Embed Size (px)
Citation preview
Structural design of an office building in reinforced
concrete in Aljezur
Francisco Ribeiro Guardado de Sousa e Silva
Dissertation to obtain a master’s degree in
Civil Engineering
Advisor: Prof. Rui Vaz Rodrigues
Jury
President: Prof. Dr. José Joaquim Costa Branco de Oliveira Pedro
Advisor: Prof. Rui Vaz Rodrigues
Examiner: Prof. Dr. Pedro Guilherme Sampaio Viola Parreira
Instituto Superior Técnico, Lisbon, Portugal
October 2016
1
Abstract
The purpose of this dissertation is the development and practical application of the acquired knowledge during the Civil Engineering course, through a structural design of a building.
Taking into consideration initial data from an existent project, originally located in a region with low seismic action, the design is now performed in a region with high seismic action. In this work the following steps are going to be considered: an initial conception, followed by the geometry verification via a pre-design, then seismic analysis, design, insertion of higher stiffness elements and their implications, and finalizing with the detailing drawings of the most relevant structural elements.
The analyses were carried out according with the principles set in the Eurocodes. A tridimensional model was made, in the appropriate software, to put into practice the necessary analyses.
The main components were designed and finalized in detailing drawings. Keywords: Pre-design; Seismic analysis; Design; Structural cores; Eurocodes.
Introduction The intent of this work is to put to test the acquired knowledge in the Civil Engineering
course with a practical application, in this instance it’s a structural design of a building. The focus is the study of a building’s behavior in a place of strong seismic activity in the
context of Portugal, since it was originally designed for a low seismic zone. In addition, the structure will be evaluated by its proximity to the sea, that is also relevant to its elements.
The first step, since it’s a previously conceived project, is to verify the structure dimensions by means of a preliminary design, followed by an analysis of elements and their design with the mandatory requirements. They’re correctly met if the two most important aspects are assured, safety against the actions, and the adequate serviceability behavior of the global structure during the lifetime to which it’s designed.
In order to evaluate the effects due to static and dynamic actions, it’s essential to create a tridimensional model of finite elements, in this case, in the SAP200 software. This model enables a more rigorous design, particularly in elements more susceptible to a seismic action.
To conclude, the structure will be completed with cores consisted of orthogonal walls, then the global analysis and design procedure. So, to finish, other elements were designed, in addition to a core and its respective foundation.
1. Project bases The idea of this project is to design the main structural elements of an office building,
while placing it in a new location with a frame structure, originally conceived in a low seismic region. Any necessary additions or changes will be made until a safe and well-designed structure is achieved.
1.1 General concept The new building location is in Aljezur, Portugal, associated with being a high seismic
region in the Portuguese context and near the coast, so the structure faces a new set of loads for which it wasn’t planned, also the site has a soft rock as soil foundation with a maximum stress level of 1,5MPa.
1.2 Initial changes In this new structure traditional concrete slabs are implemented, there are five floors,
identified from 0 (zero) to 4 (four) with a horizontal structure reduction in the two highest floors. The first floor slab will be extended to the edge of the building where an additional beam (V609) will be created. Columns P23, P26, P04, P05, P06 e P07 will now have 1,60-meter square based footing, with 0,70-meter height, respectively, S10, S15, S11, S12, S13 and S14, with strap beams combining each pair of footing.
2. Materials and concrete cover After the initial remarks concerning the overall appearance of the structure, the following
step is the choice in materials, concrete and steel, and the concrete cover as well.
2.1 Concrete class Concrete class depends on each element class of exposure.
2
2.1.1 Class of exposure Table 4.1 in the Eurocode EN 1992-1-1 2010, also belonging to the regulation document EN 206-1, contains the possible classes of exposure that are summed for this case (Table 1).
Table 1 – Classes of exposure for each structural element
Structural element Foundation Columns Beams Slabs
Class of exposure XC3 XS1 XA2 XC3 XS1 - XC3 XS1 - XC3 - -
2.1.2 Class of resistance The document E464-2005 established by the national laboratory of civil engineering (LNEC) states some recommendations for the classes of resistance due to the classes of exposure, leading up to a class of resistance of C35/45 for slabs and C40/50 for the foundation, columns and beams.
