3.predimensioning

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. Slab A 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 (this stiffened 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:

o Flexural design will ordinarily consist in selecting a slab depth which will permit to use of an economical low steel ratio and which will not allow unsightly or damaging deflections. 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. Girder A 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 mm and 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 considering architectural and rigidity criteria:

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

(

)

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

3. Column Columns 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 force which acts at the basis of the column) in the long term Service Limit State (G+0.4L+0.4S); o Ac – the necessary cross sectional area; o υd– normalized axial force which takes into account the indirect effect of the seismic action over the structure; υd =0.4(for marginal column), 0.5(for central column) (according to STAS 10107/90) ;

o fcd=20/1.5=13.33 (N/mm2) – (for concrete class C20/25) design compression strength 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

NcSLT2 for 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

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