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Design of new scaffold anchor based on the updated finite element model
Engineering Structures 118 (2016) 334–343
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Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Design of new scaffold anchor based on the updated finite element model Jiri Ilcik a, Vikas Arora b,⇑, Jakub Dolejs a a b
Faculty of Civil Engineering – Department of Steel and Timber Structures, Czech Technical University in Prague, Thákurova 7, 166 29 Praha 6, Czech Republic Department of Technology and Innovation, University of Southern Denmark, Campusvej 55, Odense 5230, Denmark
a r t i c l e
i n f o
Article history: Received 20 April 2015 Revised 25 January 2016 Accepted 29 March 2016 Available online 13 April 2016 Keywords: Optimization Tubular scaffold Fixing anchor Facade Stability Nonlinear finite element model
a b s t r a c t In this paper, a new scaffold anchor system is presented. The developed scaffold system overcomes the problems associated with the existing scaffold anchors. The existing scaffold anchors damage the surrounding insulation layers subsequently decreases the stability of scaffold anchors. The developed scaffold system has a new type of the facade anchor and the position pattern used for scaffolding. The developed scaffold system is based on the accurate FE models of the prototype anchor, which have been updated in the light of the experimental results i.e. force–displacement curve. It has been observed that the results of finite element model do not match with experimental results. The modelling of stiffnesses of the joints is considered to be the major source of uncertainty in the finite element model. Subsequently, stiffnesses of joints of anchor have been updated in the light of experimental data. The results have shown that after updating, the predictions of finite element model of scaffold system matches well with experimental results. Subsequently, the loading forces used during the optimization process have been obtained from the updated finite element model of the tubular scaffold construction related to the Eurocode standards. In addition to the problems associated with existing scaffold anchors, the developed scaffold anchor is also effective in transmitting support forces to the facade object along with increasing the stability of scaffold anchors. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Scaffold constructions are generally divided into two groups based on their main bearing components [1]. First group comprises of non-system tubes constructions, where the main components are mild steel tubes with diameter 48.3 mm and 4 mm thickness. Tubes are connected together by couplers. In the European countries, these types of systems are still very popular because of their variability. Based on the same principle, the bamboo scaffolds, which are very often used in East Asia countries, can be also added into this group. Second larger group comprising of prefabricated parts, mostly frames, in the certain system configuration; this group is called proprietary scaffolds. Scaffoldings in both groups are generally very weak constructions because of the loose connections of parts [2,3]. The stability of scaffold anchor systems can be increased significantly by the anchoring and bracing [4,5]. Many scaffold constructions collapses every year. According to the past research, the majority of failures occur due to inadequate site supervision and poor design [1]. ⇑ Corresponding author. E-mail address: [email protected] (V. Arora). http://dx.doi.org/10.1016/j.engstruct.2016.03.064 0141-0296/Ó 2016 Elsevier Ltd. All rights reserved.
These reasons are compounded, when the scaffold is fixed to a facade with a thermal insulation layer, because there are not many ways how to fix the anchor through this layer [6], and none of them have been sufficiently analyzed yet [7]. The presence of thermal insulating layer increases the possibilities of the failure. In the most of the cases, a long scaffold screw is used to overcome the thermal insulation as shown in Fig. 1. The use of long scaffold screw often results in deformation of the screw during the impact of the high wind load [8], which subsequently results in damage of the surrounding insulation layer and additional repairs are required [7]. Moreover, the deformation of the screw decreases the stability of scaffold anchor systems. To overcome these problems, a new facade anchor has to be developed. In this paper the developed anchor shapes are presented. One of the shapes, the ‘‘Lever Anchor” has been fabricated and experiment has been carried out to determine it’s the real load bearing capacity. It has been observed that the force–displacement curve is nonlinear because of permanent deformation of the anchor due to loading. Two FE models (beam model and solid model) have been developed for making out the numerical analyses. The experimental results have been compared with the corresponding predictions of these finite element models. It has been observed that the force–
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Fig. 2. The prototype of the Lever anchor.
Fig. 1. Vertical section of the fixed anchor.
displacement curves of these initial finite elements models did not match with the experimental results. It is well known that finite element predictions are often called into question when they are in conflict with experimental results. Inaccuracies in finite element model and errors in results predicted by them can arise due to use of incorrect modelling of boundary conditions, incorrect modelling of joints, and inaccurate size of the mesh, etc. This has led to the development of model updating techniques, which aim at reducing the inaccuracies present in an analytical model in the light of measured experimental data as shown in the surveys by Imregun and Visser [9] and Mottershead and Friswell [10]. Since the geometry of the finite element models have been known well, the stiffness of the joints and material properties have been considered as major sources of uncertainties. To reduce the uncertainties in the joints, the joint stiffnesses have been updated by using parametric optimization approach. The experimental results have been used for parametric optimization to reduce the error between experimental results and predictions of finite element models. The similar process has been used in [11–13]. Arora [14] concluded that parametric iterative optimization of finite element gives better results than direct optimization of finite element model. Subsequently it has been observed from that the experimental and corresponding updated finite element models force– displacement curves matches very well with each other. It can be concluded from the experimental updating of finite element of anchors that the updated anchor represents the reality accurately. As the developed scaffold anchor system is deformed permanently which results in non-linear behavior, a scaffold anchor system has been redesigned to behave linearly. The loading forces used during the optimization process have been obtained from the finite element model of the tubular scaffold construction related to the Eurocode standards [15,16]. The maximum support force from the scaffold construction has been applied on the anchors finite element models and material and geometrical optimizations have been done. The updated finite element model can be used for design of the structure [17]. As the result of these investigations, the accurate finite element solid model has been created. It carries the support force within the area of linear behavior in all its parts. 2. The updating of finite element models of prototype anchor in the light of experimental results After initial investigations of the scaffolding’s stability, three potential shapes of the new anchor [18–20] have been developed by simple basis. Two of them – ‘‘The Lever Anchor” and ‘‘The Oblique Scaffold Anchor”, showed in Figs. 2 and 3, are using innovative oblique arm. The principle of the obliquity is demonstrated in
Fig. 4. As it can be observed from Fig. 4 two anchors in the horizontal plane are used for fixing, these two anchors are placed in the opposite orientation to create a notional trapezoid with the surface of the facade. The outer scaffold plane is stiffened because of the vertical X-bracing and the inner plane is moved in a direction parallel with the facade [7]. By using the oblique arms, the displacement of the inner plane is significantly restricted, so the scaffold stability is increased. Also the anchors provide minimum deformation in its parallel threaded bars, which are joined into the facade through an insulation layer. This type of mechanism ensures that there is no damage to the surrounding insulation. For a backup there is also ‘‘The Rigid Scaffold Anchor”, see Fig. 3, which has the conventional straight arm. This shape has been developed for the case of an arm obliquity idea failure. For the further analysis, only the ‘‘Lever anchor” is selected. The reason is that the single parts of this anchor can be adjusted in different positions, so the installation process is easier and the variability of the anchor is greater than in ‘‘The Oblique Scaffold Anchor”. From the static point of view, the anchor parts ‘‘Threaded bars”, ‘‘Slider” and ‘‘Span” create a rigid frame. These parts are shown in Fig. 2. Furthermore, the anchor provides a semi-rigid support along vertical axis. Thus, this paper focuses only on optimizing the value of the torsional stiffness from experiments will be handled in the next stages of the development. In this paper, for further analysis, the anchor is considered as a fixed support in horizontal plane. After fabricating, the Lever anchor prototype, the pilot experiment on the real masonry wall has been carried out. The forces have been applied at the end of the lever arm in 4 directions as is shown in Fig. 5. These four directions represent all the possible force directions arisen during the standard load combinations [16]. The reason of this pilot experiment is to determine an optional loading direction for the first laboratory experiment and followed by finite element verification. It has been concluded that the +Y direction is optional, because only the tension force is applied and the interference of the buckling and imperfections is restricted. It will ensure accurate laboratory experiment set up and verification of initial FE models. The behavior of scaffold anchor system under the compressive force will be investigated in the next stages of the development. The pictorial view of the experimental set up is shown in Fig. 6 whereas scheme diagram of the laboratory experiment is shown in Fig. 7. The anchor has been loaded continually by tension force only in vertical direction. The range of force varies from 0 to 3 kN and the displacement of the lever arm has been recorded in real time. The anchor has been loaded by the single acting hollow plunger cylinder with the one-handed pump. The cylinder has been situated on the top of the supporting steel construction made from two parallel steel columns with reversed T-shape. Tensometric pressure dynamometer has been placed between the cylinder and the upper surface of the construction, which is connected with
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Fig. 3. The Rigid Scaffold Anchor and The Oblique Scaffold Anchor.
