Document Type : Research Note

**Authors**

Department of Civil Engineering, National Institute of Technology Rourkela, Odisha, India-769008

**Abstract**

Proper assessment of wind load enables durable design of structures under varying wind load conditions. The accurate prediction of pressure coefficient on any irregular plan shaped buildings is essential for the assessment of wind loads and the structural design. The main objective of this study is to present an equation in the line of Multivariate Adaptive Regression Spline (MARS) approach using experimental data of surface mean pressure coefficient. This developed equation can be used satisfactorily for the prediction of pressure coefficient values accurately on the surfaces of C-shaped buildings. An extensive experimentation was carried out to obtain coefficient of pressure over the surfaces of C-shaped models under varying sizes, corner curvature and angle of incidence in a sub-sonic wind tunnel. The predicted values of pressure coefficient of different C-shaped buildings using developed model are compared with equations developed by Swami and Chandra’s (S&C) and Muehleisen and Patrizi’s (M&P). The comparison indicates that the proposed MARS model predicts pressure coefficient values more accurately than those by S&C and M&P models on frontal as well as side surfaces. Further, the model is used to validate with the actual building, Tokyo Polytechnic University (TPU) data to show the applicability of the proposed equation.

**Keywords**

1. Lin, N., Letchford, C., Tamura, Y., Liang, B., and

Nakamura, O. Characteristics of wind forces acting

on tall buildings", Journal of Wind Engineering and

Industrial Aerodynamics, 93(3), pp. 217{242 (2005).

2. Macdonald, A.J., Wind Loading on Buildings, Halsted

Press (1975).

3. Meroney, R.N. Wind-tunnel modelling of the

ow

about blu bodies", Journal of Wind Engineering and

Industrial Aerodynamics, 29(1{3), pp. 203{223 (1988).

4. Cook, N.J. The designer's guide to wind loading of

building structures", Building Research Establishment

Report, Part 2: Static Structures, Butterworths, London

(1990).

5. Suresh Kumar, K., Irwin, P.A., and Davies, A.

Design of tall building for wind: wind tunnel vs.

codes/standards", Third National Conference on Wind

Engineering, Calcutta, India, pp. 318{325 (2006).

6. Stathopoulos, T. and Zhou, Y.S. Numerical simulation

of wind-induced pressures on buildings of various

geometries", Computational Wind Engineering, 1, Elsevier,

pp. 419{430 (1993).

7. Zhou, Y. and Stathopoulos, T. A new technique for

the numerical simulation of wind

ow around buildings",

Journal of Wind Engineering and Industrial

Aerodynamics, 72, pp. 137{147 (1997).

8. Ahmad, S. and Kumar, K. Interference eects on

wind loads on low-rise hip roof buildings", Engineering

Structures, 23(12), pp. 1577{1589 (2001).

9. Ho, T.C.E., Surry, D., and Davenport, A.G. The

variability of low building wind loads due to surrounding

obstructions", Journal of Wind Engineering and

Industrial Aerodynamics, 36, pp. 161{170 (1990).

10. Lou, W., Jin, H., Chen, Y., Cao, L., and Yao, J. Wind

tunnel test study on wind load characteristics for

double-skin facade building with rectangular shape",

Journal of Building Structure, 26(1), pp. 65{70 (2005).

2982 M. Mallick et al./Scientia Iranica, Transactions B: Mechanical Engineering 27 (2020) 2967{2984

11. Lu, S., Chen, S.F., Li, J.H., and Jiao, Y.F. Numerical

study on the eects of curved annex on the wind loads

on a spherical tall building", Engineering Mechanics,

2, p. 021 (2007).

12. Chakraborty, S., Dalui, S.K., and Ahuja, A.K. Experimental

and numerical study of surface pressure on

'+' plan shape tall building", International Journal of

Construction Materials and Structures, 8(3), pp. 251{

262 (2013).

13. Gomes, M.G.R., Rodrigues, A.M., and Mendes, P.

Experimental and numerical study of wind pressures

on irregular-plan shapes", Journal of Wind Engineering

and Industrial Aerodynamics, 93(10), pp. 741{756

(2005).

