Terms of Reference This report is the final report on Structural Design for AR0026 MEGA, given at the Delft University of Technology during the academic year of 2017-2018. Authors are Yamuna Sakthivel (4738578) and Mark Schilder (4316355).
Table of Contents Terms of Reference .........................................................................................................................................................................2 1.
Introduction ................................................................................................................................................................................. 5
2.
Highrise........................................................................................................................................................................................... 6 2.1.
Architectural Concept ............................................................................................................................................. 6
2.2 Input for analysis .................................................................................................................................................................. 8 2.2.1
Load Case .................................................................................................................................................................... 8
2.2.2
Wind load ..................................................................................................................................................................... 9
2.2.3
Equivalent Core Thickness ..................................................................................................................... 10
2.3 Structural Evolution .......................................................................................................................................................... 11 2.3.1 Preliminary Structural considerations ....................................................................................................... 11 2.3.2 Analysis of Diagrid Structural Concept.................................................................................................... 11 2.3.3 Alternate Approach ................................................................................................................................................ 13 2.4.
GSA Analysis.................................................................................................................................................................. 16
2.4.1 Load Conditions ......................................................................................................................................................... 16 2.4.2 GSA Model ..................................................................................................................................................................... 19 2.4.3 GSA Outcome............................................................................................................................................................. 20 2.4.4 Remarks .......................................................................................................................................................................... 20 2.5
Build-up of the Final Model ..............................................................................................................................22
2.6
Checks & sizes .............................................................................................................................................................25
2.6.1 Tube member .............................................................................................................................................................25 2.6.2. Floor system ...............................................................................................................................................................27 2.6.3 Interior columns ....................................................................................................................................................... 30 2.6.4 Hand calculation.......................................................................................................................................................32
3
2.7
Tube connection ........................................................................................................................................................34
2.8
Fire safety ....................................................................................................................................................................... 36
Low rise ....................................................................................................................................................................................... 38 3.1 Architectural concept .................................................................................................................................................... 38 3.2 Build up..................................................................................................................................................................................... 39 3.2.1 Eastern plinth .............................................................................................................................................................. 39 3.2.2 Western plinth ........................................................................................................................................................... 40 3.3 Sizing............................................................................................................................................................................................ 41 3.4 Analysis......................................................................................................................................................................................42 3.4.1 Eastern plinth ...............................................................................................................................................................42 3.4.2 Western plinth ........................................................................................................................................................... 44 3.4.3 Western plinth Truss ............................................................................................................................................ 46
4
Foundations ............................................................................................................................................................................. 48
4.1 Underground ........................................................................................................................................................................ 48 4.2 Site ................................................................................................................................................................................................ 50 4.3 Input for calculation ........................................................................................................................................................ 51 4.3.1 Common elements ................................................................................................................................................. 51 4.3.2 Main Building ...............................................................................................................................................................52 4.3.3 Low rise (plinth)..........................................................................................................................................................52 4.4 Analysis......................................................................................................................................................................................53 4.4.1 Characteristics.............................................................................................................................................................53 4.4.2 High Rise calculation ............................................................................................................................................ 55 4.5 Foundation stiffness........................................................................................................................................................57 4.6 Second order effects .................................................................................................................................................... 58 4.7 Subway settlements ...................................................................................................................................................... 59 5
Construction Sequence ................................................................................................................................................. 60 5.1 Foundation/Basement Construction................................................................................................................ 60 5.2 Super-structure construction .................................................................................................................................. 61
6
Conclusion and reflection ............................................................................................................................................ 63
7
References ............................................................................................................................................................................... 64 Topographical/Geographical ................................................................................................................................... 64 Engineering .............................................................................................................................................................................. 64
1. Introduction Directly near the central train station of Rotterdam, an unused parcel of land is situated with rough dimensions of 180 x 20 metres on the Conradstraat. The local government owns this land and is planning to sell it to a project developer. Placement right in between the train and bus station would create the need for a special building.
The possibility of placing high rise on this plot has been discussed with the locals, and it has been concluded a maximum height of 180 metres would result in minimum shading disturbance to the Provenierswijk, just north of the station. Such a tower on a narrow spot like the one on the Conradstraat creates structural challenges.
Figure 1: Situation of the building plot (red outline) within Rotterdam Central district. Source: Google Maps
The municipality of Rotterdam has shared these thoughts with the Technical University of Delft. For the course of AR0026 “MEGA�, this situation has been the main input for a project combining architects, climate-, facade-, computational- and structural designers, all trying to find an optimal solution for this challenge from their own viewports. This report is the final report on the structural design part of group 06 for this course. In the following chapters, the reader will find out on the first ideas and calculations of the outcome of the project, starting from the High Rise in chapter 2. The following chapter continues on the Low Rise, while chapter 4 has its focus on the foundation. Finally, a reflection is given based on the design decisions taken at various stages of the project.
2. Highrise 2.1. Architectural Concept Synergy tower is going to be the newest trend in Rotterdam with an inviting and accessible plinth for the users. The design goal is to return the existing landscape to the city and not overshadow the landmark Rotterdam central station. The concept is a reflection of the award-winning Rotterdam central station as seen in Figure 2. The built form is distinguished with two levels of volumes: one which is a high rise and the other a low rise that forms the plinth. The pivot of the architecture is the sloping green pedestrian accessible plinth that gradually leads into the building. The high rise emerges from the center of the plinth.
Figure 2: Conceptual Sketch of the Synergy tower
It was an important design goal for the building not just address the needs of the users but also contribute to the immediate environment. Hence, the mass of the high rise is not just a reflection of the station. It is also shaped with three major parameters to respond to the users, urban surroundings and attain required architectural volume. The optimization in Octopus (Plugin in grasshopper) gives a form Figure 3. that captures highest solar radiation, encompasses the required architectural volume and reduce the reflection from the building into the surroundings. The result is an undulating mass with various inclinations on the structures that makes it an interesting challenge for structural design.
Figure 3: Overall mass as a result of parametric optimization
Figure 4: View of the rendered tower from south-east
2.2 Input for analysis It is highly important to get an indication of the dimensions of the structural elements for performing the preliminary structural analysis. The deflection limit of the building at the top excluding the foundation is the major driving parameter to conclude on the structural system and this is derived from the formula below. δ ≤ h/750 Where, δ is the deflection due to the building’s stiffness It is understood that for height of 177 m, a maximum allowable deflection is 0.24 m.
2.2.1
Load Case
Since this part of the building complex is over 70 metres tall, it is officially a high rise building according to Dutch regulations. It incorporates multiple functions: Hotel, Residences, Offices and some Shopping areas. In case of structural failure, the consequence in terms of deaths and injuries would be very high, since the building is packed with people. Also, the escape time would be considerably higher than for an average building. Therefore, consequence class 3 is necessary for any structural calculations. Hence, the following factors are used for loading. Design Situation 1 2
Permanent unfavourable 1,49 1,32
loads, Permanent loads, Variable loads, favourable leading 0,9 0,9 1,65
Variable loads, others 1,65 1,65
Table 1: CC3 load factors
Since the (variable) wind load is an important influencing factor for the modelling of the tower, design situation 2 is taken. In the table below, an overview is given of the load cases used as input for the FEM models. Load Case
Permanent: G
SLS1 ULS1 SLS2 ULS2 ULS_0,9G *
1,0 1,32 1,0 1,32 0,9
Variable Leading: Qwind 1,0 (North-South) 1,65 (North-South) 1,0 (East-West) 1,65 (East-West) 1,65 (North- South)
Variable Qfloor Ψ0 * 1,0 Ψ0 * 1,65 Ψ0 * 1,0 Ψ0 * 1,65 0
Secondary:
Table 2: Analysed load cases in GSA Oasys
(*) This loadcase has only been used for the GSA Oasys and Foundation analysis. Both analyses are made for two wind load directions. These directions are according to the expected primary directions of the building, meaning the building is loaded perpendicularly to its face.
2.2.2
Wind load
In many examples, maximum wind load is taken to model the behaviour of the tower. As the Eurocode states a stepped approach for wind loading, this seemed an overestimation. A quick test was set up in Matrix frame to find out if a reduced wind load could be used. Since deflections were expected to be the leading factor, this was the compared output. Three cases were compared: 1. Deflection under three stepped loading according to NEN EN 1991-4, with linearized 2nd step; 2. Deflection under maximum loading (for maximum height); 3. Deflection under equivalent bending moment load* * This load is taken from Mbase due to load case 1: stepped loading. Equivalent constant load ‘q’ has been then applied under case 3, using Mbase = ½ q l2. The loading and heights in the following figure are exact, while deflections are not (a random stiffness was assigned to the elements). As a reference: (+0,8 - -0,7) * 1700 N/m2 * 1m= 2550 N/m = 2,55 kN/m for a 1 m wide strip.
Figure 5: Three Loadcases for comparison
Figure 6: Deflections for comparison
As can be seen from the last figure, case 2 approximates the true deflection better than case 3. Case 2 overestimates with 4,7%, while case 3 underestimates with 13,8%. As case 2 is not overestimating a lot, maximum height loading is used for the final model.
2.2.3 Equivalent Core Thickness For modelling purposes, a 4 walled core was preferred, rather than a complex extruded shape with openings. For this reason, an equivalent core model was set up. The core has been set up by the climate designers ensuring that all elevators, safety measures, ducts and services are accommodated. Inputs were provided by the structural team in assigning the thickness of the walls and opening in the core. Some inner walls are also included in a cross-section analysis, as seen in Figure 7. Neutral centre, A (m2), Iyy (m4) and Izz (m4) have been computed. To compensate for openings, factor 0,7 has been used for reduction in stiffness on the second moment of areas. The equivalent wall thicknesses (ty and tz) used for the FEM modelling have been fine tuned for these two numbers (Iyy and Izz). Figure 8 shows wall sizes, while Figure 9 shows neutral centre positioning. Table 3 shows the outcome of the effective thickness of walls obtained for modelling. The drawback of this method would be that the area used in the modelling is also reduced. For self-weight, a reduction of 1,0 is used (no reduction), as this compensates for inner walls.
