16)

With notations:

a1- Distance from the wall to the nearest edge of the area that is transmitted load;

Ab0.45 Aefarea that the load is appliedHo- wall height from the base to the level to which the concentrated load is applied;Aef- effective loaded area;

Aef= t Lef

Where


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- . is the effective length of taking the load measured at half height of the wallresulting from downloading vertical force at an angle of 60 with the horizontal (see Fig.

6.2 ) .

- tis the thickness of the wall

The values of equation (6.16) will be limited as follows:

a. max= 1.25 if

= 0b. max= 1.50 if

= 1.0

c. For 0.00 < 1.0values are obtained by linear interpolation(2) Applying eccentricity of the concentrated load comparing to the median plane of the wall, willbe t/4.

(3) In cases where the effects of concentrated forces are overlapped (Fig. 6.2) the middle height

section of the wall height will be checked with (6.15).

(4) In the case of masonry elements of groups 2 and 2B and the AAC (BCA), the concentratedload must be applied by using of a rigid material to allow for vertical charge distribution at an

angle of 30 to the vertical, for ensuring the achievement of a length L efload as shown in fig. 6.2a.

In the case of burnt clay masonry elements from Group 1 the concentrated force can be applieddirectly to masonry.

(5) If the concentrated force is applied according to (4) the compressive stress under concentrated

force (cl) must not exceed 1.5fd for masonry elements of groups 1 and 2 and fd for masonryelements of group 2B and AAC (BCA).

6.6.3. The design strength due to compression and bending of structural walls

6.6.3.1. Calculation Conditions(1) General assumptions for determining the design strength to axial force and bending moment in

the plane of unreinforced and reinforced masonry wall are given in the article. 6.6.1.2 (2) with the

specifications of:a. Article 6.6.3.2. for unreinforced masonry walls (ZNA)

b. Article 6.6.3.3. for confined masonry walls (ZC and ZC+AR)

c. Article 6.6.3.4. reinforced core masonry (ZIA)

(2) In the case of reinforced masonry the unitary stress-strain relationship () for reinforcement

will be taken according to EN 1992-1-1.

(3) In the case of walls with complex cross-sectional shape (I, L, T) the design strength to axial

force and bending moment in the plane of the wall shall be determined with the calculation sectionwith the flange lengths determined due to art.6.3.1 (3);

(4) The intersections of the web and flanges of walls with complex form (I, L, T) but also for weak

sections by vertical slits will be checked for vertical sliding efforts calculated according to 6.8.1.1.

(2). If the connection between the web and flanges with deep slits are higher than the limits givenin Table 7.2 the connection between the web and flange is neglected.

(5) Verification of (4) is not required if, in the slits, the link between the web and flanges of the

wall are made following the conditions:a. unreinforced masonry (ZNA)

i. the walls in the both directions are made simultaneously (fully woven);


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ii. connecting section between the walls is not impaired by vertical slits ;

iii. at the corners, intersections and branches minimum reinforcement areas set in P

100-1 are provided in horizontal bed joints and in this Codeb. confined masonry, with or without reinforcement in horizontal bed joints (ZC/ZC+AR):

i. strips represents 50 % of the area of contact between masonry and concrete;

ii.

connecting section between the walls is not impaired by vertical slits ;iii. at the corners, intersections and branches minimum reinforcement areas set in P100-1 are provided in horizontal bed joints and in this Code

6.6.3.2. The design strength due to compression and bending of unreinforced masonry

structural walls (ZNA)(1) The design strength to bending (MRd) associated to the design axial force (NEd), applied to the

median plane of a wall, is calculated considering that compression efforts block is rectangular with

0.85fdvalue.(2) For the conditions of (1) to a horizontal wall composed section (I, T, L) the design bending

strength (MRd) is calculated as follows:

a.

Determine the area of compression of the wall= . (6.17)b. Determineyzcdistance from center of gravity of the wall (G) to the center of gravity for

compression zone. (G1)

c. Determine the design bending strength (MRd) with the relation =

Figure 6.8. Calculation of the design bending strength (MRd) for a given axial force

Note. In the fig. 6.8, lcis the actual length of the compression zone corresponding to masonry

constitutive law .