Fig. 4. The plane view – the principle of the obliquity.
Fig. 6. Photo from the end of the laboratory experiment.
Fig. 5. The force directions considered in pre-experiment.
the computer to measure an actual force in real-time. The draw bar made of steel has been connected to a hydraulic cylinder at the end of Lever arm. Vertical displacement of the lever arm has been measured by an absolute potentiometer sensor in real-time. It has been observed that during the initial stage the ‘‘Span bar” has reached the plastic behavior as it is deformed permanently. After applying the force of approximately 3.0 kN, first small cracks on the span’s bars have been detected, these cracks become larger at the end of the experiment. It has been observed that the weakest member of the scaffold anchor system is span member. The output of the experiment is a force–displacement curve as shown in Fig. 8. After carrying out of the experiment, the beam and solid finite element models have been developed in the ANSYS Workbench software [21]. In the beam model, members of the scaffold anchor system are connected together by using both the longitudinal (along X and Y axes) and also torsional stiffnesses (along the Z axis). Since the values of these joint stiffnesses are unknown as well as
the exact values of the material properties, these have been considered to be the source of error in the finite element model. Subsequently, the finite element model has been optimized considering stiffnesses and material properties as updating parameters in the light of experimental force–displacement curve. Whereas in the solid model, unknown variables are material properties, subsequently the solid model has been also optimized considering material properties as updating parameters for finite element model. As the permanent deformation has been observed during experimentation, the material properties are considered non-linear. Overlay of the experimental and updated finite element models predictions are shown in Fig. 9. The initial and final values of the optimization parameters are given in Tables 1 and 2 for beam and solid FE models respectively. It can be observed from Table 1 that the torsional stiffness values of springs have been changed significantly whereas, it can be observed from Table 2 that there has been some reduction in the values of material in case of solid model. It can be observed that the updated finite element models predictions matches well with the experimental results (force–displacement curve), so it can be concluded from optimization study that updated finite element models represents the reality accurately.
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J. Ilcik et al. / Engineering Structures 118 (2016) 334–343 Table 1 Initial and final values of optimized variables for beam model. Initial beam model
Fig. 7. The setting up of the laboratory experiment.
3.5 3
FORCE [kN]
Stiffness
Named
Longitudinal Longitudinal Longitudinal Longitudinal
R L L R
MN/m
MN/m
406.90 406.90 1070.00 1070.00
406.90 406.90 1070.00 1070.00
Torsional Torsional
L R
MN m/rad 0.10 0.10
MN m/rad 2.41 2.41
Longitudinal Longitudinal Longitudinal Longitudinal
RN RN RN RN
D D U U
MN/m 21630.00 387.90 21630.00 387.90
MN/m 21630.00 387.90 21630.00 387.90
Torsional Torsional
RN RN
D U
MN m/rad 0.10 0.10
MN m/rad 0.11 0.11
Longitudinal Longitudinal Longitudinal Longitudinal Longitudinal
UL LN LN LN LN
X D D U U
MN/m 0.10 9000.00 351.90 9000.00 351.90
MN/m 0.10 9000.00 351.90 9000.00 351.90
Torsional Torsional
LN LN
D U
MN m/rad 0.01 0.01
MN m/rad 0.34 0.34
MPa 200 300 580
MPa 200 275 550
2 1.5
0.5 0
10
20
30
40
50
60
70
80
90
DISPLACEMENT [mm] EXPERIMENT
Y X Y X
3.5 3 2.5 2 1.5 1 0.5 0
10
20
30
40
50
60
70
80
90
DISPLACEMENT [mm] EXPERIMENT
BEAM MODEL
Structural steel NL S235 Structural steel NL 4.8 Structural steel NL 8.8
Initial solid model MPa
Updated solid model MPa
200 300 580
200 260 500
INIT. SOLID
INIT. BEAM
Fig. 8. Force–displacement curves of initial models.
FORCE [kN]
Y X Y X
Table 2 Initial and final values of optimized variables for solid model.
1
0
Y Y X X
Material Structural steel NL S235 Structural steel NL 4.8 Structural steel NL 8.8
2.5
0
Updated beam model
SOLID MODEL
Fig. 9. Force–displacement curves of updated models.