Figure 7: Used core faces for equivalent thickness. Holes taken into account by reduction factor only.
Figure 8: Thickness and positioning of the walls in question.
Figure 9: Positioning of the Neutral centre (black dot)
ty, outer (m) tz, outer (m) A (m^2) Iyy (m^4) Izz (m^4)
From Analysis 0,8 0,6 59,6 3262,0 936,6
Reduction 0,7 0,7 0,7
41,7 2283,4 655,6
Equivalent used for FEM modelling 0,68 0,43 42,9 2296,0 655,6
Table 3: Outcome of the thickness analysis
2.3 Structural Evolution 2.3.1 Preliminary Structural considerations
Figure 10: Options considered for selection of structural system and analysis
2.3.2 Analysis of Diagrid Structural Concept Initial stages of design had its core outside the building as a free structure and the building faรงade had to act as the structure. Hence, a diagrid system was considered as it is the most efficient and sustainable structural system which does not rely on the core for stability.
Mega structures are possible from large bracings to smaller diagonals running throughout the structure. The efficiency of the mega frame is a result of the angle of the bracing that range from 30-60 degrees, sizing of diagonals and form of the building it takes upon. The diagrid was scripted in grasshopper to make it parametric to analyse for various spacings and angles with different profile sizes. Three major angles of the diagonal were considered to analyse its performance for this form in Karamba.
Figure 11: Analyzed diagrid models with angles of braces as 53°, 64°and 45° (from left to right)
The goal of this analysis was to understand the deflections attained at the top of the building with various spacing and angles of bracing. Figure
Angle of the bracing (m)
Height of a unit (m)
a b c
53 64 45
16 16 4
Spacing between the diagonals (m) 12.0 8.6 8.4
Column profile (SHS in cm) 90 x 90 x 10 90 x 90 x 10 90 x 90 x 10
Mass of the stability system (Kg) 2.16 x e7 2.45 x e7 3.65 x e7
Deflection (cm) 22 14 16
Table 4: Preliminary analysis of global deflection of diagrid systems analyzed in Karamba
From the above table, it can be concluded that for this tower a diagrid system with 53degree angle uses the least material with higher spacing between the diagonals for a deflection of 0.22m (which is lesser than the maximum allowable deflection of 0.24m). Diagrid system express visual dominance compared to other conventional structural systems. Before optimizing this structure, it was necessary to discuss if this structure would be most suitable to express the architectural ideologies. The following were the considered disadvantages that was collective inference from various disciplines:
1. 2. 3. 4. 5.
The diagrid formed an envelope around the building overpowering the sharp kinks that neglected the architectural reflection of the Rotterdam central station. Complicated nodes arise due to various change in angles that increases the cost of fabricating the nodes Optimizing the diagrid system would lead a change in the architectural form that disregards radiation analysis. The tower being a mixed-use tower, the diagrid interferes with the clean view in the residence that affects the market value of the properties. The clean architecture expression on the faรงade was lacking.
Understanding the design and aesthetic requirements of the architects, it was necessary to make a subtle structural system that efficiently resolves the lateral forces on the shorter axis and not overpower the structure. To keep the essence of the architecture, an innovative structural system that flows along the building to offer major views and wider spacing between the structural elements should be adopted.
2.3.3 Alternate Approach Design with research was the adopted strategy to come up with a suitable structural concept. Projection of a bounding grid of vertical lines was the starting point to create an envelope and test how the tube system works on an undulated architectural form.
Figure 12: Projection of structural envelope onto the architectural mass
The projected grid wraps around the form generating a tubular envelope with columns and beams. A grid of 1.5 m the spacing strategy to decide on the incremental spacing between the columns. The spatial planning could also be achieved effectively for architectural purposes using the same multiples of dimensions.
Model 1: Tube structure with diagonal bracings In the initial design, core could not be considered as the stability member as it was not centrally located. A pure tubular structure with 4.5 m spacing was analyzed in Karamba and GSA. The stand alone could not resolve the lateral forces and keep deflection in
control for serviceability limit state. Addition of diagonal members, increasing the size of corner framework were necessary to reduce the deflection. And this leads to complicated nodes in the structure, high self-weight and less porosity through the structure.
Figure 13: Result of Karamba structural analysis of Model 1
Model 2: Tube structure with core In this model, core placement had been decided and this has been considered as a stability member for further analysis. The consideration of core led to drastic decrease in the size of the columns and beams. A uniform sizing of structural elements and elimination was achieved unlike model 1. Half of the structural mass has been reduced and connection between the structural elements has been simplified.
Figure 14: Result of Karamba structural analysis of Model 2
Model 3: Tube structure with 6m Spacing With architectural demand for more spacing between the columns, a spacing of 6 m was experimented to check the stability of the tube with core. Increase in the size of column profile helped in coping the increased spacing between the structural elements.
Figure 15: Result of Karamba structural analysis of Model 3 Figure
Spacing between the columns (m)
Size of the Column profile (SHS in cm)
Mass of the tube (Kg)
Deflection (cm)
a b c
4.5 4.5 6
90 x 90 x 10 50 x 50 x 10 80 x 80 x 10
3.17 x e7 1.5 x e7 2.7 x e7
18 19 24
Table 5: Deflection in lateral stability system for the chosen structural concept
Optimisation of Model 3 The kinks present in building at level 0 and 12 results in high horizontal forces due to lateral loads from winds. The diaphragm action given by the floor would be insufficient for even distribution of lateral forces on to the tube and the core. Hence, addition of horizontal bracing was necessary to transfer the lateral forces more effectively at the two mentioned levels.
Figure 16: Structural section indicating the kinks in the tower
Figure 17: Plan depicting the arrangement of horizontal bracing on the composite floor system
2.4. GSA Analysis 2.4.1 Load Conditions The loads used for the FEM model have been set up as follows. An overview of the loads is included in the end of this paragraph.
Distribution of Loads The distribution of loads is adapted to the model itself (see paragraph “2.4.2 GSA Model�) and therefore no loads are applied to the floors directly. Since the floor is spanning between the facade and the core, 50% of its loads is distributed along the perimeter beams of the tube system, and 50% is assigned to the core. An average floor size of 22,9 x 50,4 m is used for computation of the total load. On the perimeter beams, this results in a line load (N/m), while on the core mesh face the input is a 2D load (N/m2).
Figure 18: Average floor widths.
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Wind forces are distributed along the nodes of the facades, which are evenly distributed due to the applied grid of 6 m width and 4 m height. The area is computed by grasshopper for the facades in question. This is an area of 8767 m2 for the north facade and 4308 m2 for the west facade. No distinction is made between pressure and suction; both components are applied on the same facade.
Figure 19: Highlighted facades used for loading
Permanent Loads Permanent loads used for the modelling are composed of floor self-weight, core selfweight and structural facade self-weight. The floor beams have a relatively low weight and are neglected for now. Shallow deck floors with a 6 m span are 23 cm thick according to the product specification of HODY (Ir. Soons, F.A.M. & al, (2014), page cd10). This is including the 6 cm corrugated sheet, which means the average thickness is 20 cm. Using the specific weight of reinforced concrete, this results in a load of 5 kN/m2.
The structural facade consists of composite elements and is heavy. In fact, its weight per floor is higher than the core’s weight per floor. Its weight is modelled as a line load along all the tube elements. The cross section ‘A’ multiplied by 1 m gives a line load of 31,74 KN/m, see the Table 9. For more information on the cross section, see paragraph 2.6.1 Tube member. As mentioned before, the core area with no reduction (factor 1.0) is used for the weight of the core. It gives a face load of 21,3 kN/m2.
Variable Loads Variable loads used in the modelling are variable floor loads and wind loads. The floor functions are changing and so are the imposed variable loads. A weighted average of 2.25 KN/m2 is used for each floor, to keep the modelling simple and flexible. Since the wind load is taken as the main variable load, a combination factor of Ďˆ=0,5 is used on all the floors. Only two floors are taken with maximum variable load, which is modelled with the combined load twice (0.5 * 2 gives 1.0; maximum variable loads on these floors). Those two floors are the two highest floors that are not situated in the tip. For the wind loads, the maximum wind pressure (being 1.70 KN/m2) is used accordingly to the wind load research, as stated in section 2.2.2Wind load). The number is according to wind region 2, Urban terrain, height of 170 metres (Ir. Soons, F.A.M. & al, (2014), page gl12). The building is 177 metres tall, but the top two floors are left out, which enables the wind to pass through. The slightly smaller maximum load is the only way this is taken into account for loading, since the area without windows is in the tip and very small. Thus, full area is considered to be taking up the wind. The factor for pressure has been taken as +0,7, while for suction as -0,8. Together, they add up to 1,5. The load has been distributed along the nodes of the facades. đ??šđ?‘¤đ?‘–đ?‘›đ?‘‘,đ?‘›đ?‘œđ?‘‘đ?‘’ = đ?‘žđ?‘? (đ?‘§đ?‘’ ) ∗ đ?›´đ?‘?đ?‘“ ∗
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Overview Characteristic loads: Type
Pointload (kN) Permanent
Lineload (kN/m)
Faceload (kN/m^2)
Remarks
19,68
10,97
Lineload on facade beams, faceload on core.
31,74
-
-
-
22,65
Floor
-
4,43
2,47
Wind
28,02 / 25,97
-
-
Floor
-
Facade Core Variable
Lineload on facade beams, faceload on core. Combination factor Ďˆ=0,5 included here. In North-South / West-East directions respectively.