Figure 6.9. The design bending strength calculation for a composed section


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(3) If a rectangular wall, lwlength and thickness trelations (6.17) and (6.18) become:

The depth of compression

= . (6.19)The design bending moment

=

=

(6.20)

(4) With the notations:

= = Equations (6.19) and (6.20) are written in the form

= 1.175 = 1.175 (6.19a)= 11.175 (6.20a)

(5) If the axial force is applied eccentrically to the plane of the wall, the depth of compression will

be determined by the relationship:

= . (6.19b)Where i(m)constant shall be determined as specified in 6.6.2.1.1

(5) In the case of unreinforced masonry walls for which the strength verification for earthquake

design for SLS the design bending resistance (MRd) associated to the design axial force (NEd) willbe determined as (2) and (3) but with the limitation of the area in which the subject develops tensile

under condition:

yzc< 1.2rsc (6.21)Where rscis the distance from the gravity center of the horizontal section of the wall up to the

central kernel which is on the same side with compressed fiber.

(6) If a rectangular wall length lw, the relation (6.21) followsMRd= 0.2 lwNEd

6.6.3.3. Compressive and flexural strength of confined masonry walls

(1) The calculation of design strength to bending in the plane of the wall (MRd) associated to designaxial force for seismic loads (NEd) for confined masonry walls (ZC, ZC+AR), built with burnt clay

masonry elements of groups 1, 2 and 2S, and AAC (BCA) have the following assumptions:

a. Neglect :

i. The tensile strength of the concrete column tie (belt) subjected to stretching ofthe wall;

ii. tensile strength of masonry mortar in horizontal bed joints ;

iii. section of intermediary RC column ties (belts) (if any);

iv. concrete compressive strength of compressed RC column tie (belt) for masonry

with ultimate specific strain mu= 2.0 (the RC column tie aria is included inthe area of masonry)

b. It takes into account the strength of confinement vertical elements

i. The compressive strength of the concrete in the compressed RC column tie it take

into account for masonry with ultimate specific strain of mu= 3.5 (area becomes

the area of concrete masonry equivalent to the relation (6.10 ));

ii. The reinforcement strength of both column ties from the extremities.


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(2) The design bending strength (MRd) associated to the design axial force (NEd) for confined

masonry walls of certain shape, will be calculated by summing the flexural design strength ofreinforced ideal masonry section MRd(zna,i)with the corresponding design bending strength from

the edges column ties reinforcementMRd(As) calculated in accordance with (5) (7).

MRd= MRd(zna,i)+MRd(As) (6.23)(3) The area of the ideal unreinforced masonry section is calculated based on the ultimate specificstrain of masonry (mu) as 6.6.1.3. (4).

(4) The compressed area of ideal unreinforced masonry (Azci) is calculated with (6.17).

(5) The design bending moment of unreinforced masonry ideal section is calculated by therelationship

,= (6.24)Where yzci is the distance from the center of gravity of the wall to the center of gravity of

compression in ideal masonry section(6) The design bending strength of reinforcement from column ties MRd(As) is calculated by the

relationship

= (6.25)Where notations are:ls- the distance between the centers of gravity of the two column belts from the extremities;

Asthe smallest of areas for reinforcement of the two column belts;

fyddesign strength of the reinforcement of the two column belts.

6.6.3.4. Compressive and flexural strength of reinforced core masonry walls (ZIA)

(1) Design strength to bending (MRd) in the plane of the wall associated with the design axial force(NEd), for building with reinforced core masonry (ZIA) is calculated using general assumptions in

6.6.1.2. (2) and the following specific assumptions:

a.

parallel layers of masonry and concrete work together until the final stage correspondingto the weakest of materials;

b. unitary compressive efforts have value of 0.85fd and are uniformly distributed over a zone

with a depth xconv=0.80xwhere xis the distance from the most compressed fiber to the

neutral axis of the horizontal wall section;

c. the ultimate specific stain of masonry (mu) and concrete (cu) will be limited as follows:

i. masonry elements from burnt clay in group 1: cu mu 3.5

ii. For masonry elements made of burnt clay in Groups 2 and 2S and AAC (BCA)

elements: cu mu 2.0d. The central core reinforcement is uniformly distributed along the wall (As in mm2 / m).