2.2 Concrete cover To obtain the concrete cover it’s enough to consult table NA. II in the national annex in EN 1992-1-1 2010 with the class of exposure, resulting in 35 millimeters for slabs and 45 millimeters for elements of foundation, columns and beams.
2.2 Steel Due to being a reinforced concrete building in a seismic region it must be class C A500NR Special Ductility steel.
3. Definition of actions Actions are separated in vertical (gravitational) and horizontal.
3.1 Gravitational actions Gravitational actions are permanent loads, self-weight and remaining dead load, and live loads, only uniform.
3.1.1 Self-weight Calculated by the product of the relevant dimension of each element times the weight by volume of a reinforced concrete piece, γb, with the value of 25,0 kN/m3.
3.1.2 Remaining dead load The remaining dead load is fixed with a constant value of 2,0 KN/m2.
3.1.3 Uniform live load Defined in the forward chapter 4.1.1 for slab elements.
3.2 Horizontal actions Two horizontal actions were defined, wind and seismic action, but only the dominant one will be applied.
3.2.1 Wind Wind is defined in EN 1991-1-4 2010 regulation document and in this instance calculated by the maximum force it applies on the building and summed up with all relevant data in table 2.
Table 2 – Wind data
Cf vb qb(z) qp(z) Fw
Cf,0 cdir cseason vb,0 (Zone B)
[m/s2] vb
[m/s2] ρ
[Kg/m3] qb(z)
[N/m2] cE(z)
qp(z) [kN/m2]
cscd Aref [m2]
Fw [kN]
1,50 1,00 1,00 30,00 30,00 1,25 562,5 3,25 1,83 1,00 356,94 652,52
3.2.2 Seismic action Seismic action is defined in EN 1998-1 2010 in two types that differ on the earthquake distance, distant (Type 1) and near (Type 2), by using response spectrums made from the table 3 data.
Table 3 – Data of each seismic type
Smax [m/s2] TB [s] TC [s] TD [s] ag [m/s2] S [m/s2] β
Seismic Type 1.1 1,00 0,10 0,60 2,00 2,50 1,00 0,20
Seismic Type 2.3 1,00 0,10 0,25 2,00 1,70 1,00 0,20
3
Frequency and period are obtained through the formulas expressed in the regulation document leading to a 0,65-second period, and it to a spectral acceleration. After the total structure mass is calculated, the consequent equivalent earthquake force is achieved (Table 4).
Table 4 – Spectrum acceleration and resulting seismic force
Sd (T) [m/s2] Main S.T. Sd (T) [m/s2] λ Total mass [ton] Fb [kN] βtheoretical
S.T. 1.1 1,93 A.S. 2.3 1,93 0,85 994 1631,60 0,17
S.T. 2.3 0,55
3.2.3 Wind vs Seismic action The seismic force is much higher than wind force, therefore the relevant horizontal action.
4. Preliminary-design New loads imply a verification of structural dimensions, and if needed the proper
adjustments, specifically in slabs and in the more axially stressed column footing.
4.1 Load definition Thickness is the relevant dimension in slabs and all volumetric dimensions of a footing
need to be guaranteed.
4.1.1 Slabs Self-weight (Table 5), not constant throughout the building, remaining dead load, fixed
value, and three types of uniform live loads, interior, porch and roof, determine the existing loads. Tables 6.1 and 6.9 in EN 1991-1-1 2009 and NA-6.2 and NA-6.10 tables of the national annex contain, respectively, the pavement use categories and live loads. When consulted, the results for this case are in table 5.
Table 5 – Loads by floor and pavement
Element h (m) γb
[kN/m3] SW
[kN/m2] RDL
[kN/m2] PL
[kN/m2] Pavement Use category Live load
Floor 0 0,15 25,00 3,75 2,00 5,75 Interior Category B qk = 3,0 kN/m2
Floor 1 0,20 25,00 5,00 2,00 7,00 Roof Category H qk = 0,4 kN/m2
Floor 2 0,20 25,00 5,00 2,00 7,00 Porch Category A qk = 5,0 kN/m2
Floor 3 0,20 25,00 5,00 2,00 7,00
Floor 4 0,20 25,00 5,00 2,00 7,00
Floor 5 0,15 25,00 3,75 2,00 5,75
4.1.2 Foundation – Footing Loads used in slabs are also relevant for the foundation, in addition to the self-weight of
columns (Table 6).