Table 6: Loading of the GSA model
2.4.2 GSA Model The GSA model consists of 3 parts: Core face (mesh), Floor areas (meshes), tube elements (1d beams). The core mesh has 4 sides, according to the equivalent core thicknesses, the two long sides in weak direction have been assigned 0,43 m thick, while the two short ones in the strong direction are 0,68 m thick. The floor meshes are automatically loaded with fully rigid connections to both the core and the tube elements. An alternative modelling with floor beams and no floors has been considered, but this did not result in a workable model in GSA. It has been used in karamba analysis for comparison, which showed very comparable deflections (see paragraph “Model 3: Tube structure with 6m Spacing”)To make sure the floors are not cooperating in the stiffness of the tower, they have been modelled as 1 cm thin, so they have a negligible out of plane rigidity. They only act as membranes that spread the wind load and connect the core with the facade. This is the reason for placement of the floor loads on the tube and core only. For the tube, a differentiation has been made for the beams and the columns. They could be loaded separately, and properties could vary as well. Finally, the same section has been used for both.
When creating the meshes, it has been made sure nodes were placed in overlap with the nodes of the facade, so that FEM software could link the two together, as the sources were different: meshes were imported using the GeometryGym function built in in Rhinoceros’ Grasshopper, while the facade has been imported as a DWG file.
Connection to the underground has been ensured by encastring all the nodes on height z=0. Another part to note is the exclusion of the floor slab on level 4, according to the wishes of the architect. The horizontal tube elements have been taken out here as well on the east and west facades, see figure below. This does result in some unused nodes, showing red diamonds in the model.
Figure 20: Removed floor slab and beams on two facades. Red diamonds indicate unused nodes.
2.4.3 GSA Outcome The GSA Oasys analysis has been used to check for deflections in SLS and member forces in ULS.
Figure 21: Outcome under different loadcases
2.4.4 Remarks From the model outcome, some remarks can be made. The first one is that tensile reactions only occur at the core corners, according to this model (see Figure 22) Any basement influences are not included. They will be for the foundation calculation.
Figure 22: Vertical reaction forces at the nodes. Tension found in the core corner only.
Another one is that the architect’s plan to leave out a beam at level 4 has produced the governing member, as in this part of the tube bending moment increases due to double height of the member, as does buckling length.
Figure 23: Deflected shape at the location of the kink (Level +3)
One can also see the core face being pushed inside via the floor by the facade, at the location of a kink. This model has a core that is composed of 4 faces, while in real, the building would have a core with interior walls. The core face would react stiffer, which means it would deform less, which also means less deformation would occur at the facade itself. It is therefore doubtful if the bending moment found on the southern facade members (the right side of this picture), is realistic.
Figure 24: Stresses in the core base under load case 5
Another observation is that the core shows a tensile stress at the bottom under load case ULS_0.9G, which means the used cracked E modulus was the right one.
Figure 25: Stresses in core top in ULS (Load case 2)
The last significant observation shows tensile stresses at the top of the core, at the spots the floors are attached. Since a bending beam (core) and a shear frame (tube) are combined, this is the effect of different.
2.5 Build-up of the Final Model
1
Core: The core was designed to be a major transportation hub that contains the lift shafts based on architectural and service demands. It is 21.8m x 11.2m in dimension which makes it a large central element that can be taken advantage for the overall stability of the structure. The core is connected to the exterior structure by means of floor slabs and primary beams spanning between the columns and core. The effective dimensions and stiffness of the core are discussed in paragraph “Equivalent Core Thickness�.
2
The maximum floor span range for the shallow deck floor system (Discussed in Floor system) is 14.6m. The eastern volume of the structure has varying floor spans ranging from 17m in ground floor to maximum of 24m in Level 14. Hence, intermediate columns are required for supporting the shallow deck floor system. Element : Internal Column Material : Steel (S355) Support type : Fixed at the bottom and hinged to the floors Section Profile : HD 400 744+
3
Floor beams span from the columns of the lateral stability system to the core and they are modelled as hinged connections in GSA and Karamba for structural analysis. Element : Primary Beams Material : Steel (S355) Type of connection: Hinged Section Profile : HE 800M (at largest)
4
Horizontal bracing between the floor beams help in even distribution of the resultant horizontal forces over the tube and core. Element : Lateral bracing Material : Steel (S355) Type of connection: Hinged Section Profile : Square Hollow section Width – 0.1m Height: 0.1 m Thickness : 0.02 m
5
The floor slabs contribute to diaphragm effect that reduces the global deflection of the structure. A typical floor in the tower consists of a reinforced shallow deck floor integrated with concrete core activation. Though the maximum achievable continuous span is 3m for shallow deck floor system, a 6m span could be achieved by using extra props for support during casting. The section detail of the floor is elaborated in paragraph “2.6.2. Floor system”.
6
The tube structure consists of columns and beams that resolve lateral forces. The spacing between the two columns is 6m. Element : Columns and beams Material : Steel (S460) Type of connection: Moment transfer Section Profile : Square Hollow section Width – 0.8m Height: 0.8 m Thickness : 0.1 m
Table 7: Sequential build-up of the structural system of the high rise
The infill elements used are listed in the summary table below. Tower Members
Profile
Tube members
SHS 800/800/10 , composite
Interior Columns
HD 400 744+
Maximum size floor beams
HE800M
Floor Slabs
Shallowdeck HODY SB60 floor, t = 23 cm
2.6 Checks & sizes 2.6.1 Tube member The used member consists of steel, concrete and reinforcement. At first, this has been done with bearing in mind fire safety, and with the thought, the concrete could significantly add up to the stiffness of the tube as a whole. At the end of the project, it has been found that additional fire safety measures needed to be taken anyway, and that the steel is doing almost all of the work. But, an addition to the composite area reflects in stiffness of the tube in the large scale. This addition achieved by adding the concrete is 14%. In torsion, the rectangular section has been added up to the hollow section component of the steel. To enter the cross sectional properties into GSA Oasys, scaling has been done to the concrete properties, in order to be able to use the Young's modulus of Steel. This has been done as follows: I_c_eq = (0,6*Ecm/Es)*I_c (*) A_c_eq = (0,6*Ecm/Es)*A_c It_c_eq = (0,6*Gc/Gs)*It_c (*) According to NEN-EN 1994-1-1+C1:2011 6.7.3.3
Figure 26: Cross section of the structural part of the tube element Component
(Scaled) A [m^2]
(Scaled) It [m^4]
Npl,Rd [MN]
0,032
99,4
Steel
0,28
(Scaled) I [m^4] 0,0233
Reinforcement
0,0097
0,00045
-
4,2
Concrete
0,0318
0,00096
0,028
6
TOTAL
0,3215
0,02474
0,06
109,6
Table 8: Section properties and plastic axial resistance (used for member classification). Component
Area [m^2]
Steel
0,28
Specific weight [N/m^3] 78500
Reinforcement
0,0097
78500
761
Concrete
0,36
25000
9000
TOTAL
Load [N/m] 21980
31741 Table 9: Weight of the element
Check Governing member is member 10415, as can be seen in the GSA report. It is not that strange, because as stated earlier, the tube system misses out on a beam row at this location.
Figure 27: Loading on the governing member.
This element NEd = 39,01 MN MEd = 10,32 MNm VEd = 2,44 MN
is
tested
with
the
following
values.
Steel Approach The member is designed as composite, but regulation says it is officially a steel section, since δ = Npl,steel,Rd / Npl,composite,Rd = 99,4 / 109,6 = 0,91. For composite sections, 0,2<δ<0,9. Therefore, a steel analysis is made for the governing member, bearing in mind that the concrete and rebars will only add up to the resistance. Steel class: S355 Cross section class: c/t = 0,6/0,1 = 6 c/t < 33ξ = 26,73 for compression (flanges box) c/t < 72ξ = 58,32 for bending (webs box) Therefore: Cross section class 1 Normal force calculation: NEuler = 3230 MN, with lbuc = 0,5*lsys = 4 m. nEuler = NEuler/NEd = 82
đ??´đ?&#x2018; đ?&#x2018;Ąđ?&#x2018;&#x2019;đ?&#x2018;&#x2019;đ?&#x2018;&#x2122; â&#x2C6;&#x2014; đ?&#x153;&#x17D;đ?&#x2018;Ś đ?&#x153;&#x2020;đ?&#x2018;&#x;đ?&#x2018;&#x2019;đ?&#x2018;&#x2122; = â&#x2C6;&#x161; = 0,175 â&#x2030;¤ 0,2 đ?&#x2018; đ??¸đ?&#x2018;˘đ?&#x2018;&#x2122;đ?&#x2018;&#x2019;đ?&#x2018;&#x; Therefore, Ď&#x2021;buc =1,0 independent of the buckling curve; NRd = Npl,Rd U.C. = NEd/NRd = 39,01/99,40 = 0,39 [-] OK
Combined bending with normal force calculation: For rectangular hollow sections of uniform thickness and for welded box sections with equal flanges and equal webs, according to the formula sheet of the course CIE4115 :Steel Structures II (Ir. Nijgh, M.P & al, 2017). đ?&#x2018;&#x20AC;đ?&#x2018; ,đ?&#x2018;&#x2026;đ?&#x2018;&#x2018; = đ?&#x2018;&#x20AC;đ?&#x2018;?đ?&#x2018;&#x2122;,đ?&#x2018;&#x2026;đ?&#x2018;&#x2018; â&#x2C6;&#x2014; (1 â&#x2C6;&#x2019; đ?&#x2018;&#x203A;)(1 â&#x2C6;&#x2019; 0,5đ?&#x2018;&#x17D;) n = a = (A-2btf)/A = 0,42
NEd/Npl,Rd
=
0,39
đ?&#x2018;&#x20AC;đ?&#x2018; ,đ?&#x2018;&#x2026;đ?&#x2018;&#x2018; = 26,27 đ?&#x2018;&#x20AC;đ?&#x2018; đ?&#x2018;&#x161; â&#x2C6;&#x2014; 0,77 = 20,32 đ?&#x2018;&#x20AC;đ?&#x2018; đ?&#x2018;&#x161; U.C. = MII,Ed/MRd = 10,44/20,32 = 0,51 [-] OK Stress check: Assuming Av = 2*Afl đ?&#x2018;&#x2030;
đ?&#x153;?=đ??´ = đ?&#x2018;Ł
đ?&#x2018;
2,44â&#x2C6;&#x2014;106 0,16 đ?&#x2018;&#x20AC;
đ?&#x153;&#x17D; = đ??´ + đ?&#x2018;&#x160;đ??źđ??ź = đ?&#x2018;
đ?&#x2018;&#x2019;đ?&#x2018;&#x2122;
= 15 MPa
39,01â&#x2C6;&#x2014;106 0,28
+
10,44â&#x2C6;&#x2014;106 0,058
Ď&#x192;vonM,
= 320 MPa
outer web fibre
Ď&#x192;vonM,
outer fibre
= â&#x2C6;&#x161;Ď&#x192;2 + 3 â&#x2C6;&#x2014; đ?&#x153;? 2 = 317 đ?&#x2018;&#x20AC;đ?&#x2018;&#x192;đ?&#x2018;&#x17D;
= â&#x2C6;&#x161;Ď&#x192;2 + 3 â&#x2C6;&#x2014; đ?&#x153;? 2 = 320 đ?&#x2018;&#x20AC;đ?&#x2018;&#x192;đ?&#x2018;&#x17D;
U.C. = Ď&#x192;Ed,vonM / Ď&#x192;y = 320 / 355 = 0,90 [-] OK
2.6.2. Floor system For the floor system, a composite floor is taken, with an H section as steel section and a shallow deck system on top. The beams are connected as hinges on both sides. Concrete core activation is included in the slab.
