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TECHNICAL UNIVERSITY OF CIVIL ENGINEERING BUCHAREST
FACULTY OF ENGINEERING IN FOREIGN LANGUAGES
Diploma Project
B+GF+5S
1 Technical report .......................................................................................................................... - 6 1.1 Building description .......................................................................................................... - 6 1.2 Architectural characteristics .............................................................................................. - 6 1.3 Structural characteristics and materials used .................................................................... - 6 1.4 Structural computational aspects ...................................................................................... - 6 1.5 Data regarding the building site ........................................................................................ - 7 2 Load evaluation .......................................................................................................................... - 8 3 Predimensioning ....................................................................................................................... - 10 3.1 Slab.................................................................................................................................. - 10 3.2 Beams .............................................................................................................................. - 10 3.2.1 Longitudinal beams ............................................................................................... - 10 3.2.2 Transversal beams ................................................................................................. - 10 3.3 Columns .......................................................................................................................... - 10 3.3.1 Column 1 - corner column ..................................................................................... - 11 3.3.2 Column 2 - marginal column ................................................................................. - 11 3.3.3 Column 3 - central column .................................................................................... - 11 4 Walls ......................................................................................................................................... - 12 5 Evaluation of the seismic loads and load combination ............................................................ - 14 5.1 Equivalent seismic force ................................................................................................. - 14 5.2 Computational model for lateral and vertical load .......................................................... - 15 5.3 Vibration modes .............................................................................................................. - 16 6 Design of rigidity to lateral forces ............................................................................................ - 20 6.1 Serviceability Limit State Check (SLS) .......................................................................... - 20 6.2 Ultimate Limit State Check (ULS) ................................................................................. - 21 7 Dimensioning of the structural elements .................................................................................. - 23 7.1 Slab.................................................................................................................................. - 23 7.1.1 General computation scheme................................................................................. - 23 7.1.2 Static computation in the elastic-range slabs reinforced on one direction ............ - 23 7.1.3 Static computation in the elastic-range slabs reinforced on two directions .......... - 24 7.1.4 Dimensioning the reinforcement ........................................................................... - 29 7.2 Beams .............................................................................................................................. - 35 7.2.1 Design of the longitudinal reinforcement .............................................................. - 35 7.2.2 Design of the transversal reinforcement of the beams .......................................... - 41 7.3 Columns .......................................................................................................................... - 46 7.3.1 Geometrical characteristics.................................................................................... - 46 7.3.2 Provisions regarding the materials used ................................................................ - 46 7.3.3 Longitudinal reinforcement provisions ................................................................. - 46 -2-
7.3.4 Longitudinal reinforcement design ........................................................................ - 46 7.3.5 Transversal reinforcement provisions ................................................................... - 47 7.3.6 Transversal reinforcement design .......................................................................... - 47 8 Structural Walls ........................................................................................................................ - 51 8.1 General considerations for the computations of the structural walls .............................. - 51 8.2 The values of the design sectional efforts in the walls ................................................... - 51 8.3 The longitudinal and transversal reinforcement.............................................................. - 52 8.4 Material provisions for structural walls .......................................................................... - 59 8.5 Geometric Exigencies ..................................................................................................... - 59 9 Foundation ................................................................................................................................ - 60 9.1 General Information ........................................................................................................ - 60 9.2 Predimensioning.............................................................................................................. - 60 10 Stairs ......................................................................................................................................... - 61 10.1General issues ................................................................................................................. - 61 10.2Loads ............................................................................................................................... - 61 10.3Reinforcement ................................................................................................................. - 61 11 Bibliography ............................................................................................................................. - 65 -
Table 1-1 Geotechnical Conditions .......................................................................................... - 7 Table 2-1 Load on current floor ............................................................................................... - 8 Table 2-2 Load from terrace .................................................................................................... - 8 Table 2-3 Load from faade ..................................................................................................... - 8 Table 5-1 Modal Participating Mass Ratios ........................................................................... - 19 Table 6-1 SX drift check ........................................................................................................ - 21 Table 6-2 SY drift check ........................................................................................................ - 21 Table 6-3 SX drift check ........................................................................................................ - 21 Table 6-4 SY drift check ........................................................................................................ - 22 Table 7-1 Moment computation for the current floor slabs ................................................... - 26 Table 7-2 Moment computation for the terrace slabs ............................................................ - 28 Table 7-3 Current floor slab reinforcement ........................................................................... - 31 Table 7-4 Terrace slab reinforcement .................................................................................... - 33 Table 7-5 Field reinforcement for beams in Frame C-C ........................................................ - 37 Table 7-6 Support reinforcement for beams in Frame C-C ................................................... - 38 Table 7-7 Field reinforcement for beams in Frame 6-6 ......................................................... - 39 Table 7-8 Support reinforcement for beams in Frame 6-6 ..................................................... - 40 Table 7-9 Transversal reinforcement for beams in frame C-C .............................................. - 42 Table 7-10 Transversal reinforcement for beams in frame 6-6 .............................................. - 44 Table 7-11 Longitudinal reinforcement for Central Column ................................................. - 49 Table 7-12 Transversal reinforcement for Central Column ................................................... - 49 Table 8-1 Longitudinal reinforcement for the Structural Wall .............................................. - 58 Table 8-2 Transversal reinforcement for the Structural Wall ................................................ - 58 -
Figure 1 Ground level snow load - CR-1-1-3-2012 ................................................................. - 9 Figure 2 Peak ground acceleration IMR 225 years - P100-1-2013 ........................................ - 14 Figure 3 Tc response spectrum zoning - P100-1-2013 .......................................................... - 14 Figure 4 Normalized elastic acceleration spectrum - P100-1-2013 ....................................... - 14 Figure 5 First mode of vibration ............................................................................................ - 16 Figure 6 Second mode of vibration ........................................................................................ - 17 Figure 7 third mode of vibration ............................................................................................ - 18 Figure 8 Wall 1 Zone A M-N interaction diagram ............................................................. - 54 Figure 9 Wall 1 Zone B M-N interaction diagram .............................................................. - 56 Figure 10 Stair Etabs Diagram ............................................................................................... - 61 -
The purpose of the current project is to compute, design and detail the structural elements
for a B+GF+5S dual type concrete structure. The structure will be located on Grigore Manolescu
street nr 10-14, District 2, Bucharest.