Table 6 – Self-weight of columns
Column P01/ /P04
P05/P06/P07/P08/ /P09/P10/P11/P12
P13/ /P14/P15
P23 P26 P28/
/P29/P30 P33
P34/ /P35/P26
P37/ /P38
Self-weight [kN] 66,75 51,75 20,25 63,45 51,75 11,70 8,13 11,70 1,10
4.2 Load combinations Only one load combination is necessary for ultimate limit state verification in pre-design, the fundamental combination of equation 4.1.
𝑃𝑆𝑑 = 𝛾𝐺 × 𝑃𝐿 + 𝛾𝑄 × 𝐿𝐿 [𝑘𝑁 𝑚2⁄ ] Equation 4.1
4.2.1 Slabs In each floor the live load distribution is different and in accordance with the pavement use. Table 7 presents the final loads applied on this verification.
Table 7 – Loads by each floor
Element h
[m] SW
[kN/m2] RDL
[kN/m2] PL
[kN/m2] LLpavement [kN/m2]
LLporch [kN/m2] Psd_pavement
[kN/m2] Psd_porch [kN/m2]
Floor 0 0,15 3,75 2,00 5,75 3,00 5,00 12,26 15,26
Floor 1 0,20 5,00 2,00 7,00 3,00 5,00 13,95 16,95
Floor 2 0,20 5,00 2,00 7,00 3,00 5,00 13,95 16,95
Floor 3 0,20 5,00 2,00 7,00 3,00 5,00 13,95 16,95
Floor 4 0,20 5,00 2,00 7,00 0,30 5,00 9,90 16,95
Floor 5 0,15 3,75 2,00 5,75 0,30 - 8,21 -
4
4.2.2 Footing The same load combination and resulting loads for slabs contribute to the footing verification as well as the self-weight of columns, added as another dead load.
4.3 Pre-design verifications Now, it will be determined if any dimension needs to be altered, amplified or reduced.
4.3.1 Slabs To control a slab’s thickness is to limit the highest value of a reduced negative moment. That happened in floor 1 with a 30,80 kNm/m moment value and a reduced one of 0,05, which is inferior to a commonly used limit of 0,25, therefore the thickness in each floor is adequate.
4.3.2 Footing As long as the tension, only depending of axial stress, transmitted to the soil can be supported, all footing dimensions can be used. Column P10 is most axially stressed with a 1400kN value, leading to a 546,87 kPa tension, lesser than the admissible of 1500kPa.
5. Modulation A tridimensional model of finite elements is the best way to analyze a structure behavior
and, to create it, the software SAP2000 was chosen. The x (lengthier direction) and y axis are in accordance to the horizontal display of the building. Beams and columns were modeled with bar like finite elements and slabs with Shell elements, the foundation was not necessary to module due to its good soil, only represented by the proper support element.
5.1 Material properties In terms of concrete, C35/45 is used in slabs, C40/50 in beams and columns, and as a steel material S500NR SD. All defined with the respective modules and coefficients that can be found in the proper material description tables.
5.2 Columns The identification and dimension of columns remains from the initial project. To simulate the loss of stiffness due to cracking, EN 1998-1 2010 allows the consideration of stiffness reduction to half and to apply it the resistance properties were reduced to 50% of their capacity.
5.3 Beams Same process of identification used in columns is repeated for beams.
5.4 Slabs Slabs were divided just like two-way slabs are divided into panels, with the use of four node Shell element, as detailed as needed.
5.5 Foundation It is enough to put a fixed support onto the columns base, in the ones who reach the foundation level, because the soil demonstrates good mechanical characteristics.
5.6 Tridimensional model Putting together all definitions in the previous modulation subchapters the tridimensional model is reached.
6. Seismic analysis After the module is finalized, a seismic analysis is next, beginning with the behavioral
structure study in its deformed state through a modal analysis to determine the frequency and period of the structure. Then, classify it and define the needed loads. The objective of this analysis is to make sure the two obligations in a structural design project of a building in a seismic zone are abided, non-occurrence of collapse and limitation of damages.