Figure 28: Floor plan of level 0. Maximum span on the left. Intermediate columns placed on the right.
It has been considered to use a composite beam, but analysis showed it added up a lot to the bending moment resistance, and much less to the stiffness. Since stiffness is normative for this situation, no shear connection between the deck and the beam will be applied, other than necessary to have the floor supported by the beam.
Figure 29: Build-up of the floor section rendered.
The deck itself spans the same width as the spacing of the facade: 6 m. According to the specifications of HODY (found in Quick Reference (Ir. Soons, F.A.M. & al, (2014), page cd10)) this can be achieved with 4 temporary props during construction. This is a drawback, but in return, proper diaphragm action is achieved (if compared to e.g. hollow core slabs). An important part of the solution was the inclusion of facilities for the climate designers in our team. The challenge was to include an air duct in the beam, as placing it under the beam would significantly raise the overall ceiling/floor thickness. A rigid H beam with a local cut out for ducts is preferred over the castellated beam for flow of forces and stiffness. That is why a solid section would be used with a local cut. Since less cutting and welding would have to be done, this would also result in a cheaper solution. For the calculation though, the tables with section properties for equivalent castellated beams have been used. The chosen castellated beam has been specially chosen with an opening high enough to accommodate the duct: a 64 cm opening for a 60x80 cm duct. As removing the web locally has a high impact for shear loads, it has been strongly advised to the climate designers to place it in the middle of the span. The governing floor beam is the one on the westside of the core. From the faรงade to the core, the beam has to span 14,6 metres. Calculation characteristics have been shown below.
HEM 450 into Castellated HEM 800: Specifications A 403 h 80 I_T section 381530 W_T section 9536 opening height 64
cm^2 cm cm^4 cm^3 cm
Floor: Specifications Span beam to beam height height steel sheet average height of concrete selfweight imposed variable load
m m m m kN/m^2 kN/m^2
Type of load Characteristic qG,floor,k qG,beam,k qQ,floor,k Design qG,d qQ,d
6 0,23 0,06 0,2 5 4
lineload [kN/m] 30 2,7 24 43,2 39,6
ULS M_Ed (1/8ql^2) M_Rd (W*Ď&#x192;) U.C.
2205 3385 0,65
kNm kNm [-]
SLS w_allowed (l/300) w_Ed (5ql^4/EI) U.C.
4,8 4 0,83
cm cm [-]
Table 10a to 8d: in and output of the simply supported floor beam .
It has to be stated that for residential and hotel functions different ducts are used. If such a duct has to pass a beam that spans on the north/south faces of the building (a span of 5 m), a simpler solution would be preferred where the duct is running underneath the beam, so that no cut has to be made.
2.6.3 Interior columns Three interior columns are placed, as can be seen in the floor plan in the previous section. This means three out of four floor spans (all except for the floor span east of the core) are column free, assuring a lot of flexibility for the user. The three columns are placed on the east part, at a distance of 7,5 metres from the core face, so it could fit best with the functional floorplans. As the interior column crosses most of the floor functions, all separate functions and load cases have been taken into account. These functions are from top to bottom : Residential, Hotel, Office and Shopping, inter crossed thrice with a Mechanical/Electrical/Plumbing (MEP) floor.
Figure 30: Interior columns in a vertical cross section (marked red)
The column itself is an HD type, for easy attachment of the floor beams. These beams are not of equal length for all floors, and as a result, a part of the load will cause an asymmetric loading. As the beams are attached hinged, the eccentricity between the connection and middle of the column section will create a bending moment. This eccentricity has been taken as h/2+5 cm.
A table with all loading explanations is included as an appendix. The resulting forces and checks are shown below. Steel class: S355 Cross section class: c/t = 0,3611/0,106 = 3,4 c/t < 33Îľ = 26,73 for compression (flanges) c/t = 0,289/0,0659 = 4,4
c/t < 72Îľ = 58,32 for bending (web) Therefore: Cross section class 1 Profile specifications: HD400 x 744 + Width 442 Depth 531 t_web 65,9 t_flange 106 r 15 A 0,1149 I_weakest_direction 0,00153 W_el_loaded direction 0,0137
mm mm mm mm mm m^2 m^4 m^3
Table 11: Product specificatioins of the HD 400x744+ profile.
As with the tube column, a check has been made on combined stress with a buckling analysis, and on the reduced bending moment capacity (MN,Rd). Buckling check nbuc = NEuler/NEd l_buc EI N_Euler labda_rel buckling curve Xbuc
8,63 4 321300000 198193,66 0,45 d 0,8
[-] m Nm^2 kN [-]
N_Ed M_2_Ed (second order) Sigma_N_Ed Sigma_M2_Ed Sigma_Ed_total
22963,97 413,04
kN kNm
199,86 30,15 230,01
N/mm^2 N/mm^2 N/mm^2
Xbuc Sigma_Rd
0,8 284
[-] N/mm^2
U.C. = 230/284 =
0,81
[-] OK
[-]
Table 12: Buckling analysis of the column.
For H sections, a slightly different formula is used then seen before for the tube section, according to the formula sheet of the course CIE4115 :Steel Structures II (ir. Nijgh, M.P. & al (2017)). For n>a: đ?&#x2018;&#x203A;â&#x2C6;&#x2019;đ?&#x2018;&#x17D; 2 đ?&#x2018;&#x20AC;đ?&#x2018; ,đ?&#x2018;&#x2026;đ?&#x2018;&#x2018; = đ?&#x2018;&#x20AC;đ?&#x2018;?đ?&#x2018;&#x2122;,đ?&#x2018;&#x2026;đ?&#x2018;&#x2018; [1 â&#x2C6;&#x2019; ( ) ] 1â&#x2C6;&#x2019;đ?&#x2018;&#x17D;
With n = NEd/Npl,Rd, a = (A-2btf) Reduced bending moment capacitycheck n
3815801,08
[-]
a
0,18
[-]
M_2_Ed
413,04
kNm
MN,Rd
3815,80
kNm
U.C. = 413/3815 =
0,11
[-] OK
Table 13: Reduced bending moment capacity analysis.
2.6.4 Hand calculation To find out how accurate a hand calculation would be in comparison to the finite element modelling of GSA Oasys, a hand calculation was set up. The effective width method mentioned by Ham and Terwel in the high-rise reader (ir. Ham, P.H., ir. Terwel, K.C. (2017)) has been used. The columns have been scaled to equivalent concrete columns and have been spread out over the perimeter, after which a part of it has been declassified to be useless due to the shear lag effect. The equivalent stiffness of the core calculated earlier has been added to the overall bending stiffness EI. For the calculation, a wind load has been used only. To relativize the validity of the experiment, it has to be said that in the GSA model, the building clearly showed a larger deflection due to self weight, as the building has cantilevering floors on the southern facade. Therefore it is even more interesting why the hand calculation shows an actually larger deflection than found with FEM, especially since the facade area is only overestimated by 0.4% in the former (average floor width has been used). The calculation parameters are shown below.
Figure 31: Section of the equivalent width model used for the hand calculation. Original picture from (ir. Ham, P.H., ir. Terwel, K.C. (2017),page 41).
SIZES Building L W H
21 52,4 177
m m m
Columns ctc columns Depth equivalent concrete columns Width columns Equivalent thickness
6 1,94 1,94 0,63
m m m m
LOADS Windload qp(ze) Pressure factor Suction factor Safety factor Area Facade Lineload q
1,7 0,7 0,8 1 8803,2 133,6
kN/m^2 [-] [-] [-] (SLS) m^2 kN/m
STRENGHTS Concrete Tube & Core W_eq (effective width)
10,5
m
L
21
m
c_L_eq
0,5
[-]
I_eq_tube
1936,4
m^4
E_tube
18600
N/mm^2
EI_concrete_tube
3,60165E+13
Nm^2
E_core
10000
N/mm^2
I_core
656
m^4
EI_core
6,56E+12
Nm^2
EI_total
4,26E+13
Nm^2
REACTIONS Deflections ql^4/8EI
0,312
m
Allowed deflection (h/750)
0,236
m
Table 14a to c: Modelling input and output siizes, equivalent tube, wind loads, bending stiffness and deflections respectively
2.7 Tube connection Accurate modelling of all the connections and their performance analysis in different loading conditions for this project would require more time. Hence, a conceptual approach and design of these connections has been elaborated in this section. The inclinations and kinks on the structural mass gives rise to seven types of inclination of columns and different connection typologies between them.