The building will have a residential function. Moreover the basement will be used for
parking space.
The height regime of the structure is of 18 m. Each story has a height of 3 m, including
the base one. The basement is also 3 m height. The surface of the ground floor is of 274.56 m2
and of the current floors is of 307.17. As a result the construction has a developed area of
1810.41 m2.
In plane the building has a regular shape.
Architectural characteristics
Partitioning made of vertical hollow brick walls finished with paint or natural stone,
according to the room.
Ceilings are executed from gypsum boards on metallic structure, with a paint cover
over the support layer.
Flooring made from stratified parquet in the living rooms and bedrooms, and natural
stone in kitchens, bathrooms and entrance halls.
Outdoor swimming pool on the top terrace.
Installations have separate meters for water, heating and electricity, better to value the
under floor heating system connected to the buildings common heating system.
Preinstalled phone, internet and TV cable connections mean no cables hanging from
The parking access with remote control gate and the video surveillance system add an
extra layer of security to the building.
Defrosting system on the access ramp for the parking lot and on the terraces from
upper floors increase the comfort of the inhabitants during the cold season.
Structural characteristics and materials used
The superstructure is designed based on a series of functional and architectural
requirements, but also by taking into consideration the seismic behavior. The design solution is
based on the dual structural system: structural system in which the vertical loads are taken over
mainly by spatial frames, while the lateral load is partially carried by the frames and partially by
the structural walls. The floors are reinforced concrete slabs with hp=17cm.
The structural walls, the columns, the beams and the slabs are made from reinforced
monolithic concrete
Concrete used for superstructure: reinforced concrete C20/25 with fcd=13.3 N/mm2
For leveling and cross slope C8/10
Steel: PC52 with fyd=300 N/mm2, OB37 with fyd=210 /mm2
The foundation solution is mat foundation made from reinforced concrete C20/25.
The infrastructure consists of concrete walls and frames. The basement is enclosed by a 30
cm thick reinforced concrete walls. The slab over the basement is 17 cm thick.
Structural computational aspects
Designing structures with structural walls must satisfy all the exigencies (functional,
structural, esthetics, placement in the urban layout, execution, maintenance and repair
/consolidation) based on the location conditions (geotechnical, climatic, seismic, influences on
neighborhood buildings) and the importance of the building. In this way a favorable behavior can
be assured during exploitation, at an acceptable safety level. The satisfaction of the structural
exigencies imply taking over the different actions, especially the seismic ones. This is achieved
by applying the structural mechanism of elastic-plastic deformation which incorporates also the
mechanism of dissipating energy.
The adequate modeling with respect to the real behavior and using the proper
computational models for determining the efforts and dimensioning the structural elements is
also essential.
The computations are performed in accordance with the design codes EUROCODE, the
corresponding National Annex, but also National Regulations. The structural modeling is
achieved using software based on finite elements methods: ETABS 9. 7. The design is done in
order to assure a proper seismic behavior. The actions have been considered from the
fundamental combination, but also from the special combinations. The seismic force is
established according to P100-1/2013.
Data regarding the building site
The building will be located in Bucharest. As a result:
The class of importance and exposure III with 1=1.
The ground acceleration for design MRI 225 years is ag=0.3g.
The control period of vibration is Tc=1.6s.
Ductility class H.
Snow characteristic value so,k=2kN/m2
Reference wind pressure, measured at a mean of 10 min, at 10m above ground level, for a
mean recurrence interval of 50 years, is 0.5kPa; also the building is situated in a urban area
with high density of buildings.
Table 1-1 Geotechnical Conditions
0 - 0.7m Infill materials (pavements, 50 cm sand bed,
broken and unbroken bricks)
0.7 - 3m Dark brown plastic silt sand
3 - 6.5m Plastic stiff clay
6.5 - 12m Sandy silt
Due to the soil stratification and the building layout
mat foundation.
e=0.5 pconv=300kPa
the chosen foundation solution is a
LOAD EVALUATION
Table 2-1 Load on current floor
Nominal Coefficient
Self-weight
Flooring load 1.75
Live load
Interior walls 1.5
Long term Coefficient Design
qDV=13.125kN
Table 2-2 Load from terrace
Terrace insulation 1.5
Snow load
Table 2-3 Load from faade
Thickness Height
Colored plastering
Thermo insulation
Interior plastering
(kN/m3)
qDV=10.1625 kN
qDV= 1.5886 kN
The snow load on the roof takes into account the quantity of snow depending on the roof shape,
and the variation of snow height due to wind and snow melt.
sk = Isi Ce Ct s0,k
Is - the exposure-importance coefficient for the snow load
i - the shape coefficient
s0,k - the charcteristic vale of snow load at the ground level [kN/m2], at the
location;
Ce - the exposure coefficient of the locatiom
Ct - the termic coefficient
Due to the importance of the structure, Is=1
Due to the small slope of the terrace roof 00 300, i=0.8
Due to its location, the structure has partial exposure, Ce=1
Due to good insulation of the roof, Ct=1
The values of the characteristic value of snow at ground level in Romania are presented
on the map:
Figure 1 Ground level snow load - CR-1-1-3-2012
The building is located in Bucharest so s0,k =2.0
sk=1*0.8*1*1*2=1.6kN/m2
PREDIMENSIONING
The slab taken as basis of computation is the most unfavorable one, one way slab with
dimensions of L1 = 5 m and L2 = 14.7 m
The height of the slab: hpl = (/ 30)
hpl = thickness of the slab
Lmin = short length of the slab = 5 m
hpl = 5 m / 30= 0.166 m = 17 cm
3.2 Beams
3.2.1 Longitudinal beams
The dimensions of the longitudinal beams will be Hb.long and Wb.long, where:
Hb.long = the height of the longitudinal beam Hb.long = t / (10..12)
Wb.long = the width of the longitudinal beam Wb.long = Hb.long / (2..3)
Where t represents the bays.