The developed updated two FE models (beam and solid) are subsequently used to calculate the exact support force on the loaded scaffold anchor system. The support force has been calcu-
lated from the finite element model of the tubular scaffold construction, which uses Lever anchors as supports. A finite element model of tubular scaffolding was described originally by Dolejš in [7]. Dolejs’ model has experimentally conducted torsional stiffness of the joints, which is necessary for the more accurate solution [22]. The dimensions of this scaffolding and position pattern of anchors correspond with the commonly used 12-storey high scaffolding with the netted cladding, see Fig. 10. His model contains fixing system provided by commonly used short anchors and these anchors are modelled by using simple beams with pinned supports. To demonstrate the influence of the long scaffold screw used in a fixing (as is shown in Figs. 1 and 11) the same FE model of anchor has been used by adding these screws (see Fig. 12) and it has been solved out using the same software as Dolejs used [23]. Subsequently, the same model has been analyzed again by considering Lever anchors in their own original position pattern as is shown in Fig. 13. The Lever anchor has been modelled as short oblique beams with fixed supports. The stability results are demonstrated by critical load coefficients obtained from geometrical non-linear analyses (GNIA) and the results are shown in Table 3. It can be observed that the load combinations match the Eurocode standard [14], there are four combinations S1–S4. The first two S1 and S2 represent in-service conditions and next S3 and S4 are out-of-service conditions. In
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Fig. 13. Lever anchors position pattern of the Model 3. Dots represent positions of the anchors.
Table 3 Critical load coefficient from the stability computing. Fig. 10. The model of the tubular scaffolding [7].
Fig. 11. A scaffold anchoring provided by long scaffold screw penetrating an insulation layer.
Load combination
Model 1
Model 2
Model 3
acr
acr
acr
The service condition S1 Perpendicular to façade S2 Parallel to façade
1.68 1.67
1.68 1.67
2.03 1.96
The out of service condition S3 Perpendicular to façade S4 Parallel to façade
2.19 2.74
0.37 2.73
3.24 3.2
made by Dolejs is indicated in this paper as Model 1. It has been mentioned above that Dolejs’ model represents scaffold construction fixed only by anchors to the facade without insulated layer. The Model 2 represents the phenomenon of damaged insulation layer by adding FE models of screws between anchors and facade. It is the same model as Model 1, but with the enhanced fixing as is shown in Fig. 12. Finally, Model 3 represents a model with newly developed Lever anchors, as is shown in Fig. 13. The Lever anchor has been modelled as an oblique beam with the rigid support in all three ways and also with the torsional rigid stiffness along the Z-axis. The axis orientation is shown in Fig. 12. It can be observed from Table 3, that most critical constant is 0.37 relates to the load combination S3 in Model 2. The load combination S3 is dominated by the wind load in the direction perpendicular to the facade. This critical constant is the smallest as expected, because the damage of the insulation layers occurs mostly during the high wind load [24,25]. It can be also observed, that by using Lever anchor the coefficient rises up significantly to 3.24. After that, the support forces from Model 3 have been obtained by using GNIA analysis, as shows Table 4. In Table 4 it can be seen, that the highest values relates to the S3 with the value of 17.36 kN as a pressure force in the way perpendicular to the facade. These sup-
Table 4 Support forces of the Lever anchors, combination S3 is chosen as crucial. Fig. 12. The axonometric view on the scaffold anchoring.
the service conditions, the load acts mainly in the vertical direction and in the out-of-service conditions the load dominates in the horizontal direction, because of the wind impact. The original model
Load combinations Maximum according to Rx
Rx [kN]
Ry [kN]
Rz [kN]
Mz [kN m]
Mx, My [kN m]
S1 S2 S3 S4
1.38 0.59 17.36 0.38
0.01 0.15 0.35 0.00
0.00 0.00 0.00 0.00
0.06 0.04 0.91 0.00
0.00 0.00 0.00 0.00
Perpendicular to façade Parallel to façade Perpendicular to façade Parallel to façade
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Fig. 14. (A) Initial geometry, (B) geometry after optimization with (C) the maximum permitted distances [mm].
Fig. 16. Enhanced Lever arm cross section.
Fig. 15. The optimized Lever arm.
port forces will be placed on the end of the lever arm in the optimization process. Also it has been decided, that despite S3 forces have a pressure impact on the anchor, and these support forces will be also placed on the anchor reversely to deduce tension strains.
3. The initial geometry optimization After obtaining loading forces and accurate FE models matching the previous experiment data, the optimization process was carried out. Arora et al. [17] obtained the updated finite element model and subsequently used for further design of the structure. First of all the initial geometry are adjusted. The Czech scaffolding standard [26] states the maximum free gap between the facade and scaffolding by the value 250 mm, because of that, the distance between the span member and the point, where the loading force is placed, is set up axially as 220 mm. Also the maximum possible depth of the insulation layer is for the further investigations considered as 300 mm [27], subsequently the axial distance between a span member and the facade is 310 mm. The difference between axial geometry of previous finite element models and subsequent optimized models shows Fig. 14. Design of the anchor has been practically tested during the pilot experiment and the installation on the facade was difficult. Thus newly developed anchor overcomes problems associated with a previous design the span member has been divided into 4 parts. Now, the anchor consists of 2
identical sliders with the 2 parallel single threaded rods placed between them as is shown in Fig. 15.
4. The optimization of the anchor under tension force In this subsection stress analysis under tension is described. The main goal is to, that the stress values in all anchor parts have to be below the yield strength values of the materials, i.e. the actual stresses must be placed in the elastic area. The procedure consists of two steps. In the first step, the initial developed beam and solid models are dimensionally updated and loaded by Lever arm support forces. If the total deformations are the same in both of the models, then in the second step the stress analyze of the solid model could be done. It has been observed, that one of the most limiting point is at the lever arm, where the support bar penetrates this arm (see Fig. 15). The tube diameter of the lever arm cross section cannot be changed, because the lever arm will be joined to the scaffold construction by the commonly used coupler and these couplers are connecting two tubes with the diameter 48.3 mm only. It has been decided to improve the lever arm tube cross section by the reinforcing the lever arm with two parallel plates made of steel S355J0, as is shown in Fig. 16. Since the lever arm tube is made of steel S235J0, the modelling of these two parts together as a one single beam used in FE beam model could be complicated, it has been decided to split these parts and assume the cross section as the two parallel plates only. These plates have thickness 6 mm each. The cross sections types of all other parts remain same, but
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Table 5 Maximum stresses in FE3 tensioned model. Parts
Details
Cross section
Material
Max. stress [MPa]
Threded bars Threded rods Slider Support bar
Left/right Upper/bottom Left/right Threaded rod Steel plates of joint Reinforced steel plates Tube upper/bottom Steel plates of joint
M20 M20 Plates 3 mm M20 Plates 3 mm Plates 6 mm 48,3/3,2 Plates 3 mm
8.8 8.8 S235J0 8.8 S235J0 S355J0 S235JRG2 S235J0
166.08 345.24 190.76 167.78 142.01 215.65 151.15 179.71
Lever arm
Fig. 17. The FE1 beam model, maximum deformation under tension.
they have been enhanced in the light of the linear behavior. The final cross sections are shown in Table 5. Three materially non-linear finite element models have been developed. FE1 and FE2 models represent beam and solid models
with the simplified lever arm cross section made of two parallel steel plates only and FE3 is a more accurate solid model with the full lever arm cross section – two plates and the rests of the steel tube welded together as it can be seen in Figs. 15 and 16. In all
Fig. 18. The FE2 solid model, maximum deformation under tension.