Figure 32: Illustration of the various faces the structural mass
Figure 33: Types of nodes that arises between column and beam elements (1-6 left to right)
Every structure relies on strong connection between the elements that allows efficient transfer of loads and resistance to movements. Generally, tubular structures made of HDprofiles or I-profiles are connected by means of rigid connections using angles and high strength steel bolts. But, use of rectangular hollow sections poses a challenge in the design of connections. Direct bolting between the structural elements and welding are the
most commonly used connection typologies in Steel structures. For this structure, a SHS profile of 90 x 90 x 10 cm is used for both columns and beams. And connection between two SHS sections is convenient by welding methods than bolting. It requires special slots with web in the structural profiles for a person to bolt it manually. Welding is the convenient option and handling these bulky sections would cause delay in the workmanship. Hence, an alternative and easier way to assemble the structural elements is necessary. The below diagram shows the bending moment in framed structure due to lateral forces. The bending moment is the highest at the junctions where the beams and columns meet.
Figure 34: Illustration of bending moments in a framed structure
At those junctions, a highly rigid connection is a requirement. In practice, achieving such a connection between SHS profiles is difficult. Hence, the framed structure is added with nodes that would connect the beams and columns such that planes of connections are pushed away from the critical bending moment zones. The design goals for the for the connection was to avoid: 1. in-situ welding 2. Bolting slots on SHS sections that would reduce the strength of the structural profiles. To satisfy the above two criteria; nodes, columns and beams were introduced with end plates enhanced with stiffeners. These end plates could be bolted between the stiffeners that avoids the need of special holes to bolt the elements together. The figure below indicates the detail of Node 1 which is a 90-degree connection between the columns and beams. Such a connecting node eliminates the need for welding, blind bolting and bolting slots which makes it an efficient connection with high rigidity.
Figure 35: Detail connection model of Node 1
2.8 Fire safety Fire is a serious risk in any building and therefore fire safety objective must be established first. Design for fire safety can be achieved by two ways: active and passive strategies. Passive fire protection is more of fire resistance which is the component of overall fire safety. Structural design is a subset of passive fire strategies applied in building. The structural elements should be provided with fire resistance for either controlling the spread of fire or preventing the collapse of the structure depending on the function of the structure and evacuation time required. For high rises that are more than 30 storeys a minimum fire escape time of 120 minutes is a requirement according to Eurocode which is the design goal behind the conceptual design development for fire resistance. The Synergy tower has been designed with composite columns of rectangular hollow sections filled with reinforced concrete. The concrete inside the steel offers a fireresistance of 60 minutes. Bu, the structural steel that is exposed will collapse in a fire when the temperature reaches a critical level (500-100 degree). Hence, additional safety measures are required to seal the steel elements. To ensure this, the square hollow composite sections are encapsulated in 50 mm reinforced Gypsum board as an insulating layer that can provide fire resistance up to 120 minutes. The figure below illustrates the detail of the composite column.
Figure 36: Cross section of the column encapsulated in reinforced gypsum boards for fire safety
Also, the shallow deck floor system rests on the HE 800 M steel profiles in the largest span that are perforated for the service ducts to pass through them. These perforations and services below puts them at higher level of fire risk exposure. But unlike the column and beam elements of the tube structure, they cannot be encased in gypsum boards. An alternate protection should be provided such that the service ducts pass through without hinderance. A fire-resistant coating of intumescent paint would be the most convenient option. The thickness of this coating decides the duration of fire resistance. A 6 â&#x20AC;&#x201C; 7.5 mm thickness of epoxy resin- based thick coat can offer a fire resistance up to 120 minutes. The thin film coatings under the influence of heat produce an insulating layer blown up to 50 times thicker than the original film thickness.
Figure 37: HE 800 profiles coated with intumescent paint fire resistance
3 Low rise 3.1 Architectural concept The low rise has been designed as a connection between the NS station, the urban are on the ground floor, the bus station and the tower. It has a sloping roof on the eastern side, so that people could climb upwards while enjoying the plants along the way.
Figure 38: Architectiral concept: easthern plinth
This green roof continues on storey 4 of the high rise and on the other side of the tower, on the western plinth. Another interesting point in this part of the building are the conference rooms in the western corner. These required column free spaces with a maximum span of 15.6 metres. These two inputs were the major influencing factors for the structural design. The elements analysed are two typical sections and the longest truss.
3.2 Build up Both of the buildings are steel portal frames, which is the stability system used. The base are H-profiled columns and H- and I-profiled beams. However, to accommodate the wishes of the architect, some trusses are included as well.
Figure 39: Easthern plinth, 1. Additional core highlighted in red
3.2.1 Eastern plinth Shown in Figure 39 is the eastern plinth. It consists of two buildings, attached underground. A visitor would be able to look downwards into the building from the rooftop. An atrium is placed in the back, which narrows the buildings. On the right, near to the high-rise, one could see a core for elevators (highlighted red), which is used for stability in the other direction. For the left side, the portal frame is doing the work on its own. It has to be noted that the high rise and low rise are attached only with a â&#x20AC;&#x2DC;rollerâ&#x20AC;&#x2122; joint, so that both can settle independently. The floors are spanning partly 9 metres, and partly 6. Hollow core slabs have been chosen as floor system, on top of the H-beams. The span is in longitudinal direction, perpendicular to the Matrixframe portal analysed further on in this paragraph.
Figure 40: Eastern plinth, 2
Visible in the figures are the trusses, these are placed to include the possibility of placing trees, locally reaching a depth of 120 cm of soil instead of the 30 cm of soil placed elsewhere. These trusses do require double columns, which would increase material cost. In order not to overdesign the entire portal, the second column rows only carry the roof, not the floors. Although attached to the rest of the frame, the frame with the floor beams will act stiffer and therefore is accounted to take the entire wind load. This has been shown in Figure 41.
Figure 41: Roof - floor set up. Only one of the two portals is attached to the internal floor beam.
Figure 42: Truss detail
Shown above is a detail of the Tree-truss. Perpendicular to the picture, soil would interchange with air- and electricity ducting and struts that interlock the two trusses with each other.
3.2.2 Western plinth The western plinth also includes an atrium close to the high rise, but continues in one piece. The roof at this place is still a green roof, but does not have special accommodation for trees. This means the soil thickness is 30 cm over the entire roof. Towards the western end, the roof cuts into a point The top floor here is a restaurant, the floor underneath are occupied by column-free conference halls. To make sure no conference hall has columns in it, the green roof and restaurant floor had to be supported
in a different way. This way, the architectural gesture that had a structural outcome of a 33 m long truss (marked red in Figure 43). This truss is simply supported, and its stability is ensured by the rigid connection on the other side of the building.
Figure 43: Westher plinth. Truss highlited in red.
Since all floor spans are 6 metres or less, and an irregular floor plan is faced around the atrium, the preference has been given to use a shallow deck floor system, just as in the tower. Only the green roof is supported by hollow core slabs. The floor span direction is again in longitudinal direction, perpendicular to the Matrixframe portal analysed.
3.3 Sizing Eastern plinth: Members
Profile
Truss outline
RHS300/200/6,3
Truss diagonals & verticals
RHS200/100/5,6
Floor beams
IPE500
Columns
HE400B
Balcony beams
HE200B
Balcony columns
HE200B
Roof slabs
H320 HCSlabs
Floor slabs
T255 HCSlabs Table 15: Profiles used in the Easthern Plinth.
Western plinth: Members
Profile
Floor beams restaurant and roof
HE700M
Floor beams conference centre
IPE750x196
Columns
HE600B
Balcony beams
HE400B
Truss horizontals and governing diagonal
RHS500/300/16
Truss verticals and diagonals
RHS300/300/16
Roof Slabs
H320 HCSlabs
Floor Slabs
U200 HCSlabs Table 16: Profiles used in the Western Plinth
3.4 Analysis The analysis has been made with use of Matrixframe. In ULS, stresses have been checked, while in SLS, the deflection has been checked. The connections to the foundations have been modelled as rigid connections, as the moment frame continues in the underground. Since for both buildings imposed variable floor loads are governing over wind loads, and Ď&#x2C6;0 for wind loads is 0, the load combinations including wind load are not shows below.
3.4.1 Eastern plinth Loading is explained in the following table. Self weight of the elements is also included in Matrixframe. This part of the plinth is the only part of the structure that is calculated in Consequence Class 2. G [kN/m^2] Roof Structure Soil Imposed Total faceload,k *load factor (1,2 G + 1,5Q) width to be taken by beam element: 4,5 m Floor Structure Imposed Total faceload *load factor (1,2G+1,5Q) width to be taken by beam element: 9 m Wind qp(ze) cf_pressure (left facade) cf_suction (right facade) Width to be taken by column element: 9 m
Q [kN/m^2]
4,3 6 10,3 12,36 G [kN/m^2] 3,1
5 5 7,5 Q [kN/m^2]
3,1 3,72
4 4 6
0,8 0,7 -0,8
kN/m^2 [-] [-]
Table 17a and b: Loading
It has to be noted that for the truss, not lineloads but pointloads are used for modelling. Geometry is based on the 1,5 m grid, as seen in the figure below.
Figure 44: Sizing of the portal frame
Results
Figure 45: Stresses in the double portal under ULS
As can be seen, all beam stresses are under 355 MPa , while the maximum column stress is around 150 MPa. An HE400B buckling analysis is made for a fast check. As the nodes most probably will not give the columns a fully clamped support, lbuc=0,7lsys is chosen. HE400B Lbuc = 0,7*lsys = 0,7*4 = 2,8 m Iz = 1,082 * 10-4 m^4 A = 0,0198 m^2 NEuler = 28 604 kN Nsquash = 7 029 kN λrel = 0,50 [-] Buckling curve b χbuc = 0,88 σmax,Rd = 0,88*355 = 312 Mpa Therefore, all stresses are within limit, although any torsional effects due to the placement of coupled columns and trusses are not taken into account.