6.1 Modal analysis Seismic response is evaluated with the vibration modes, that represent the deformed states and within each there is an assigned frequency, dependable on structure stiffness. Only the more important modes matter and chosen with the defined criteria in EN1998-1 2010. In this case, the 26 first modes fit this category and the very first mode determines the frequency, with a
5
0,80 hertz value, and period, of 1,25 seconds. Since the third mode is rotation, and the two previous are displacement, the structure does not suffer from elevated torsion. In that case, these are pleasant results because the desired conclusion was for the displacements to be dominant when compared against rotations.
6.2 Vertical regularity Applying the criteria set in EN 1998-1 2010 section 4.2.3.3, the building has no vertical regularity.
6.3 Horizontal regularity Applying the criteria set in EN 1998-1 2010 section 4.2.3.2, the building has no horizontal
regularity.
6.4 Structural system classification In EN 1998-1 2010 the possible structural systems are defined, which lead, for this building, to a framed system classification, as a result of the presence of beams and columns.
6.5 Behavior coefficient The behavior coefficient can be calculated, to assure that the previously adopted one is adequate, in accordance to EN 1998-1 2010 and resulting in a 3,9 value, therefore the 3,0 chosen value doesn’t need changing.
6.6 Actions
6.6.1 Permanent loads 6.6.1.1 Self weight and remaining dead load These loads are the same as the ones defined in chapter 4.1.1.
6.6.2 Live loads The live loads are the uniform live load and seismic action.
6.6.2.1 Uniform live load Already defined in chapter 4.1.1.
6.6.2.2 Seismic action Just like in chapter 3.2.2, the seismic action is defined through response spectrums.
6.6.2.2.1 Response spectrums This time, the response spectrums were defined in the software SAP with the data in chapter 3.2.2.
6.7 Load combinations To perform a seismic analysis, the definition of a seismic combination is required alongside a fundamental combination.
6.7.1 Seismic combination
All coefficients belonging the seismic combination in equation 6.1 can be found in EN 1990 2009 and EN 1998-1 2010, and resulting in a total of four combinations, two for each earthquake type and within them two others for both horizontal directions. In every combination, the seismic action has a dominant direction, represented in full, and the orthogonal direction is only represented by 30% of its influence. Also, after consulting the second document’s national annex, the need for a vertical component is disregarded, leaving the combinations to depend solely to horizontal seismic action.
𝑆𝑑 = 𝐺𝑘 + 𝜓𝐸 × 𝑄𝑘 + 𝐸 = 𝐶𝑃 + 𝜓𝐸 × 𝑆𝐶 + 𝐸 Equation 6.1
6.7.2 Fundamental combination
In equation 6.2, seismic action is not included, since it’s only applied in accidental combinations. However, if wind was applied than it would be, with the proper coefficient.
𝑆𝑑 = 𝛾𝐺 × 𝐺𝑘 + 𝛾𝑄 × 𝑄𝑘 = 𝛾𝐺 × 𝐶𝑃 + 𝛾𝑄 × 𝑆𝐶 = 1,35 × 𝐶𝑃 + 1,50 × 𝑆𝐶 Equation 6.2
6
6.8 Seismic coefficient The most important seismic action determines the seismic coefficient, β, and in this case
it’s for the y direction type 1.1 with a value of 0,11, well within the expected value between 0,10 and 0,20, and also in agreement with the 0,17 value calculated manually.
7. Design In this chapter one of every element type is designed. In the specific case of the slab, the
seismic analysis will not be used for stress evaluation, only for deformation.
7.1 Design of Slab The chosen slab is from floor 2, with a thickness of 0,20 meters and a small portion of 0,15 metros at an edge. To design it, the safety to the ultimate limit states (ULS) and serviceability limit states (SLS) must be guaranteed.
7.1.1 Ultimate Limit States (ULS)
7.1.1.1 Moment
The same procedure and methods used in chapter 4.3.1 are applied along with loads from the fundamental combination. The resulting moments lead to a steel reinforcement applied in an overall rectangular mesh of ϕ8//0,15 (3,35 cm2/m). In two support sections and one frame section, an additional reinforcement of ϕ6//0,15 is included. Near the edges, there is another rectangular mesh reinforcement of ϕ8//0,15.