(2) The assumptions referred to in (1) design bending strength (MRd) in the plane of the wall, the

associated design axial force (NEd), is calculated by summing the flexural design strength ofunreinforced masonry section with reinforce design strength from median layer:

MRd(ZIA)=MRd(zna,i)+MRd(as) (6.26)(3) Equivalent thickness of unreinforced masonry ideal section is calculated using:

tech=2tz+ntm (6.27)

Where notations are:tz - the thickness of the outer layer of masonry ;

tm- median thickness of mortar / concrete ( grout ) ;


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n - equivalence constant is taken under 6.6.1.3 . (4)

(4) The design strength of unreinforced masonry ideal section MRd(zna,i) is calculated accordingart.6.6.3.3 .

(5) The design resistance of reinforcements distributedMRd(as), is calculated using:

= 0.25 (6.28)Where notations are:as -is the area per unit length of the core layer reinforcement

fyd-is the reinforcement design strength of the core layer

6.6.4. Shear design strength of structural walls

(1) The shear design strength of structural masonry walls (VRd) for all masonry types (ZNA, ZC

and ZIA) will be equal to the lesser of the amounts calculated for:a. failure by sliding the horizontal bed joints (VRd l)

b. failure in the sloping section from main tensile efforts along the compressed diagonal

(VRd i)(2) For the walls in the form of I, L, T the shear design strength is taken equal to the shear design

strength of the web (rectangular section).

6.6.4.1. Shear strength of unreinforced masonry walls(1) The design shear strength of reinforced masonry structural walls will be taken equal to the

lesser of the design resistance valuesa. Slip in a horizontal bed joints, calculated with the relations (6.29) and (6.29b)

b. In the inclined section, calculated with (6.34).

6.6.4.1.1. Slip strength in horizontal bed joints(1) The design shear strength of rectangular masonry walls shall be calculated considering the

design unitary slip stress in horizontal pointfvd,l, it is evenly distributed along the length of the wallof compression (lc).

(2) The constructive reinforcement arranged in beam belts will not be considered for calculation

of shear strength.

6.6.4.1.1.1. Slip strengths in horizontal bed joints for no seismic charges

(1) The design strengths to sliding in a horizontal sense V Rdfor unreinforced masonry walls in

case of no seismic requests will be calculated by the relation:VRd,l= fvd,ltlc (6.29a)

Where notations are:fvd,l-design unitary slip strength in horizontal masonry bed joint set with (4.6A)t -thickness of the wall web;

lccompression length of the wall web.


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(2) Length of compression region (lc) is calculated from sectional design requests (bending

moment and axial force-M-N) finding that tensile stresses are distributed linearly on the

compression zone (fig.6.10a) relationship:

= 1.5 3 (6.30)

Figura.6.10. the distribution tangential unitary strengths(a) Non-seismic requests (b) seismic demand (by reversing the action)

Using the relative intensity of unitary compression effort by relation (6.30) can be written insimplified form

lc= 1.75sdlw (6.30a)Wheresdis defined in 6.6.3.2. (4)

(3) The unitary average compressive effort ( d) used for determining the design unitary strengths(fvd,l), is calculated considering the design vertical load of grouping that load, NSd or NEd is

uniformly distributed on the compressed wall (lc) determined by the relation (6.30).

6.6.4.1.1.2. The slip strengths into the horizontal bed joint due to seismic loads(1) If the request due to seismic action the grip effect is canceled fvk0onto loose areas/cracked the

previous cycle of the seismic force (lw-lc) - Fig. 6.10b.(2) The sliding design strengths in a horizontal sense VRd for unreinforced masonry walls due to

seismic loads, shall be calculated by the relation

,= 0.40=

0.40 (6.31)


lcis the length of compression determined by the relation (6.30) or (6.30)

lad- is the length that is active adherence determined by the relationship

= 2 =3.5 1 (6.32)From (6.32) it follows that if the case of alternating seismic actions the grip lad length remainsactive only if the condition is satisfied