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Fig. 19. The FE3 solid model enhanced, maximum deformation under tension.
models the amount of the elements has been set up according to the convergence studies with the interaction to the final results. In the solid models the meshing is the mix of tetrahedral and hexahedral methods while the dominant method is tetrahedral. Also the local re-sizing of elements has been used for the optimal efficient solution. The final displacements in the end of the lever arm for each finite element model are shown in Figs. 17–19. The results shown as the force–displacement curves of these models are plotted together in Fig. 20. Because of the loose connection and the gaps between all parts, the initial displacement in all models has been set up approximately as 10 mm as it was observed during the pilot experiment on the real wall and during the laboratory experiment as well. It can be also observed that the final displacement curve of the FE3 model is linear, so the full lever arm cross section has the sufficient capacity to carry internal forces. Maximum Von-Mises stresses have been analyzed in solid FE3 model. The results are
Fig. 21. Side view on FE4 model with initial imperfections.
given in Table 5. All stress values belong under the yield strengths of materials. In Table 5 if a part consists of two similar members (for example the threaded bars consist of the left and right threaded bar) then only one value of maximal stress from both parts is shown. Also in some complex parts (for example lever arm), the maximum stress is shown separately for all their segments (in the case of the lever arm the stress is shown separately for steel plates making a connection, then reinforced steel plates and both upper and bottom rests of the tube). 5. The optimization of the anchor under a compression force
Tension Force
20 18 16
FORCE [kN]
14 12 10 8 6 4 2 0
8
9
10
11
12
13
14
15
16
DISPLACEMENT [mm] FE1 - BEAM
FE2 - SOLID
FE3 - SOLID ENHANCED Fig. 20. The force–displacement curves of all 3 models models).
In previous investigations in this paper the 3 finite elements models of the anchor have been developed. Since the anchor was tensioned all these models were centric. If the compressive force is applied, it is necessary to add a model with an initial geometrical imperfection. This model is indicated as FE4, it is the same like FE3 solid model but contains the initial imperfections based on the gaps between parts, as demonstrates Fig. 21. Since in this stage of the development the optimized anchor is not manufactured yet, these values of the angles have been measured from the FE model. It is expected that the real values on the manufactured anchor will be smaller, because the anchor will be produced with the maximum focusing on the minimization of these initial imperfections. The FE4 model is the most accurate of all developed models, it consists of 23 075 elements with 46 380 nodes. Its weight is 8.57 kg. The force magnitude is same as in the tensioned anchor; however in this model the loading is compressive. The results of the force–displacement curves of all FE1–FE4 models are plotted together in Fig. 22. The curve of FE4 model has a linear character. Table 6 demonstrates that all decisive members of FE4 model are in linear parts even if the cross sections remain the same as in the previous tensional analysis. The updated finite element model obtained from the previous investigations, have been optimized to carry out the increased loading force as shown in Fig. 23. It can be
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Compression Force
20 18 16
FORCE [kN]
14
FE1 - BEAM
12 10
FE2 - SOLID
8
FE3 - SOLID ENHANCED
6 4
FE4 - SOLID ENHANCED IMPERFECTIONS
2 0
0
1
2
3
4
5
6
7
8
DISPLACEMENT [mm] Fig. 22. The force–displacement curves of all models.
Table 6 Maximum stresses in FE4 compression model. Parts
Details
Cross section
Material
Max. stress [MPa]
Threded bars Threded rods Slider Support bar
Left/right Upper/bottom Left/right Threaded rod Steel plates of joint Reinforced steel plates Tube upper/bottom Steel plates of joint
M20 M20 Plates 3 mm M20 Plates 3 mm Plates 6 mm 48,3/3,2 Plates 3 mm
8.8 8.8 S235J0 8.8 S235J0 S355J0 S235JRG2 S235J0
426.64 321.48 190.23 376.07 195.07 251.41 151.15 187.17
Lever arm
observed from Fig. 23 that the optimized updated finite element model has able to carry more loading force. 6. Conclusions In this paper, a new scaffold anchor system has been developed. The newly developed scaffold anchor system overcomes the prob-
COMPARSION - TENSION FORCE
3.5 3
FORCE [kN]
2.5 2 1.5 1
lem associated with the existing scaffold anchor system. An initial finite element model of scaffold anchor system has been updated using experimental data. The updated finite element model has been used to calculate accurate loading forces on scaffold anchor system and further design of scaffold anchor system. The updated finite element models have been optimized to carry out the increased loading force. The loading force has been obtained from the more accurate finite element model of the scaffold construction. In this paper, the newly developed anchors have been positioned in a special pattern to carry more loading force. It has also been shown that using these anchors the scaffold stability can be increased. Optimization has been related to the modification of the initial geometry and reinforcement of weak parts. The finite element models have been loaded in both directions to investigate compression and tension behaviors. As the results the 4 new finite element models of the anchor have been obtained, the solid model in the position with initial imperfections is the most accurate. It has been shown that this optimized model is able to carry those support forces, because the stresses in all parts are under the yield strength of the materials.
0.5 0
0
20
40
60
Acknowledgements
DISPLACEMENT [mm] UN-OPTIMIZED "UPDATED SOLID MODEL" OPTIMIZED "FE3 - SOLID ENHANCED" Fig. 23. The final comparison between un-optimized and optimized solid tensioned models.
The authors are grateful to the financial supports by the Czech Technical University (Project no. SGS13/168/OHK1/3T/11) and also to the program ERASMUS+ (CZ PRAHA10). The technical support and a supervision during experiments by J. Jonáš of HILTI is gratefully acknowledged as well as support from Experimental Centre of
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Faculty of the Civil Engineering, CTU in Prague, and Z. Picek, PKL servis.
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[12] Arora V, Singh SP, Kundra TK. Finite element model updating with damping identification. J Sound Vib 2009;324:1111–23. [13] Arora V. Constrained antiresonance frequencies based model updating method for better matching of FRFs. Inverse Probl Sci Eng 2014;22:873–88. [14] Arora V. Comparative study of finite element model updating methods. J Vib Contr 2011;17:2023–39. [15] European Committee for Standardization (CEN). EN 12811-1: temporary works equipment – Part 1: Scaffolds – performance requirements and general design; 2003. [16] European Committee for Standardization (CEN). EN 1991-1-4 Eurocode 1 – actions on structures, general actions, Part 1–4: Wind actions; 2007. [17] Arora V, Singh SP, Kundra TK. Damped FE model updating using complex updating parameters: its use for dynamic design. J Sound Vib 2009;324:350–64. [18] Ilcˇík J, Dolejš J. The oblique sliding scaffold anchor. Utility model CZ26024, Prague; 2013. [19] Ilcˇík J, Dolejš J. The oblique scaffold anchor. Utility model CZ26023, Prague; 2013. [20] Ilcˇík J, Dolejš J. The rigid scaffold anchor. Utility model CZ26022, Prague; 2013. [21] ANSYS Workbench, version 14.0.0 – static structural. [22] Beale RG, Godley MHR. Numerical modeling of full-scale tube and fitting scaffold tests. In: 7th Euromech solid mechanics conference; 2009. [23] SCIA Engineer, version 13.1.64. [24] Peng J, Wu Ch, Chan S, Huang C. Experimental and numerical studies of practical systems scaffolds. J Constr Steel Res 2013;9:64–75. [25] Peng J, Chan S, Wu C. Effects of geometrical shape and incremental loads on scaffold systems. J Constr Steel Res 2006;63:448–59. ˇ NI). CˇSN 73 8101: scaffolding – common [26] Czech Normalization Institution (C regulations; 2005. [27] Dolejš J. Designing of scaffolding construction I; 2011. p. 25–35.