7.1.1.2 Shear
Applying the formulas for shear resistance indicated in EN 1998-1 2010, it comes to a value of 94,29 kN, much higher than the calculated shear stress of 31,60 kN, which means the safety for ELU is verified.
7.1.2 Serviceability Limit States (SLS)
The safety of the slab to SLS is guaranteed by controlling the occurring crack width and slab deflection.
7.1.2.1 Cracking (Crack opening)
Normally, the crack width is calculated from stresses obtained with a quasi-permanent combination, but in this case, it was preferred to use a frequent combination (Equation 7.1) because it leads to bigger loads and stresses.
𝑃𝑠𝑑 = 𝐺𝑘 + 𝜓1 × 𝑄𝑘 = 7,0 + 0,50 × 3,0 = 8,5 𝑘𝑁 𝑚2⁄ Equation 7.1
The highest moment is 18,5 kNm/m and applying the formulas in EN 1992-1-1 2010 for crack width it results in a 0,19-meter crack, which is lower than the maximum recommended width in the same document of 0,30 meters for the slab class of exposure.
7.1.2.2 Deformation (Deflection)
To better estimate the deflection in a slab, and just for this instance, it’s best to resort to the model created in SAP, which lead to a 1,8 millimeter deformation. The deformation limit is L/250, with L being the smaller length in the panel registering the deflection, coming up to a maximum of 18 millimeters. Meaning, that in a long term, the deflection had to increase 10 times to cause any protuberance on the slab and this not to be expected.
7.2 Design – Column The seismic combination is more relevant than the fundamental combination for columns, to be designed through a combined compression and bending method. Column P06, primary, and P10, secondary, were chosen for design, since they are the most stressed for each column type.
7.2.1 Primary Column (P06)
P06’s section is 0,30 meters (b) by 0,50 meters (h) and 4,5-centimeter concrete cover.
7
7.2.1.1 Longitudinal reinforcement
The necessary reinforcement can be determined through a series of recommendations and impositions of the regulations EN 1992-1-1 2010 and EN 1998-1 2010 (Table 8).
Table 8 – Stresses and reinforcement for column P06
Column Nsd [kN] Msd [kNm] µ ν ωtot As,tot [cm2] Solution As [cm2] ρL
P06 -299,87 187,17 0,094 -0,075 0,14 12,88 < As,min 6ϕ20 + 4ϕ16 26,89 0,018
7.2.1.2 Transverse reinforcement
In a column it’s easier to achieve a transverse reinforcement through constructive regulation and then verify that it’s enough to comply with the resistance regulation (Table 9). In the critical zone the reinforced spacing is reduced to 0,10 meters and has a 0,70-meter length.
Table 9 – Stress and transverse reinforcement for column P06
Column Vsd [kN]
d [m]
z [m]
cotg θ Asw/s
[cm2/m] (Asw/s)min [cm2/m]
As,adopted [cm2/m]
As [cm2/m]
P06 90,82 0,44 0,40 2,0 2,64 3,04 ϕ8//0,15 + ϕ8//0,15 6,70
7.2.2 Secondary Column (P10) P10’s section is 0,30 meters (b) by 0,50 meters (h) and 4,5-centimeter concrete cover.
7.2.2.1 Longitudinal reinforcement
Equal requirements for P06 and P10, since the cross section is the same (Table 10).
Table 10 – Stresses and reinforcement for column P10
Pilar Nsd [kN] Msd [kNm] µ ν ωtot As,tot [cm2] Solution As [cm2] ρL
P06 -934,16 -201,31 0,10 -0,23 0,04 3,68 < As,min 6ϕ16 + 2ϕ16 16,09 0,015
7.2.2.2 Transverse reinforcement
Regulation EN 1992-1-1 2010 is enough to achieve transverse reinforcement in P10, because it was categorized as a secondary column (Table 11). The critical zone has a 0,50-meter length and the reinforcement spacing is once again reduced to 0,10 meters.
Table 11 – Stress and transverse reinforcement for column P06
Column Vsd [kN]
d [m]
z [m]
cotg θ Asw/s
[cm2/m] (Asw/s)min [cm2/m]
As,adopted [cm2/m]
As [cm2/m]
P10 97,61 0,44 0,40 2,0 2,84 3,04 ϕ8//0,15 + ϕ8//0,15 6,70
7.2.3 Particulars Although the fundamental combination was applied, it led to inferior stresses than the
seismic combination, lesser even than the minimum requirements imposed by the regulations.
