- Email: [email protected]
Investigation of buckled truss bars of a space truss roof system
Engineering Failure Analysis 106 (2019) 104156
Contents lists available at ScienceDirect
Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal
Investigation of buckled truss bars of a space truss roof system Cüneyt Vatansever
T
Department of Civil Engineering, Istanbul Technical University, 34469 Maslak, Istanbul, Turkey
A R T IC LE I N F O
ABS TRA CT
Keywords: Space truss roof Flexural buckling Support settlement Nonlinear analysis Mero node
Some bars of space truss roof a major shopping market chain in Adana, Turkey have experienced flexural buckling without any circumstance of overloading induced by snow and rain together with wind that has led to the buckling phenomenon. However, according to the on-site geotechnical surveys that have demonstrated that an increase in consolidation settlement of foundation soil has occurred, it has been realized that differential support settlements may cause the truss bars to buckle. This paper investigates the probable cause of the buckling phenomenon observed in some truss bars based on the soil condition. For this, a photogrammetric survey has initially been performed to determine the existing vertical position of the roof supports located on the top of the cantilever columns. To obtain the amount of settlements of the supports, initial vertical coordinates of the tips of the columns that were determined before assembling of the roof are subtracted from those obtained by the photogrammetric measurement with respect to the reference point. An observation has also been made in site to visually inspect the distribution pattern of the buckled truss bars. A 3D analytical model of the roof has been developed to understand whether or not the buckling failure of the truss bars is resulted from the soil settlement under the individual foundations. When the observed distribution pattern of the buckled truss bars is compared to that obtained by the nonlinear analysis, a reasonably good agreement has been achieved, which shows that the truss bars have buckled because of the effects caused by differential settlements among the individual foundations due to increase in consolidation settlement occurred within the soil that surrounds the structure.
1. Introduction Space truss roof systems have widely been used to cover large areas because of their less weight. A special type of space truss roof, called Mero space truss roof, has often been employed since the use of prefabricated straight tubular elements with bolts and sleeves (truss bars) and a sphere (Mero node) designed in so as to allow connection among the truss bars (Fig. 1) [1], make the handling and assembly work easier. Despite of the advantages of the space truss roof systems mentioned above, these types of systems are very prone to progressive collapse initiated by buckling of the truss bars. In particular, a space truss roof in which the buckled truss bars gather in a certain region across the roof may entirely collapse suddenly without any indication and warning. A numerical investigation [2] on the progressive collapse behavior of double-layer space truss roofs has proved the sensitivity of these structures against the progressive collapse when subjected to increasing applied load. However, even though some truss bars buckle in flexural mode, the entire roof may not collapse because the system is capable of allowing redistribution of axial forces to a small extent. For instance, if a space truss roof is subjected to soil-induced settlements resulting in disproportionately relative displacements among the roof supports in time, axial force redistribution in truss bars is likely, but still limited to negligible level.
E-mail address: [email protected]. https://doi.org/10.1016/j.engfailanal.2019.104156 Received 5 August 2016; Received in revised form 18 January 2018; Accepted 26 August 2019 Available online 29 August 2019 1350-6307/ © 2019 Elsevier Ltd. All rights reserved.
Engineering Failure Analysis 106 (2019) 104156
C. Vatansever
Slot Bolt Tubular member
Sphere Fig. 1. Typical components and details of a Mero connection.
Many researches have been conducted on the investigation of collapse behaviors of the space truss roof systems. One has reported the investigation of a space truss roof designed to cover a reinforced building that has totally collapsed due to snow load initially underestimated and some mistakes made in the design [3]. Additionally, the partial collapse of a space truss roof of an industrial plant has been investigated in [4] and it has been reported that the collapse was because of ice ponds after exceptional snow load. Another research [5] has addressed a long-span steel roof structure collapsed during construction as a result of an out-of-plane buckling phenomenon caused by a gust of wind. The partial collapse of a space truss roof structure that occurred during strong winds and heavy rains was investigated based on the site observation and experimental study on the bolts [6]. An experimental study was performed to investigate the ductility behavior of a space truss roof system that consists of cold-formed hollow square sections attached to a joint through the special welded joint plates and bolted connections [7]. A methodology allowing to perform nonlinear postbuckling analysis of space truss systems was developed and applied to double-layer space truss to obtain the vertical loaddisplacement response [8]. A numerical research based on a nonlinear stepwise linearization analysis method was carried out to investigate the nonlinear behavior of space truss members [9]. A space truss roof of a major shopping market chain in Adana, Turkey has been addressed in this study, whose some bars have buckled flexurally without any circumstance of overloading induced by snow and rain together with wind. The officers responsible for structural system of the shopping market also confirmed that neither ponding roof water nor heavy snow that led to buckling failure of the truss bars was experienced. However, it was realized, based on the on-site geotechnical survey conducted between the dates December 12th, 2013–January 7th, 2014, that another potential cause of this failure may be changes within the foundation soils that surround and support the structure over time because the risk of the consolidation settlement appeared to be high. It was also reported that when findings had been compared to those obtained by previous geotechnical surveys dated on August 1995 and April 2006, soil condition had negatively been affected over the years. As a result, these findings showed that changes occurred in foundation soil that can lead to differential support settlements might play a role in the buckling of the truss bars. This paper investigates the possible relation between buckling of the truss bars and the consequences of changes that have taken place with time in condition of foundation soil. 2. Description of the space truss roof system The structural system of entire building consists of steel built up box columns cantilevered to foundation and space truss roof supported by these columns, as shown in Fig. 2. The space truss roof system considered herein is composed of two planar networks of bars which form the top and bottom layers parallel to each other and interconnected by diagonal web bars. The roof plan with the dimensions of 32.5 m by 90.0 m and elevation across the longitudinal direction of the roof are shown in Fig. 3. Transverse elevation is also illustrated in Fig. 4. The roof has been simply supported on the top of 28 steel built up box columns of 450 mm × 450 mm that have been constructed with 12 mm thick plates. The heights of the columns along the longitudinal axis of 20 are 6.70 m while the columns along the axis of 17 and 15A are 7.15 m and 7.50 m long, respectively. The axis of 15A is shared by adjacent building. So, the columns located on axis 15A are existing columns which have been erected during construction of the existing adjacent building. All supports are indicated by solid dots in Fig. 3. The column located at the intersection point of axis 15A and axis F was not marked with solid dot because the roof did not rest on this column. Each column was supported by 0.70 m thick square spread footing with the width of 4.0 m. The total height of the roof that corresponds to the distance between top and bottom layer is 1.768 m. While dashed line shows the members in the plane of the bottom layer, the members of top layer are depicted by the solid lines, as shown in Fig. 3. The characteristics of typical truss bars used in the design, such as tubular members' diameters, their wall thicknesses and corresponding bolt diameters are tabulated in Table 1. A dowel pin, which goes through the bolt, must also be used to allow the bolts to be tightened by means of spanner sleeve. The diameters of the holes drilled in each individual bolts for dowel pins are also listed in Table 1. The material of the tubes was S235JR possessing the yield stress Fy = 235 N/mm2 and tensile strength Fu = 360 N/mm2. All bolts were made of steel with the tensile strength Fub = 1000 N/mm2 and the yield stress Fyb = 900 N/mm2 which was nominally designated as 10.9 bolts. Sleeves' material was denoted by A1030 whose yield stress and tensile strength were 345 N/mm2 and 520 N/ mm2, respectively. The Mero nodes use the steel of C45 with yield stress of 430 N/mm2 and tensile strength of 750 N/mm2. 2
Engineering Failure Analysis 106 (2019) 104156
C. Vatansever
Fig. 2. Typical view of structural system.
