Metoda Simplificata de Calcul Pentru Cladiri Cu Structura Din Zidarie - Varianta 3

7/29/2019 Metoda Simplificata de Calcul Pentru Cladiri Cu Structura Din Zidarie - Varianta 3

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THIRD DESIGN SIMPLIFIED METHOD

FOR MASONRY BUILDING STRUCTURES

1. ESTABLISHING THE STIFFNESS AND STRENGTHCAPACITIES FOR INTERNAL OR EXTERNAL

MASONRY WALLS

The infill panels, the piers or masonry structural walls increase the stiffness and

strength capacities for the entire structural system.

During the earthquakes the masonry walls (including infill panels) suffer a lot of

damages, starting with fissures, cracks, expulsions and ending with local or generalcollapse.

Taking into account the shape of the building we shall make the general

appreciation separately for each principal resistance direction.

Figure 1Exterior masonry walls (infill panels)

RC Column RC ColumnRC Column

RC Beamsor Floor

Masonry pier Masonry pier

hw

hw

lw

hl

hl


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Taking into consideration the period of the design and erection for these masonry

walls, we may accept that:

If the building is an existing building, made without design codes or withincipient rules it happened that the masonry walls to consist the firstresistance line against the earthquakes, before the frame system;

If the building is designed under the actual design codes, the connectionbetween frames and infill panels must be very wise considered to assure thatthe first resistance is represented by frames. It happens that the piers or

masonry structural walls to remain one of the first resistance line in abuilding structural system.

To consider the infill panels contribution at the entire system stiffness and strengthcapacities it is necessarily to identify the failure mechanism of these and the shear

forces according with the fissure stage. (fig.3, 4 and 5)

Figure 2Interior masonry walls (infill panels)

The masonry piers and walls having the same height but different lengths offer

different fissure stages for the same drift values. These fissures are in generallyproduced by shear forces and present inclined traces.

Considering all of these we may classify the masonry walls in function of severalparameters:

RC Column RC ColumnRC Column

RC Beamsor Floor

Masonry pier Masonry pier

hw

hw

lw

hl

hl

nte s


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The masonry walls thickness (tsw, tmw, tlw) which are usually multiple of thebrick units dimensions;

The ratio between the length and the height of the wall (l w/hw) and infunction of this ratio we may divide the masonry walls in the next categories:

Short walls or piers; Medium walls or piers;

Long walls or piers.

Figure 3

Short wall

Figure 4

Middle wall

Figure 5

Long wall

6.0

sw

sw

h

l 5.16.0 mw

mw

h

l 5.1lw

lw

h

l 6

,

swy 4

,

mwy 2

,lwy

We may calculate the level drifts (y) according with the angular level deformation(y -relative level rotation) corresponding to different type of walls with an elastic-plastic behavior.

swswyswy h ,, (1)

mwmwymwy h ,, (2)

lwlwylwy h ,, (3)

The shear forces develop in the masonry piers and walls, according with an elastic-

plastic behavior, considering that the fissures stage is produce by the principal

tension stresses or from horizontal shear stresses may be computed as:swswssw fAV , (4)

mwmwsmw fAV , (5)

lwlwslw fAV , (6)

Where:

swswsws tlA , (7)

mwmwmws tlA , (8)

lwlwlws tlA

, (9)

Fissure

y,sw

hsw

lsw

tsw

y,sw

Fissure

hmw

y,mw

Fissure

hlw

y,lw


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2. ESTABLISHING THE STIFFNESS AND STRENGTHCAPACITIES FOR INTERNAL OR EXTERNAL

EQUIVALENT MASONRY WALLS STICKS

2.1. Stiffness capacities for internal or external equivalent

masonry walls sticks

For the general structural system analyses we may implant a condensed special

model for structural walls (including piers and infill panels) consist in condensedsticks for each masonry walls types (short, medium and long).

To establish the equivalent geometrical characteristics we determine first therelative levels stiffness as:

swy

sw

swstick

V

S,

,

(10)

mwy

mw

mwstick

VS

,

,

(11)

lwy

lw

lwstick

VS

,

,

(12)

Knowing the material characteristics (Ew) starting with relative levelsstiffness we may determine the equivalent inertial moment for each type of sticks

like:

swy

sw

sw

swstickw

swstick

V

h

IE

S,

3

,

,

12

(13)

mwy

mw

mw

mwstickw

mwstick

V

h

IES

,

3

,

,

12

(14)

lwy

lw

lw

lwstickw

lwstick

V

h

IES

,

3

,

,

12

(15)

and

swyw

swswswsw

swyw

swswsws

swswyw

swswsws

swyw

swsw

swstickE

htlf

E

hfA

hE

hfA

E

hVI

,

2

,

2

,

,

3

,

,

3

,12121212

(16)

mwyw

mwmwmwmw

mwyw

mwmwmws

mwmwyw

mwmwmws

mwyw

mwmw

mwstickE

htlf

E

hfA

hE

hfA

E

hVI

,

2

,

2,

,

3,

,

3

,12121212

(17)

lwyw

lwlwlwlw

lwyw

lwlwlws

lwlwyw

lwlwlws

lwyw

lwlw

lwstickE

htlf

E

hfA

hE

hfA

E

hVI

,

2

,

2

,

,

3

,

,

3

,12121212

(18)

Where:

y,sw;

y,mw;

y,lwlevel drifts corresponding to short, medium or longwalls according with an elastic-plastic behavior;


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y,sw; y,mw; y,lw - relative angular level deformation (relative levelrotation) corresponding to short, medium or long walls

hwthe clear height of the wall; lwthe clear length of the wall;

Vsw; Vmw; Vlw - level shear forces corresponding to short, medium orlong walls according with an elastic-plastic behavior considering that

the fissures stage is produce by the principal tension stresses or fromhorizontal shear stresses;

As,sw; As,mw; As,lwshear area corresponding to short, medium or longwalls according with an elastic-plastic behavior

fwThe masonry shear or tension resistance; Sstick,sw; Sstick,mw; Sstick,lwrelative level stiffness I stick,sw; I stick,mw; I stick,lw - equivalent inertial moments for different

masonry walls type grouping in short, medium or long as equivalent

sticks; My,stick,sw; My,stick,mw; My,stick,lw - equivalent bending moments according

with an elastic-plastic behavior for different masonry walls typegrouping in short, medium or long as equivalent sticks;

2.2 Strength capacities for internal or external equivalent

masonry walls sticks

The strength capacities for the real masonry walls are represented by the shear

forces corresponding to an elastic-plastic behavior. Starting from the shear forcesvalues we may compute each levels bending moments for the condensed model:

n

i

sw

l

swstickyV

hM

1

,,2

(19)

n

i

mw

l

mwstickyV

hM

1

,,2

(19)

n

i

lw

l

lwstickyV

hM

1

,,2

(19)

The values of shear forces and bending moments are the same for both senses ofthe seismic action in the chosen direction.

The distance between the equivalent sticks ds have a value big enough to assure

that the equivalent frame work for shear and not for axial forces (recommendedaround 10 m).


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Figure 6Equivalent shear frame subsystem

ds ds

Infinite rigid beams

Short walls stick:- I- M- E

stick,sw

y,stick,sw

w

Long walls stick:- I- M- E

stick,lw

y,stick,lw

w

Middle walls stick:- I- M- E

stick,mw

y,stick,mw

w

hl

hl

hl

hl

Metoda Simplificata de Calcul Pentru Cladiri Cu Structura Din Zidarie - Varianta 3

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