Probing the Probabilistic Effects of Imperfections on the Load Carrying Capacity of Flat Double-Layer Space Structures

Document Type : Regular Paper


Assistant Professor, Department of Civil Engineering, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran


Load carrying capacity of flat double-layer space structures majorly depends on the structures' imperfections. Imperfections in initial curvature, length, and residual stress of members are all innately random and can affect the load-bearing capacity of the members and consequently that of the structure. The double-layer space trusses are susceptible to progressive collapse due to sudden buckling of compression members. Progressive collapse is a chain of local failures leading to the collapse of either the entire or a part of the structure. In this paper, the effects of the probabilistic distribution of initial curvature and length imperfections on the bearing capacity of flat double layer grid space structures for different member’s length and support conditions have been studied. First, equal to the number of the members of the structure, two sets of random numbers have been generated using the Gamma and Gaussian distributions to account for the initial curvature and the length imperfections, respectively. Thereupon, the amount of the imperfection randomly varies from one member to another. Afterward, based on the Push-Down analysis, the ultimate load-bearing capacity of the structure was determined through nonlinear analyzes performed through the OpenSees software and this procedure for certainty was repeated numerous times. Finally, based on the Monte Carlo simulation method, the structure’s reliability diagrams and tables were procured. The acquired results indicate that the behavior of flat double-layer space grids are sensitive to and can be affected by the random distribution of initial imperfections.


Main Subjects

[1] ANSI/AISC360–10 (2010). “Specification for Structural Steel Buildings.” American Institute of Steel Construction, Chicago, USA.
[2] Bruno L, Sassone M, Venuti F. (2016). “Effects of the equivalent geometric nodal imperfections on the stability of single layer grid shells.” Eng Struct., Vol. 112, pp.184–99.
[3] Chen X, Shen SZ. (1993). “Complete load–deflection response and initial imperfection analysis of single-layer lattice dome.” Int J Space Struct, Vol.8(4), pp.271–8.
[4] Chryssanthopoulos MK, Poggi C. (1995).  “Stochastic imperfection modelling in shell buckling studies.” Thin-Wall Struct., Vol. 23(1–4), pp.179–200.
[5] El-Sheikh A.L., (1997). “Effect of member length imperfections on triple-layer space trusses.” Journal of Engineering Structures, Vol. 19(7), pp. 540–550. DOI:10.1016/S0141-0296(96)00120-4.
[6] El-Sheikh A.L., (2002). “Effect of geometric imperfections on single-layer barrel vaults.” International Journal of Space Structures, Vol. 17(4), pp. 271–283. DOI: 10.1260/026635102321049538.
[7] El-Sheikh A.L., (1995). “Sensitivity of space trusses to member geometric imperfections.” International Journal of Space Structures, Vol. 10(2), pp. 89–98. DOI: 10.1177/026635119501000202.
[8] El-Sheikh, A., (1991). “The effect of composite action on the behavior of space structures.” Ph.D. Thesis, University of Cambridge, UK.
[9] European Standard. 3: (2004).  “design of steel structures.” Parts 1–6: Strength and stability of shell structures. European Committee for Standardization.
[10] Hurtado, J. E., & Barbat, A. H., (1998). “Monte Carlo techniques in computational stochastic mechanics.” Archives of Computational Methods in Engineering, Vol. 5(1), pp. 3-29. DOI: 10.1007/BF02736747.
[11] Lin X, Teng JG. (2003). “ Iterative Fourier decomposition of imperfection measurements at non-uniformly distributed sampling points.” Thin-Wall Struct., Vol. 41 (10), pp. 901–24.
[12] Liu H, Zhang W, Yuan H. (2016). “Structural stability analysis of single-layer reticulated shells with stochastic imperfections.” Eng Struct., Vol. 124, pp.473–9.
[13] M.R. Sheidaii, and M. Gordini, (2015). “Effect of Random Distribution of Member Length Imperfection on Collapse Behavior and Reliability of Flat Double-Layer Grid Space Structures.” Advances in Structural Engineering, Vol. 18(9), pp.1475-1486. DOI: 10.1260/1369-4332.18.9.1475.
[14] Mazzoni S., McKenna F. and Fenves G.L., (2005). “The OpenSees Command Language Manual.” Department of Civil And Environmental Engineering, University Of California, Berkeley, USA.
[15] McKenna F., Fenves G.L. and Scott M.H., (2010). “Open System for Earthquake Engineering Simulation.” Pacific Earthquake Engineering Research Center, University Of California, Berkeley, USA.
[16] Melchers, R.E., (1999). “Structural Reliability Analysis and Prediction.” John Wiley & Sons, Second Edition.
[17] Moghadasa, R. K., & Fadaeeb, M. J. (2012). “Reliability assessment of structures by Monte Carlo simulation and neural networks.” Asian Journal of Civil Engineering (Building and Housing), Vol. 13(1), pp. 79-88.
[18] Nowak A.S. and Collins K.R., (2000). “Reliability of Structures.” Mc. Graw Hill.
[19] Papadrakakis, M., & Lagaros, N. D., (2002). “Reliability-based structural optimization using neural networks and Monte Carlo simulation.” Computer methods in applied mechanics and engineering, Vol. 191(32), pp. 3491-3507. DOI:
[20] Schmidt L.C. and Morgan P.R. and Hanaor A., (1982). “Ultimate load testing of space trusses.” Journal of Structural Division, ASCE, Vol. 180(6), pp. 1324–1335.
[21] Schmidt L.C., Morgan PR. and Hanaor A., (1980). “Ultimate load behavior of a full scale space truss. Proceeding of Institution of Civil Engineering.” Vol. 69(2), pp. 97–109. DOI: 10.1680/iicep.1980.2489.   
[22] Shen SZ, Chen X. (1999). “Stability of single-layer reticulated shells.” Beijing: Science Press; (in Chinese).
[23] Smith, E. A., Epstein, H. I., (1980). “Hartford Coliseum roof collapse: structural collapse sequence and lessons learned.” Civil Engineering. ASCE, Vol. 50(4), pp. 59–62.
[24] TahamouliRoudsari, Mehrzad, and Mehrdad Gordini. (2015), “Random imperfection effect on reliability of space structures with different supports.” Structural Engineering and Mechanics, Vol. 55(3), pp. 461-472.
[25] Technical Specifications for Space frame structures (JGJ7-2010). Beijing: Ministry of housing and Urban-Rural Construction of P.R. China.
[26] The European Standard EN 10210-2., (2006). “Hot finished structural hollow sections of non-alloy and fine grain steels.” British Standard, UK.
[27] Yamada S, Takeuchi A, Tada Y, Tsutsumi K. (2001).  “Imperfection-sensitive overall buckling of single-layer latticed domes.” J Eng Mech, Vol.4, pp.382–6.
[28] Yan J, Qin F, Cao Z, Fan F, Mo YL. (2016). “Mechanism of coupled instability of single layer reticulated domes.” Eng Struct., Vol.114, pp.158–70.
[29] Zhou HZ, Fan F, Zhu EC. (2010). “Buckling of reticulated laminated veneer lumber shells in consideration of the creep.” Eng Struct, Vol. 32(9), pp.2912–8.