3. Overview of the structural design In design, the self-weight of the structural system was automatically taken into account by analysis software, SAP2000 v8 [10]. The weight of purlins and roof cladding were taken as 0.35k N/m2. The load from equipment was assumed to be 0.225 kN/m2. Snow load for the roof without considering drift was 0.75 kN/m2 in accordance with the TS 498/1997 [11]. Wind pressures acting on the surfaces and pressure distribution were determined in conformity with the TS 498/1997 [11]. Self-straining forces arising from restrained dimensional changes because of temperature fluctuation were also considered. The magnitude of the fluctuation was estimated as ± 25 °C. Equivalent lateral force procedure stipulated in Turkish Seismic Code (TSC) [12] was used for the design of the structure against earthquake. Seismic Zone 2 is assigned to the area where the structure is located. The effective ground acceleration coefficient, Ao was accordingly taken to be 0.30. For the equivalent static lateral forces, spectrum coefficient, S(T) was taken as the maximum value of 2.5 regardless of the local site class. The building importance factor and structural behavior factor were taken to be I = 1.2 and R = 4, respectively. For this structure, structural behavior factor, R is found to be convenient since seismic loads are fully resisted by single-story frames with columns pinned at top as defined in TSC [12]. 4. On-site observation Before analytical investigation, an observation has been made in site to visually inspect the buckled truss bars and their distribution pattern over the roof. Fig. 5 shows the typical flexural deformation of the buckled truss bars. No indication of any damage on the bolts, spheres and sleeves has been observed. Welds connecting the conic parts to the ends of the tubular elements have not experienced any damage as well. 5. Determination of differential support settlements Three, as aforementioned, geotechnical surveys have been performed to characterize the soil condition in site. It has been stated in the report from the geotechnical survey on August 1995 that cohesion values of 100–280 kN/m2 were obtained by the Vane shear test while those values, by the hand penetrometer test, were found as 125–225 kN/m2. The allowable soil stress was given as 250 kN/ m2. According to the report from the survey conducted on April 2006, the maximum consolidation settlement and subgrade reaction of the soil were reported as 11.7 mm and 40,000 kN/m3, respectively. The allowable soil stress was specified as 225 kN/m2. In the third survey lasted between December 25th, 2013 and January 7th, 2014, the cohesion values were obtained as 73–119 kN/m2, which indicated that changes leading to larger consolidation settlement occurred within the foundation soil that support the structure. It was also reported that the values of consolidation settlements reached to 70–120 mm. The final report concluded that the occurrence possibility of non-uniform consolidation settlement was found to be high and the superstructure must be protected from the undesirable effect of the foundation settlement because of the reduced ability of the soil to support the load. Accordingly, the most probable reason for the buckled truss bars is seemed to be increase in axial compressive forces induced by differential settlements of the foundations supporting the structure due to gradual reduction in the bearing capacity of the soil. Therefore, a set of photogrammetric surveying has been performed to obtain the amount of vertical settlement of each roof support located on the top of the columns. For this, a total station, which is an instrument to measure angles and distances from itself to points under survey, has been used. By this equipment, coordinates of surveyed points have been calculated using trigonometry and triangulation. The relative vertical settlement values, which are tabulated in Table 2, have been computed by subtracting the 3
Engineering Failure Analysis 106 (2019) 104156
C. Vatansever
Fig. 3. Plan view, typical longitudinal elevation and dimensions of the roof.
4
Engineering Failure Analysis 106 (2019) 104156
C. Vatansever
Fig. 4. Typical transverse elevation of the roof. Table 1 Dimensions of tubular members and corresponding bolts with dowel pin holes. Tube diameter [mm]
Wall thickness [mm]
Bolt [mm]
Dowel pin hole diameter [mm]
42.4 42.4 48.3 48.3 60.3 76.1 76.1 88.9 88.9 88.9 88.9 88.9 88.9 114.3 114.3
2.5 2.5 2.5 2.5 2.5 3.0 3.0 3.0 3.0 4.0 4.0 5.0 5.0 4.5 4.5
M12 M16 M12 M16 M16 M16 M20 M20 M24 M20 M24 M24 M24 M24 M24
4 5 4 5 5 5 8 8 8 8 8 8 8 8 8
initial levels of the tip of the columns measured during the assemblage of the roof from those obtained by the photogrammetric survey performed within this study. As clearly seen from Table 2, the largest soil settlements have occurred along axis 15A that belongs also to the adjacent building, because vertical loads from both buildings act on each column on axis 15A. Furthermore, as settlement potential of foundation soil has increased with the change of consolidation characteristics, the foundations of the columns on the axis have settled deeper into soil. 6. Analytical model Since the roof is supported on the top of the cantilever steel columns, the lateral stiffness of columns can be used in modeling the support conditions in lieu of explicit modeling of columns. Thus, elastic springs can then simply be utilized to rationally represent the lateral behavior of roof supports in orthogonal directions (i.e. x and y). The lateral stiffness of each column has been computed by considering the response of a cantilever column with a point load acting on the top. Then, Eq. (1) can be used and the values obtained for each column can be defined as spring coefficients, denoted ks, which are assigned to the springs represented the supports of the roof for both lateral directions. Therefore, the columns were not directly included in the analytical model developed by SAP2000 v19 [13]. As the influence of the axial stiffness of columns on analysis results was found to be negligible when compared to flexural stiffness, the axial stiffness of columns was not incorporated into the analytical model. In Eq. (1)h, E and I are the height of the column, elastic modulus and moment of inertia, respectively.