7.3 Design – Beam The agglomerate of applying the seismic combination, of the dominant earthquake type in both directions, and the fundamental combination led to the design of V734, V834, V714, V816 and V923 beams. To simplify, only the V834 beam will be described.
7.3.1 Beam V834 (Floor 2 beam)
The beam’s cross section is 0,30 meters (b) by 1,15 meters (h) with a concrete cover of 4,5 centimeters.
7.3.1.1 Longitudinal reinforcement
After making sure the necessary requirements in EN 1992-1-1 2010 and EN 1998-1 2010 are met, the resulting reinforcement is displayed in table 12.
8
Table 12 – Longitudinal reinforcement for V834 beam
As [cm2/m] Ac [cm2/m] ρ [%]
M+ [kNm] 6ϕ16 (12,06) 3ϕ16 (6,03) 0,37
M- [kNm] 6ϕ16 (12,06) 3ϕ16 (6,03) 0,40
7.3.1.2 Transverse reinforcement
Just like in the previous chapter, the required regulations must be guaranteed to achieve the transverse reinforcement of table 13. In critical zones the spacing is reduced to 0,125 meters.
Table 13 – Transverse reinforcement for V834 beam
Vsd [kN] (Asw/s) [cm2/m] (Asw/s),adopted [cm2/m]
170,40 2,31 < As,min 2R ϕ8//0,25 (4,02)
7.3.1.3 Longitudinal reinforcement in the web
This reinforcement has the function to control and minimize cracking, to do so ϕ10//0,15 meters in each side of the web will be placed.
7.3.2 Beam V923 (Floor 3 beam)
Designed via the fundamental combination and with a transverse reinforcement spacing of 0,15 meters instead of 0,25 meters, in current zones. Same solution for critical zones.
7.3.3 Particulars
All longitudinal reinforcements need to resort to ϕ16 bars due to restrictions regarding the node between columns and beams. In beam V923 there are two different transverse and longitudinal reinforcements because of the two distinct cross sections.
7.4 Design – Foundation The foundation is constituted by the agglomerate of footing and strap beams.
7.4.1 Footing
There are two kinds of footing, differing in their volumetric dimensions. The same combinations used in beams are applied and S03, S14 and S07 will be designed. Only the S03 footing will be described.
7.4.1.1 Footing S03
The footing has a 1,60-meter side square base, 0,70-meter height and 4,5-centimeter concrete cover.
7.4.1.1.1 Inferior reinforcement
Resorting to a simple and commonly used footing reinforcement calculation model, the necessary reinforcements can be reached (Table 14) and displaced in a rectangular mesh.
Table 14 – Inferior reinforcement for footing S03
Footing As [cm2] As [cm2/m] As,needed [cm2/m] As,adopted [cm2/m] ρ [%]
S03 6,51 4,53 < As,min 11,47 ϕ16//0,15 (13,40) 0,21
7.4.1.1.2 Superior reinforcement
It’s enough to choose a reinforcement based on the inferior solution, with a smaller diameter for the bars and a larger spacing. Therefore, the solution is ϕ12//0,25 meters with same kind of disposition.
7.4.1.2 Particulars
In S07 footing the solution is ϕ16//0,20 meters for the inferior reinforcement and ϕ12//0,20 meters for the superior reinforcement, both with a rectangular mesh displacement.
9
7.4.2 Strap beam
L01, L07 and L09 strap beams are going to be designed and with same procedures previously used in beams. The impositions to the cross sections, according to EN 1998- 2010, will not be put into effect since this element isn’t structurally indispensable. Strap beam L01’s design is described.
7.4.2.1 Strap beam L01
The strap beam exists in the x direction, with a cross section of 0,50 meters (b) by 0,70 meters (h) and 4,5 centimeters of concrete cover.
7.4.2.1.1 Longitudinal reinforcement
The longitudinal reinforcement is displayed in table 15.
Table 15 – Reinforcement for strap beam L01
Msd [kNm] µ ω As [cm2] As,adopted [cm2] ρ [%]
46,64 0,008 0,008 1,67 < As,min 7ϕ16 (14,07) 0,43 > ρ,min
7.4.2.1.2 Transverse reinforcement
Table 16 contains the transverse reinforcement.