Contents lists available at ScienceDirect
Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Design of new scaffold anchor based on the updated finite element model Jiri Ilcik a, Vikas Arora b,⇑, Jakub Dolejs a a b
Faculty of Civil Engineering – Department of Steel and Timber Structures, Czech Technical University in Prague, Thákurova 7, 166 29 Praha 6, Czech Republic Department of Technology and Innovation, University of Southern Denmark, Campusvej 55, Odense 5230, Denmark
a r t i c l e
i n f o
Article history: Received 20 April 2015 Revised 25 January 2016 Accepted 29 March 2016 Available online 13 April 2016 Keywords: Optimization Tubular scaffold Fixing anchor Facade Stability Nonlinear finite element model
a b s t r a c t In this paper, a new scaffold anchor system is presented. The developed scaffold system overcomes the problems associated with the existing scaffold anchors. The existing scaffold anchors damage the surrounding insulation layers subsequently decreases the stability of scaffold anchors. The developed scaffold system has a new type of the facade anchor and the position pattern used for scaffolding. The developed scaffold system is based on the accurate FE models of the prototype anchor, which have been updated in the light of the experimental results i.e. force–displacement curve. It has been observed that the results of finite element model do not match with experimental results. The modelling of stiffnesses of the joints is considered to be the major source of uncertainty in the finite element model. Subsequently, stiffnesses of joints of anchor have been updated in the light of experimental data. The results have shown that after updating, the predictions of finite element model of scaffold system matches well with experimental results. Subsequently, the loading forces used during the optimization process have been obtained from the updated finite element model of the tubular scaffold construction related to the Eurocode standards. In addition to the problems associated with existing scaffold anchors, the developed scaffold anchor is also effective in transmitting support forces to the facade object along with increasing the stability of scaffold anchors. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Scaffold constructions are generally divided into two groups based on their main bearing components [1]. First group comprises of non-system tubes constructions, where the main components are mild steel tubes with diameter 48.3 mm and 4 mm thickness. Tubes are connected together by couplers. In the European countries, these types of systems are still very popular because of their variability. Based on the same principle, the bamboo scaffolds, which are very often used in East Asia countries, can be also added into this group. Second larger group comprising of prefabricated parts, mostly frames, in the certain system configuration; this group is called proprietary scaffolds. Scaffoldings in both groups are generally very weak constructions because of the loose connections of parts [2,3]. The stability of scaffold anchor systems can be increased significantly by the anchoring and bracing [4,5]. Many scaffold constructions collapses every year. According to the past research, the majority of failures occur due to inadequate site supervision and poor design [1]. ⇑ Corresponding author. E-mail address: [email protected] (V. Arora). http://dx.doi.org/10.1016/j.engstruct.2016.03.064 0141-0296/Ó 2016 Elsevier Ltd. All rights reserved.
These reasons are compounded, when the scaffold is fixed to a facade with a thermal insulation layer, because there are not many ways how to fix the anchor through this layer [6], and none of them have been sufficiently analyzed yet [7]. The presence of thermal insulating layer increases the possibilities of the failure. In the most of the cases, a long scaffold screw is used to overcome the thermal insulation as shown in Fig. 1. The use of long scaffold screw often results in deformation of the screw during the impact of the high wind load [8], which subsequently results in damage of the surrounding insulation layer and additional repairs are required [7]. Moreover, the deformation of the screw decreases the stability of scaffold anchor systems. To overcome these problems, a new facade anchor has to be developed. In this paper the developed anchor shapes are presented. One of the shapes, the ‘‘Lever Anchor” has been fabricated and experiment has been carried out to determine it’s the real load bearing capacity. It has been observed that the force–displacement curve is nonlinear because of permanent deformation of the anchor due to loading. Two FE models (beam model and solid model) have been developed for making out the numerical analyses. The experimental results have been compared with the corresponding predictions of these finite element models. It has been observed that the force–
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Fig. 2. The prototype of the Lever anchor.
Fig. 1. Vertical section of the fixed anchor.