ks =
3EI h3
(1)
One single plastic hinge, as shown in Fig. 6, was assigned to the mid-length of each truss bar to represent the nonlinear behavior in tension and compression. The behavior, which is defined by axial force-deformation relationship, was assumed to be as shown in Fig. 7 [14]. The parameters governing the force-deformation curve were adopted from FEMA 356 [14] and tabulated in Table 3. In Fig. 7, point B indicates the axial force, Fy, and corresponding deformation, ΔT, at when the tubular element starts to yield. A strain hardening behavior between point B and point C is defined with a slope of 3%. The amount of plastic deformations corresponding to 5
Engineering Failure Analysis 106 (2019) 104156
C. Vatansever
Fig. 5. Photographs showing typical buckled truss bars. Table 2 Support settlements. Columns
Amount of relative settlements to reference support [mm]
Columns
Amount of relative settlements to reference support [mm]
Columns
Amount of relative settlements to reference support [mm]
(20-L) (20-A) (20-B)a (20-C) (20-D) (20-F) (20-G) (20-I) (20-J) (20-K)
−19.2 −16.8 0.0 −22.8 −40.8 −64.8 −91.8 −88.8 −94.8 −88.8
(17-L) (17-M) (17-N) (17-C) – (17-E) (17-P) (17-I) (17-J) (17-K)
−55.5 −57.3 −55.5 −65.7 – −71.1 −69.9 −78.3 −84.3 −90.3
(15A-L)c (15A-A) (15A-B) (15A-C) (15A-D) (15A-F)b (15A-G) (15A-I) (15A-J) (15A-K)
−162.3 −138.3 −138.3 −132.3 −138.3 – −120.3 −123.3 −144.3 −144.3
a b c
Reference support. The column not supporting the roof. Point monitored during analysis under displacement control.
Fig. 6. Analytical model for each truss bar.
point C and point E is characterized by the parameters a and b, respectively. The line from point D to point E represents the residual strength illustrated by the parameter c. Initial slope of the curve in compression side is defined as the same as in tension side. The critical buckling load, Fcr, is the load obtained depending on slenderness ratio (may be defined as the ratio of the system length of a member to the least radius of gyration). The corresponding axial deformation is designated as ΔC. The contribution of the residual compressive strength is shown by the horizontal line defined by parameter c depending on the diameter-to-wall thickness ratio in 6
Engineering Failure Analysis 106 (2019) 104156
C. Vatansever
F
b
a Fy
ΔC A Compression
C
B
Tension
D
E c Δ
ΔT Fcr
Fig. 7. Axial behavior of typical truss bar. Table 3 Properties of axial plastic hinges for tubular elements. Case
Members in tension Members in compression
Diameter – to – thickness ratio
d t
≤
1500 Fy
d t
≥
6000 Fy
1500 Fy
≤
d t
≤
Plastic deformation
Residual strength ratio
a
b
c
11ΔT 0.5ΔC
14ΔT 9ΔC
0.8 0.4
0.5ΔC
3ΔC
0.2
Linear interpolation shall be used.
6000 Fy
Table 3. No any initial imperfection amplitude was explicitly considered in modeling truss bars. The study carried out by Alcicek [15] has also demonstrated that axial force-deformation responses of the truss bars with characteristics tabulated in Table 3 are in harmony with those from the analyses performed under cycling loading (compression and tension) on individual truss bars with the initial imperfection amplitude of L/300 (L is length of truss bar). Hence, compressive strengths of truss bars have been computed by SAP2000 v19 [13] indirectly considering the effect of initial imperfection. Since no any bolt failure, as seen in Fig. 8, was observed during site investigation, bolts were not explicitly included in the analytical model. Similarly, as sleeve and sphere failure were not detected during observation shown in Fig. 8, these elements were not incorporated into the model. It is thought that each truss bar has buckled in different moments over time. Therefore, this situation has caused the roof structure to behave in nonlinear manner with differential settlements increasing. Accordingly, displacement-controlled pushover analysis has been found to be more appropriate for the investigation. The analytical model used for the nonlinear analysis performed by using SAP2000 v19 [13] is shown in Fig. 9. The relative displacements that correspond to the differential settlements were considered as displacement loads and imposed to the relevant supports. Dead loads [11] including weight of the structural members of the roof, cladding with purlins and equipment were taken into account combining with the displacement loads. 7. Analysis results and discussion The model has been nonlinearly analyzed under combined gravity loads whose details are given in Section 3 and relative support settlements listed in Table 2 to simulate the loading condition likely to cause the truss bars to buckle. The total self-weight of the structural members of the roof was taken as 0.112 kN/m2 based on the weight of existing structural member sizes. In performing the nonlinear pushover analysis, relative displacements in Table 2 were applied to the relevant supports in a manner of which they would increase monotonically. All gravity loads were remained constant throughout the loading process. According to the analysis results, the distribution pattern of the truss bars failed by buckling across the roof are shown in Fig. 10. Moreover, analysis results showed that the truss bars which are composed of tubular elements with outside diameter of 42.5 mm and wall thickness of 2.5 mm are much more susceptible to flexural buckling because of their relatively higher slenderness ratio, obtained as 176. This slenderness ratio is less than 200 as stipulated in ANSI/AISC 360-16 [16] for members in compression. However, as the slenderness ratio is larger than the value of 137.4 calculated from 4.71 E / Fy [16] that divides the strength curve of members in axial compression into two regions; elastic and inelastic, it is clear that these truss bars with slenderness ratio of 176 buckled in elastic region. This led to redistribution of axial forces among the other neighboring truss bars and development of nonlinear response of the roof. Although bolts were not explicitly introduced into the analytical model, the ratio of the nominal tensile strength to the required tensile strength (axial tensile force experienced by the truss bar) for each bolt was also obtained to see how far the ratio is from unity 7
Engineering Failure Analysis 106 (2019) 104156
C. Vatansever
Fig. 8. Typical Mero node indicating no failure of bolts, sleeves and spheres.