Bay Computed Round up Computed
up width
Same size beams are chosen for ease of execution and symmetry.
3.2.2 Transversal beams
The dimensions of the longitudinal beams will be Hb.trans and Wb.trans, where:
Hb.trans = the height of the longitudinal beam Hb.trans = t / (10..12)
Wb.trans = the width of the longitudinal beam Wb.trans = Hb.long / (2..3)
Each column will have its axial load computed. For this task we will consider the loads
supported by the slabs, which are carried to the beams, and the beams then transfer the loads to
the column. We will also take into consideration the loads coming from faade, nonstructural
walls, and also self-weight of each column.
qfacade=1.59 kN/m2 - Load from the weight of the facade
qter=10.16 kN/m2 - Load from the terrace
qcl=13.13 kN/m2 - Load from the current level
3.3.1 Column 1 - corner column
The tributary areas are A1=2.05 m2 and A2=3.02m2, the dimensions of the beams are
Hb=0.55m and Wb=0.3 and dimensions of the slab are L1=4.05m, T1=5m.
The chosen cross section will be a rectangle of 30 cm x 60 cm with Area = 0.18 m2.
Nter =83.13 kN-the axial load from the terrace
Ncf =120.32 kN-the axial load from the terrace
N=5*Ncf+Nter N=684.73 KN
3.3.2 Column 2 - marginal column
The tributary areas are A1=1.90 m2, A2=3.46m2, A3=3.75 m2, A4=3.13 m2, the
dimensions of the beams are Hb=0.55m and Wb=0.3 and dimensions of the slab are L1=5.2m,
T1=5m, T2=3.9.
The chosen cross section will be a square of 60 cm x 60 cm with Area = 0.36 m2.
Nter =162.45 kN-the axial load from the terrace
N=5*Ncf+Nter N=1365.76 KN
3.3.3 Column 3 - central column
The tributary areas are A1=2.62 m2, A2=2.59m2, A3=1.9 m2, A4=1.8 m2, A5=1.12 m2,
A6=1.12m2, A7=2.04 m2, A8=2.2 m2, the dimensions of the beams are Hb=0.55m and Wb=0.3
and dimensions of the slab are L1=4.3m, T1=4.05m, L2=3, T2=4.2.
The total area of the web on one direction will be at least:
is the sum of the horizontal sections of walls, laid parallel with the direction of the
action of the lateral loads
is the importance factor of the structure according to 4.4.5 from P100-1:2013
ks=ag/g the ratio between the peak value of the acceleration and the gravitational
n is the number of slabs of the building
is the area of the slab in m2
The thickness of the walls will be at least 15 cm. For structures that have less than 12
stories it is recommended to keep constant dimensions of the wall sections on the whole height.
On x direction:
On y direction:
The area of the flanges situated at the margins of the walls will respect the rule:
Where, NEd is the axial compression stress.
Wall 1:
Dimensions of the slab: L=9.675m, T=2.5m.
The tributary area is A=24.56m2.
The dimensions of the corresponding beams: L1=3.75m, L2=2.6m, T2=5m.
This check is performed to identify the cases in which the sections need strengthening by
means of flanges.
Dimensions of the slab: L=8.25m, T=2.5m.
The tributary area is A=20.625m2.
The dimensions of the corresponding beams: L2=2.6m, L3=1.4m, T3=5m.
Dimensions of the slab: L=4.175m, T=5.825m.
The dimensions of the corresponding beams: L6=2.6m, L7=3m, T7=1.45m.
The dimensions of the corresponding beams: L16=1.55m, L17=2.6m, T13=4.05m,
T14=4.05m.
Dimensions of the slab: L=8.1m, T=2.1m.
The dimensions of the corresponding beams: L17=2.6m, L18=1.4m, T14=4.05m,
EVALUATION OF THE SEISMIC LOADS AND LOAD COMBINATION
Equivalent seismic force
The seismic loads are determined with the method of seismic equivalent force according
to P100-1/2013
is the importance factor of the
( ) is the design acceleration
spectrum which takes into account the
characteristics of ground motion and the
dynamic properties of the structural
is the fundamental vibration period
of the structural system
q is the behavior factor
( ) represents the elastic acceleration
is the design acceleration of the peak
ground acceleration
( ) is the normalized elastic
acceleration spectrum
takes into account the over strength
Figure 2 Peak ground acceleration IMR 225
years - P100-1-2013
Figure 3 Tc response spectrum zoning - P1001-2013
and redundancy of the structural system
is a correction factor that takes into account the contribution of the fundamental
vibration mode through its modal mass making the equivalence between real
multi degree of freedom(MDOF) and a single degree of freedom system.
=0.85 if
and the building has two levels or =1 otherwise
T=0.3331
TB< T <TC
Figure 4 Normalized elastic acceleration
spectrum - P100-1-2013
Computational model for lateral and vertical load
The computation of the efforts is done with ETABS. The superstructure is considered
fixed at the level of the slab above the basement.
In order to define the model the following steps are followed:
Choose the units of measurement KN and m and define the geometry of the structure
(axes, spans, bays, story height);
Define the materials and the linear cross sections (beam, columns), the plane elements
(walls, slabs); define the geometrical characteristics, the materials and the rigidity of the
structural elements;
Define the load cases due to gravitational loads: from the self-weight of the structural
elements, terrace layers, floorings, partitioning elements, attic, facade, but also from
variable load: live load and snow;
Define the horizontal load from the design seismic situation. The equivalent seismic
forces are defined as a fraction of the weight of the superstructure. The response
spectrum is defined. The additional eccentricities are considered 5% from the length of
the building on each direction, on one side and the other of the center of the masses.