displacement curves of these initial finite elements models did not match with the experimental results. It is well known that finite element predictions are often called into question when they are in conflict with experimental results. Inaccuracies in finite element model and errors in results predicted by them can arise due to use of incorrect modelling of boundary conditions, incorrect modelling of joints, and inaccurate size of the mesh, etc. This has led to the development of model updating techniques, which aim at reducing the inaccuracies present in an analytical model in the light of measured experimental data as shown in the surveys by Imregun and Visser [9] and Mottershead and Friswell [10]. Since the geometry of the finite element models have been known well, the stiffness of the joints and material properties have been considered as major sources of uncertainties. To reduce the uncertainties in the joints, the joint stiffnesses have been updated by using parametric optimization approach. The experimental results have been used for parametric optimization to reduce the error between experimental results and predictions of finite element models. The similar process has been used in [11–13]. Arora [14] concluded that parametric iterative optimization of finite element gives better results than direct optimization of finite element model. Subsequently it has been observed from that the experimental and corresponding updated finite element models force– displacement curves matches very well with each other. It can be concluded from the experimental updating of finite element of anchors that the updated anchor represents the reality accurately. As the developed scaffold anchor system is deformed permanently which results in non-linear behavior, a scaffold anchor system has been redesigned to behave linearly. The loading forces used during the optimization process have been obtained from the finite element model of the tubular scaffold construction related to the Eurocode standards [15,16]. The maximum support force from the scaffold construction has been applied on the anchors finite element models and material and geometrical optimizations have been done. The updated finite element model can be used for design of the structure [17]. As the result of these investigations, the accurate finite element solid model has been created. It carries the support force within the area of linear behavior in all its parts. 2. The updating of finite element models of prototype anchor in the light of experimental results After initial investigations of the scaffolding’s stability, three potential shapes of the new anchor [18–20] have been developed by simple basis. Two of them – ‘‘The Lever Anchor” and ‘‘The Oblique Scaffold Anchor”, showed in Figs. 2 and 3, are using innovative oblique arm. The principle of the obliquity is demonstrated in
Fig. 4. As it can be observed from Fig. 4 two anchors in the horizontal plane are used for fixing, these two anchors are placed in the opposite orientation to create a notional trapezoid with the surface of the facade. The outer scaffold plane is stiffened because of the vertical X-bracing and the inner plane is moved in a direction parallel with the facade [7]. By using the oblique arms, the displacement of the inner plane is significantly restricted, so the scaffold stability is increased. Also the anchors provide minimum deformation in its parallel threaded bars, which are joined into the facade through an insulation layer. This type of mechanism ensures that there is no damage to the surrounding insulation. For a backup there is also ‘‘The Rigid Scaffold Anchor”, see Fig. 3, which has the conventional straight arm. This shape has been developed for the case of an arm obliquity idea failure. For the further analysis, only the ‘‘Lever anchor” is selected. The reason is that the single parts of this anchor can be adjusted in different positions, so the installation process is easier and the variability of the anchor is greater than in ‘‘The Oblique Scaffold Anchor”. From the static point of view, the anchor parts ‘‘Threaded bars”, ‘‘Slider” and ‘‘Span” create a rigid frame. These parts are shown in Fig. 2. Furthermore, the anchor provides a semi-rigid support along vertical axis. Thus, this paper focuses only on optimizing the value of the torsional stiffness from experiments will be handled in the next stages of the development. In this paper, for further analysis, the anchor is considered as a fixed support in horizontal plane. After fabricating, the Lever anchor prototype, the pilot experiment on the real masonry wall has been carried out. The forces have been applied at the end of the lever arm in 4 directions as is shown in Fig. 5. These four directions represent all the possible force directions arisen during the standard load combinations [16]. The reason of this pilot experiment is to determine an optional loading direction for the first laboratory experiment and followed by finite element verification. It has been concluded that the +Y direction is optional, because only the tension force is applied and the interference of the buckling and imperfections is restricted. It will ensure accurate laboratory experiment set up and verification of initial FE models. The behavior of scaffold anchor system under the compressive force will be investigated in the next stages of the development. The pictorial view of the experimental set up is shown in Fig. 6 whereas scheme diagram of the laboratory experiment is shown in Fig. 7. The anchor has been loaded continually by tension force only in vertical direction. The range of force varies from 0 to 3 kN and the displacement of the lever arm has been recorded in real time. The anchor has been loaded by the single acting hollow plunger cylinder with the one-handed pump. The cylinder has been situated on the top of the supporting steel construction made from two parallel steel columns with reversed T-shape. Tensometric pressure dynamometer has been placed between the cylinder and the upper surface of the construction, which is connected with
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Fig. 3. The Rigid Scaffold Anchor and The Oblique Scaffold Anchor.
Fig. 4. The plane view – the principle of the obliquity.
Fig. 6. Photo from the end of the laboratory experiment.
Fig. 5. The force directions considered in pre-experiment.
the computer to measure an actual force in real-time. The draw bar made of steel has been connected to a hydraulic cylinder at the end of Lever arm. Vertical displacement of the lever arm has been measured by an absolute potentiometer sensor in real-time. It has been observed that during the initial stage the ‘‘Span bar” has reached the plastic behavior as it is deformed permanently. After applying the force of approximately 3.0 kN, first small cracks on the span’s bars have been detected, these cracks become larger at the end of the experiment. It has been observed that the weakest member of the scaffold anchor system is span member. The output of the experiment is a force–displacement curve as shown in Fig. 8. After carrying out of the experiment, the beam and solid finite element models have been developed in the ANSYS Workbench software [21]. In the beam model, members of the scaffold anchor system are connected together by using both the longitudinal (along X and Y axes) and also torsional stiffnesses (along the Z axis). Since the values of these joint stiffnesses are unknown as well as
the exact values of the material properties, these have been considered to be the source of error in the finite element model. Subsequently, the finite element model has been optimized considering stiffnesses and material properties as updating parameters in the light of experimental force–displacement curve. Whereas in the solid model, unknown variables are material properties, subsequently the solid model has been also optimized considering material properties as updating parameters for finite element model. As the permanent deformation has been observed during experimentation, the material properties are considered non-linear. Overlay of the experimental and updated finite element models predictions are shown in Fig. 9. The initial and final values of the optimization parameters are given in Tables 1 and 2 for beam and solid FE models respectively. It can be observed from Table 1 that the torsional stiffness values of springs have been changed significantly whereas, it can be observed from Table 2 that there has been some reduction in the values of material in case of solid model. It can be observed that the updated finite element models predictions matches well with the experimental results (force–displacement curve), so it can be concluded from optimization study that updated finite element models represents the reality accurately.
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J. Ilcik et al. / Engineering Structures 118 (2016) 334–343 Table 1 Initial and final values of optimized variables for beam model. Initial beam model
Fig. 7. The setting up of the laboratory experiment.
3.5 3
FORCE [kN]
Stiffness
Named
Longitudinal Longitudinal Longitudinal Longitudinal
R L L R
MN/m
MN/m
406.90 406.90 1070.00 1070.00
406.90 406.90 1070.00 1070.00
Torsional Torsional
L R
MN m/rad 0.10 0.10
MN m/rad 2.41 2.41
Longitudinal Longitudinal Longitudinal Longitudinal
RN RN RN RN
D D U U
MN/m 21630.00 387.90 21630.00 387.90
MN/m 21630.00 387.90 21630.00 387.90
Torsional Torsional
RN RN
D U
MN m/rad 0.10 0.10
MN m/rad 0.11 0.11
Longitudinal Longitudinal Longitudinal Longitudinal Longitudinal
UL LN LN LN LN
X D D U U
MN/m 0.10 9000.00 351.90 9000.00 351.90
MN/m 0.10 9000.00 351.90 9000.00 351.90
Torsional Torsional
LN LN
D U
MN m/rad 0.01 0.01
MN m/rad 0.34 0.34
MPa 200 300 580
MPa 200 275 550
2 1.5
0.5 0
10
20
30
40
50
60
70
80
90
DISPLACEMENT [mm] EXPERIMENT
Y X Y X
3.5 3 2.5 2 1.5 1 0.5 0
10
20
30
40
50
60
70
80
90
DISPLACEMENT [mm] EXPERIMENT
BEAM MODEL
Structural steel NL S235 Structural steel NL 4.8 Structural steel NL 8.8
Initial solid model MPa
Updated solid model MPa
200 300 580
200 260 500
INIT. SOLID
INIT. BEAM
Fig. 8. Force–displacement curves of initial models.
FORCE [kN]
Y X Y X
Table 2 Initial and final values of optimized variables for solid model.