Fig. 9. Analytical model of the roof.
when the increase in axial force due to the consequence of the redistribution is considered. The maximum ratio was obtained as 0.06, which indicates no damage occurred on the bolts as observed in site. Similarly, the axial compressive strengths of the spanner sleeves that correspond to their yield strengths were found to be adequate to transmit the maximum axial compressive forces occurred. Since any type of failure in sphere connectors was not observed in site and also until now no damage on sphere connector has been reported 8
Engineering Failure Analysis 106 (2019) 104156
C. Vatansever
Fig. 10. Distribution pattern of buckled truss bars based on analysis. 9
Engineering Failure Analysis 106 (2019) 104156
C. Vatansever
x
Buckled bars inspected in site Buckled bars based on analysis
Fig. 11. Comparison between on-site and analysis-based distribution pattern of buckled truss bars. 10
Engineering Failure Analysis 106 (2019) 104156
C. Vatansever
plus none of sphere has failed in the tests [3], no further check was performed for these connector elements. For the axial strengths of bolts and sleeves, the principals specified in ANSI/AISC 360-16 [16] have been considered. Nominal tensile strengths of bolts were calculated with the minimum net tensile area which is equal to the smaller of cross sectional area passing through the thread part and that at the dowel pin hole. For the nominal axial compressive strengths of sleeves, net cross sectional area at dowel pin hole was used. The on-site distribution pattern of buckled truss bars is shown in Fig. 11 superimposed with the analysis-based distribution pattern. It can be seen from Fig. 11 that there is a good agreement between the distribution pattern of the observed buckled truss bars and that of the truss bars attained their nominal axial compressive strengths except for a fewer truss bars. This lack of harmony may be attributed to the displacement history including relative vertical movements of the supports applied in monotonically incremental manner in the analysis, which indicates proportional and proper loading condition. Such case, however, is different from the real situation. In reality, foundations have settled down disproportionately due to changes that took place in foundation soil with time. Uncertainties in the nonlinear behavior of the steel material which leads to different yield strength may also be of the reasons of this discrepancy. Furthermore, only settlements of the supports were determined by the photogrammetric survey and accounted for in the analysis. However, foundation soil with a higher degree of consolidation may cause the column footings to move differentially in vertical direction which allows the columns to rotate, resulting in horizontal movements of the supports which have not been taken into account in the analysis. Additionally, the nominal buckling strength is also affected by the order of initial imperfection subjected to truss bars [15]. As the initial imperfection increases in magnitude, the nominal buckling strength decreases. Moreover, undesirable forces may be applied to truss bars to align the bolts with their holes in the spheres during the construction. However, when compared the analysis-based distribution pattern of the buckled truss bars to on-site distribution pattern of those, a reasonably good agreement has been achieved, which shows that the truss bars have buckled because of the effects caused by differential settlements among the individual foundations due to changes occurred within the soil that surrounds the structure. 8. Conclusion The buckling failure of some bars of a space truss roof has been investigated by means of nonlinear analysis considering site observations. During the site survey, it has been first learned from the officers that no any meteorological event resulting in overloading which could cause the truss bars to buckle has occurred. However, the last geotechnical survey has revealed that occurrence of increase in consolidation settlement within foundation soil with time may play an important role for the buckling failure of the truss bars. Photogrammetric survey demonstrated that differential support settlements have taken place because a higher degree of consolidation has caused each spread foundation of each column supporting the roof to settle at different rates. The study showed that some structural damages could be caused by the behavior of the foundation soil over time. Therefore, the effect of differential support settlements due to the soil having a potential of consolidation settlement on the structural systems of buildings should be assessed in detail. Based on the site inspections and the nonlinear analysis results, the following conclusions can be drawn:
• The increase in consolidation settlement with time has caused the foundations to experience differential downward movement. This has led to development of relative support settlements. • Nonlinear behavior of the space truss roof caused by buckled truss bars has been estimated with a sufficient accuracy by means of •
displacement-controlled pushover analysis. Thus, a reasonably good agreement has been achieved between the analysis-based distribution pattern and on-site distribution pattern of buckled truss bars. Displacement-controlled pushover analysis has been found to be an appropriate way to predict the response of the roof to the relative support settlements.
Acknowledgements The author would like to express his appreciate to Assist. Prof. Dr. Serdar Bilgi for his valuable contribution during the process of photogrammetric measurement. References [1] J. Chilton, Space Grid Structures, Architectural Press, 2000. [2] Y. Sahol Hamid, P. Disney, G.A.R. Parke, Progressive collapse of double layer space trusses, IABSE-IASS Symposium London, 2011. [3] Ö. Çağlayan, E. Yüksel, Experimental and finite element investigations on the collapse of a Mero space truss roof structure-a case study, Eng. Fail. Anal. 15 (2008) 458–470. [4] F. Piroğlu, K. Özakgül, Partial collapses experienced for a steel space truss roof structure induced by ice ponds, Eng. Fail. Anal. 60 (2016) 155–165. [5] N. Augenti, F. Parisi, Buckling analysis of a long-span roof structure collapsed during construction, J. Perform. Constr. Facil. 27 (1) (2011) 77–88. [6] F. Piroğlu, K. Özakgül, H. İskender, L. Trabzon, C. Kahya, Site investigation of damages occurred in a steel space truss roof structure due to ponding, Eng. Fail. Anal. 36 (2014) 301–313. [7] A. Fülöp, M. Iványi, Experimentally analyzed stability and ductility behavior of a space-truss roof system, Thin-Walled Struct. 42 (2) (2004) 309–320. [8] C.D. Hill, G.E. Blandford, S.T. Wang, Post-buckling analysis of steel space trusses, J. Struct. Eng. 115 (4) (1989) 900–919. [9] A.E. Smith, Space truss nonlinear analysis, J. Struct. Eng. 110 (4) (1982) 688–705. [10] SAP2000 v8.3.8, Static and Dynamic Finite Element Analysis of Structures, Computers and Structures, Inc., Berkeley, California, 2019. [11] TS 498, Specification for Design Loads for Buildings, TSE Turkish Standards Institution Ankara, Turkey, 1987. [12] Turkish Seismic Code (TSC), Specification for Buildings to Be Built in Earthquake Areas, Government of Republic of Turkey, Ministry of Public Works and Settlement, Ankara (Turkey), 2007.
11
Engineering Failure Analysis 106 (2019) 104156
C. Vatansever
[13] SAP2000 v19.0.1, Static and Dynamic Finite Element Analysis of Structures, Computers and Structures, Inc., Berkeley, California, 2019. [14] FEMA 356, Pre-Standard and Commentary for the Seismic Rehabilitation Buildings, Federal Emergency Management Agency, November 2000. [15] H.E. Alçiçek, Nonlinear Analysis of Space Roof Trusses under Monotonically Increasing Vertical Load, MSc Thesis ITU Graduate School of Science Engineering and Technology, Istanbul, 2015. [16] ANSI/AISC 360-16, Specification for Structural Steel Buildings, American Institute of Steel Construction, 2016.
