To investigate the behavior of the studied walls, a total of nine reinforced concrete walls were analyzed, each of which was subjected to boiler pressure loading. Dynamic nonlinear time history analyzes were performed to study the behavior of the walls.
INTRODUCTION
- General
- Research Objectives
- Methodology of Work
- Scope of the Research Work
- Organization of Thesis
The overall aim of the research work is to investigate the response of the RC wall under blast loading using the Finite Element Method (FEM). This research provides a thorough understanding of the behavior of RC wall subjected to boiler blast loading.
LITERATURE REVIEW
Introduction
Review of Previous Literatures
- Works performed by Zhou et al. (2008)
- Works performed by Yin et al. (2009)
- Works performed by Li et al. (2014)
- Works performed by Xia et al. (2014)
- Works performed by Mooty et al. (2014)
- Works performed by Ibrahim et al. (2014)
- Works performed by Xiao et al. (2017)
- Works performed by Schuldt et al. (2017)
- Work performed by Islam (2022)
The same experimental setup was modeled in LS-DYNA to observe the blast wall response. The effectiveness of the blast wall depends on the arrangements and design considerations of the walls.
Limitation of Past Works
Theoretical prediction indicates that the weight of equivalent TNT has a significant effect on the blast pressure-time history. Finally, the structural design of RC walls will be proposed using available dynamic design method of walls.
FINITE ELEMENT METHOD AND BLAST RESISTANT DESIGN
Introduction
Analysis Approach
- Finite element software
- Mander concrete model
- Rebar parametric stress-strain curve
- Nonlinear direct integration time-history analysis
The model is basically a stress-strain relationship developed for both unconfined and confined concrete subjected to uniaxial compressive loading. Another widely used stress-strain curve for structural steel in FEM software is the Rebar Parametric Stress-Strain Curve.
Blast Resistant Design
- Static vs. dynamic response
- Single degree of freedom system
Decreasing time steps should always be selected because the accuracy of the analysis depends on it. This is why in explosion design the yield is acceptable in explosion design and the energy applied to the structure is somewhat balanced by the strain energy of the structure. Failure to use this factor can significantly underestimate the bending capacity of the part.
Due to the nature of the load and the uncertainty in the intensity of the load, impact-resistant design depends on the deformation rather than the stress limit. 25 Figure 3.3: Typical bilinear resistance-deflection curve (Design of Blast Resistant Buildings in Petrochemical Facilities, 2nd Edition, Energy division of ASCE, 2010). The procedure, which involves obtaining the equivalent SDOF system for a structural element, requires a deformed shape of the structure.
The vibration frequency of a SODF system is primarily dependent on the corresponding stiffness and mass of the system.
RESULTS OF DYNAMIC ANALYSIS AND DESIGN OF RC WALL
Introduction
Time History Data Acquisition
FEM Model of RC wall
- Mesh size
- Time history load application
The wall type was "Shell (Layered)", which reflects the non-linear properties of the materials used in the wall as indicated in Table 4.2. However, in the case of concrete, the nonlinear property of the wall was assigned in the same direction. The accuracy of the results (tension, displacement, support reaction, etc.) depends on the mesh size.
Again the reliability of the model is also directly related to the mesh size used in numerical analysis and finite element programs. Each of the time history load functions was applied to the center of the RC wall in this research with the help of a unit load as mentioned in Figure 4.2 (a). 32 The magnitude of the concentrated load at the center of the wall is kept low enough so as not to interfere with the actual boiler blast load.
The intent of applying the unit load at the center of the wall was to specify the location of the time history load application.
Mesh Sensitivity Analysis
It should be noted that reducing the mesh size significantly increases the computation time, the memory required for the computation, and the size of the analysis file. Thus, an optimized mesh size of 304.8 mm (12 inches) was selected as the optimal mesh size.
Mesh Size
Validation of the Numerical Model
- Comparison of maximum central displacement
35 The finite element model of the RC walls used in this research was modeled in SAP 2000. The concrete material used in the model has a stress-strain relationship defined by Mander et al. The time history of the load was defined by the linear equation (equation 23) below-.
A typical wall of mesh size 50 mm x 50 mm along with support conditions are mentioned in figure 4.6. The change in the results of the maximum central displacements of the walls is shown in figure 4.7. From the analysis results, it can be seen that the percent difference in displacements between the current technique used in this research and the technique used by Mooty et al.
38 Based on the evaluation of the FE modeling techniques used in this research work against the published literature with different parameters, it can be concluded that the technique provides reliable and consistent results in case of blast load analysis.
Response of RC Wall Subjected to Boiler Blast Time-History Load
- Effect of standoff distance on maximum stress
- Effect of filling degree on maximum stress
- Effect of standoff distance on maximum deflection
- Effect of filling degree on maximum deflection
As confirmed by the sensitivity analysis performed in the previous section, the results obtained from 304.8 mm (12 in) mesh sizes for 40%, 50% and 60% fill rates will be compared and shown in Figure 4.9. 40 The figure shows that the curves follow a similar pattern for the filling degree of 40% and 60%, with the exception of the filling degree of 50%. For all deadlock distances, the maximum stresses obtained at a filling degree of 40% are the smallest, 60% the largest and 50% lies between these two extreme values.