1
0
Y Y X X
Material Structural steel NL S235 Structural steel NL 4.8 Structural steel NL 8.8
2.5
0
Updated beam model
SOLID MODEL
Fig. 9. Force–displacement curves of updated models.
The developed updated two FE models (beam and solid) are subsequently used to calculate the exact support force on the loaded scaffold anchor system. The support force has been calcu-
lated from the finite element model of the tubular scaffold construction, which uses Lever anchors as supports. A finite element model of tubular scaffolding was described originally by Dolejš in [7]. Dolejs’ model has experimentally conducted torsional stiffness of the joints, which is necessary for the more accurate solution [22]. The dimensions of this scaffolding and position pattern of anchors correspond with the commonly used 12-storey high scaffolding with the netted cladding, see Fig. 10. His model contains fixing system provided by commonly used short anchors and these anchors are modelled by using simple beams with pinned supports. To demonstrate the influence of the long scaffold screw used in a fixing (as is shown in Figs. 1 and 11) the same FE model of anchor has been used by adding these screws (see Fig. 12) and it has been solved out using the same software as Dolejs used [23]. Subsequently, the same model has been analyzed again by considering Lever anchors in their own original position pattern as is shown in Fig. 13. The Lever anchor has been modelled as short oblique beams with fixed supports. The stability results are demonstrated by critical load coefficients obtained from geometrical non-linear analyses (GNIA) and the results are shown in Table 3. It can be observed that the load combinations match the Eurocode standard [14], there are four combinations S1–S4. The first two S1 and S2 represent in-service conditions and next S3 and S4 are out-of-service conditions. In
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Fig. 13. Lever anchors position pattern of the Model 3. Dots represent positions of the anchors.
Table 3 Critical load coefficient from the stability computing. Fig. 10. The model of the tubular scaffolding [7].
Fig. 11. A scaffold anchoring provided by long scaffold screw penetrating an insulation layer.
Load combination
Model 1
Model 2
Model 3
acr
acr
acr
The service condition S1 Perpendicular to façade S2 Parallel to façade
1.68 1.67
1.68 1.67
2.03 1.96
The out of service condition S3 Perpendicular to façade S4 Parallel to façade
2.19 2.74
0.37 2.73
3.24 3.2
made by Dolejs is indicated in this paper as Model 1. It has been mentioned above that Dolejs’ model represents scaffold construction fixed only by anchors to the facade without insulated layer. The Model 2 represents the phenomenon of damaged insulation layer by adding FE models of screws between anchors and facade. It is the same model as Model 1, but with the enhanced fixing as is shown in Fig. 12. Finally, Model 3 represents a model with newly developed Lever anchors, as is shown in Fig. 13. The Lever anchor has been modelled as an oblique beam with the rigid support in all three ways and also with the torsional rigid stiffness along the Z-axis. The axis orientation is shown in Fig. 12. It can be observed from Table 3, that most critical constant is 0.37 relates to the load combination S3 in Model 2. The load combination S3 is dominated by the wind load in the direction perpendicular to the facade. This critical constant is the smallest as expected, because the damage of the insulation layers occurs mostly during the high wind load [24,25]. It can be also observed, that by using Lever anchor the coefficient rises up significantly to 3.24. After that, the support forces from Model 3 have been obtained by using GNIA analysis, as shows Table 4. In Table 4 it can be seen, that the highest values relates to the S3 with the value of 17.36 kN as a pressure force in the way perpendicular to the facade. These sup-
Table 4 Support forces of the Lever anchors, combination S3 is chosen as crucial. Fig. 12. The axonometric view on the scaffold anchoring.
the service conditions, the load acts mainly in the vertical direction and in the out-of-service conditions the load dominates in the horizontal direction, because of the wind impact. The original model
Load combinations Maximum according to Rx
Rx [kN]
Ry [kN]
Rz [kN]
Mz [kN m]
Mx, My [kN m]
S1 S2 S3 S4
1.38 0.59 17.36 0.38
0.01 0.15 0.35 0.00
0.00 0.00 0.00 0.00
0.06 0.04 0.91 0.00
0.00 0.00 0.00 0.00
Perpendicular to façade Parallel to façade Perpendicular to façade Parallel to façade
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Fig. 14. (A) Initial geometry, (B) geometry after optimization with (C) the maximum permitted distances [mm].
Fig. 16. Enhanced Lever arm cross section.
Fig. 15. The optimized Lever arm.
port forces will be placed on the end of the lever arm in the optimization process. Also it has been decided, that despite S3 forces have a pressure impact on the anchor, and these support forces will be also placed on the anchor reversely to deduce tension strains.
3. The initial geometry optimization After obtaining loading forces and accurate FE models matching the previous experiment data, the optimization process was carried out. Arora et al. [17] obtained the updated finite element model and subsequently used for further design of the structure. First of all the initial geometry are adjusted. The Czech scaffolding standard [26] states the maximum free gap between the facade and scaffolding by the value 250 mm, because of that, the distance between the span member and the point, where the loading force is placed, is set up axially as 220 mm. Also the maximum possible depth of the insulation layer is for the further investigations considered as 300 mm [27], subsequently the axial distance between a span member and the facade is 310 mm. The difference between axial geometry of previous finite element models and subsequent optimized models shows Fig. 14. Design of the anchor has been practically tested during the pilot experiment and the installation on the facade was difficult. Thus newly developed anchor overcomes problems associated with a previous design the span member has been divided into 4 parts. Now, the anchor consists of 2
identical sliders with the 2 parallel single threaded rods placed between them as is shown in Fig. 15.
4. The optimization of the anchor under tension force In this subsection stress analysis under tension is described. The main goal is to, that the stress values in all anchor parts have to be below the yield strength values of the materials, i.e. the actual stresses must be placed in the elastic area. The procedure consists of two steps. In the first step, the initial developed beam and solid models are dimensionally updated and loaded by Lever arm support forces. If the total deformations are the same in both of the models, then in the second step the stress analyze of the solid model could be done. It has been observed, that one of the most limiting point is at the lever arm, where the support bar penetrates this arm (see Fig. 15). The tube diameter of the lever arm cross section cannot be changed, because the lever arm will be joined to the scaffold construction by the commonly used coupler and these couplers are connecting two tubes with the diameter 48.3 mm only. It has been decided to improve the lever arm tube cross section by the reinforcing the lever arm with two parallel plates made of steel S355J0, as is shown in Fig. 16. Since the lever arm tube is made of steel S235J0, the modelling of these two parts together as a one single beam used in FE beam model could be complicated, it has been decided to split these parts and assume the cross section as the two parallel plates only. These plates have thickness 6 mm each. The cross sections types of all other parts remain same, but
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Table 5 Maximum stresses in FE3 tensioned model. Parts
Details
Cross section
Material
Max. stress [MPa]
Threded bars Threded rods Slider Support bar
Left/right Upper/bottom Left/right Threaded rod Steel plates of joint Reinforced steel plates Tube upper/bottom Steel plates of joint
M20 M20 Plates 3 mm M20 Plates 3 mm Plates 6 mm 48,3/3,2 Plates 3 mm
8.8 8.8 S235J0 8.8 S235J0 S355J0 S235JRG2 S235J0
166.08 345.24 190.76 167.78 142.01 215.65 151.15 179.71
Lever arm
Fig. 17. The FE1 beam model, maximum deformation under tension.