. (6.33)

6.6.4.1.2. The release strength in the inclined section(1) The design strength to failure on the sloping section of unreinforced masonry wall construction

is calculated by the relationship

, = , (6.34)


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fvd,i is the design value of the strength for a failure on inclined sections calculated with

relations (4.4), and (4.6B)

bis a correction factor that accounts for the masonry panel aspect ratio values:

- b = 1.5 for h/lw1.5

- b = 1.0 for h/lw< 1.0- b = h/lwfor 1.0 h/lw< 1.5

Masonry panel height shall be taken:- h = htotfor walls working as cantilevers

- h = hspfor piers who can be double embedded in the extremities

6.6.4.2. Shear strength of confined masonry walls6.6.4.2.1. Design strength to horizontal slip

(1) The design strength to horizontal slip into the horizontal bed joint of confined masonry walls,

VRdwill be calculated by adding the following values:

a.

The design strength to horizontal slip in masonry panel corrected to take into accountthe effect of confinement elements (VRd1*);

b. The design shear strength of corresponding design of the reinforcement from thecompressed RC column tie at the wall edges (VRd2)

c. The design shear strength of the compressed RC column tie (VRsc).

VRd= VRd1*+VRd2+VRsc (6.35)

(2) The design strength to horizontal slip of the unreinforced masonry (VRd1*) will take:

a. For non-seismically requests a value VRd1 calculated with ( 6.29 )

b. For seismic applications will take into account the effect of confinement and cooperationbetween the elements and masonry panel will use the relationship

, = 0.40 (6.35a)Where

= 0.80 (6.35b)Where hpanand lpanare confined masonry panel sizes.

VEdvalue of equation (6.35b) is limited according to the relationVEd lpantfvd0 (6.35c)

Wherefvd0 is the design unitary strength to slip in horizontal bed joints under a zero unitary

compression strength (shear adhesion).

(3) The design shear strength of vertical reinforcement from the compressed RC column tieunder the mandrel effect (VRd2) is calculated using:

VRd2= cAascfyd (6.36)Where notations are:

Aasc- reinforcement area from the compressed RC column tie;fyddesign strength of the RC column tie reinforcement

c reinforcement participation factor by the mandrel effect

The cvalues are from 6.3 table.


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Factor cvalues for shear strength calculation due to vertical reinforcement

from confine column tie - Table 6.3

Stirrups Vertical reinforcement in column ties (belts)

SteelStrengths category 1 Strengths category 2

1st

strengthscategory

0.250 0.200 0.150 0.200 0.150 0.100

0.400 0.350 0.250 0.300 0.250 0.200

0.400 0.300

2nd

strengthscategory

Not used

0.250 0.200 0.150

0.400 0.350 0.250

0.400

(4) The design shear strength of the concrete of compressed column tie is calculated from therelationship:

VRsc= Abscfcvd (6.37)


Absc- the concrete area of the compressed RC column tiefcvd - unitary design shear strength of concrete in compressed RC column tie.

6.6.4.2.2. The release strength in the inclined section(1) The design strength to failure on the sloping section of confined masonry walls, VRd,i, is

calculated by adding the following values:a. The design strength to failure on sloping section of simple masonry panel corrected to take

into account the effect of confinement elements (VRdi*)

b. The design shear strength of corresponding design of the reinforcement from the

compressed RC column tie at the wall edges (VRd2)c. The design shear strength of the compressed RC column tie (VRsc).

VRd= VRdi*+ VRd2+VRsc (6.38)

(2) The design strength to horizontal slip of the unreinforced masonry (VRd1*) will take:

a. For non-seismically requests a value VRdi calculated with (6.34) with fvd,i strengths

calculated with relations ( 4.4) and ( 4.6A )

b. For seismic applications will use relation ( 6.34 ) and will take into account the effect of

cooperation between elements of confinement and masonry panel replacing the relations

(4.4a ) and (4.4b ) the unitary effort 0d with 0d* value calculated with relationship

=

(6.39)

TheNEd*is given by (6.35b)(3) VRd2and VRscstrengths will be calculated in accordance with 6.6.4.2.1. (3), and 6.6.4.2.1 (4).