The results for the 304.8 mm (12 inch) mesh size will be used to discuss the effect of fill rate on peak load. After examining the effect of offset and fill rate on the maximum wall load, it is now time to examine the effect of offset and fill rate on the maximum wall deflection in this research work. The maximum deflection for the 40% fill level was found to be the lowest (1.34 mm), the highest maximum deflection (1.46 mm) found at the 60% fill level, and the maximum deflection (1.50 mm) for the of filling 50% lies between these two extreme values for all offset distances, i.e.
This section presents the effect of fill grade on maximum deflection for the walls analyzed in this research work.
Dynamic Design of RC Wall Subjected to Boiler Blast Load
- Effect of wall thickness on maximum deflection
- Effect of concrete strength on maximum displacement
Hopefully the design charts will help produce economical design of the walls with respect to the boiler blast loading to which they will be subjected. However, this section will discuss the effect of wall thickness on the maximum displacement of the walls. The maximum displacements of the walls together with corresponding peak load are expressed in Table 4.13.
After studying the effect of wall thickness on the maximum displacement of the walls, the effect of different strength of concrete on the peak displacement of the RC walls will be thoroughly investigated in a systematic manner. So a total of 81 walls will be designed and the results of the peak displacements will be investigated. The results are presented in Figure 4.16, which shows the variation in the maximum displacement for these three strength categories in the case of a wall thickness of 152.4 mm (6 inches).
52 For the last group of walls, the effect of concrete strength on the maximum displacement of the walls is graphically expressed in Figure 4.18.
Proposed Design Charts for RC Walls Subjected to Boiler Blast Load
The wall is subjected to the boiler explosion load with the duration of the load applied to the wall being within the range of 40 seconds or more. If the maximum allowable peak pressure on the wall is greater than that of the maximum pressure acting on the wall, The unit strength of walls is defined as the minimum between the unit flexural strength and the unit shear strength.
This is the primary capacity of the RC wall per unit width of the wall while subjected to boiler blasts. On the other hand, the shear resistance of the wall is the shear resistance capacity of the same RC wall under application of dynamic load. The minimum bar ratio at which the resistance of the wall no longer increases is the ultimate resistance of the wall (Kim et al., 2006).
These cards are developed for the ductility requirements that will ensure the wall's durability under these pressures.
CONCLUSION AND RECOMMENDATIONS
Introduction
Conclusion
The maximum deflection for the 40% fill level is the lowest (1.34 mm), the highest maximum deflection (1.46 mm) found at the 60% fill level, and the maximum deflection (1.50 mm) at the 50% fill level is between these two extreme values for all offset distances, i.e. Another observation is that the maximum deflection for 50% and 60% charge rates varies by only 0.9%. The proposed design charts are used only for the design of supported cantilever AB walls subjected to uniformly distributed boiler shock loads with a blowing duration of 40 seconds and more.
The basis of the design is to ensure a satisfactory response from the wall by adjusting the safe distance based on real life scenarios. It is applicable to a wide range of boiler water holding capacities, making it a simple and suitable tool for designers. For existing walls, these design diagrams will also assist designers in selecting an appropriate distance at which the wall will support the maximum explosion pressure in the event of a boiler explosion.
Recommendations for Future Study
Issa, “Numerical evaluation of the performance of bidirectional RC panels under impact loads,” WIT Transactions on the Built Environment, vol. Solomon, "Calculation of Blast Loads for Applications to Structural Components", Publications Office of the European Union (JRC Technical Reports), p. Cho, Design of Blast-Resistant Buildings in Petrochemical Facilities. 2nd Edition, Task Committee on Blast Resistant Design of Petrochemical Committee of the Department of Energy of the American Society of Civil Engineers, 2006.
The pressure time histories were then converted to strain time history by multiplying the pressures by the area of the RC walls, i.e. Design of Blast-Resistant Buildings in Petrochemical Facilities.2nd Edition, Task Committee on Blast Resistant Design of the Petrochemical Committee of the Energy Division of the American Society of Civil Engineers, 2006", unless otherwise noted]. Reinforcing steel in bending, DIFs = 1.17 Stress increase factor for concrete, SIFc = 1 Stress increase factor for reinforcing steel, SIFs = 1.1 Effective duration of blasting, td = 50 sec.
Reinforcing steel in bending, DIFs = 1.17 Stress increase factor for concrete, SIFc = 1 Stress increase factor for reinforcing steel, SIFs = 1.1 Effective duration of the explosion, td = 40 sec. Reinforcing steel in bending, DIFs = 1.17 Stress increase factor for concrete, SIFc = 1 Stress increase factor for reinforcing steel, SIFs = 1.1 Effective duration of the explosion, td = 31.9 sec. The base of the wall is fixed and the top is hinged, making it a supported cantilever.