12
Contents lists available at ScienceDirect
Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal
Investigation of buckled truss bars of a space truss roof system Cüneyt Vatansever
T
Department of Civil Engineering, Istanbul Technical University, 34469 Maslak, Istanbul, Turkey
A R T IC LE I N F O
ABS TRA CT
Keywords: Space truss roof Flexural buckling Support settlement Nonlinear analysis Mero node
Some bars of space truss roof a major shopping market chain in Adana, Turkey have experienced flexural buckling without any circumstance of overloading induced by snow and rain together with wind that has led to the buckling phenomenon. However, according to the on-site geotechnical surveys that have demonstrated that an increase in consolidation settlement of foundation soil has occurred, it has been realized that differential support settlements may cause the truss bars to buckle. This paper investigates the probable cause of the buckling phenomenon observed in some truss bars based on the soil condition. For this, a photogrammetric survey has initially been performed to determine the existing vertical position of the roof supports located on the top of the cantilever columns. To obtain the amount of settlements of the supports, initial vertical coordinates of the tips of the columns that were determined before assembling of the roof are subtracted from those obtained by the photogrammetric measurement with respect to the reference point. An observation has also been made in site to visually inspect the distribution pattern of the buckled truss bars. A 3D analytical model of the roof has been developed to understand whether or not the buckling failure of the truss bars is resulted from the soil settlement under the individual foundations. When the observed distribution pattern of the buckled truss bars is compared to that obtained by the nonlinear analysis, a reasonably good agreement has been achieved, which shows that the truss bars have buckled because of the effects caused by differential settlements among the individual foundations due to increase in consolidation settlement occurred within the soil that surrounds the structure.
1. Introduction Space truss roof systems have widely been used to cover large areas because of their less weight. A special type of space truss roof, called Mero space truss roof, has often been employed since the use of prefabricated straight tubular elements with bolts and sleeves (truss bars) and a sphere (Mero node) designed in so as to allow connection among the truss bars (Fig. 1) [1], make the handling and assembly work easier. Despite of the advantages of the space truss roof systems mentioned above, these types of systems are very prone to progressive collapse initiated by buckling of the truss bars. In particular, a space truss roof in which the buckled truss bars gather in a certain region across the roof may entirely collapse suddenly without any indication and warning. A numerical investigation [2] on the progressive collapse behavior of double-layer space truss roofs has proved the sensitivity of these structures against the progressive collapse when subjected to increasing applied load. However, even though some truss bars buckle in flexural mode, the entire roof may not collapse because the system is capable of allowing redistribution of axial forces to a small extent. For instance, if a space truss roof is subjected to soil-induced settlements resulting in disproportionately relative displacements among the roof supports in time, axial force redistribution in truss bars is likely, but still limited to negligible level.
E-mail address: [email protected]. https://doi.org/10.1016/j.engfailanal.2019.104156 Received 5 August 2016; Received in revised form 18 January 2018; Accepted 26 August 2019 Available online 29 August 2019 1350-6307/ © 2019 Elsevier Ltd. All rights reserved.
Engineering Failure Analysis 106 (2019) 104156
C. Vatansever
Slot Bolt Tubular member
Sphere Fig. 1. Typical components and details of a Mero connection.
Many researches have been conducted on the investigation of collapse behaviors of the space truss roof systems. One has reported the investigation of a space truss roof designed to cover a reinforced building that has totally collapsed due to snow load initially underestimated and some mistakes made in the design [3]. Additionally, the partial collapse of a space truss roof of an industrial plant has been investigated in [4] and it has been reported that the collapse was because of ice ponds after exceptional snow load. Another research [5] has addressed a long-span steel roof structure collapsed during construction as a result of an out-of-plane buckling phenomenon caused by a gust of wind. The partial collapse of a space truss roof structure that occurred during strong winds and heavy rains was investigated based on the site observation and experimental study on the bolts [6]. An experimental study was performed to investigate the ductility behavior of a space truss roof system that consists of cold-formed hollow square sections attached to a joint through the special welded joint plates and bolted connections [7]. A methodology allowing to perform nonlinear postbuckling analysis of space truss systems was developed and applied to double-layer space truss to obtain the vertical loaddisplacement response [8]. A numerical research based on a nonlinear stepwise linearization analysis method was carried out to investigate the nonlinear behavior of space truss members [9]. A space truss roof of a major shopping market chain in Adana, Turkey has been addressed in this study, whose some bars have buckled flexurally without any circumstance of overloading induced by snow and rain together with wind. The officers responsible for structural system of the shopping market also confirmed that neither ponding roof water nor heavy snow that led to buckling failure of the truss bars was experienced. However, it was realized, based on the on-site geotechnical survey conducted between the dates December 12th, 2013–January 7th, 2014, that another potential cause of this failure may be changes within the foundation soils that surround and support the structure over time because the risk of the consolidation settlement appeared to be high. It was also reported that when findings had been compared to those obtained by previous geotechnical surveys dated on August 1995 and April 2006, soil condition had negatively been affected over the years. As a result, these findings showed that changes occurred in foundation soil that can lead to differential support settlements might play a role in the buckling of the truss bars. This paper investigates the possible relation between buckling of the truss bars and the consequences of changes that have taken place with time in condition of foundation soil. 2. Description of the space truss roof system The structural system of entire building consists of steel built up box columns cantilevered to foundation and space truss roof supported by these columns, as shown in Fig. 2. The space truss roof system considered herein is composed of two planar networks of bars which form the top and bottom layers parallel to each other and interconnected by diagonal web bars. The roof plan with the dimensions of 32.5 m by 90.0 m and elevation across the longitudinal direction of the roof are shown in Fig. 3. Transverse elevation is also illustrated in Fig. 4. The roof has been simply supported on the top of 28 steel built up box columns of 450 mm × 450 mm that have been constructed with 12 mm thick plates. The heights of the columns along the longitudinal axis of 20 are 6.70 m while the columns along the axis of 17 and 15A are 7.15 m and 7.50 m long, respectively. The axis of 15A is shared by adjacent building. So, the columns located on axis 15A are existing columns which have been erected during construction of the existing adjacent building. All supports are indicated by solid dots in Fig. 3. The column located at the intersection point of axis 15A and axis F was not marked with solid dot because the roof did not rest on this column. Each column was supported by 0.70 m thick square spread footing with the width of 4.0 m. The total height of the roof that corresponds to the distance between top and bottom layer is 1.768 m. While dashed line shows the members in the plane of the bottom layer, the members of top layer are depicted by the solid lines, as shown in Fig. 3. The characteristics of typical truss bars used in the design, such as tubular members' diameters, their wall thicknesses and corresponding bolt diameters are tabulated in Table 1. A dowel pin, which goes through the bolt, must also be used to allow the bolts to be tightened by means of spanner sleeve. The diameters of the holes drilled in each individual bolts for dowel pins are also listed in Table 1. The material of the tubes was S235JR possessing the yield stress Fy = 235 N/mm2 and tensile strength Fu = 360 N/mm2. All bolts were made of steel with the tensile strength Fub = 1000 N/mm2 and the yield stress Fyb = 900 N/mm2 which was nominally designated as 10.9 bolts. Sleeves' material was denoted by A1030 whose yield stress and tensile strength were 345 N/mm2 and 520 N/ mm2, respectively. The Mero nodes use the steel of C45 with yield stress of 430 N/mm2 and tensile strength of 750 N/mm2. 2
Engineering Failure Analysis 106 (2019) 104156
C. Vatansever
Fig. 2. Typical view of structural system.
