Chapter 4: RESULTS OF DYNAMIC ANALYSIS AND DESIGN OF RC WALL
4.9 Proposed Design Charts for RC Walls Subjected to Boiler Blast Load
52 For the last group of walls, the effect of concrete strength on the maximum displacement of the walls have been expressed graphically in Figure 4.18. From the figure, it can be observed that in case of a peak load of 38.038 kN, 37.252 kN, 30.233 kN, 41.380 kN, 37.463 kN, 30.292 kN, 41.128 kN, 39.107 kN and 31.188 kN, the maximum displacement of the wall with a concrete strength of 24.14 MPa (3.5 ksi) is 4.81%, 4.81%, 4.80%, 4.83%, 4.79%, 4.77%, 4.81%, 4.80% and 4.77% more respectively than that of the maximum displacement with a concrete strength of 27.6 MPa (4 ksi) and 9.45%, 9.46%, 9.42%, 9.47%, 9.43%, 9.42%, 9.48%, 9.46% and 9.40% more respectively than of the maximum displacement with a concrete strength of 31.03 MPa (4.5 ksi).
38.038 37.252 30.233 41.38 37.463 30.292 41.128 39.107 31.188 6
8 10 12 14
0.24 0.31 0.39 0.47 0.55
Maximum Displacement (inch)
Maximum Displacement (mm)
Load (kN)
3500 psi 4000 psi 4500 psi
Figure 4.18: Maximum displacement vs. peak load curve for 254.0 mm (10 inch) wall.
After perceiving the results, it can be settled that for an increase in concrete strength from 24.14 MPa (3.5 ksi) to 27.6 MPa (4 ksi), the peak displacement decreases roughly by 4.5% and 9.5% for all thicknesses considered respectively.
53 It is to be noted that the proposed method shall be applicable if and only if all of the following conditions are met-
i. The wall is subjected to boiler blast load with the duration of the load being applied on the wall is within the range of 40 seconds or higher.
ii. The support condition is propped cantilever.
iii. The loading is distributed evenly on the surface of the wall.
The design steps are as follows-
i. First, a standoff distance (R) of the boiler is selected and the scaled distance (Z) is calculated for the respective standoff distance using the following equations (Karlos et al., 2013).
WTNT = 0.01089×M (24)
Z = R
√WTNT
3 (25)
Where,
M = Weight of water inside the boiler in kilograms R = Standoff distance of the boiler in meters Z = Scaled distance for the boiler (m/kg0.333)
Instead of using these two equations, Figure 4.19 may also be used for convenience. It has been developed for a wide range of water holding capacity of boiler and standoff distances.
ii. Next, from Figure 4.20 as proposed by Islam 2022, the maximum positive pressure exerted due to the explosion of a boiler blast is to be picked up using the scaled distance calculated from the previous step.
iii. After that, the unit resistance of the wall to be designed is to be selected using one of the three charts shown in Figure 4.21, Figure 4.22 and Figure 4.23.
iv. Then, using the selected wall resistance in the previous step, the maximum allowable peak pressure on the wall can be found.
v. Finally, the maximum allowable peak pressure on the wall is compared to the peak pressure acting on the wall in the second step. If the maximum allowable peak pressure on the wall be more than that of the peak pressure acting on the wall,
54 then the wall will said to withstand the boiler blast load for which it is intended to be designed for.
0 2500 5000 7500 10000 12500 15000 17500 20000 22500 0.00
0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00
Scaled Distance, Z (m/kg0.333 )
Water Holding Capacity, M (Kg) Standoff distance 1.524 m Standoff distance 2.439 m Standoff distance 3.049 m Standoff distance 3.659 m Standoff distance 4.573 m
Figure 4.19: Scaled distance vs. water holding capacity curve
1.2 1.4 1.6 1.8 2.0 2.2
0.45 0.50 0.55 0.60 0.65 0.70 0.75
9.40 10.44 11.49 12.53 13.58 14.62 15.66
Maximum Positive Pressure (psf)
Maximum Positive Pressure (kPa)
Scaled Distance, z (m/kg0.333) 40% Filling Degree
50% Filling Degree 60% Filling Degree
Conservative Assumption ignoring the efffect of FD y = -0.1872x2 + 0.4337x + 0.424
Figure 4.20: Proposed Peak pressure on wall vs. Scaled distance curve (Islam, 2022).