14. Amin, J.A. and Ahuja, A.K. Experimental study

of wind pressures on irregular plan shape buildings",

BBAA VI International Colloquium on: Blu Bodies

Aerodynamics and Applications, Milano, Italy, pp. 20{

24 (2008).

15. Amin, J.A. and Ahuja, A.K. Experimental study

of wind-induced pressures on buildings of various

geometries", International Journal of Engineering,

Science and Technology, 3(5), pp. 1{19 (2011).

https://www.ajol.info/index.php/ijest/issue/view/

8314

16. Kim, Y.C. and Kanda, J. Wind pressures on tapered

and set-back tall buildings", Journal of Fluids and

Structures, 39, pp. 306{321 (2013).

17. Chakraborty, S., Dalui, S.K., and Ahuja, A.K. Wind

load on irregular plan shaped tall building-a case

study", Wind Struct., 19(1), pp. 59{73 (2014).

18. Bhattacharyya, B., Dalui, S.K., and Ahuja, A.K.

Wind induced pressure on E plan shaped tall buildings",

Jordon Journal of Civil Engineering, 8(2), pp.

120{134 (2014).

19. Bhattacharyya, B. and Dalui, S.K. Investigation of

mean wind pressures on 'E' plan shaped tall building",

Wind and Structures, 26(2), pp. 99{114 (2018).

20. Yi, J. and Li, Q.S. Wind tunnel and full-scale study of

wind eects on a super-tall building", Journal of Fluid

Structure, 58, pp. 236{253 (2015).

21. Li, Y. and Li, Q. Across-wind dynamic loads on

L-shaped tall buildings", Wind Structure, 23(5), pp.

385{403 (2016).

22. Mallick, M., Mohanta, A., Kumar, A., and Raj,

V. Modelling of wind pressure coecients on Cshaped

building models", Modelling and Simulation

in Engineering, 2018, Article ID 6524945, 13 pages

(2018). https://doi.org/10.1155/2018/6524945

23. Akins, R.E. Wind pressures on buildings", CER;

76/77-15 (1976).

24. Walton, G.N. Air

ow and multiroom thermal analysis",

ASHRAE Transactions, 88, pp. 78{91 (1982).

25. Walker, I.S. and Wilson, D.J. Evaluating models for

superposition of wind and stack eect in air inltration",

Building and Environment, 28(2), pp. 201{210

(1993).

26. Ginger, J.D. and Letchford, C.W. Net pressures

on a low-rise full-scale building", Journal of Wind

Engineering and Industrial Aerodynamics, 83(1{3),

pp. 239{250 (1999).

27. Ohkuma, T., Marukawa, H., Niihori, Y., and Kato,

N. Full-scale measurement of wind pressures and

response accelerations of a high-rise building", Journal

of Wind Engineering and Industrial Aerodynamics,

38(2{3), pp. 185{196 (1991).

28. Swami, M.V. and Chandra, S. Procedures for calculating

natural ventilation air

ow rates in buildings",

ASHRAE Final Report FSEC-CR-163-86, ASHRAE

Research Project (1987).

29. Swami, M.V. and Chandra, S. Correlations for

pressure distribution on buildings and calculation of

natural-ventilation air

ow", ASHRAE Transactions,

94(3112), pp. 243{266 (1988).

30. Grosso, M. Wind pressure distribution around buildings:

a parametrical model", Energy and Buildings,

18(2), pp. 101{131 (1992).

31. Crawley, D.B., Lawrie, L.K., Winkelmann, F.C., Buhl,

W.F., Huang, Y.J., Pedersen, C.O., Strand, R.K.,

Liesen, R.J., Fisher, D.E., and Witte, M.J. EnergyPlus:

creating a new-generation building energy

simulation program", Energy and Buildings, 33(4), pp.

319{331 (2001).

32. Cook, N., Designers' Guide to EN 1991-1-4 Eurocode

1: Actions on Structures, general actions part 1-4.

Wind actions, Thomas Telford Publishing (2007).

33. Costola, D., Blocken, B., and Hensen, J.L.M.

Overview of pressure coecient data in building

energy simulation and air

ow network programs",

Building and Environment, 44(10), pp. 2027{2036

(2009).

34. Costola, D., Blocken, B., Ohba, M., and Hensen,

J.L.M. Uncertainty in air

ow rate calculations due

to the use of surface-averaged pressure coecients",

Energy and Buildings, 42(6), pp. 881{888 (2010).