3. Overview of the structural design In design, the self-weight of the structural system was automatically taken into account by analysis software, SAP2000 v8 [10]. The weight of purlins and roof cladding were taken as 0.35k N/m2. The load from equipment was assumed to be 0.225 kN/m2. Snow load for the roof without considering drift was 0.75 kN/m2 in accordance with the TS 498/1997 [11]. Wind pressures acting on the surfaces and pressure distribution were determined in conformity with the TS 498/1997 [11]. Self-straining forces arising from restrained dimensional changes because of temperature fluctuation were also considered. The magnitude of the fluctuation was estimated as ± 25 °C. Equivalent lateral force procedure stipulated in Turkish Seismic Code (TSC) [12] was used for the design of the structure against earthquake. Seismic Zone 2 is assigned to the area where the structure is located. The effective ground acceleration coefficient, Ao was accordingly taken to be 0.30. For the equivalent static lateral forces, spectrum coefficient, S(T) was taken as the maximum value of 2.5 regardless of the local site class. The building importance factor and structural behavior factor were taken to be I = 1.2 and R = 4, respectively. For this structure, structural behavior factor, R is found to be convenient since seismic loads are fully resisted by single-story frames with columns pinned at top as defined in TSC [12]. 4. On-site observation Before analytical investigation, an observation has been made in site to visually inspect the buckled truss bars and their distribution pattern over the roof. Fig. 5 shows the typical flexural deformation of the buckled truss bars. No indication of any damage on the bolts, spheres and sleeves has been observed. Welds connecting the conic parts to the ends of the tubular elements have not experienced any damage as well. 5. Determination of differential support settlements Three, as aforementioned, geotechnical surveys have been performed to characterize the soil condition in site. It has been stated in the report from the geotechnical survey on August 1995 that cohesion values of 100–280 kN/m2 were obtained by the Vane shear test while those values, by the hand penetrometer test, were found as 125–225 kN/m2. The allowable soil stress was given as 250 kN/ m2. According to the report from the survey conducted on April 2006, the maximum consolidation settlement and subgrade reaction of the soil were reported as 11.7 mm and 40,000 kN/m3, respectively. The allowable soil stress was specified as 225 kN/m2. In the third survey lasted between December 25th, 2013 and January 7th, 2014, the cohesion values were obtained as 73–119 kN/m2, which indicated that changes leading to larger consolidation settlement occurred within the foundation soil that support the structure. It was also reported that the values of consolidation settlements reached to 70–120 mm. The final report concluded that the occurrence possibility of non-uniform consolidation settlement was found to be high and the superstructure must be protected from the undesirable effect of the foundation settlement because of the reduced ability of the soil to support the load. Accordingly, the most probable reason for the buckled truss bars is seemed to be increase in axial compressive forces induced by differential settlements of the foundations supporting the structure due to gradual reduction in the bearing capacity of the soil. Therefore, a set of photogrammetric surveying has been performed to obtain the amount of vertical settlement of each roof support located on the top of the columns. For this, a total station, which is an instrument to measure angles and distances from itself to points under survey, has been used. By this equipment, coordinates of surveyed points have been calculated using trigonometry and triangulation. The relative vertical settlement values, which are tabulated in Table 2, have been computed by subtracting the 3
Engineering Failure Analysis 106 (2019) 104156
C. Vatansever
Fig. 3. Plan view, typical longitudinal elevation and dimensions of the roof.
4
Engineering Failure Analysis 106 (2019) 104156
C. Vatansever
Fig. 4. Typical transverse elevation of the roof. Table 1 Dimensions of tubular members and corresponding bolts with dowel pin holes. Tube diameter [mm]
Wall thickness [mm]
Bolt [mm]
Dowel pin hole diameter [mm]
42.4 42.4 48.3 48.3 60.3 76.1 76.1 88.9 88.9 88.9 88.9 88.9 88.9 114.3 114.3
2.5 2.5 2.5 2.5 2.5 3.0 3.0 3.0 3.0 4.0 4.0 5.0 5.0 4.5 4.5
M12 M16 M12 M16 M16 M16 M20 M20 M24 M20 M24 M24 M24 M24 M24
4 5 4 5 5 5 8 8 8 8 8 8 8 8 8
initial levels of the tip of the columns measured during the assemblage of the roof from those obtained by the photogrammetric survey performed within this study. As clearly seen from Table 2, the largest soil settlements have occurred along axis 15A that belongs also to the adjacent building, because vertical loads from both buildings act on each column on axis 15A. Furthermore, as settlement potential of foundation soil has increased with the change of consolidation characteristics, the foundations of the columns on the axis have settled deeper into soil. 6. Analytical model Since the roof is supported on the top of the cantilever steel columns, the lateral stiffness of columns can be used in modeling the support conditions in lieu of explicit modeling of columns. Thus, elastic springs can then simply be utilized to rationally represent the lateral behavior of roof supports in orthogonal directions (i.e. x and y). The lateral stiffness of each column has been computed by considering the response of a cantilever column with a point load acting on the top. Then, Eq. (1) can be used and the values obtained for each column can be defined as spring coefficients, denoted ks, which are assigned to the springs represented the supports of the roof for both lateral directions. Therefore, the columns were not directly included in the analytical model developed by SAP2000 v19 [13]. As the influence of the axial stiffness of columns on analysis results was found to be negligible when compared to flexural stiffness, the axial stiffness of columns was not incorporated into the analytical model. In Eq. (1)h, E and I are the height of the column, elastic modulus and moment of inertia, respectively.
