The Eighth Asia-Pacific Conference on Wind Engineering, December 10 14, 2013, Chennai, India Simulation and Analysis of Cylindrical wall of Ground Elevated RC Silo with Transverse Shear due to Wind Load : A Case Study. Desh Bandhu Mukherjee 1, Prasanta Patra 2, Amiya K. Samanta 3 1 M.Tech Student, NIT Durgapur, W. B., India, email-mdeshbandhu@yahoo.com 2 Senior Lecturer, K.G. Engineering Institute, Bishnupur, W. B., India, email- ppnitd@gmail.com 3 Associate Professor, Department of Civil Engineering, NIT Durgapur, W. B., India, email-aksnitd@gmail.com ABSTRACT Ground elevated reinforced concrete (RC) silo is a very important structure in material handling plant and food grain processing plants so as to supply it throughout the year. The configuration of the structure is normally vertical, right circular and cylindrical. When such a structure is analyzed under wind load, the distribution of internal forces does not follow the typical pattern expected from the beam bending theory due to nonaxisymmetric variation of wind pressure along the circular periphery considering the silo as a thin walled tubular structure. The silo wall deforms considerably in its cross section due to ovalisation instability. Various past investigations indicate that circular silo having ratio of height of wall to diameter exceeding one (H/D>1) is susceptible to such deformation to greater extent. In case of long cylindrical steel silo ring stiffeners are provided at intermediate levels of the cylindrical wall in order to reduce this ovalisation effect due to wind load. But, in case of reinforced concrete silo, ring stiffeners are not normally provided to avoid construction hazards during slip forming. After a brief review of the previous investigations in connection with the same, it has been observed that wind pressure distribution in cylindrical silo wall had been taken into consideration for the purpose of pre-buckling and post-buckling analysis of mainly steel silo. Little investigation has been found regarding the deformation pattern of wall of cylindrical wall, in particular which is made up of reinforced cement concrete. Author(s) are deeply motivated to find a direction in this context through review of work pertinent to the field and an attempt has been made to simulate the wind load exactly as prescribed by the Indian code of Practice on the cylindrical wall of a typical silo using a highly sophisticated platform of finite element software and studied deformation of the cylindrical wall pertinent to the ovalisation phenomena. This particular study /investigation also reveals important data and throw light on assessing area of hoop reinforcement and their curtailments along the height of the cylindrical wall for the typical configuration only for the structural engineers so as to make design safe and economic. Keywords: Simulation, Wind load, Cylindrical wall, Ground elevated RC silo, Ovalisation. Introduction Bin or, bunker or, silo structures are used to store granular or fine material to supply it throughout the year. This type of structure is not only subjected to gravity load, but also there is an effect of lateral load in this structure. The lateral load may be wind or seismic load. When a cylindrical structure having circular cross section is subjected to wind loading then there will be an ovalization phenomenon and an associated considerable deformation in the cross section of the silo wall. Various past investigations indicates that when the height to diameter ratio is less than or equal to 1 (H/D 1) then this ovalisation phenomenon does not produce severe deformation to the said structure. But, when this height to diameter ratio exceeds 1 (H/D>1) then this ovalization and deformation plays a very significant role in design of the cylindrical wall. Due to the ovalisation phenomenon the shell wall will get Proc. of the 8th Asia-Pacific Conference on Wind Engineering Nagesh R. Iyer, Prem Krishna, S. Selvi Rajan and P. Harikrishna (eds) Copyright c 2013 APCWE-VIII. All rights reserved. Published by Research Publishing, Singapore. ISBN: 978-981-07-8011-1 doi:10.3850/978-981-07-8012-8 133 32
deformed and this deformation is totally different as compared to the beam bending deformation. From the review of the literature done so far, it is evident that most of the researchers did not pay their attention regarding the analysis (or, behaviour) of RC cylindrical silo under static wind load except the investigation done by Samanta et. al (2010). Rather most of the investigation / experiments deal with the ovalisation effect on steel cylindrical or, conical wall due to static or dynamic wind load phenomena. Since the author is trying to converge towards the exact circumferential static wind load effect on RC silo wall, the summary of the literature review done so far related to that issue has been listed below. Chen and Rotter (2012) have generated numerical models in finite