Equivalent static analysis of box culvert for fire tender loading

Transcription

1 Equivalent static analysis of box culvert for fire tender loading Prasad R. Vaidya Dynamic moving live load can be considered as an equivalent static wheel load for the particular vehicle class and its wheel configuration. This paper elaborates loading considerations, modeling and analysis of double cell box culvert for fire tender loading. The critical loading conditions for cover slab, base slab and walls are discussed. The culvert is modeled by using finite element software. The interpretations of analysis results for different elements are presented. The present study aims to establish a procedure for computer aided analysis of box culvert especially used under pavement for cross drainage work. 1. Introduction Box culvert is a closed RC structure generally used for water flow across the river while simultaneously allowing traffic over it. The structural elements consist of cover slab, base slab and walls build monolithically. Live load due to moving traffic is considered as a significant load which mainly governs the design. Dynamic analysis for moving load is a difficult and tedious procedure for small and moderate construction. The box culverts are used frequently in modern constructions as a cross drainage work. The airside drainage works in airports are usually with single cell or double cell box culvert with intermediate RC chambers. The culverts which are under runways subjected to aircraft loading are structurally important since they are subjected to heavy loads with impact. The culverts which are used as a cross drainage work under the road are often proved to be more economical than a bridge with abutment and deck slab. The culvert can be a single cell, double cell or multiple cells based on the requirements. The culvert is considered as a rigid frame with cover slab, base slab and vertical walls. The box may be provided with or without cushion depending on road level requirement. In the culvert with considerable cushion, the live loads on cover slab get dispersed due to cushion depth. However the dead load due self weight of cushion is the predominant load and will govern the design of cover slab. Designs of vertical walls depend upon the lateral thrust exerted by the wheel load in addition to active earth pressure. Earthquake forces are not considered in design of box culvert as per IS 1893:2002 [1]. Haunch is provided at the junction of vertical wall and cover slab for the smooth flow of forces. Base slab is provided with some projection to satisfy bearing requirements of the soil underneath. The thickness of cover slab and the wall is generally kept same to avoid variation in stiffness. The lateral pressure on side walls due to submerged soil can be effectively reduced by providing perforations for vertical walls with pipe sleeves. As the span of culvert increases flexural demand for cover slab will also increase, which is controlled by introducing vertical wall in between and thus making the culvert as multicell. 2. Load cases and support conditions Loading consideration plays a very crucial role in the analysis of the box culvert. Live load due to wheels of the fire tender vehicle will exert lateral pressure on side walls along with active earth pressure. The reasonable estimate is required to predict the behavior of the walls under the action of these forces. There is a monolithic connection of tank wall and slab. Hence it can be treated as a fixed one. Base slab is supported on soil with full bearing so that the horizontal thrust is resisted by the frictional force developed between concrete and soil. Once the sliding check is satisfied, there is no translation at bottom. At the top the only resistance is passive earth pressure, which is not sufficient for large horizontal trust and hence there will be a translation at the The Indian Concrete Journal February

2 top. Accordingly the support condition of culvert wall will be effectively held in position and restrained against rotation at the bottom and restrained against rotation but not held in position at top [2]. For the exact analysis, box full with water and box empty conditions may be considered, but the box full condition will not govern most of the time. The critical loading conditions for vertical walls are as follows Case 1: Box empty - Active earth pressure (AEP) and lateral thrust due to wheel load (WL) from outside. Case 2: Box full - Active earth pressure and lateral thrust due to wheel load from outside along with water pressure (WP) from inside. Case 3: Box full Water pressure from inside and Active earth pressure from outside. Case 4: Box full Water pressure from inside. The case 4 can be neglected since this may not happen practically in case of cross drainage work. The cover slab needs to be analyzed for critical wheel load position over cover slab. The wheel configuration shall also be taken into account because these will simultaneously exert a lateral pressure on the walls. Wheel load positions need to be considered separately for wall and cover slab. Finally, all loads are combined to get worst effect and the corresponding forces. 3. Methodology Two cell box culvert selected for analysis is shown in Figure 1. Fire tender vehicle wheel configuration and its loads are shown in Figure 2. It is considered that the top of the cover slab exactly match with the pavement top and the vehicle moves across the culvert. The front elevation of culvert along with wheel load position and load dispersion is shown in Figure 3. The plan of culvert along with wheel load path is shown in Figure 4. Considering the critical wheel load positions for cover slab and walls separately, case 1 and case 2 are further subdivided into 7 cases as 72 The Indian Concrete Journal February 2017