Define the load combinations which contain the action of the earthquake and the vertical
associated loading.
Define the mass source for computing the basic seismic force.
Position the elements in the structure, define the piers, define the slab diaphragm
Define the location and value of the loads associated to different loading hypothesis
Define the supports
Choose the type of analysis-elastic analysis
After having the spatial model for computation, the structural computation is performed
by determining the first 3 vibration modes (translation on X, translation on Y and rotation
on Rz) and the values of displacements and efforts. The displayed results have the units in
the international units: m, KN, KNm, seconds depending on each case.
Vibration modes
Figure 5 First mode of vibration
Figure 6 Second mode of vibration
Figure 7 third mode of vibration
Table 5-1 Modal Participating Mass Ratios
UZ SumUX
SumUY SumUZ
SumRX
SumRY
SumRZ
DESIGN OF RIGIDITY TO LATERAL FORCES
Is considered the check at two limit states, to the Serviceability Limit State (SLS) and the
Ultimate Limit State (ULS) (Appendix E, P100/2013)
Serviceability Limit State Check (SLS)
The aim of checking is to limit the degradation of nonstructural elements and equipment
for frequent seismic action (recurrence period of 30 years). This check also aims to reduce the
cost of the post-earthquake repair works.
Considering the criteria of interaction between the structural and nonstructural elements,
the present structure is in the situation where the nonstructural walls interact with the structure,
so the admissible inter story drift is 0.005.
The displacement check is done based on the expression (relation E.1-appendix E, P1001-2013):
- inter-story drift associated to the conventional elastic analysis
- reduction factor which considers the shorter recurrence period of the earthquake
- the value of is: 0.5 for the buildings in the importance classes III
q - behavior factor specific to the structures type
- the relative displacement, determined by static computation under the seismic loads
- allowable value of the relative story displacement
Displacement values dr are calculated using calculation assumptions of structural
elements rigidity in accordance with the actual cracking condition, depending on the degree of
interaction between structural elements and the nonstructural elements (partitioning and
closures). At the action of a moderate intensity earthquake is assumed that connections between
closures and partitioning elements and columns and beams will not be compromised and damage
of nonstructural elements to be insignificant as a result of limiting lateral movement. In such
circumstances it is justified the contribution of nonstructural elements in the global stiffness of
the structure. Because it cannot build rigorous models , but sufficiently simple structure elements of partitioning for design practice, it is permitted in a simplified way, the global
evaluation of structural rigidity by considering the deformation properties of not cracked sections
(stage I behavior) of the structural elements and neglect the contribution of non-structural
elements. In the case where the nonstructural elements are not deforming in the same way with
the structure, the rigidity of the structure is evaluated considering the deformation properties of
structural elements in the cracked stage.
So, in my case the values of dr are estimated in the hypothesis of the sectional
stiffness of the structural elements in the not cracked stage:
Ec Elasticity modulus of the concrete
Ic inertia moment of the cross section
From the table below, the structure with the dimensions of the elements, obtained from
preliminary design, obey the lateral displacement check corresponding to SLS.
The admissible displacement is 0.5% of Hs.
Table 6-1 SX drift check
Direction Combination
PSXPSY
0.000378 0,5 5,75
d,r,sls
dadm
Table 6-2 SY drift check
PSYNSX
0,5 5,75
Ultimate Limit State Check (ULS)
The aim is to avoid the loss of human life during a major earthquake (with a long
recurrence period) by preventing the collapse of the closures and partitioning elements, limiting
the structural degradation and the second order effects. The earthquake associated to this limit
state is considered when designing the resistance to lateral forces of the building. All the
horizontal seismic action will be resisted by the reinforced concrete walls and frames, which will
be heavily cracked so their stiffness is equal to 0.5EcIc.
The check is made based on the expression E.2., Appendix E, P100/2013.
- relative story displacement under the seismic action associated to ULS
dr -the relative displacement, determined by static computation under the seismic loads
c- the displacement amplification factor, which takes into account that for T<Tc the
seismic displacements computed in the inelastic domain are larger than those corresponding to
elastic seismic response.
- allowable value of the relative story displacement, equal to 2.5% of Hs
DIMENSIONING OF THE STRUCTURAL ELEMENTS
7.1.1 General computation scheme
In the case of continuous beams and slabs the permanent load together with the
temporary load can determine several loading schemes. The efforts are determined for the most
unfavorable loading scheme corresponding to each section.
To determine the maximum positive moment in a field, the permanent load is considered
to be applied in all the spans and the temporary load in the respective opening, and in alternative
spans.
To determine the maximum negative moment in a field, the permanent load is considered
to be applied in all openings and the temporary load in the adjacent openings, but also in
alternate openings.
For determining the maximum negative moment in the support, the permanent load is
considered to be applied in all openings and temporary load in the adjacent openings of the
respective support and in that alternate openings.
7.1.2 Static computation in the elastic-range slabs reinforced on one direction
The slabs are computed on one direction if
where =
The computation of the efforts in the section of the slabs reinforced on one direction due
to permanent or temporary loads, applied uniform, is done like in the case of isolated or
continuous beams, computed in the elastic range for a strip of slab with the width equal to the
The slab is loaded with the sum of the temporary and permanent loads.
one way slab (which is reinforced on the shorter direction)
Positive moment in field:
Negative moment in support:
Slab 2
Current floor
q(kN/m2)
l(m)
M field(KN*m)
M support (KN*m)
7.1.3 Static computation in the elastic-range slabs reinforced on two directions
The slabs are computed on two directions if
, where
The maximum and minimum moments are computed based on two loading schemes,
based on the support type of the slab.