element software for cylindrical thin shells considering various (L/D) ratio to check their buckling behaviours under wind pressure. In that investigation the non-uniform distribution of wind load along circumference was expressed /derived in terms of Fourier cosine series. Godoy and Degró (1998) have tried to explain the bifurcation buckling of the steel shell wall under static wind pressure in peripheral direction with finite element modeling. In the investigation done by Macdonald et al. (1988) wind tunnel pressure measurements on scale models of low-rise cylindrical structures was carried out with the help of 50 pressure taps by arranging them in circumferential direction. From the experiment it is clear that the maximum magnitude mean pressures occur at 60-90% of the height of a silo. Below 50% of the height, the magnitude of the mean pressures reduces noticeably. Circumferential distribution of axial membrane stress for thin walled cylinder under wind load was graphically represented in the investigation done by Pecknold (1989). Also this investigation deals with the ovalisation phenomena for the cylindrical shell under peripheral wind pressure. The buckling behaviour of silo-like cylindrical shells (stiffened by one or two rings) under wind pressure has been summarized by Uchiyama et al.(1987). Wind pressure distributions along the circumferences of a rigid cylinder at various L/R ratio have been shown by the investigators. In the investigation the authors have also tried to explain the pre-buckling behaviour of various stiffened specimen comprises of different flexural rigidity (EI). In the investigation of Samanta et.al (2010) comparison between approximate analysis and Finite Element analysis using Abaqus has been done. In the analysis it has been shown that vertical stress developed in the silo wall is significant, which can not be predicted at all by approximate analysis. It has also been shown by Samanta et. al (2010) that, the different variation of stresses developed (hoop stress as well as vertical stress) for different H/D ratio. In the investigation of Samanta et. al (2010) the wind loading was considered as surface loads act as point load at different nodes. This configuration can t give the proper wind pressure distribution at the circumference of the RC silo wall. It is also true that the effect of reinforcement has also not been considered by Samanta et. al (2010). Motivation and Model DIN / Indian Standard code does not say more about the wind pressure distribution on circular cylindrical silo. The distribution of wind load on cylindrical silo does not follow the same pattern as a rectangular beam. From that point of view we can consider the silo as a tubular beam. There is a considerable deformation in cylindrical silo due to the effect of wind loading. This deformation is called the ovalization phenomenon. From the structural point of view our aim will be to protect the silo from any kind of failure. Functional design must provide for adequate volume, proper protection of the stored materials and satisfactory 33
method of filling and discharge. Whereas structural considerations are stability, strength and control (minimizing) of crack width and deflection of silo. Φ (A) : Plan of RC silo Model (B) Vertical section of RC silo Model Fig. 1 : Vertical section and plan of Elevated RC silo (Ordinary) Ovalisation / Deformation of circular cylindrical shell wall (closed roof of an empty ordinary RC silo as shown in Fig.-1) due to static wind loading at peripheral direction of the RC silo has been considered in this study. In the RC silo model there is a ring beam (with conical hopper) at (+) 5.00m level. In the silo model the column height is 6.00m. The bottom of the supporting column is fixed at the top of foundation beam. Also the external diameter of the cylindrical wall is 6400mm; and the wall thickness is 200mm. There is a slab at roof (200mm thick) at (+) 11.30m level. It s important to note that the height of silo wall to diameter ratio is very close to 2.0 and hence may be considered as long. The wind pressure has been applied in circumferential direction of the cylindrical wall throughout the entire altitude of the silo starting from (+) 5.00m level. Wind load on wall has been calculated as per the relevant clause of Indian standard code of practice. For the exact representation the wind pressure has been expressed in terms of Fourier coefficient. Then this application of the peripheral pressure has been done in Abaqus. Due to the circumferential wind pressure, some stresses will develop at various levels of the silo wall. The intension of the author(s) is to provide the graphical representation of the three major stresses (Hoop, Vertical and Von Mises) at various levels of the cylindrical wall so as to understand the critical deformation of shell wall required to be taken care of by the designers. The main objective of this study is to evaluate the deformation of 11.50m high silo wall when subjected to wind load and infer about the necessary steps to be taken up by the designers /practicing professionals. 34