Table 16 – Transverse reinforcement for strap beam L01
Vsd [kN] z [m] θ [º] cotg θ (Asw/s) [cm2/m] As,adopted [cm2/m]
27,82 0,59 30 1,73 0,63 < As,min 2R ϕ8//0,15 (6,70)
7.4.2.1.3 Longitudinal reinforcement in the web
The longitudinal reinforcement in the web is ϕ8//0,075 meters in each side of the element.
7.4.2.1 Particulars
L07a has smaller dimensions so lesser needs of reinforcement (Table 17).
Table 17 – Reinforcements for strap beam L07a
As [cm2] (Asw/s) [cm2/m] Acracking [cm2/m]
4ϕ16 (6,03) ϕ8//0,25 (4,02) ϕ8//0,20 (each side)
8. Inclusion of structural cores The goal is to complete the structure with cores, register its influence and designed them.
8.1 Inclusion of stairs and elevator cores to the structure As a last step to this work, the intent is to add structural cores to the building, defined by
a group of walls, that will later perform a stairway and elevator function. The walls are in reinforced concrete and treated just like columns, with the same materials and actions defined in chapters 2 and 3. They will be placed as if they were one element, with a 0,30-meter thickness, and located in the lateral facade that has no porches, and go as high as 3,0 meters above the floor 4 slab. A 0,20-meter slab will be placed to top them off.
8.2 Modulation The cores were modeled as independent walls linked by rigid elements at their top that guarantee the functioning of the walls as a group and as higher stiffness elements.
8.3 Changes provoked by the cores The presence of the cores forced some changes. Firstly, a height reduction in the cross section of beam V966 (Floor 4). Afterwards, suppressing columns P28, P33 and P34 (Floor 3) and replacing them with the creation of column P40, with a square section of 0,40-meter side, and extending column P26 all the way to floor 3. This alteration also meant a relocation, in direction y, of beam V953 (Floor 4) to align it with P40, which in turn relocated P38 (beginning in floor 4) so that it has its own vertical alignment with P30 (ending in floor 4 and continued by P30). Finally, the structure is now classified as a mixed system.
10
8.4 Design of columns, beams and footing In design, the only elements in need of reprocessing were others beams with higher stresses (Table 18).
Table 18 – Reinforcement for beams V828, V911, V951 and V958
Beam
Longitudinal reinforcement Transverse reinforcement Cracking reinforcement
Msd+ / Msd
- Current Zones Critical Zones Web
As [cm2] Ac [cm2] Asw/s [cm2/m] Asw/s [cm2/m] Asw/s [cm2/m]
V828 / V911 6ϕ16 (12,06) 3ϕ16 (6,03) 2R ϕ8//0,25 (4,02) 2R ϕ8//0,125 (8,04) ϕ10//0,10 (7,85) / ϕ10//0,15 (5,24)
V951 / V958 8ϕ16 (16,08) 4ϕ16 (8,04) 2R ϕ8//0,25 (4,02) 2R ϕ8//0,125 (8,04) ϕ10//0,10 (7,85)
8.5 Design of a core The stairway core was chosen for design because its walls have the biggest cross
sections and was consequently responsible for higher stresses in the seismic analysis. Its reinforcements will be determined per wall.
8.5.1 Vertical reinforcement
Once again, with the proper requirements indicated in both EN 1992-1-1 2010 and EN 1998-1 2010 and also with a reinforcement calculation model applied to each wall, the reinforcements in table 19 can be reached. In each side of every wall a reinforcement of ϕ10 bars spaced by 0,20 meters will be placed. Reinforcements in the two critical lengths of each wall are mainly responsible for the resistance to moment stresses. The critical length (lc) is 0,80 meters in walls 1 and 3 and 0,55 meters in wall 2.
Table 19 – Reinforcement by critic length for each wall
Element Reinforcement by lc As,total [cm2]
Wall 1 / Wall 3 4ϕ16 +6ϕ12 25,51
Wall 2 4ϕ16 +4ϕ12 22,37
8.5.2 Horizontal and transverse reinforcement
Horizontal and transverse reinforcement for every wall are displayed in table 22, obtained with the EN 1992-1-1 2010 and EN 1998-1 2010 regulation.