Figure 46: Deflections of the structure under SLS
In SLS, the maximum deflection allowed for the lower beam, columns and trusses are 30, 20 and 13,3 mm respectively (l/300). Overall deflection in height is (l/500), that is 24 mm. These deflections are not reached, therefore, in SLS, the building suffices. SLS with floor variable loads over wind loads was governing.
3.4.2 Western plinth Loading of the building is as follows: G [kN/m^2]
Q [kN/m^2]
Roof Structure
3,7
Soil
6
Imposed
5
Total faceload,k
9,7
5
*load factor (1,32 G + 1,65Q)
12,804
8,25
Floor
G [kN/m^2]
Q [kN/m^2]
Structure
3,1
width to be taken by beam element: 6 m
Imposed
4
Total faceload
3,1
4
*load factor (1,32G+1,65Q)
3,72
6
qp(ze)
0,8
kN/m^2
cf_pressure (left facade)
0,7
[-]
cf_suction (right facade)
-0,8
[-]
Width to be taken by beam element: 6 m
Wind
Width to be taken by column element: 6 m Table 18a and b: Loading
Geometry of the building:
Table 19: Sizing of thel Easthern plinth section with largest span.
Stress in the members in ULS:
Table 20: Stresses under ULS
All beam members have stresses under 355 MPa, maximum column stress is around 160 MPa. Again, a quick buckling check has been made. HE600B Lbuc = 0,7*lsys = 0,7*4 = 2,8 m Iz = 1,353 * 10-4 m^4 A = 0,027 m^2 NEuler = 35 769 kN Nsquash = 9 585 kN λrel = 0,52 [-] Buckling curve b χbuc = 0,88 σmax,Rd = 0,88*355 = 312 Mpa Therefore, the main ULS criterion is met.
Deformation of the building in SLS:
Figure 47: Deflections of the portal under SLS
Beam deflections are 36, 36, 18 and 18 mm respectively for the roof, floor+2, floor +1 and floor 0. This is less than l/300 = 48 mm for the 14,8 m span. Overall building horizontal deflection should be less then l/500 = 24 mm. Since it is 21,5, it also suffices.
3.4.3 Western plinth Truss The truss has a length of 33,4 m and supports 6 roof beams (top), as well as 7 floor beams (bottom). The loads are equal to that of the overall western plinth (see Table 18 ). The difference for load input lies in the widths taken for computing of the point loads. The next image explains this. The red line is the truss.
Figure 48: Division of the two trapezoids into 4 rectangles with average widths.
Instead of a continuous inclination, four rectangle areas with an average width shown above have been used for load calculation (2 for the roof (blue), 2 for the floor (black)). The left ones are used for the triangular part of the truss ; the right ones for the flat part of the truss. Centre to centre distance of the roof beams remains 6 m, but as the truss is inclined, the distance between the nodes equals 6,2 m. Geometry of the truss:
Figure 49: Sizing of the truss.
Figure 50: Loading of the truss. Roof loading on the top horizonals, Floor loading on the bottom ones.
Stress in the members in ULS:
Figure 51: Stresses in the members in ULS.
All the elements in tension are under 355 MPa, the highest compressive stress found is 260 MPa, in a member of length 6,2 metres. A quick buckling check is set up.
RHS 500/300/16 Lbuc = 1,0*lsys = 6,2 m Iz = 3,68 * 10-4 m^4 A = 0,0243 m^2 NEuler = 19 842 kN Nsquash = 8 627 kN λrel = 0,67 [-] Buckling curve a χbuc = 0,82 σmax,Rd = 0,82*355 = 291 Mpa Therefore, the main ULS criterion is met. Deflection of the structure in SLS:
Figure 52: Deflections of the members in metres.
The maximum deflection is 5,6 mm, while the maximum allowed deflection is l/300 = 33,4/300 = 11,3 mm. Therefore, the structure suffices for SLS.
4 Foundations This chapter handles the designed building pit, basement and pile plan. The base for the fundaments of the building is the underground.
4.1 Underground In Figure 53 a CPT scan can be seen (source: Dinoloket (2018)). A soil classification is shown in Figure 54. It shows a sandy humus layer, followed by a clay layer, and a sand layer again (from now on called sand layer 1). Underneath, as can be seen in the CPT, there is another clay layer and a deep sand layer (sand layer 2). Height of the ground floor is on average around 0 NAP (source: Algemeen Hoogtebestand Nederland), and the depth of the ground water level is around -2 m (as seen in Figure 55).
Figure 53: Cone penetration test on the plot of the building. Source: Dinoloket.
Figure 54: Soil layer interpretation. Since it shows only 35 m of depth, the secondary sand layer is not shown. Source: Dinoloket
Figure 55: Waterlevel measurements. Source: Dinoloket.
4.2 Site On one side of the plot, a metro tube is located, as seen in Figure 56. On the other side, the Rotterdam Centraal station influences the possibilities to build underground. Also, a building crane has been set up for the construction of the Rotterdam Centraal station, its fundaments overlap with the site.
Figure 56: Lay out of the plot in current situation. Original image retreived from https://brightspace.tudelft.nl/d2l/le/content/65741/Home.
At one spot, the subway outline touches the border of the plot. The foundation of the railway station ends approximately at the northern border of the site. A minimum distance of 0,5 m is chosen for placement of sheet piles from existing underground structures, but the municipality took this into account already. Sheet pile size is taken as 0,5 m, which results in an offset of the original borders, decreasing the buildable area.
The building crane fundament consists of 70 piles (27 m deep) and a slab (RTV Rijnmond, (2011)). The piles have an unknown diameter, and therefore are not taken into account as a possible foundation. Therefore, it is a good fact that the slab and part of the piles have been removed, so that one has only to build around it. This information has been shared with MEGA students by the municipality.
4.3 Input for calculation With the boundary conditions given, it has been chosen to make the following building pit. As the pit has been split up (to make differentiated settlements less problematic), various depths are chosen.
4.3.1 Common elements Use of sheet piles and concrete prefabricated prestressed concrete piles. Building pits will make use of underwater concrete. Steel sheet piles are vibrated to a depth of -20 m NAP, at a distance of at least 0,5 m from the train station foundation and the subway. The clay layer is penetrated, therefore, inflow of water from the side is prevented. Next, the soil is removed, and props are placed to keep the walls stable. Water is left in the pit while soil is excavated. Piles and/or anchors are driven from the surface to the desired depth. The following step is installation of the underwater concrete, 1 m thick slab, after which compressive girders are placed and water is pumped out.
Figure 57: Cross section of the high rise foundation
4.3.2 Main Building The concrete piles act as tensile elements during building stage. The reinforced slab poured on top is 2 m thick. This slab makes sure the forces from both the core and the tube system are redistributed over the whole slab area. Depth is 15 m (see Figure 57). Prefabricated piles are used as their strength is guaranteed and not affected by the wet environment of the building pit before it gets pumped dry. Also, as they are prestressed, tensile forces are less of a problem, and crack formation could be prevented. The first sand layer is reached.
Figure 58: Cross section of the low rise foundation
4.3.3 Low rise (plinth) The plinth consists of two separate, though similar basements. The difference is that its depth is only 13,5 m, as a less thick structural foundation slab would be necessary (0.5 m is chosen). Anchors are used to counteract the tensile stresses during and after construction, as more space is available than underneath the high-rise. Directly near the station, space is limited to pull the steel sheets out, and some material will be left behind. Any ground penetrating elements are placed in a way that they do not interact with the old building crane foundation. Prefabricated piles are used again. The pile plan is added in the appendix. A pile is placed on every crossing of lines. Underneath the high-rise, a dense grid of piles is set up. The size of the piles is 40 x 40 cm^2. The centre to centre distance is 1,2 metres, that is using the rule of thumb for maximum density of 3*Diameter. Underneath the low rise, piles are only placed underneath columns, but always in pairs, so they can take up the bending moment from the moment frame structure.
Three places underneath the low-rise got extra attention. The first one is the placement of piles around the old foundations of the building crane (indicated with white circles in the eastern plinth). In order to prevent conflicting placement, or too dense placement, the grids have been shifted, to ensure at least a 1 m distance between the piles. Next, the grid has been densified on the right side of the western plinth, to accommodate placement of a building crane. At last, some extra piles have been placed at the left side of the eastern plinth, to have piles placed along the entire width of the small core placed here.
4.4 Analysis To find out what size of piles would be needed, stresses underneath the foundation were plotted. This reveals tensile stresses occurring underneath the high-rise and plinth alike. Next images give an overview of the steps taken in the analysis: windload, load takedown and uplift water pressure are super positioned to result in the final stress distribution.
Figure 59: Stresses for the analysis. Up left: wind loads. Up right: vertical loads. Down left: vertical watterpressures. Down right: total stress distribution
4.4.1 Characteristics Characteristics and assumption made for the analysis are listed below. Characteristics of the high rise building are: Height (loaded by wind): 168 m
Width foundation in weakest direction (width 1): 20,2 m Average building width in 2nd direction (width 2): 50,4 m Number of floors: above ground - 42, underground â&#x20AC;&#x201C; 3 Depth foundation: 15 m Of which : thickness structural slab: 2 m underwater concrete: 1 m Loading of the High rise: The loading table is shown below. All loads have been transferred to kN/m 2, that means that for the façade and core, the load has been spread. For the structural tube this means: đ?&#x2018;?