3 shown in Figures 5 to 11. The lateral load distribution for wall as per Reynolds handbook [3] is shown in Figure 12. Wheel loads are considered as a concentrated load and lateral load on the wall is calculated using Figure 12 [3]. The impact factor is considered as per IRC 6:2014 [4]. The length of the culvert wall affected due to surcharge is calculated with 45 o dispersion, however on conservative side the loads are applied on the wall for maximum length. All the load cases are combined as per IRC 6:2014 [4] and IRC 112:2011 [5] to extract the critical forces for cover slab, base slab and walls. Load combinations used for analysis are shown in Table 1. Interpretation of results is also discussed. 4. Software Modeling It has been proved that software analysis and design of box culvert compare well with manual method [6]. Attempts are made for finite element modeling [7] and analysis of a double cell box culvert using finite element software package. Four nodded shell element is used to model walls, base slab and cover slab. In shell type behavior, both in-plane and out-ofplane bending stiffness are considered. All loads are applied as per shell local coordinate system. Wheel load on a cover slab is applied by converting concentrated load as a line load of length equal to length of shell element. Soil stiffness is modeled using point spring considering safe bearing The Indian Concrete Journal February

4 Table 1. Details of load positions and combinations Load position Description Designation Load combinations - LSM Culvert empty (E) Culvert full (F) a Front wheel touch the front wall of culvert E1, F1 1.35DL+1.5AEP+1.5a 1.35DL+1.5AEP+1.5a+1.35WP b Front wheel on the front wall of culvert E2, F2 1.35DL+1.5AEP+1.5b 1.35DL+1.5AEP+1.5b+1.35WP c Back wheels on the front wall of culvert E3, F3 1.35DL+1.5AEP+1.5c 1.35DL+1.5AEP+1.5c+1.35WP d Front wheel just crosses the front wall of culvert E4, F4 1.35DL+1.5AEP+1.5d 1.35DL+1.5AEP+1.5d+1.35WP e Front wheels on the centre of cover slab E5, F5 1.35DL+1.5AEP+1.5e 1.35DL+1.5AEP+1.5e+1.35WP f Front wheel just crosses the middle wall of culvert E6, F6 1.35DL+1.5AEP+1.5f 1.35DL+1.5AEP+1.5f+1.35WP g Back wheels on the centre of cover slab E7, F7 1.35DL+1.5AEP+1.5g 1.35DL+1.5AEP+1.5g+1.35WP AEP- Active earth pressure, WP- Water pressure capacity of soil and corresponding settlement. Passive earth pressure exerted by the soil is also modeled by considering half spring stiffness. The mathematical model of double cell box culvert is shown in Figure Results and Discussion The results obtained from analysis are presented for cover slab, base slab and walls for culvert empty and culvert full conditions. The load combinations are adopted for limit state of strength [8] as per IRC: Seismic, wind, hydrodynamic and accidental effects are ignored in the analysis. Outer and middle wall The variations of bending moments for outer and middle walls (along line 1 shown in Figure 3) are presented in Figures 14 to The Indian Concrete Journal February 2017

5 The maximum vertical bending moments for different load combinations are presented in Figures 18 and 19. For horizontal bending the maximum values of moments anywhere in the wall are represented in Figures 20 and 21. The Indian Concrete Journal February

6 The maximum values of shear force for different load combinations are shown in Figures 22 and 23. It can be seen from the above results that combination E1 and F1 will be critical for design compared to all other combinations, this is true for horizontal as well as vertical bending. The middle wall is stressed more than the outer wall. The horizontal moments are found to be less than vertical moments. The maximum bending moments for outer and middle wall are shown in Table 2. The maximum values of shear force for different load combinations are presented in Table 3. Table 2. Maximum horizontal bending moment for outer and middle wall Load combination Outer wall Horizontal bending moment (KN-m/m) Middle wall Culvert empty (E) Culvert full (F) Culvert empty (E) Culvert full (F) Max. +ve Max.-ve Max. +ve Max.-ve Max. +ve Max.-ve Max. +ve Max.-ve E1, F E2, F E3, F E4, F E5, F E6, F E7, F Table 3. Maximum shear force for outer and middle wall (KN) Load combination Outer wall Shear force (KN/m) Middle wall Culvert empty (E) Culvert full (F) Culvert empty (E) Culvert full (F) Along length (V23) Across length (V13) Along length (V23) Across length (V13) Along length (V23) Across length (V13) Along length (V23) Across length (V13) E1, F E2, F E3, F E4, F E5, F E6, F E7, F The Indian Concrete Journal February 2017

7 The shear force is critical for combination E1 and F1. The shear force in outer wall is found to be more than middle wall. Cover slab The cover slab will be stressed more along the path of the wheel. The variations of bending moment along the path of the wheel (along line 2 shown in Figure 4) for different load combinations are presented in Figures 24 and 25. The Indian Concrete Journal February