In the first load scheme the panels are considered fixed supported or simply supported
based on their contour. The load applied is:
, where:
g is the permanent load
p is the variable load
In the second conventional scheme the panels are considered simply supported on all the
sides. On all the panels is applied a conventional load directed up-down and respectively downup in all the possible ways. This load is:
Scheme 2a
Scheme 2b
Scheme 2c
Total moment
Table 7-1 Moment computation for the current floor slabs
q+p/2= 11.63
L1= 4.05
p/2= 1.50
M1'
(kN*m) (kN*m) (kN*m)
(kN*m)
Table 7-2 Moment computation for the terrace slabs
q+p/2= 7.76
7.1.4 Dimensioning the reinforcement
Based on the mean of the maximum values of the bending moment in each support the
reinforcement can be determined for each slab.
The computation is performed by considering a rectangular cross section with the length
equal to unit. If the length of the strip is considered 1 m, the resulting reinforcement will be laid
on 1 m of slab. On the drawing the representation of the reinforcement is done by the number of
bars on meter.
The necessary reinforcement is:
Where: b=1000 mm - the unitary strip
x - the depth of the neutral axis
Where: d - the width without the concrete covering
fcd - the strength of concrete in compression
fyd - the yielding strength of steel
The constructive rules which have to be respected are:
The minimum diameter of the bars is 6 mm for the bottom part and 8 mm(OB37)
or 6 mm(PC52) for the upper part and for the inclined bars.
For hp<30, the minimum number of bars per meter is 5 and the maximum number
The minimum reinforcement area (SR-EN-1992-1-1-2004).
, is equal to 443.3 mm2 for the computed slab.
From the Romanian codes, the minimum reinforcement percentage should be
>0.20%.
Perpendicular on the direction of the strength reinforcement, found by
computations, repartition reinforcement has to be placed. This reinforcement has
the following purposes: constructive because it takes over bending moments from
the lower part, from the vicinity of the support and serves to ensure a good
behavior in case of concentrated loads; for mounting the reinforcement nets
because it holds the reinforcement bars from migrating before and during the
pouring and the vibrating of concrete.
For the regular slabs the repartition reinforcement should be at least 15%of the
load strengthening reinforcement, but minimum 46.
The number of bars should be multiple of 2.5 and 3.
The length of the bars on one support is the minimum between l1/4, l2/4.
Table 7-3 Current floor slab reinforcement
SLAB TYPE
Mid-span
x direction
y direction
y direction up
y direction down
x direction left
x direction right
[kN
m]
[N/mm2]
fyd
[N/mm]
38+212/m
[%)
Table 7-4 Terrace slab reinforcement
[kNm]
The bending moments were obtained through automatic computation in ETABS. To
obtain the needed moments, the building was loaded with the envelope of the load combinations.
The results displayed the maximum value of the bending moment as shown in the figure below:
7.2.1 Design of the longitudinal reinforcement
MEd = Mdesign the effective bending moment from the envelope.
In the present project the beams were declared as T-shape but in computation the cross
|>|
section is considered rectangular because |
| so
. As a result beff is
involved in the computations for the beams which are done on a rectangular section.
The necessary area of reinforcement is:
is the maximum value of the effective bending moment from ETABS.
c is the concrete cover
Based on the chosen diameters of reinforcement the area given by the actual reinforce
layout is computed: As1
The reinforcement percentage is:
The capable moment of the section is:
For the top reinforcement we assume that x<2*c
As a result:
Then x is computed for the effective reinforcement:
If x<2a the area of reinforcement is computed correctly, otherwise the section is
computed as a double reinforced section.
Provisions for the longitudinal reinforcement:
The minimum diameter is 12.
At least 2 bars 14 should be placed in the bottom and top parts of the beams.
The compressed reinforcement at the ends of the beams should be at least 50% of
the tensioned reinforcement.
At the upper part of the beam at least one quarter of the top reinforcement should
be continuous.
The reinforcement ratio
Only 2 or maximum 3 nonconsecutive diameters are used.
The minimum clear distance between rebars is 30 mm, and at least one space of
50 mm for the top rebars. For the bottom rebars the distance should be 25mm.
The maximum clear distance is 200 mm.
(for C20/25
0. 32%)
Example for beam 4 frame C-C
The chosen diameter is 112 and 216 so the
The reinforcement percentage is
The chosen diameter is 412 + 216 so the
=25.45 <2*c
Table 7-5 Field reinforcement for beams in Frame C-C
Story Field
[kNm] [N/mm2] [mm] [mm] [mm]
hs=hb
As2nec
-2as
[mm2]
Aeff =
n2/4
MRd+
Table 7-6 Support reinforcement for beams in Frame C-C
hs=hb Aeff=n
MEdfyd
As2nec Diameter
[kNm] [N/mm ] [mm] [mm] [mm]
[mm ] [mm]
[mm ]
88 112+216
419 112+216
MRd[kNm]
Table 7-7 Field reinforcement for beams in Frame 6-6
Table 7-8 Support reinforcement for beams in Frame 6-6
0.0046 81.52
0.0046 103.14
7.2.2 Design of the transversal reinforcement of the beams
The shearing forces for computations were found using equilibrium of the beam under the
action of the transversal loading due to earthquake and the moments acting on the ends of the
beam. The design is performed in order to place the plastic hinges at the ends of the beam.
The principle of computation is based on computing two values of the shear force
corresponding to the maximum and minimum positive moments developing in the two ends of
the beams. Since the shear failure is brittle we have to amplify the shear force produced by the
earthquake with a safety coefficient and finally the design shear forces will be computed with the
following equation
coefficient which takes into account a possible over resistance due to increased
rigidity of the steel to deformation = 1. 2
Provisions for computing the transversal reinforcement:
wmin= 6 mm for h 800mm
Choose w and the spacing s which can have values between 75. . . 200mm with a 25 mm
For =
because =45 and cot =1
The diameter and the bars are chosen in order to comply with the conditions 1 and 2.
and |
are needed inclined
reinforcement in two orthogonal directions and half of the design shear force should be resisted
by stirrups and half by the inclined reinforcement.