Wind Pressure assessment The basic wind pressure, which varies along the height of the silo at Durgapur has been calculated as per IS 875 1987 (Part III) with Basic wind speed (V b ) = 47 m/s. Risk coefficient (K 1 ) and Topography factor (K 3 ) are taken as 1.07 and 1.00 respectively, whereas Terrain height factor (K 2 ) varies with the height of the silo wall. Now the design wind speed, (V des ) becomes equal to K 1 K 2 K 3 V b and design wind pressure (p) = 0.60 (V des ) 2 = 1.52(k 2 ) 2 kn/m 2. This variation wind pressure along the height is calculated in Table-1 and also has been shown in Fig.-1. Table-1 Variation of wind pressure along the height of silo Height up to (m) K 2 (Ref: table 2 of IS 875 (III).) Pressure (kn/m 2 ) 30 1.06 1.708 20 1.01 1.55 15 0.97 1.43 10 0.91 1.259 At any level of the cylindrical structure, the wind pressure as calculated above is again not uniform on the surface area as the external coefficient value changes with the angle subtending at centre of cross section as shown in the adjacent sketch (Fig.-2). The respective external coefficients(c s ) are calculated for height to diameter ratio, h/d =16.5/6.4 =2.58 by interpolation from the relevant table of IS code by interpolation. Now these coefficients are being multiplied by wind pressure as calculated in Table-1 to get actual wind load(f) on the cylindrical surface of the silo. In view of applying the same load pattern on the structure in the Abaqus platform, the Cs needs to expressed in terms of Fourier Series for the purpose of representing the wind load in a close form solution for the said analysis. Here the Fourier cosine series upto 8th harmonic representing the coefficient in (0,2 ) has been used and the resulting equation has been derived as ; θ C s = -0.66 + 0.302 Cos ( ) + 0.997 Cos (2 ) + 0.438 Cos (3 ) - 0.075 Cos (4 ) - 0.0 Cos (5 ) + 0.064 Cos (6 ) - 0.015 Cos (7 ) - 0.042 Cos (8 ) Fig. 2 : Vertical section The wind loads calculated thus has been applied on cylindrical wall of the silo in the models. Methodology The typical model of the silo as described above has been generated (Fig.-3) and a Finite Element analysis has been performed using Abaqus. The material properties of all the parts have been simulated as homogeneous, isotropic, elastic with Young s modulus = 25000 MPa, Poisson s ratio = 0.17 and mass density = 2.4E-9 t/mm3. After the assembly of all the parts a complete silo model has been generated. Then the peripheral wind load in the silo wall has been applied. Fig. -3(C) indicates the loading diagram of the silo. In meshing operation all 35
the components (column, wall and roof) except hopper were meshed using hexagonal (C3D8I) elements; whereas the conical hopper configuration was meshed using tetrahedral (C3D4H) elements. For meshing operation sweep technique with medial axis algorithm has been considered by the author(s). The approximate global size of all the elements has been considered as 200mm. (A) Model (B) Mesh (C) Wind load Fig. 3 RC Silo analysed in Abaqus 6.10 The support condition of all the structures has been simulated as fixed with ring beam at foundation level. The wall and the conical hopper is supported on the ring beam at (+) 5.0m level. There may be a lateral sway of the ring beam as a whole depending on the slenderness of the columns or supporting wall as the case may be, but same will take place together with the silo wall. The 3D silos modeled such a way, have been analysed using Abaqus to get the values of deformation and stress contours developed at different level. Finally, the design stresses are noted and compared with Samanta et. al (2010). Result and discussion The deformation pattern observed on the application of the wind pressure on the cylindrical wall of the RC silo is shown in Fig. 4, 5 and 6, which depicts a cross sectional deformation silo wall referred here as ovalisation phenomenon using a deformation scale factor of 5000 in Abaqus. From the deformed configuration it is obvious that contours developed are very smooth. The amount of deformation is slightly on lowers at roof level as well as ring beam at (+5)m level due to in-plane rigidity provided by the roof slab and ring beam respectively. Fig. 5(B) shows the contours of Von Mises stress for the cylindrical wall of the silo wall only. The cross sectional distortion at maximum stress level and maximum displacement level are shown in Fig. 6. From the distorted shape of the wall cross section (refer Fig. 6), it may be said that the cross section of the silo wall takes the shape of an ellipse. 36
(A) Deflected Configuration (B) Stress Contours Fig. 4 RC Silo analyzed in Abaqus (A) Deflected Configuration (B) Stress Contours Fig. 5 Contour of cylindrical wall of silo (A) At maximum displacement level (B) At maximum stress level Fig. 6 Cross sectional deformation 37