they have been enhanced in the light of the linear behavior. The final cross sections are shown in Table 5. Three materially non-linear finite element models have been developed. FE1 and FE2 models represent beam and solid models
with the simplified lever arm cross section made of two parallel steel plates only and FE3 is a more accurate solid model with the full lever arm cross section – two plates and the rests of the steel tube welded together as it can be seen in Figs. 15 and 16. In all
Fig. 18. The FE2 solid model, maximum deformation under tension.
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Fig. 19. The FE3 solid model enhanced, maximum deformation under tension.
models the amount of the elements has been set up according to the convergence studies with the interaction to the final results. In the solid models the meshing is the mix of tetrahedral and hexahedral methods while the dominant method is tetrahedral. Also the local re-sizing of elements has been used for the optimal efficient solution. The final displacements in the end of the lever arm for each finite element model are shown in Figs. 17–19. The results shown as the force–displacement curves of these models are plotted together in Fig. 20. Because of the loose connection and the gaps between all parts, the initial displacement in all models has been set up approximately as 10 mm as it was observed during the pilot experiment on the real wall and during the laboratory experiment as well. It can be also observed that the final displacement curve of the FE3 model is linear, so the full lever arm cross section has the sufficient capacity to carry internal forces. Maximum Von-Mises stresses have been analyzed in solid FE3 model. The results are
Fig. 21. Side view on FE4 model with initial imperfections.
given in Table 5. All stress values belong under the yield strengths of materials. In Table 5 if a part consists of two similar members (for example the threaded bars consist of the left and right threaded bar) then only one value of maximal stress from both parts is shown. Also in some complex parts (for example lever arm), the maximum stress is shown separately for all their segments (in the case of the lever arm the stress is shown separately for steel plates making a connection, then reinforced steel plates and both upper and bottom rests of the tube). 5. The optimization of the anchor under a compression force
Tension Force
20 18 16
FORCE [kN]
14 12 10 8 6 4 2 0
8
9
10
11
12
13
14
15
16
DISPLACEMENT [mm] FE1 - BEAM
FE2 - SOLID
FE3 - SOLID ENHANCED Fig. 20. The force–displacement curves of all 3 models models).
In previous investigations in this paper the 3 finite elements models of the anchor have been developed. Since the anchor was tensioned all these models were centric. If the compressive force is applied, it is necessary to add a model with an initial geometrical imperfection. This model is indicated as FE4, it is the same like FE3 solid model but contains the initial imperfections based on the gaps between parts, as demonstrates Fig. 21. Since in this stage of the development the optimized anchor is not manufactured yet, these values of the angles have been measured from the FE model. It is expected that the real values on the manufactured anchor will be smaller, because the anchor will be produced with the maximum focusing on the minimization of these initial imperfections. The FE4 model is the most accurate of all developed models, it consists of 23 075 elements with 46 380 nodes. Its weight is 8.57 kg. The force magnitude is same as in the tensioned anchor; however in this model the loading is compressive. The results of the force–displacement curves of all FE1–FE4 models are plotted together in Fig. 22. The curve of FE4 model has a linear character. Table 6 demonstrates that all decisive members of FE4 model are in linear parts even if the cross sections remain the same as in the previous tensional analysis. The updated finite element model obtained from the previous investigations, have been optimized to carry out the increased loading force as shown in Fig. 23. It can be
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Compression Force
20 18 16
FORCE [kN]
14
FE1 - BEAM
12 10
FE2 - SOLID
8
FE3 - SOLID ENHANCED
6 4
FE4 - SOLID ENHANCED IMPERFECTIONS
2 0
0
1
2
3
4
5
6
7
8
DISPLACEMENT [mm] Fig. 22. The force–displacement curves of all models.
Table 6 Maximum stresses in FE4 compression model. Parts
Details
Cross section
Material
Max. stress [MPa]
Threded bars Threded rods Slider Support bar
Left/right Upper/bottom Left/right Threaded rod Steel plates of joint Reinforced steel plates Tube upper/bottom Steel plates of joint
M20 M20 Plates 3 mm M20 Plates 3 mm Plates 6 mm 48,3/3,2 Plates 3 mm
8.8 8.8 S235J0 8.8 S235J0 S355J0 S235JRG2 S235J0
426.64 321.48 190.23 376.07 195.07 251.41 151.15 187.17
Lever arm
observed from Fig. 23 that the optimized updated finite element model has able to carry more loading force. 6. Conclusions In this paper, a new scaffold anchor system has been developed. The newly developed scaffold anchor system overcomes the prob-
COMPARSION - TENSION FORCE
3.5 3
FORCE [kN]
2.5 2 1.5 1
lem associated with the existing scaffold anchor system. An initial finite element model of scaffold anchor system has been updated using experimental data. The updated finite element model has been used to calculate accurate loading forces on scaffold anchor system and further design of scaffold anchor system. The updated finite element models have been optimized to carry out the increased loading force. The loading force has been obtained from the more accurate finite element model of the scaffold construction. In this paper, the newly developed anchors have been positioned in a special pattern to carry more loading force. It has also been shown that using these anchors the scaffold stability can be increased. Optimization has been related to the modification of the initial geometry and reinforcement of weak parts. The finite element models have been loaded in both directions to investigate compression and tension behaviors. As the results the 4 new finite element models of the anchor have been obtained, the solid model in the position with initial imperfections is the most accurate. It has been shown that this optimized model is able to carry those support forces, because the stresses in all parts are under the yield strength of the materials.
0.5 0
0
20
40
60
Acknowledgements
DISPLACEMENT [mm] UN-OPTIMIZED "UPDATED SOLID MODEL" OPTIMIZED "FE3 - SOLID ENHANCED" Fig. 23. The final comparison between un-optimized and optimized solid tensioned models.
The authors are grateful to the financial supports by the Czech Technical University (Project no. SGS13/168/OHK1/3T/11) and also to the program ERASMUS+ (CZ PRAHA10). The technical support and a supervision during experiments by J. Jonáš of HILTI is gratefully acknowledged as well as support from Experimental Centre of
J. Ilcik et al. / Engineering Structures 118 (2016) 334–343
Faculty of the Civil Engineering, CTU in Prague, and Z. Picek, PKL servis.
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