đ?&#x2018;&#x2DC;đ?&#x2018; đ?&#x2018;Ąđ?&#x2018;˘đ?&#x2018;?đ?&#x2018;&#x2019; [ 2 ] đ?&#x2018;&#x161;
= đ?&#x2018;&#x201A;đ?&#x2018;&#x201C;đ?&#x2018;&#x17D;đ?&#x2018;?đ?&#x2018;&#x17D;đ?&#x2018;&#x2018;đ?&#x2018;&#x2019; â&#x2C6;&#x2014; đ??şđ?&#x2018;Ąđ?&#x2018;˘đ?&#x2018;?đ?&#x2018;&#x2019; [
đ?&#x2018;&#x201A;đ?&#x2018;&#x201C;đ?&#x2018;&#x17D;đ?&#x2018;?đ?&#x2018;&#x17D;đ?&#x2018;&#x2018;đ?&#x2018;&#x2019; đ?&#x2018;&#x2DC;đ?&#x2018; đ?&#x2018;&#x2DC;đ?&#x2018; â&#x2C6;&#x2014; â&#x201E;&#x17D;đ?&#x2018;&#x201C;đ?&#x2018;&#x2122;đ?&#x2018;&#x153;đ?&#x2018;&#x153;đ?&#x2018;&#x; â&#x2C6;&#x2014; đ??şđ?&#x2018;Ąđ?&#x2018;˘đ?&#x2018;?đ?&#x2018;&#x2019; [ ] ]+ đ?&#x2018;&#x161; 6[đ?&#x2018;&#x161;] đ?&#x2018;&#x161;
With: ptube = load on foundation per floor [kN/m^2] Ofacade = perimeter of façade [m] 6 [m] = grid spacing Gtube = selfweight tube [kN/m] hfloor = height floor = 4 [m] Weight building Facade Floor Core
G [kN/m^2] 6,7 5 5,1
Q [kN/m^2] 2,25 -
Total 1,0G 1,32G+0,5*1,65Q
16,8 16,8 24,1
2,25
Figure 60: Parts contributing to the vertical loading by the building
Characteristics of the low rise building are: Height: 16 m Number of floors: above ground â&#x20AC;&#x201C; 4, underground â&#x20AC;&#x201C; 3 Depth foundation: 13,5 m Of which : thickness ground floor: 0,5 m underwater concrete: 1 m Analysis assumptions 2nd order effects: neglected (for foundation analysis) Section modulus foundation slab: 1/6*width 1*width 22 Wind profile: 3 stepped, with linearized 2nd step Building is analysed with an equivalent rectangular building Compressive loads are indicated positive Pile prestressing has not been taken into account
4.4.2 High Rise calculation Analysis 1: 0,9G+1,65Qwind EQUILIBRIUM finished stage (vertical loading) height building (loaded)
168
m
height/floor
4
m
amount of floors
42
-
load per floor
16,9
kN/m^2
total vertical tower loads
709,2
kN/m^2
basement floor loads
50,7
kN/m^2
Concrete slab weight
50
kN/m^2
UW_concrete slab
22
kN/m^2
Total overall structure downwards
831,8
kN/m^2
Total downwards, d (0,9 factor)
749,3
kN/m^2
Total upwards, d (1,0 factor)
130
kN/m^2
Compressive vertical stress
619,3
kN/m^2
Windload phase 1 (NAP+50)
1,21
kN/m^2
Windload phase 3 (NAP+168)
1,7
kN/m^2
Suction/pressure factor
1,5
[-]
Safety factor
1,65
[-]
M Ed_total
2765421
kNm
W_slab_North-south
3427,536
m^3
Max stress Compressive
806,8
kN/m^2
Max stress Tensile
-806,8
kN/m^2
EQUILIBRIUM finished stage (with windloads)
Distribution wind over slab:
EQUILIBRIUM finished stage (vertical and wind combined) pressure under slab_max
1426,1
kN/m^2
pressure under slab_min
-187,6
kN/m^2
Table 21: Equilibria in different building stages
PILE ANALYSIS Diameter pile
0,4
m
ctc grid
1,2
m
A_taken by pile
1,44
m^2
A_pile
0,16
m^2
To be taken per pile (max)
2053,5
kN
To be taken per pile (min)
-270,1
kN
Sigma_pile_max
12834,7
kN/m^2
12,8
Mpa
-1688,2
kN/m^2
-1,7
Mpa
Sigma_pile_min
Table 22: Pile Analysis
Figure 61: Stress distribution
Analysis 2: 1,32G+1,65Qwind+0,5*1,65*Qfloors The information similar to situation above has been left out. Due to the new load combination, the load / floor has been altered. EQUILIBRIUM finished stage (vertical and wind combined) load per floor
24,1
kN/m^2
Compressive vertical stress
1051,3
kN/m^2
Max stress Compressive, wind
806,8
kN/m^2
Max stress Tensile, wind
-806,8
kN/m^2
pressure under slab_max
1858,2
kN/m^2
pressure under slab_min
244,5
kN/m^2
PILE ANALYSIS To be taken per pile (max)
2675,8
kN
To be taken per pile (min)
352,1
kN
Sigma_pile_max
16723,5
kN/m^2
Sigma_pile_min
16,7
Mpa
2200,6
kN/m^2
2,2
Mpa
Table 23: New equillibrium pile analysis
Figure 62: Stress distribution
Conclusion As the most realistic situation under full wind load would be somewhere in between both the loading cases, it can be said that no severe tensile reaction is expected in the foundation. If brought back to the stresses in the piles themselves, the additional tensile load would be at most 1,7 N/mm2, which after including eventual prestressing in the piles, would be most probably neutralised. If the slab itself would start to tilt, equilibrium with partial contact should be analysed.
4.5 Foundation stiffness The stiffness of the foundation has been analysed using an analogy incorporating an infinitely stiff foundation slab and springs that model the piles. This model is set up according to the 2 m thick slab used underneath the high-rise. Since 16 rows of piles fit in the foundation, the following formula has been used: 8
đ?&#x2018;&#x2DC;đ?&#x2018;&#x201C;đ?&#x2018;&#x153;đ?&#x2018;˘đ?&#x2018;&#x203A;đ?&#x2018;&#x2018;đ?&#x2018;&#x17D;đ?&#x2018;Ąđ?&#x2018;&#x2013;đ?&#x2018;&#x153;đ?&#x2018;&#x203A; = 2 â&#x2C6;&#x2014; â&#x2C6;&#x2018; đ?&#x2018;&#x2DC;đ?&#x2018;?đ?&#x2018;&#x2013;đ?&#x2018;&#x2122;đ?&#x2018;&#x2019; â&#x2C6;&#x2014; đ?&#x2018;&#x17D;đ?&#x2018;&#x2013;2 đ?&#x2018;&#x2013;=1 đ??¸đ??´
With đ?&#x2018;&#x2DC;đ?&#x2018;?đ?&#x2018;&#x2013;đ?&#x2018;&#x2122;đ?&#x2018;&#x2019; = 2â&#x2C6;&#x2014;đ?&#x2018;&#x2122;
Figure 63: mechanics scheme of foundation stiffness analysis assuming infinitely stiff foundation slab
With this model, a displacement of 6 cm is found. Together with the 24,5 cm displacement found in the GSA model, the total 1st order deformation gets 30,5 cm. Foundation stiffness spacing # piles along the smaller width A_pile E_pile l_pile alpha k_pile k_foundation M_wind Theta_foundation height building delta_top_foundation delta_top_building delta_total
1,2 16 0,16 20000 8 2 200000000 117504000 39905,1 0,0003396 177 0,060 0,245 0,305
m [-] m^2 N/mm^2 m [-] m^-1 kNm/rad kNm rad m m m m
Table 24: Parameters for stiffness calculation
4.6 Second order effects The second order effects have been taken into account for the entire building with the use of a simple mechanics scheme. The first order deflections at the top of the building (δ) will conclude in a certain rotational stiffness of the building as a whole (foundation and tower included). The weight of the building (centre of gravity is assumed to be exactly in the middle) will then account for a secondary deflection, with lever arm δ/2. With the rotational stiffness found earlier, a new rotation can be found (θ2), and therefore a new deflection. This results in a 7% increase in deflections.
Figure 64: Mechanics scheme of the simplified 2nd order analysis.
The bending moment M1 resulting from the wind is taken as the three stepped bending moment according to NEN EN 1991-4, as used in the foundation pile analysis. Additional data can be found in the table below. Second order effect M_wind_Ed
1669361,96
kNm
delta_1
0,305
m
Theta_1
0,00172
rad
k_total
968427154
kNm/rad
1/2*delta_1
0,153
m
G_building
842502,3
kN
M_G_2nd order_Ed
128528,0
kNm
Theta_2
0,0001327
rad
delta_2
0,0235
m
Second order effect
7,7
%
New delta_total
0,329
m
delta_allowed
0,354
m
0,93
[-]
U.C.
Table 25: Final deflection analysis
This means, that the total deflection would become δbuilding + δfoundation + δ2ndorder = 0,245+0,060 +0,023 = 0,329 m. With the building height of 177 m, the allowed deflection is 177/1000 = 0,356 m. Therefore, the SLS criterion has been met.
4.7 Subway settlements From previous projects in the neighbourhood of the building, such as the Delftse Poort complex, it is known that settlements of nearby situated subway caissons could be problematic. Since those caissons need to be properly connected to be watertight, any local settlements of the underground need to be restricted. As the high rise of the designed building is founded on the 1st sand layer, it could cause such settlements by
compressing the clay layer between the 1st and 2nd sand layer in the underground. It is not known though, what the exact settlement would be. Therefore, the foundation has been placed on the first sand layer, assuming the subway would not be a problem. If however, an analysis would show that the settlements are problematic, the building would need to be founded to the deeper sand layer. As no 40 m deep prefabricated piles could be used, steel piles would be advised to use. They would not corrode as the environment along the entire length is wet. However, with a larger pile length, the pile stiffness and foundation stiffness would reduce. The SLS criterion could be not met in this situation, and further adaptations to the building and / or foundation would need to be made.