6.6.4.3. Shear strength of confined masonry walls with horizontal bed joints reinforcement

(ZC+AR)

(1) The design shear strength of structural walls with confined masonry and reinforced inhorizontal bed joints is calculated by summing the shear strength of confined masonry


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(VRd1*+VRd2+VRsc) - determined from 6.6.4.3 relations and the design strength given by horizontal

reinforcement from bed joints resistance time of reinforcement design of horizontal joints (VRd3).

VRd= VRd1+ VRd2+ VRsc+ VRd3 (6.40)(2) The design strength of reinforcement in horizontal bed joints (VRd3) is calculated, where the

total wall height (htot) wall length (lw) by the relationship:

= 0.80 (6.41)Where notations are:lwlength of the wall ;

Asw- purpose area of horizontal reinforcement (for taking shear force);s -the vertical distance between two successive rows of reinforcement Asw;

fysd- design strength of reinforcement in horizontal joints.

If the total wall height (htot) < length of the wall (lw) in (6.41) will be replaced the lwwith htot

(3) A part of not more than 50 % of the reinforcement of the slabs beam ties may be added to the

reinforcement from the horizontal bed joints intersected by a fissure at 45 (Asw).

Figure 6.11 Design strength of masonry with reinforcement in horizontal bed joints

6.6.4.4. Shear strength of masonry walls with reinforced core(1) The design shear strength for masonry with reinforced central core - VRd (ZIA)is determined by

summing the design shear strength of the three constituent materials:

VRd (ZIA)= VRdz+ VRdb+ VRda (6.42)

Where notations are:VRdzdesign shear strength of unreinforced masonry;

VRdbdesign shear strength of the core layer of concrete or grout;

VRdadesign shear strength of the horizontal reinforcement in the core layer.(2) Length of compressed masonry with reinforced central core wall and the amount of unitary

compression strength in the wall is determined based on the assumptions of 6.6.4.4.

(3) The design shear strength of the masonry VRdzis determined according to 6.6.4. (1)


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(4) The design shear strengths of concrete layer (VRdb) and horizontal reinforcement (VRda) shall be

calculated according to CR 2-1-1.1.

6.6.4.5. The strength at vertical sliding force associated with bending of the wall

(1) The design strength at vertical sliding between the web and flanges for the walls with (I, L, T)sections and / or weakened section of the slits is calculated on the vertical height of the floor (VLhd)assuming that the tensile stresses shear are uniformly distributed over the height of the floor, by

the relationship:

= (6.43)Where notations are:

hetfloor height;

tLwall thickness in the section in which the strength of the wall is calculated;fvk0characteristic shear strength of masonry under compressive stress equal to zero;

Msafety factor for the material group established under load.

6.6.4.6. The design strength of spandrels (coupling beams)(1) The design shear strength of reinforced concrete coupling beams (spandrels) Vrcwill determine

by relationship

= . + (6.44)

Where notations are:Mcap

susandMcapjosare design bending strengths values at the ends of the coupling beam,

top and bottom, calculated using the design strength of the reinforcement;

Lgcis the length of the coupling beam calculation (between piers faces);

Vgis the maximum shear for vertical loads from seismic load grouping;(2) For the calculation of design strength to bending (Mcap) in equation (6.44) will take account of

the reinforcement bars arranged in the slab connected with the concrete coupling beam, on a strip

having the width equal with six times the thickness of the slab for each part.

6.6.5. The design strength of the walls subjected to bending perpendicular to the median

plane(1) For the calculation of design strength to bending perpendicular to the masonry wall (MRxd1and

MRxd2) for all walls (structural, non-structural panels and framed masonry), use design tensile

strength of bending perpendicular plan masonryfxd1, fxd2.(2) For the confined masonry walls with horizontal reinforcement in bed joints, for the calculation

of MRxd2 (the plane perpendicular to the horizontal joints breaking) will take account of thehorizontal reinforcement in bed joints are properly anchored in the edge RC column ties. .