Table 20 – Transverse reinforcement for each wall
Element Ash [cm2/m] Involving truss [cm2/m] Interior truss [cm2/m]
Wall 1 / Wall 3 2R ϕ8//0,20 (5,03) ϕ8//0,10 (5,03) 2x2R ϕ8//0,10 (20,1)
Wall 2 2R ϕ8//0,20 (5,03) ϕ8//0,10 (5,03) 2R ϕ8//0,10 (10,05)
8.5.3 Confinement and local ductility
Applying the necessary verifications in EN 1998-1 2010 it was concluded that the safety in terms of confinement and local ductility in the walls is guaranteed.
8.6 Design of the core’s footing The footing of the cores is 6,80 meters (B) by 7,60 meters (L) by 1,00 meters (H), and
with a useful height (d) of 0,90 meters. This element belongs to all walls and will embody S10 and S15, associated to columns P23 and P26. To design it, a similar model to the one used in chapter 7.4.1 was created. A solution of #ϕ20//0,15 for the inferior reinforcement and #ϕ12//0,20 for the superior reinforcement was chosen, and as indicated all displaced in a rectangular mesh.
Conclusions
This work supplemented the concepts acquired throughout the course and developed even further the problem solving creativity and execution. The main results were the proven importance of walls against other elements regarding stiffness in a current building, better understanding of the European regulations, which aspects of design can be trickier and need greater detail and also the importance of tridimensional models nowadays to improve the quality of the project.
11
References [1] NP EN1990:2009. “Eurocódigo 0 – Bases para o projeto de estruturas, 2009”.
[2] NP EN1991-1-1:2009. “Eurocódigo 1 – Ações em estruturas: Ações gerais – Pesos volúmicos, pesos próprios, sobrecargas em edifícios, 2009”.
[3] NP EN1991-1-4:2010. “Eurocódigo 1 – Ações em estruturas: Ações gerais – Ações do vento, 2010”.
[4] NP EN1992-1-1:2010. “Eurocódigo 2 – Projeto de estruturas de betão: Regras gerais e regras para edifícios, 2010”.
[5] APEB – Associação Portuguesa das Empresas de Betão Pronto. “A especificação do Betão: Guia para a utilização da norma NP EN 206-1. 2008”.
[6] E 464-2005. Documentação Normativa, Especificação LNEC – Laboratório Nacional de Engenharia Civil: Betões - Metodologia prescritiva para uma vida útil de projeto de 50 e de 100 anos face às ações ambientais, 2005.
[7] Camara, José Noronha da. “Estruturas de Betão I”. IST, 2014/2015.
[8] Costa, António. “Estruturas de Betão II”. IST, 2013/2014.
[9] Florindo, Nuno Miguel Queiroz. “Projeto de Estruturas duma Torre Habitacional em Sines”. 2013. 300f. Dissertation (Masters in Civil Engineering) – Instituto Superior Técnico, Lisboa, 2013.
[10] Costa, António. “Durabilidade de Estruturas de Betão”. IST.
[11] Costa, António. “EC8-1: Projeto de estruturas para resistência aos sismos – Exemplo de aplicação 2”. Ordem dos Engenheiros, 2011.
[12] Romãozinho, Manuel Francisco Bacelar de Ornelhas Ruivo. “Dimensionamento para a ação do EC8: Análise das prescrições da EN1998-1 aplicadas a estruturas de edifícios de betão armado com recurso a um exemplo prático”. 2008. 176f. Dissertation (Masters in Civil Engineering) – Instituto Superior Técnico, Lisboa, 2008.
[13] Gama, Catarina Morais. “Dimensionamento Sísmico de edifícios de betão armado: Estudo de diferentes soluções envolvendo paredes estruturais”. 2014. 116f. Dissertation (Masters in Civil Engineering) – Faculdade de Engenharia da Universidade do Porto, Porto, 2014.
[14] Appleton, Júlio. “Estruturas de Betão I: Capítulo 9.7”. 2012/2013.
[15] Computers & Structures Inc. Introductory Tutorial for SAP200®: Linear and Nonlinear Static and Dynamic Analysis and Design of Three-Dimensional Structures – Berkley, California, USA, 2011.
