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Preliminary design

In the case of reinforced concrete, structural elements preliminary design stage has a high

importance due to the contribution to the dead loads (the weight of the sectional elements) and to

the total mass of the construction. Pre-dimensioning depends on various conditions such as

stiffness (admissible deflection), ductility (proper sizing of structural elements so as to create

areas with sufficient seismic energy dissipation capacity of deformation in post-elastic domain or

in order to avoid soft storey mechanisms of energy dissipation), or architectural and

technological requirements.

1. SlabA slab can be defined as a shallow, reinforced-concrete structural member that is very

wide compared with its depth. Slabs are straight surface members loaded perpendicularly to their

middle plane. From functional point of view slabs are used to divide the space on the vertical

direction. If they are cast integrally with beams or girders, they may be considered the top flange

of those members and act with them as a T beam.

As a structural element, the slab has two main functions regarding the structure:

o to carry and transfer vertical loads to the linear structural members (ribs, beams, girders,columns);

o to work as a diaphragm, distributing the horizontal loads to all vertical members (thisstiffened plate effect is important in case of earthquake actions, because the structure can

still work under the seismic loads although one member fails.

A slab supported on four sides and with reinforcing steel perpendicular to all sides is

called a two-way slab. Such slabs generally are designed by empirical methods. A two-way slab

is divided into strips for design purposes.

In order to have a two-way reinforced slab, the ratio between the length and width of the

member should satisfy the following conditions:

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o Flexural design will ordinarily consist in selecting a slab depth which will permit to useof an economical low steel ratio and which will not allow unsightly or damagingdeflections. For slabs elastically fixed on perimeter, the rigidity condition is:

where

a =max (3.9, 4.5, 5.2, 5.4, 5.7) =5.7 m -is the maximum opening parallel with the short

side, a = 5.7 m

(mm);o The minimum depth from technological condition for a monolith slab is hp=50 (mm);o From the fire condition the minimum depth is hp= 90 (mm);o The condition for the slab to act as horizontal diaphragm according to P100/2006 is hp=

80 (mm);

The thickness from the above conditions will be hp = 150 mm

2. GirderA girder is defined as a linear member loaded in bending, which carries the loads from

slabs and/or secondary beams and transfers them to the columns. Also, girders carry horizontal

earthquake loads. In case of monolith structures, the girder and the slab work together, so that the

cross section of the girder is a T-section.

o From technological conditions the width of girders (bg) can be between 200 mmand 350 mm.

o From fire resistance condition b 120 mm.The width from the above conditions will be bg = 250 mm.

o In case of girders, the height hg is preliminary established consideringarchitectural and rigidity criteria:

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(rounded in addition at 0.05m), where L=5.7 m (max) is the span ofthe girder;

( )

The height from the above conditions will be hg = 500 mm.

3. ColumnColumns are linear vertical structural members in buildings carrying the loads from the

girders to the foundations. Columns primarily carry axial loads, but most columns are subjected

to moment as well as axial load.

Preliminary design for columns is mainly related to ensuring local ductility of the

element by limiting the compressive stress. Code P100-2006 recommends taking the conditions

stipulated by STAS 10107/90, which limits the axial average stress to 0.65 if additional

confinement reinforcement is provided and 0.4 in normal cases.

Imposing the ductility conditions requires the evaluation of the compressive axial force

and determining an area of the slab that distributes the load to each specific column.

The cross section of the column is determined with the following relation:

, where:

o NcSLT- the axial force which proceeds over the evaluated section (the axial forcewhich acts at the basis of the column) in the long term Service Limit State

(G+0.4L+0.4S);

o Acthe necessary cross sectional area;o dnormalized axial force which takes into account the indirect effect of the

seismic action over the structure; d =0.4(for marginal column), 0.5(for central

column) (according to STAS 10107/90) ;

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o fcd=20/1.5=13.33 (N/mm2)(for concrete class C20/25) design compressionstrength of the concrete.

Aacc=(5.4+5.7)/2*5.7=31.635 m2

(afferent area for the central column D4)

Aacm=5.7*5.4/2=15.39 m2

(afferent area for the marginal column D6)

NcSLT1

for central Column:

o at the terrace level:

o at the current floor:

o at the first floor

Nc

SLT2for Marginal Column:

o at the terrace level:

o at the current floor:

o at the first floor

The cross section of the column from the above conditions will be:

hc=bc=75 cm

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hc*bc = 0.75*0.75=0.5625 (cm2).