ks =
3EI h3
(1)
One single plastic hinge, as shown in Fig. 6, was assigned to the mid-length of each truss bar to represent the nonlinear behavior in tension and compression. The behavior, which is defined by axial force-deformation relationship, was assumed to be as shown in Fig. 7 [14]. The parameters governing the force-deformation curve were adopted from FEMA 356 [14] and tabulated in Table 3. In Fig. 7, point B indicates the axial force, Fy, and corresponding deformation, ΔT, at when the tubular element starts to yield. A strain hardening behavior between point B and point C is defined with a slope of 3%. The amount of plastic deformations corresponding to 5
Engineering Failure Analysis 106 (2019) 104156
C. Vatansever
Fig. 5. Photographs showing typical buckled truss bars. Table 2 Support settlements. Columns
Amount of relative settlements to reference support [mm]
Columns
Amount of relative settlements to reference support [mm]
Columns
Amount of relative settlements to reference support [mm]
(20-L) (20-A) (20-B)a (20-C) (20-D) (20-F) (20-G) (20-I) (20-J) (20-K)
−19.2 −16.8 0.0 −22.8 −40.8 −64.8 −91.8 −88.8 −94.8 −88.8
(17-L) (17-M) (17-N) (17-C) – (17-E) (17-P) (17-I) (17-J) (17-K)
−55.5 −57.3 −55.5 −65.7 – −71.1 −69.9 −78.3 −84.3 −90.3
(15A-L)c (15A-A) (15A-B) (15A-C) (15A-D) (15A-F)b (15A-G) (15A-I) (15A-J) (15A-K)
−162.3 −138.3 −138.3 −132.3 −138.3 – −120.3 −123.3 −144.3 −144.3
a b c
Reference support. The column not supporting the roof. Point monitored during analysis under displacement control.
Fig. 6. Analytical model for each truss bar.
point C and point E is characterized by the parameters a and b, respectively. The line from point D to point E represents the residual strength illustrated by the parameter c. Initial slope of the curve in compression side is defined as the same as in tension side. The critical buckling load, Fcr, is the load obtained depending on slenderness ratio (may be defined as the ratio of the system length of a member to the least radius of gyration). The corresponding axial deformation is designated as ΔC. The contribution of the residual compressive strength is shown by the horizontal line defined by parameter c depending on the diameter-to-wall thickness ratio in 6
Engineering Failure Analysis 106 (2019) 104156
C. Vatansever
F
b
a Fy
ΔC A Compression
C
B
Tension
D
E c Δ
ΔT Fcr
Fig. 7. Axial behavior of typical truss bar. Table 3 Properties of axial plastic hinges for tubular elements. Case
Members in tension Members in compression
Diameter – to – thickness ratio
d t
≤
1500 Fy
d t
≥
6000 Fy
1500 Fy
≤
d t
≤
Plastic deformation
Residual strength ratio
a
b
c
11ΔT 0.5ΔC
14ΔT 9ΔC
0.8 0.4
0.5ΔC
3ΔC
0.2
Linear interpolation shall be used.
6000 Fy
Table 3. No any initial imperfection amplitude was explicitly considered in modeling truss bars. The study carried out by Alcicek [15] has also demonstrated that axial force-deformation responses of the truss bars with characteristics tabulated in Table 3 are in harmony with those from the analyses performed under cycling loading (compression and tension) on individual truss bars with the initial imperfection amplitude of L/300 (L is length of truss bar). Hence, compressive strengths of truss bars have been computed by SAP2000 v19 [13] indirectly considering the effect of initial imperfection. Since no any bolt failure, as seen in Fig. 8, was observed during site investigation, bolts were not explicitly included in the analytical model. Similarly, as sleeve and sphere failure were not detected during observation shown in Fig. 8, these elements were not incorporated into the model. It is thought that each truss bar has buckled in different moments over time. Therefore, this situation has caused the roof structure to behave in nonlinear manner with differential settlements increasing. Accordingly, displacement-controlled pushover analysis has been found to be more appropriate for the investigation. The analytical model used for the nonlinear analysis performed by using SAP2000 v19 [13] is shown in Fig. 9. The relative displacements that correspond to the differential settlements were considered as displacement loads and imposed to the relevant supports. Dead loads [11] including weight of the structural members of the roof, cladding with purlins and equipment were taken into account combining with the displacement loads. 7. Analysis results and discussion The model has been nonlinearly analyzed under combined gravity loads whose details are given in Section 3 and relative support settlements listed in Table 2 to simulate the loading condition likely to cause the truss bars to buckle. The total self-weight of the structural members of the roof was taken as 0.112 kN/m2 based on the weight of existing structural member sizes. In performing the nonlinear pushover analysis, relative displacements in Table 2 were applied to the relevant supports in a manner of which they would increase monotonically. All gravity loads were remained constant throughout the loading process. According to the analysis results, the distribution pattern of the truss bars failed by buckling across the roof are shown in Fig. 10. Moreover, analysis results showed that the truss bars which are composed of tubular elements with outside diameter of 42.5 mm and wall thickness of 2.5 mm are much more susceptible to flexural buckling because of their relatively higher slenderness ratio, obtained as 176. This slenderness ratio is less than 200 as stipulated in ANSI/AISC 360-16 [16] for members in compression. However, as the slenderness ratio is larger than the value of 137.4 calculated from 4.71 E / Fy [16] that divides the strength curve of members in axial compression into two regions; elastic and inelastic, it is clear that these truss bars with slenderness ratio of 176 buckled in elastic region. This led to redistribution of axial forces among the other neighboring truss bars and development of nonlinear response of the roof. Although bolts were not explicitly introduced into the analytical model, the ratio of the nominal tensile strength to the required tensile strength (axial tensile force experienced by the truss bar) for each bolt was also obtained to see how far the ratio is from unity 7
Engineering Failure Analysis 106 (2019) 104156
C. Vatansever
Fig. 8. Typical Mero node indicating no failure of bolts, sleeves and spheres.