5 Construction Sequence 5.1 Foundation/Basement Construction S.No 1
2
3 4 5 6 7 8 9
10
11
Stage Soil Test
Process CPT test is performed on site to understand the soil condition data and find the main load bearing layer depth. Installation of Sheet Interlocking steel sheets are driven into the earth to piles obtain a continuous barrier for earth retention in the ground for permanent works. Dry Excavation The top layer of the soil is excavated. Wet Excavation Once the water table is reached, wet excavation has to be done. Building Pit After the excavation, the water in the pit is retained to avoid the failure of the sheet piles. Installation of Piles Prefabricated Piles are driven through the water into the soil Addition of Gravel Adding gravel to the bottom surface provide a good bonding surface for the underwater concrete. Underwater Concrete 1m thick underwater concrete is added as a barrier for further water penetration. Draining the water The retained water is pumped out and compression tubes (struts) are added to prevent the sheet piles from collapsing. Structural Concrete 2m thick structural concrete is casted to add weight to counter the upward water pressure from the soil. And most importantly, it provides a very stiff plate for the building to rest on and spread out the pressures from the tube and core. Dry building Construction of core and basement can commence Table 26: Construction sequence of the foundation and basement
Figure 65: Illustration of the construction sequence of the foundation and basement
5.2 Super-structure construction S.No 1
Stage Core
2
Installation of selfsupporting static tower crane and basement on the western plinth
3
Structural Assembly
4
Installing building mounted crane on the eastern facade Completion of the Once the faรงade maintenance unit is fixed the cranes Structure are removed.
5
Process Super-structure construction begins with core. Selfclimbing formwork can be used to erect the core. An external crane is installed on one side for the construction of the structural faรงade and one part of the plinth. As the core climbs upwards, columns and beams are assembled on the basements along with the floor slabs. The foundation of the plinth is used as foundation for the crane. The steel columns and beams are mechanically connected at level using prefabricated nodes which are manually bolted. This crane helps in constructing the eastern part of the plinth.
Table 27: Construction Sequence of the Super-structure
Figure 66: Illustration of the construction sequence of the super-structure
6 Conclusion and reflection The goal of this project was to design a stable structural system that would support the architectural expression. Initial goal was to achieve a sustainable structure which led to the choice of diagrid stability system. After preliminary analysis and analysing its coherence with other disciplines, it was understood that it was not the most suitable structural expression for this tower. A linear approach was adopted starting with a pure tube structure. After the finalization of the size of the core, a tube in tube structure with spacing of 4.5m and 6m was tested. From a complicated tube structure with diagonal bracing, the structure was simplified to a tube in tube with 6m spacing. The amount of material consumed by Model 3 is 20% (Comparison between table 1 and 2) more than the amount material used in a diagrid system. This structure could be further optimized by adding outriggers at the mechanical floors. This would help in making the structural elements smaller and standardized with simplified connections. . In terms of resolving the horizontal forces at the kinks of the irregular geometry, the structureâ&#x20AC;&#x2122;s horizontal bracing at level 0 and level 10 could be analysed and dimensioned. But, time constraints did not permit us to explore the structural evolution to a step ahead. If this project was to continue to the next stage, keen attention should be provided in designing the connection as they prove to be critical for any structural system. FEA of these connections and their performance in various load conditions has to be analysed for confirming its functionality.
7 References Topographical/Geographical Dinoloket. (2018). Ondergrondgegevens. https://www.dinoloket.nl/ondergrondgegevens-betaversie
Retrieved
(04-2018)
from
AHN. Algemeen Hoogtekaart Nederland. Retrieved (04-2018) from http://www.ahn.nl/index.html RTVRijnmond. (2011). Voorbereidingen bij CS voor bouw grote hijskraan. Retrieved (06-2018) from https://www.rijnmond.nl/nieuws/7088/Voorbereidingen-bij-CS-voor-bouw-grote-hijskraan CE-CS-KWARTIER_SMP_CONRADSTRAAT aangepaste rooilijn. Retrieved https://brightspace.tudelft.nl/d2l/le/content/65741/viewContent/818424/View
(04-2018)
from
Engineering Ir. Soons, F.A.M., van Raaij, B.P.M., prof. Ir. Wagemans,L.A.G., ir. Pasterkamp, S., ir. vanEs, S.H.J. (2014). Quick Reference. Ir. Nijgh, M.P., ir. deVries, P.A., dr.ir. Pavlovic, M., em.prof.dr.ir. Wardenier, J., prof.dr.ir. Veljkovic, M. (2017). Formula Sheet for examination: CIE 4115 (Steel structures II) - 2017/2018. ir. Ham, P.H., ir. Terwel, K.C. (2017). Structural calculations of High Rise structures. Composite Construction. Retrieved (06-2018) from https://www.steelconstruction.info/Composite_construction Lecture 4B.4: Practical Ways of Achieving Fire Resistance of Steel Structures. Retrieved (06-2018) from http://fgg-web.fgg.uni-lj.si/~/pmoze/esdep/master/wg04b/l0400.htm Lecture 14.7: Anatomy of Multi-Storey Buildings. Retrieved from http://fgg-web.fgg.unilj.si/~/pmoze/esdep/master/wg14/l0700.htm Gardner, A. (2014). Stability of buildings Parts 1 and 2: IStructE Ltd. Retreived 06-2018 from https://shop.istructe.org/downloads/dl/file/id/208/product/118/stability_sample.pdf Grunbauer. HE=450=M. Retrieved (05-2018) from http://www.grunbauer.nl/ned/framehem450.htm ArcelorMital. Wide Flange Columns - HD. Retrieved (06-2018) from http://orangebook.arcelormittal.com/design-data/uk-na/columns/hd/section-properties-dimensionsand-properties/
Appendix Materials Materials E_steel γ_steel σ_steel,k σ _rebar,k E_concrete_in situ,uncracked γ _concrete σ _concrete in situ, compressive ,k E_Core_cracked
210000 78500 355 500 31000 25000 25 10000
Type N/mm^2 N/m^3 N/mm^2 S355 N/mm^2 B500B N/mm^2 N/m^3 N/mm^2 C25/30 N/mm^2
Material factors Safety factors - Materials Steel_Cross sections & stability Steel_rebars Concrete_in situ
γM 1 1,15 1,5
Floor loads Variable Loads Office variable Appartments variable Hotel variable Shopping areas MEP
Distributed 4 kN/m^2 1,75 1,75 4 5
Concentrated 3 kN 3 3 7 7
Load factors Safety factors - Loading ULS CC-3 factor Design situation 1 Permanent unfavourable Permanent favourable Variable Design situation 2 Permanent unfavourable Permanent favourable Variable
Normally
Final factors
1,1 1,35 0,9 0
1,485
1,2 0,9 1,5
1,32
0
1,65
Geographical GEOLOGICAL γ clay (wet) γ dry sand γ wet sand γ concrete γ water γ underwater concrete
17 16 18 25 10 22
kN/m^3 kN/m^3 kN/m^3 kN/m^3 kN/m^3 kN/m^3
start sand 1 end sand 1 start clay 1 end clay 1 start sand 2 end sand 2
0,1 NAP 5 5 15 15 32,5 NAP
depth sand layer 1 depth clay layer depth sand layer depth hydraulic head sand layer 1 depth hydraulic head sand layer 2
4,9 10 17,5 2 2
Vertical Section
m m m m m
Horizontal Section
Foundation plan
Load input for column calculation Floor types
Loads Permanent
Floor type 1: Office width length Area Length beams taken Eccentrical beam length Eccentrical direction Variable load Ψ0 factor PSI factor TWO FLOORS Number of floors Floor type 2: Hotel/Residential width length Area Length beams taken Eccentrical beam length Eccentrical direction Variable load PSI factor Number of floors Floor type 3: MEP width length Area Length beams taken Eccentrical beam length Eccentrical direction Variable load PSI factor Number of floors Floor type 4: Shopping width length Area Length beams taken Eccentrical beam length Eccentrical direction Variable load PSI factor Number of floors Column weight height/floor #floors TOTAL
6 m 10,3 m 61,8 m^2 15,45 m 6,55 m
N/floor
Variable 462,9438 kN
N_Total Of which: N_exc
4166,4942 kN 2649,5667 kN
N/floor N/floor_two floors N_total Of which: N_exc
203,94 kN 407,88 kN
N/floor
315,74565 kN
N/floor
N_Total Of which: N_exc
6946,4043 kN
2448,072 kN
3238,3593 kN
N_total Of which: N_exc
N/floor
315,74565 kN
N/floor
347,7375 kN
N_Total Of which: N_exc
947,23695 kN
N_total Of which: N_exc
1043,213 kN
2243,34 kN 1426,59 kN
east 4 0,5 1 9
6 7,025 42,15 10,5375 3,275
kN/m^2 -
m m m^2 m m
111,276 kN
1141,272 kN
west 4 kN/m^2 0,4 22 6 7,025 42,15 10,5375 3,275
m m m^2 m m
441,59445 kN
486,3375 kN
west 5 kN/m^2 1 3 6 10,3 61,8 15,45 6,55
m m m^2 m m
N/floor N_Total Of which: N_exc
462,9438 kN 2777,6628 kN 1766,3778 kN
N/floor
163,152 kN
N_total Of which: N_exc
978,912 kN 622,512 kN
east 4 kN/m^2 0,4 6 8,829 kN/m 4 m 40 [-]
N/floor Ntotal
35,316 kN 1412,64 kN
N,G,Ed
16250,43825 kN
N,Q,Ed
6713,537 kN
Total loading Total NG Total NQ N_Ed Total load eccentrical west Total load eccentrical east Eccentricity (attachment to culumn) M_Ed_1st order
16250,43825 6713,5365 22963,97475 5307,56325 6465,0465 0,3155
kN kN kN kN kN m
365,1859654 kNm