35. Muehleisen, R.T. and Patrizi, S. A new parametric

equation for the wind pressure coecient for low-rise

buildings", Energy and Buildings, 57, pp. 245{249

(2013).

36. Deo, R.C. and Sahin, M. Application of the extreme

learning machine algorithm for the prediction of

monthly eective drought index in eastern Australia",

Atmospheric Research, 153, pp. 512{525 (2015).

37. Samadi, M., Jabbari, E., Azamathulla, H.M., and Mojallal,

M. Estimation of scour depth below free overfall

spillways using multivariate adaptive regression splines

and articial neural networks", Engineering Applications

of Computational Fluid Mechanics, 9(1), pp.

291{300 (2015).

38. Suman, S., Mahamaya, M., and Das, S.K. Prediction

of maximum dry density and unconned compressive

strength of cement stabilised soil using articial intelligence

techniques", International Journal of Geosynthetics

and Ground Engineering, 2(2), p. 11 (2016).

M. Mallick et al./Scientia Iranica, Transactions B: Mechanical Engineering 27 (2020) 2967{2984 2983

39. Mehdizadeh, S., Behmanesh, J., and Khalili, K. Application

of gene expression programming to predict

daily dew point temperature", Applied Thermal Engineering,

112, pp. 1097{1107 (2017).

40. Milukow, H.A., Binns, A.D., Adamowski, J.,

Bonakdari, H., and Gharabaghi, B. Estimation of the

darcy-weisbach friction factor for ungauged streams

using gene expression programming and extreme learning

machines", Journal of Hydrology, 568, pp. 311{321

(2018).

41. Mohanta, A., Patra, K.C., and Sahoo, B. Anticipate

Manning's coecient in meandering compound channels",

Hydrology, 5(3), p. 47 (2018).

42. Najafzadeh, M., Rezaie-Balf, M., and Tafarojnoruz,

A. Prediction of riprap stone size under overtopping

ow using data-driven models", International Journal

of River Basin Management, 16(4), pp. 1{8 (2018).

43. Shende, S. and Chau, K.W. Forecasting safe distance

of a umping well for eective riverbank ltration",

Journal of Hazardous, Toxic, and Radioactive Waste,

23(2), p. 04018040 (2018).

44. Varvani, J. and Khaleghi, M.R. A performance

evaluation of neuro-fuzzy and regression methods

in estimation of sediment load of selective

rivers", Acta Geophysica, 67(1), pp. 205{214 (2018).

https://doi.org/10.1007/s11600-018-0228-9

45. Sheikh Khozani, Z., Bonakdari, H., and Zaji, A.H.

Mean bed shear stress estimation in a rough rectangular

channel using a hybrid genetic algorithm based on

an articial neural network and genetic programming",

Scientia Iranica, 25(1), pp. 152{161 (2018).

46. Bui, D.T., Hoang, N.D., and Samui, P. Spatial

pattern analysis and prediction of forest re using new

machine learning approach of multivariate adaptive

regression splines and dierential

ower pollination

optimization: a case study", at Lao Cai province (Viet

Nam). Journal of Environmental Management, 237,

pp. 476{487 (2019).

47. Zaji, A.H., Bonakdari, H., and Shamshirband, S.

Standard equations for predicting the discharge coe

cient of a modied high-performance side weir",

Scientia Iranica, 25(3), pp. 1057{1069 (2018).

48. Samui, P., Das, S., and Kim, D. Uplift capacity

of suction caisson in clay using multivariate adaptive

regression spline", Ocean Engineering, 38(17{18), pp.

2123{2127 (2011).

49. Samui, P. and Kurup, P. Multivariate adaptive regression

spline (MARS) and least squares support

vector machine (LSSVM) for OCR prediction", Soft

Computing, 16(8), pp. 1347{1351 (2012).

50. Samui, P. Multivariate adaptive regression spline

(Mars) for prediction of elastic modulus of jointed

rock mass", Geotechnical and Geological Engineering,

31(1), pp. 249{253 (2013).

51. Cheng, M.Y. and Cao, M.T. Accurately predicting

building energy performance using evolutionary

multivariate adaptive regression splines", Applied Soft

Computing, 22, pp. 178{188 (2014).