(3) Values MRxd1and MRxd2 (in Nmm) is calculated for a wall strip width of 1,000 mm, withrelations:

MRxd1= Ww(fxd1+dp) (6.45a)

MRxd2 = Wwfxd2 (6.45b)Where notations are:


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=

Wall strength modulus (mm3);

dp- design value of the compression unitary effort in midway up the wall

t- Wall thickness in mm.

6.6.6. The design strength of masonry panels framed in frames

(1) Shall be determined in accordance with P 100-1, chapter 10

6.7. Calculation of the design strength of the floors(1) Strength of concrete slabs to vertical loads shall be calculated according to EN 1992-1-1.

(2) Strengths of wooden floors to vertical loads shall be calculated in accordance with applicabletechnical regulations in force.

6.8. Checking of safety for buildings with masonry walls

(1) Check the safety of buildings with structural masonry walls will be made by calculation, except"simple buildings" designed according to the P 100-1, cap.8.9.

(2) Safety verification of buildings with structural masonry walls shall be in accordance with:

a.

Ultimate limit states for strength and stability (ULS);b. Serviceability limit state (SLS).

6.8.1. Checking of the strength requirement

6.8.1.1. Checking of the strength requirement for loads applications in the plane of the wall(1) For loads of fundamental group situation persistent / transient design as defined in CR 0,

masonry walls will be designed to have, in all sections, design strengths for sectional efforts (NRd,

MRd, VRd) higher than sectional design efforts (NSd, MSd, VSd) resulting from the most unfavorablesituations.

(2) For the seismic group of loads the strength verification requirement will be as P100-1

art.8.6.1.1 and art. 10.9.7 (for non-structural walls and walls framed in frames).

6.8.1.2. Checking of the strength requirement for loads perpendicular to the plane

(1) The requirement of strengths to forces perpendicular to the plane, for all walls is satisfied if

there are relations:MRxd1MSxd1 (6.46a)

MRxd2MSxd2 (6.46b)

Where notations are: MSxd1 and MSxd2 are design bending moments due to forces perpendicular to the plan

established in accordance with 6.4.

MRxd1andMRxd2are design are resistances to bending perpendicular to the wall of masonrydetermined according to 6.6.6.

(2) If the load perpendicular to the action plan derived from seismic design bending moments willMExd1andMExd2values determined according P100-1, chapter 10 and art.6.4.1.din this Code.

6.8.1.3. Checking the strengths requirement for floors

(1) Check the strength to vertical load requirement will be made according to specific technical

regulations for each building material (concrete - EN 1992-1-1 and wood - NP 005).


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(2) For the horizontal earthquake loads strengths requirement will be considered satisfied if the

size and composition of the design, ensure the floors in the elastic behavior associated demands

resilience of structural walls in the final stage.

6.8.2. Checking stiffness requirements(1) Requirement of rigid structural masonry walls buildings shall be considered satisfied if thebuilding level relative displacements drunder the action of grouping seismic loads, fall within the

limits set in P 100-1.

(2) The requirement for load floors stiffness of the fundamental group and the group accidentinvolves:

a. The vertical deformation limit values laid down by specific regulations by:

i. building material (concrete or wood);

ii. building floor position (current floor, floor coverings);iii. partition walls supported onto slabs characteristics ;

iv. type of applied finishes;

b.

limit / avoid vibration for slabs:i.

Reinforced concrete slabs with large openings in buildings where occur activities

may cause vibration (gyms, dance halls, etc. );

ii. Wood floors in all categories of buildings.

(3) Verification satisfy the requirement for rigidity of slabs is as specific technical regulations for

materials.

6.8.3. Checking the stability requirements

(1) The requirement of structural stability of buildings with masonry walls shall be considered

satisfied if the requirements of the data structure for all construction 2.2.3 and geometricrequirements and design wall composition of Chapters 5 and 6.

(2) The requirement of stability filler panels and non-structural masonry walls shall be considered

satisfied if the relevant provisions of this Code and the design P 100-1, chapter 10.

6.8.4. Checking ductility requirements

(1) Requirements of ductility of masonry buildings with structural walls shall be consideredsatisfied if the conditions about overall structure, sizing and construction details provided in this

Code and the P 100-1.

Documents

Masonries Structures - Part II