Example beam 1 frame C-C
=45o
Are chosen 210 at s=100mm
=1.57 so it verifies
Table 7-9 Transversal reinforcement for beams in frame C-C
(|MRd+|+|MRd-|)
*1.2/ L [KN]
qltv*L/ VEd
2 [KN] [kN]
VEdmin
134.33 -88.25
163.74 -121.16
=VEdmin/VEdma
>-0.5
d Bars
d=hb-as
=0.6(1fck/250)
|VEdmax
| [kN]
0.5bbd
fcd[kN]
fywd
smin
Choosen
S [mm]
pw [%]
>0.2%
Table 7-10 Transversal reinforcement for beams in frame 6-6
qltv*L/2
=VEdmin/VEdmax
=0.6(1fcd
|VEdmax|
fck/250) [N/mm ]
The columns were dimensioned taking into account that the beams were of medium
ductility M, so the behavior of the columns will be in the class of ductility M. The rules and
principles for design are found in P 100-2013.
7.3.1 Geometrical characteristics
The minimum dimension of the section is 350 mm.
The dimensions of the cross-section must be a multiple of 50 mm.
The ratio between hc and bc 2. 5, where hc is the height of the column and bc is the
width of the column.
7.3.2 Provisions regarding the materials used
The minimum concrete class used for the main structural elements is C16/20 for medium
ductility buildings.
The structural elements will be reinforced only with profiled steel type PC52, PC60. The
closed stirrups and the hooks are be made of plain steel type OB37. Non ductile steel, like STNB
can be used, only if, by design, an elastic behavior can be assured.
In the critical zones of the main structural elements, steel types with a minimum strain of
7. 5% corresponding to the maximum stress will be used.
7.3.3 Longitudinal reinforcement provisions
The total reinforcement coefficient will be at least 0.01 and maximum 0.04.
The minimum reinforcement percentage on each side is pmin,side 0 . 20 %.
Between the corner reinforcement bars, at least 1 intermediate bar will be placed.
For circular columns, the minimum number of reinforcement bars is 6.
The maximum distance between the axes of the reinforcement bars is 250 mm.
The length of the critical zones at the ends of the column lcr is:
Where, hc is the largest dimension of the column and lcl is the story clear height.
, the entire column section is considered critical and will be reinforced
The minimum diameter of the reinforcement bars is 12 mm.
The maximum diameter of the reinforcement bars is 28mm.
For good adherence under normal conditions of solicitation the anchorage length will be
40 diameters.
Splicing will usually be placed in zones of minimum effort in reinforcement bars; for the
vertical bearing elements, the splicing is admitted above the level of each floor plate. For the
reinforcement bars spliced by overlapping, overlapping length will be 30d for elements with
concrete class < C20/25 and 20d in case of elements with concrete class > C20/25.
7.3.4 Longitudinal reinforcement design
The equation below will be computed on the two main directions of the seismic action.
Always consider both directions of the actions of the moments in the beams in the joints. The
values of the design shear force are obtained from the column equilibrium at each level.
is the design bending moment in the considered section of the column.
is the bending moment taken from ETABS by applying the envelope combination.
is the sum of the capable bending moments in the beams from all the spans of the
considered level associated to the direction of the seismic action.
is the effective bending moment in the beam resulted after the computation of the
is a factor taking into consideration the effect of steel and concrete consolidation in
the compressed areas and is considered 1.3 at the base of the building and 1.2 for the rest of the
levels.
The depth of the active zone is computed using the value of the axial loading given by the
LTV loading,
Based on the necessary area of reinforcement the reinforcement layout is chosen and the
capable bending moment can be computed:
7.3.5 Transversal reinforcement provisions
The minimum transversal reinforcement coefficient must be at least:
- 0.005 in the critical zone situated at the bottom part of the ground story.
- 0.0035 for the other critical zones.
- 0.0015 for the rest of the column.
The minimum diameter of stirrups is:
- d/4, where d is the maximum diameter of the longitudinal reinforcement;
- 6 mm;
- 8 mm, for perimetral stirrups.
The distance in section between consecutive bars situated at a stirrup corner or tied with
hooks will not be greater than 200 mm.
For the first 2 stories of buildings with more than 5 stories and for the first storey of
buildings with fewer stories, the stirrups will be placed beyond the critical zone on a length equal
to 0. 5lcr.
The minimum distance between stirrups is:
For the plastic zones: ae { b0/3; 7 dmin (6 dmin for the bottom part of the ground
column); 125 mm}, where b0 is the minimum dimension of the stirrup and dmin is the minimum
diameter of the longitudinal reinforcement.
Outside the plastic zones: ae { 3hc/4; 15 dmin; 200 mm}.
7.3.6 Transversal reinforcement design
The design values of the shear forces are obtained from the equilibrium of the column at
each story, considering the action of the bending moments at each end, corresponding, for each
sense of the seismic action, to the formation of plastic hinges which can occur either in the
beams or in the columns connected to the nodes.
-value of the capable bending moment at the end i
-sum of the capable moments of the beams entering the joint
-sum of the capable moments of the columns entering the joint
The design value of the shear force is:
The reinforcement is chosen and the area of reinforcement is computed taking into
account ne which refers to the number of stirrups in one section, but also their position.
In order to assure a ductile behavior, plastic and elastic zones have to be decided. The
plastic zone is found at the extremities of the column, and the elastic zone in the middle part.
Example for column 4 - intersection of axes C and 6 - the first level
=562. 348kN*m
so the Asteel=-1713.84 mm2
The chosen reinforcement is 1016 so the effective area of steel is 2009.6.
The computations are performed also on the perpendicular direction and the results show
that the same amount of reinforcement is needed.
For the transversal reinforcement
Chosen bars of 10 OB 37 spaced at 100mm:
Both conditions are fulfilled.