52. Koc, E.K. and Bozdogan, H. Model selection in

multivariate adaptive regression splines (MARS) using

information complexity as the tness function", Machine

Learning, 101(1{3), pp. 35{58 (2015).

53. Zhang, W. and Goh, A.T. Multivariate adaptive

regression splines and neural network models for prediction

of pile drivability", Geoscience Frontiers, 7(1),

pp. 45{52 (2016).

54. Mukhopadhyay, T. A multivariate adaptive regression

splines based damage identication methodology

for web core composite bridges including

the eect of noise", Journal of Sandwich Structures

& Materials, 20(7), pp. 885{903 (2017).

https://doi.org/10.1177/1099636216682533

55. Bhattacharya, S., Murakonda, P., and Das, S. Prediction

of uplift capacity of suction caisson in clay

using functional network and multivariate adaptive

regression spline", Scientia Iranica, 25(2), pp. 517{531

(2018).

56. Mirabbasi, R., Kisi, O., Sanikhani, H., and

Meshram, S.G. Monthly long-term rainfall estimation

in Central India using M5Tree, MARS,

LSSVR, ANN and GEP models", Neural Computing

and Applications, 31(10), pp. 6843{6862 (2019).

https://doi.org/10.1007/s00521-018-3519-9

57. Goh, A.T.C., Zhang, W., Zhang, Y., Xiao, Y., and

Xiang, Y. Determination of earth pressure balance

tunnel-related maximum surface settlement: a multivariate

adaptive regression splines approach", Bulletin

of Engineering Geology and the Environment, 77(2),

pp. 489{500 (2018).

58. Zhang, W., Zhang, R., and Goh, A.T. Multivariate

adaptive regression splines approach to estimate lateral

wall de

ection proles caused by braced excavations

in clays", Geotechnical and Geological Engineering,

36(2), pp. 1349{1363 (2018).

59. Friedman, J.H. Multivariate adaptive regression

splines", Annals of Statistics, 19(1), pp. 1{67 (1991).

https://doi.org/10.1214/aos/1176347963

60. Friedman, J.H. and Roosen, C.B., An Introduction to

Multivariate Adaptive Regression Splines, Sage Publications

Sage CA: Thousand Oaks, CA (1995).

61. Leathwick, J.R., Rowe, D., Richardson, J., Elith,

J., and Hastie, T. Using multivariate adaptive regression

splines to predict the distributions of New

Zealand's freshwater diadromous sh", Freshwater Biology,

50(12), pp. 2034{2052 (2005).

62. Craven, P. andWahba, G. Smoothing noisy data with

spline functions", Numerische Mathematik, 31(4), pp.

377{403 (1978).

63. Barati, R., Rahimi, S., and Akbari, G.H. Analysis

of dynamic wave model for

ood routing in natural

rivers", Water Science and Engineering, 5(3), pp. 243{

258 (2012).

2984 M. Mallick et al./Scientia Iranica, Transactions B: Mechanical Engineering 27 (2020) 2967{2984

64. Barati, R. Application of excel solver for parameter

estimation of the nonlinear Muskingum models",

KSCE Journal of Civil Engineering, 17(5), pp. 1139{

1148 (2013).

65. Akbari, G.H. and Barati, R. Comprehensive analysis

of

ooding in unmanaged catchments", Proceedings of

the Institution of Civil Engineers-Water Management,

pp. 229{238 (2012).

66. Gandomi, A.H., Yun, G.J., and Alavi, A.H. An

evolutionary approach for modelling of shear strength

of RC deep beams", Materials and Structures, 46(12),

pp. 2109{2119 (2013).

67. Ebtehaj, I., Bonakdari, H., Zaji, A.H., Azimi, H., and

Khoshbin, F. GMDH-type neural network approach

for modeling the discharge coecient of rectangular

sharp-crested side weirs", Engineering Science and

Technology, an International Journal, 18(4), pp. 746{

757 (2015).

68. Bre, F., Gimenez, J.M., and Fachinotti, V.D. Prediction

of wind pressure coecients on building surfaces

using articial neural networks", Energy and Buildings,

158, pp. 1429{1441 (2018).

Transactions on Mechanical Engineering (B)

November and December 2020Pages 2967-2984