The summary of critical values of Von Mises stress ( von ), vertical stress ( vert ) and hoop stress ( hoop ) due to the wind load acting along the periphery of the silo wall at various levels have been summarised through shown in Fig-7. The stress values due to the wind loading effect have been taken from Abaqus (6.10) output for windward side, leeward side and 78 0 to windward side. At each direction nodes have been selected for outer as well as inner portion of the silo wall. Initial nodes at each side have been selected at ring beam level (+) 5.0m. Then the second node has been considered at (+) 5.2m level. There after the selection of nodes at each 1meter interval of the wall have been considered by the author(s). 16 WINDWARD SIDE At 78 0 to WINDWARD SIDE 16 At 78 0 to WINDWARD SIDE 14 14 Level (m) 12 10 (a) Level (m) 12 10 WINDWARD SIDE (b) 8 6 LEEWARD SIDE 8 6 LEEWARD SIDE 4-0.24-0.18-0.12-0.06 0.00 0.06 0.12 0.18 0.24 Hoop Stress (MPa) 4-0.24-0.18-0.12-0.06 0.00 0.06 0.12 0.18 0.24 Vertical Stress (MPa) 16 14 At 78 0 to WINDWARD SIDE Level (m) 12 10 WINDWARD SIDE (c) 8 6 LEEWARD SIDE 4 0.00 0.06 0.12 0.18 0.24 0.30 Von Mises Stress (MPa) Fig. 7 Stress distribution at various level of cylindrical wall of RC silo A close inspection of the hoop stress values along the wind ward direction states that it is critical at almost middle one-half height of the silo wall i.e. at (+)9.2m to (+)12.20m level, whereas the same along the leeward direction is critical only at the intersection only i.e. at ring beam level and roof level and that too with one-third values of the stresses. It also depicts that junction of wall at the base /ring beam level is also affected equally due such effect of ovalisation under wind /lateral load and the same must be taken care of by the engineering professionals for the sake of designing the silo wall. 38
Comparison of Stress : The results obtained following present simulation have been tabulated (Table-2) compared with the values presented by Samanta et. al(2010) with the critical /design values so as to assess the potentiality of such method in predicting behaviour of such structural system. Table 2 Comparison of Critical Stress Direction of load Values of stress by Samanta et al.(2010) Present Simulation Critical Stress Critical Stress σ hoop σ vert σ σ hoop σ vert von σ von (MPa) (MPa) (MPa) (MPa) (MPa) (MPa) Windward 0.192 0.175 0.224 0.189 0.176 0.213 Leeward 0.095 0.201 0.242 0.094 0.205 0.245 78 0 to windward 0.148 0.153 0.188 0.171 0.197 0.255 Concluding Remarks Analysis indicates that the values of hoop stress are critical in windward side and the same occur at about middle half height (i.e. around 0.30H to 0.70H) of the silo wall, whereas at 78 0 to windward side the same values are slightly on lower side. Hoop stresses are produced due to the ovalisation phenomenon of the cross section of cylindrical wall. At the junctions of silo wall and ring beam & silo wall and roof as well as in leeward side of the silo wall hoop stresses are small. Von Mises stresses are critical at the junction in leeward side as well as mid height of the wall in windward side. The graph is very smooth except above the bottom junction (between wall and ring beam) and below the top junction (between wall and roof) where kink is formed due to sudden drops in stresses produced. It may also be noted that the values calculated in the present method using exact simulation of wind load are very close to the previous work by the author except the values for 78 0 to the windward direction. References Amiya K. Samanta, Prasanta Patra and P. Ray (2010): Assessment of Transverse Deformation of Wall of Elevated RC Cylindrical Empty Silo under Wind Load., Jr. of Instt. of Engr(I), Vol. 91, Aug 2010, pp 9-17. David A. Pecknold(1989): Load Transfer Mechanisms in Wind-loaded Cylinders., Journal of Engineering Mechanics, Vol. 115, No. 11, Nov 1989, pp. 2353-2367. IS: 875(Part 3)-1987: Code of practice for design loads (other than earthquake) for buildings and structures. K. Uchiyama, Y. Uematsu and T. Orimo(1987): Expt. on the deflection and buckling behavior of ring-stiffened cylindrical shells under wind pr., Jr. of Wind Engg. and Ind Aerodyn. Vol. 26, no. 2, 1987, pp 195 211. Lei Chen and J. Michael Rotter(2012): Buckling of anchored cylindrical shells of uniform thickness under wind load., Engineering Structures, Vol. 41, Aug 2012, pp 199-208. Luis A. Godoy and Julio C. Mendez-Degró(1998): Buckling of aboveground storage tanks with conical roof., Department of Civil Engineering, University of Puerto Rico, Mayagüez, PR 00681-9041, Puerto Rico. P.A. McDonald, J.D. Holmes, K.C.S. Kwok(1988) : Wind loads on circular storage bins, silos and tanks. I point pr. measurements on isolated structs., Jr. of Wind Engg. and Ind Aerodyn., Vol. 31, no. 1, 1990, pp 165-188. 39