8 The maximum bending moment along culvert width is shown in Table 4 and presented in Figures 26 and 27. The maximum shear force along and across the width of the culvert for cover slab is shown in Table 5 presented in Figure 28. Base slab The maximum forces for base slab are presented in Tables 6, 7 and 8. The base slab is resting on soil and has got full Table 4. Bending moment along length for cover slab Maximum bending moment along length (KN-m/m) for cover slab Load combination Culvert empty (E) Culvert full (F) E1 E2 E3 E4 E5 E6 E7 F1 F2 F3 F4 F5 F6 F7 Max. positive Max. negative Table 5. Shear force variation for cover slab (KN/m) Shear force (KN/m) variation for cover slab Load combination Culvert empty (E) Culvert full (F) E1 E2 E3 E4 E5 E6 E7 F1 F2 F3 F4 F5 F6 F7 Along length (V23) Across length (V13) Table 6. Maximum bending moment across length for base slab (KN-m/m) Maximum bending moment across length (KN-m/m) for base slab Load combination Culvert empty (E) Culvert full (F) E1 E2 E3 E4 E5 E6 E7 F1 F2 F3 F4 F5 F6 F7 Max. positive Max. negative Table 7. Maximum bending moment along length for base slab (KN-m/m) Maximum bending moment along length (KN-m/m) for base slab Load combination Culvert empty (E) Culvert full (F) E1 E2 E3 E4 E5 E6 E7 F1 F2 F3 F4 F5 F6 F7 Max. positive Max. negative The Indian Concrete Journal February 2017

9 bearing, also the wheel pressure get reduced due to dispersion and hence base slab is considered to be less critical element than a cover slab. The maximum bending moment for base slab along and across culvert width is shown in Figures 29 and 30. The maximum shear forces for base slab are shown in Figure 31. From above results the critical load combinations for each of the elements are listed in Tables 9 and 10 Table 8. Maximum shear force for base slab (KN-m/m) Shear force (KN/m) for base slab Load combination Culvert empty (E) Culvert full (F) E1 E2 E3 E4 E5 E6 E7 F1 F2 F3 F4 F5 F6 F7 Along length (V23) Across length (V13) Table 9. Critical load combinations for cover slab ad base slab Critical load combinations for slab Sr. no. Element Bending moment Shear force Across length Along length Across length Along length Positive Negative Positive Negative 1 Cover slab E7, F7 E7, F7 F7 F7 F6 E7, F7 2 Base slab E1 E1 E1 F7 E1 E1 Table 10. Critical load combinations for outer and middle wall Critical load combinations for wall Sr. no. Element Bending moment Shear force Vertical bending Horizontal bending Across length Along length Positive Negative Positive Negative 1 Outer wall E1 E1 E1 E1 F1 E1 2 Middle wall E1 E1 E1 E1 E1 E1 The Indian Concrete Journal February

10 critical for cover slab. The stresses in middle wall are found to be more than the outer wall. The vertical bending moment was found to be governed for walls where as for cover slab and base slab forces across the length was critical. Box culvert can be analyzed only for the culvert empty condition which is more critical. Not much difference in the forces was observed between culvert empty and culvert full conditions. References 6. Conclusions The fairly reasonable analysis of two cell box culvert can be made by converting moving vehicle load to an equivalent static load by considering all possible critical wheel load positions as per wheel configuration. Computer added analysis with proper interpretation of results is a very effective tool for 3D modeling and analysis of culverts. Only three wheel load positions, i.e. a, f and g are critical for analysis of two cell box culvert and with these positions of loads, probable most unfavorable combinations are E1, F1, F6 and F7. Hence analysis results can be obtained accurately by considering only four load combinations. Load combinations E1 and F1 are found to be critical for outer wall, middle wall and base slab where as the combinations F6, F7 and E7 are 1. Criteria for Earthquake Resistance Design of Structures, IS: , Bureau of Indian Standards, New Delhi 2. Indian standard code of practice for plain and reinforced concrete for general building construction IS: Bureau of Indian Standards, New Delhi 3. Reynolds C. E.and Steedman J. C. Reinforced Concrete Designer s Handbook, E & FN Spon, Taylor and Francis Group, London EC4P 4EE, 1999, pp Standard Specification and Code of Practice for Road Bridges, IRC: , Bureau of Indian Standards, New Delhi 5. Code of Practice for Concrete Road Bridges IRC: , Bureau of Indian Standards, New Delhi 6. Sinha B.N. and Sharma R.P., RCC Box Culvert- Methodology and Designs including Computer Method, Journal of Indian Roads Congress, October- December 2009, Paper No 555, pp Garg A.K., Ali A., Finite Element Modeling and Analysis of Reinforced Concrete Box Culvert, Journal of Transportation Engineering, March 2009, Vol. 135, pp Pillai S.U., Menon D., Reinforced Concrete Design, Tata McGraw-Hill Publishing Company Limited, New Delhi. Prasad R. Vaidya holds a B.E. (Civil), M.E. (Structure) from Government College of Engineering, Amravati, Maharashtra. He is an Assistant Professor at Department of Civil Engineering, Gokhale Education Society s, R.H. Sapat College of Engineering, Nashik, Maharashtra. In the past, he has worked as a structural engineer for about seven years in various organizations like Larsen and Toubro Ltd, Gammon India Ltd etc. His research interest include earthquake engineering, computer aided structural analysis and design, thermal analysis of structures and Structural planning. 80 The Indian Concrete Journal February 2017