Fig. 9. Analytical model of the roof.
when the increase in axial force due to the consequence of the redistribution is considered. The maximum ratio was obtained as 0.06, which indicates no damage occurred on the bolts as observed in site. Similarly, the axial compressive strengths of the spanner sleeves that correspond to their yield strengths were found to be adequate to transmit the maximum axial compressive forces occurred. Since any type of failure in sphere connectors was not observed in site and also until now no damage on sphere connector has been reported 8
Engineering Failure Analysis 106 (2019) 104156
C. Vatansever
Fig. 10. Distribution pattern of buckled truss bars based on analysis. 9
Engineering Failure Analysis 106 (2019) 104156
C. Vatansever
x
Buckled bars inspected in site Buckled bars based on analysis
Fig. 11. Comparison between on-site and analysis-based distribution pattern of buckled truss bars. 10
Engineering Failure Analysis 106 (2019) 104156
C. Vatansever
plus none of sphere has failed in the tests [3], no further check was performed for these connector elements. For the axial strengths of bolts and sleeves, the principals specified in ANSI/AISC 360-16 [16] have been considered. Nominal tensile strengths of bolts were calculated with the minimum net tensile area which is equal to the smaller of cross sectional area passing through the thread part and that at the dowel pin hole. For the nominal axial compressive strengths of sleeves, net cross sectional area at dowel pin hole was used. The on-site distribution pattern of buckled truss bars is shown in Fig. 11 superimposed with the analysis-based distribution pattern. It can be seen from Fig. 11 that there is a good agreement between the distribution pattern of the observed buckled truss bars and that of the truss bars attained their nominal axial compressive strengths except for a fewer truss bars. This lack of harmony may be attributed to the displacement history including relative vertical movements of the supports applied in monotonically incremental manner in the analysis, which indicates proportional and proper loading condition. Such case, however, is different from the real situation. In reality, foundations have settled down disproportionately due to changes that took place in foundation soil with time. Uncertainties in the nonlinear behavior of the steel material which leads to different yield strength may also be of the reasons of this discrepancy. Furthermore, only settlements of the supports were determined by the photogrammetric survey and accounted for in the analysis. However, foundation soil with a higher degree of consolidation may cause the column footings to move differentially in vertical direction which allows the columns to rotate, resulting in horizontal movements of the supports which have not been taken into account in the analysis. Additionally, the nominal buckling strength is also affected by the order of initial imperfection subjected to truss bars [15]. As the initial imperfection increases in magnitude, the nominal buckling strength decreases. Moreover, undesirable forces may be applied to truss bars to align the bolts with their holes in the spheres during the construction. However, when compared the analysis-based distribution pattern of the buckled truss bars to on-site distribution pattern of those, a reasonably good agreement has been achieved, which shows that the truss bars have buckled because of the effects caused by differential settlements among the individual foundations due to changes occurred within the soil that surrounds the structure. 8. Conclusion The buckling failure of some bars of a space truss roof has been investigated by means of nonlinear analysis considering site observations. During the site survey, it has been first learned from the officers that no any meteorological event resulting in overloading which could cause the truss bars to buckle has occurred. However, the last geotechnical survey has revealed that occurrence of increase in consolidation settlement within foundation soil with time may play an important role for the buckling failure of the truss bars. Photogrammetric survey demonstrated that differential support settlements have taken place because a higher degree of consolidation has caused each spread foundation of each column supporting the roof to settle at different rates. The study showed that some structural damages could be caused by the behavior of the foundation soil over time. Therefore, the effect of differential support settlements due to the soil having a potential of consolidation settlement on the structural systems of buildings should be assessed in detail. Based on the site inspections and the nonlinear analysis results, the following conclusions can be drawn:
• The increase in consolidation settlement with time has caused the foundations to experience differential downward movement. This has led to development of relative support settlements. • Nonlinear behavior of the space truss roof caused by buckled truss bars has been estimated with a sufficient accuracy by means of •
displacement-controlled pushover analysis. Thus, a reasonably good agreement has been achieved between the analysis-based distribution pattern and on-site distribution pattern of buckled truss bars. Displacement-controlled pushover analysis has been found to be an appropriate way to predict the response of the roof to the relative support settlements.
Acknowledgements The author would like to express his appreciate to Assist. Prof. Dr. Serdar Bilgi for his valuable contribution during the process of photogrammetric measurement. References [1] J. Chilton, Space Grid Structures, Architectural Press, 2000. [2] Y. Sahol Hamid, P. Disney, G.A.R. Parke, Progressive collapse of double layer space trusses, IABSE-IASS Symposium London, 2011. [3] Ö. Çağlayan, E. Yüksel, Experimental and finite element investigations on the collapse of a Mero space truss roof structure-a case study, Eng. Fail. Anal. 15 (2008) 458–470. [4] F. Piroğlu, K. Özakgül, Partial collapses experienced for a steel space truss roof structure induced by ice ponds, Eng. Fail. Anal. 60 (2016) 155–165. [5] N. Augenti, F. Parisi, Buckling analysis of a long-span roof structure collapsed during construction, J. Perform. Constr. Facil. 27 (1) (2011) 77–88. [6] F. Piroğlu, K. Özakgül, H. İskender, L. Trabzon, C. Kahya, Site investigation of damages occurred in a steel space truss roof structure due to ponding, Eng. Fail. Anal. 36 (2014) 301–313. [7] A. Fülöp, M. Iványi, Experimentally analyzed stability and ductility behavior of a space-truss roof system, Thin-Walled Struct. 42 (2) (2004) 309–320. [8] C.D. Hill, G.E. Blandford, S.T. Wang, Post-buckling analysis of steel space trusses, J. Struct. Eng. 115 (4) (1989) 900–919. [9] A.E. Smith, Space truss nonlinear analysis, J. Struct. Eng. 110 (4) (1982) 688–705. [10] SAP2000 v8.3.8, Static and Dynamic Finite Element Analysis of Structures, Computers and Structures, Inc., Berkeley, California, 2019. [11] TS 498, Specification for Design Loads for Buildings, TSE Turkish Standards Institution Ankara, Turkey, 1987. [12] Turkish Seismic Code (TSC), Specification for Buildings to Be Built in Earthquake Areas, Government of Republic of Turkey, Ministry of Public Works and Settlement, Ankara (Turkey), 2007.
11
Engineering Failure Analysis 106 (2019) 104156
C. Vatansever
[13] SAP2000 v19.0.1, Static and Dynamic Finite Element Analysis of Structures, Computers and Structures, Inc., Berkeley, California, 2019. [14] FEMA 356, Pre-Standard and Commentary for the Seismic Rehabilitation Buildings, Federal Emergency Management Agency, November 2000. [15] H.E. Alçiçek, Nonlinear Analysis of Space Roof Trusses under Monotonically Increasing Vertical Load, MSc Thesis ITU Graduate School of Science Engineering and Technology, Istanbul, 2015. [16] ANSI/AISC 360-16, Specification for Structural Steel Buildings, American Institute of Steel Construction, 2016.
12