Table 7-11 Longitudinal reinforcement for Central Column
Frame 6-6
Story Support
[N/mm2] [N/mm2]
h0=h-as
hs=h-2as
pTOTAL%
|ME'|
|NE'|
|Med|
|Ned|
Table 7-12 Transversal reinforcement for Central Column
Mcap
0.5bd
h [mm]
fcd [kN]
b [mm]
d=h-as
z [mm]
Frame C-C
Nr of
A =n /4
[mm] eff
[mm] [mm2] bars
[kNm] [kNm]
lppz
[%]
Chosen stirrups
Asnec Nr of
Aeff=n2/4
[mm] [mm ] bars [mm]
>0.35%
STRUCTURAL WALLS
General considerations for the computations of the structural walls
The main idea is to design the structural walls in order to favor the development of a
structural mechanism for dissipating energy in a favorable manner for the structure as a whole and
to assure enough ductility to the structural elements.
The dimensioning is done according to P-100-1-2013 for the class of high ductility H, and
according to the Romanian Code for designing buildings with structural reinforced concrete walls
CR 2 1 1. 1 : 2011 .
The critical zone is at the base of the wall having the length:
because the building has 6 levels.
-the height of the wall
-the clear height of the story
-the length of the wall
In the case of multistory buildings this height is rounded up to a full number of stories if the
limit of the computed plastic zone is bigger or smaller with 0.2 . In this way the base becomes
Area A with specific design performances, and the rest of the wall becomes Area B, with smaller
- the height of Area A is 3m
The values of the design sectional efforts in the walls
The values of the design bending moments MEd in the horizontal sections of the wall for the
structures which are in the classes of ductility DCH:
MEd=MEd,o for the zone A
MEd=km**MEd'< *MEd,o' for the zone B
MEd' is the bending moment due to seismic loading
MEd,o' is the value of MEd' at the base
km is the correction coefficient of the bending moments in the walls which is km=1 in zone
A and km=1.30 in zone B for the ductility class DCH
is the ratio between the capable moment and the design moment in each section
is the capable moment at the base of the wall
q is the behavior factor considered for designing the structure
The longitudinal and transversal reinforcement
In the case of longitudinal reinforcement the overlapping is in zone A:
45d in the case of horizontal bars PC52
45d in the case of vertical bars PC52 with d<20mm
Bars with d>20mm need welding
In the case of longitudinal reinforcement the overlapping in zone B is: the minimum
overlapping lengths are with 10d less than those from the table. Also, in the zone B it is not
necessary the overlapping by welding of the reinforcement with d 16(20) mm.
For the flexural reinforcement for the web the minimum web reinforcement are given in the
table below. For zone B the minimum web percentages are the ones for as<0. 12g.
Minimum reinforcement percentage
Seismic zone
Vertical bars
OB 37
PC 52, PC 60 OB 37
PC 52, PC 60
ag0.12g
ag<0.12g
The minimum bar diameter is 8 mm for horizontal bars and 10 mm for vertical bars. The
maximum distance between bars is 350 mm for horizontal bars and 250 mm for vertical bars.
For the local reinforcement at the ends on each wall one has to take into account the
The reinforcement is realized as for the columns
If the wall has no flanges the portions with the length 0. 1*lw at the ends of the beams are
considered flanges
The minimum vertical percentage is:
zone A zone B
ag0. 12g
0. 5%
ag<0. 12g
The minimum diameter is 12 mm
The layout rules are the ones in the pictures below:
0.1h
overlapping length
a) welded mesh reinforcement
b) reinforcement with independent bars
The anchorage of the vertical reinforcement of the flanges can be done by overlapping and
the length is 50dBL for the DHL class in zone A, and in zone B the lengths are smaller with 10 dbl.
In the area A should be avoided if possible the anchorage of the bars situated at the extremities. The
horizontal reinforcement should be overlapped for at least 50dBT for the class DCH.
The maximum distances between stirrups for class DCH with ag>0. 12g are:
Zone A 8dbl<125mm
Zone B 10dbl<200mm
For computing the longitudinal reinforcement the section was modeled in Response 2000.
The value of the effective bending moment was taken from the envelope of load combinations from
ETABS.
Based on the results is computed for the wall.
Wall 1 - zone A
Figure 8 Wall 1 Zone A M-N interaction diagram
From response were taken the values of the bending moments corresponding the axial range
and interpolation is performed in MathCAD.
M1 13510 .69
N1 7025.288
x M2 ( N N2 )
( M1 M2)
( N1 N2 )
x 1.171 10
MRd x
Medb 1137 9
Medb
Wall 1 - zone B
Figure 9 Wall 1 Zone B M-N interaction diagram
Dimensioning of the Transversal Reinforcement for Structural Walls
Three checks are needed:
Check the web of the concrete section to resist to compression
Check the horizontal reinforcement from the web
Check the joints
For the horizontal reinforcement:
is the design shear force
is the shear force from ETABS
is the correction factor
is the shear due to the participation of steel
is the shear due to the participation of concrete
for zone A
for zone B
is the width of the section
is the length of the section
is the sum of the vertival reinforcement from the web
is the sum of the horizontal reinforcement from the web
is the design value of the yielding limit of the vertical reinforcement
Table 8-1 Longitudinal reinforcement for the Structural Wall
Aefffl flange
11379,01 5018,57 400 3300 325+225+325 3924,96 2,4531
10139,1 4311,34 400 3300 325+225+325 3924,96 2,23009
5209,431 3594,13 400 3300 312+312+312 904,32 0,68509
3508,19 2873,2 400 3300 312+312+312 904,32 0,68509
1242,633 398,52 400 3300 312+312+312 904,32 0,68509
Field Aefffield field
2416 4823,04 0,4823
1212 2712,96 0,25691
Table 8-2 Transversal reinforcement for the Structural Wall
Ved'
Asteel
1,5*Ved'<Ved<5*Ved'
Vrd,s
bw hw
Nltv
1831,248 0,4 3,3 2476,8
0,6*bw*
hw*fcdt
Vrd,c
VRd
Material provisions for structural walls
The minimum concrete class used for the main structural elements is C20/25 for high
ductility class buildings and C16/20 for medium ductility buildings.
closed stirrups and the hooks can be made of plain steel type OB37. Non ductile steel, like STNB
can only be used as constructive reinforcement.
The ratio between the strength of the steel and its yielding limit must not be excessively
large (<1. 4).
Geometric Exigencies
The minimum thickness of the wall bw0 max {150 mm, hs/20}, where hs is the story
clear height. For buildings up to 10-12 stories it is recommended to keep the same wall section
on the entire height.
The height of the compressed wall section will not be greater than:
xu 0.10 2lw
the ratio between capable bending moment at the base, associated to the
plastification of the walls and the bending moment obtained from structural analysis in the
seismic combination; the capable bending moments must be computed for Rd=1.1.
lw is the length of the wall cross-section.
In the potentially plastic zone, when the height of the compressed zone xu exceeds the
smallest of the values 5bw0 and 0.4lw, it is necessary to make the check for loss of stability.
The same check must be made at the edges of the flanges, in the parts which exceed 4hp
on each part of the wall web. If the check cant be fulfilled, bulbs will be added.
It is recommended that for seismic zones I-IV, or for buildings with more than 6 stories,
the walls should have at their edges either bulbs or flanges.
The minimum bulb thickness is 250mm and the minimum bulb width is
bp 2 bw0.
The coupling beams for the walls with doors will have the same thickness as the rest of
the wall. If by computation this thickness is not enough, the beams will be thickened on a length
sufficient to allow the reinforcement anchorage.
The purpose of the foundation is to transmit the loads from the superstructure to the
supporting ground. From the seismic point of view the foundation should have an elastic
The chosen foundation solution is mat foundation. This is a type of direct foundation
which ensures a large support surface. The use of mat foundation is done in the following
situations:
the foundation terrain has a small bearing capacity and the raft foundation can
spread the loads on a larger area
very large loading which implies great surfaces for foundation so the loads have
to be spread on a large area, usually the whole area of the structure
non-homogenous terrain where the risk of differential settlement appears because
concrete slabs resist differential movement between loading positions
the presence of ground water above the level of the foundation
closely spaced vertical elements for which the individual pad foundation would
in the case of high rise buildings
The chosen solution is raft foundation with constant width.
For design of the raft foundation should be taken into consideration the compatibility
between the deformability of the terrain with the deformability of the structural elements. The
sectional efforts are obtained in ETABS by modeling the interaction between the foundation and
the terrain. In order to perform this task the whole structure has to be modeled including the
basements. The maximum efforts obtained are used for designing the raft foundation. The
ground is modeled as an elastic environment, a Winkler model and the efforts in each spring in
computed. Based on these results the reinforcement can be computed.
The reinforcement is made with horizontal nets of horizontal reinforcement, laid at the
upper and lower part of the element to resist the positive and negative moments. In addition to
this it is necessary an additional reinforcement on the central area of the raft for preventing
contraction phenomena. The minimum reinforcement percentage is 0.15% on each face.
The height of the raft foundation:
The length of the cantilever
The dimensions in plan of the raft foundation:
m so is chosen
10 STAIRS
10.1 General issues
Stairs should be designed in order to not influence the rigidity of the structure or to
interfere with the elements which assure the rigidity.
The design of the stairs must assure the following performance conditions:
Stability-avoid buckling or local deflection
Resistance: limit the damage in case of severe actions and avoid collapse
Ductility: no interference with the ductility of the adjacent vertical structural
elements which can be assured by avoiding uncontrolled links with the horizontal
sub-ensembles
Rigidity: limit the displacements and deflection of the stairs and of the
neighboring sub-ensembles; limit the cracking
Durability: assure a normal behavior during the lifetime of the structure under
normal exploitation conditions and limit the premature deterioration of materials
and elements
10.2 Loads
plastering qplast=plast*hplast=19*0. 015=0. 285kN/m2
flooring qflooring=flooring*hflooring=22*0. 05=1. 1kN/m2
live load qlanding=3kN/m2
For the structural elements a projection of loads has to be performed.
For the steps Atriangle=Arectangle
The height of a stair is computed considering the needed number of stairs, which is 18 in
this case and the height of the level which is 3m.
The finishing
A1=b*0. 05=0. 26*0. 05=0. 013m2
A2=0. 05*0. 05=0. 0025m2
A3=h*0. 05=0. 1676*0. 05=0. 00838m2
A1+A2+A3=0. 02388m2
qfinishing=hp*p=0. 015*19=. 0285kN/m2
The variable load :qu=qu*cos =0. 43kN/m2
where is the angle of the slope of the ramp.
tg=
Figure 10 Stair Etabs Diagram
10.3 Reinforcement
L 2.5m
l 1m
Due to the L/l ratio the landing will be reinforced on one direction
For computation we consider one strip with the length of 1 m.
b 1000mm
fcd 13.33
For concrete C20/25
fyd 300
For steel PC52 which will be used for reinforcement
Mfield 0.9kN m
Msupp 2.63kN m
d1 150mm
1 2 Mfield
b d1 fcd
x d1 1
As1 b x
As1 2.003 10 m
Asmin min b d1
Asmin 3 10
The chosen reinforcement is 6 8 with
Ast eel 6 3.14
( 8mm)
Ast eel 3.014 10
Ast eel 100
b d1
1 2 Msupp
As1 5.87 10 m
On the long direction will be used repartition reinforcement computed from the minimum
reinforcement percentage: 6 8
L 2.55m
Mfield 2.11kN m
As1 5.436 10
Asmin 2.6 10
Asmin 2.6 10 m
P100-1-2013
SREN1992-1-1-2004
CR-1-1-3-2012-ZAPADA
CR2-2006-Cod-de-Proiectare-Pereti-Structurali-Beton-Armat
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