55 Figure 4.20 shows the peak pressure exerted on the event of a boiler blast. One of the major advantages of using this graph is that the proposed peak pressure is independent of the size and filling degree of the boiler rather it depends on the standoff distance of the boiler. For example, a boiler having a water holding capacity of 6MT with a filling degree of 25% and a standoff distance of 1.524m would produce the same scaled distance if another boiler having a water holding capacity of 10MT with a filling degree of 61% and a standoff distance of 2.439m which finally in turn would yield the same maximum positive pressure. However, the green dotted line representing the relation between the scaled distance and maximum positive pressure is somewhat a bit conservative because of the absence of sufficient amount of test data.
Next, the point of interest of discussion is the unit resistance vs. rebar ratio charts (Figure 4.21, Figure 4.22 and Figure 4.23) developed exclusively for propped cantilever RC walls with varying spans. The unit resistance of the walls is defined as the minimum between the unit bending resistance and the unit shear resistance. These are the primary capacity of the RC wall per unit width of the wall while subjected to boiler blast loads. These resistances can easily be calculated by using the dynamic strength of the materials of the wall and structural mechanics (refer to appendix C for the calculations). The bending resistance is the capacity of a RC wall under bending when subjected to dynamic loads.
On the other hand, the shear resistance of the wall is the shear resisting capacity of the same RC wall under the application of dynamic load. These capacities are only dependent on the wall material strength and amount of reinforcement in the wall. Figure 4.21, Figure 4.22 and Figure 4.23 have been developed for a concrete strength of 27.6 MPa (4 ksi) and 415 MPa (60 ksi).
The unit resistance increases gradually with the increase in rebar ratio in the wall. After a certain rebar ratio, the resistance of the wall becomes constant. The minimum rebar ratio at which the resistance of the wall no longer increases is the ultimate resistance of the wall (Kim et al., 2006). Before reaching this point, the wall is controlled by bending and beyond this point, the wall is controlled by shear. Numerous observations and tests confirm that it is more economical to select a rebar ratio and thickness for which the wall is controlled by bending (Kim et al., 2006).
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0.000 0.005 0.010 0.015
0 1 2 3 4 5 6 7
0.00 6.89 13.79 20.68 27.58 34.47 41.37 48.26
Unit Resistance of Wall, Ru (KPa) Unit Resistance of Wall, Ru (psi)
Rebar Ratio 10 ft span 12 ft span 15 ft span
Figure 4.21: Proposed unit resistance of wall vs. rebar ratio curve for a wall thickness of 152.4 mm (6 inch) with f’c = 27.6 MPa and fy = 415 MPa.
0.000 0.005 0.010 0.015
0 2 4 6 8 10 12
0.00 13.79 27.58 41.37 55.16 68.95 82.74
Unit Resistance of Wall, Ru (KPa) Unit Resistance of Wall, Ru (psi)
Rebar Ratio 10 ft span 12 ft span 15 ft span
Figure 4.22: Proposed unit resistance of wall vs. rebar ratio curve for a wall thickness of 203.2 mm (8 inch) with f’c = 27.6 MPa and fy = 415 MPa.
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0.000 0.005 0.010
2 4 6 8 10 12 14
13.79 27.58 41.37 55.16 68.95 82.74 96.53
Unit Resistance of Wall, Ru (KPa) Unit Resistance of Wall, Ru (psi)
Rebar Ratio 10 ft span 12 ft span 15 ft span
Figure 4.23: Proposed unit resistance of wall vs. rebar ratio curve for a wall thickness of 254.0 mm (10 inch) with f’c = 27.6 MPa and fy = 415 MPa.
Figure 4.24, Figure 4.25 and Figure 4.26 shows the proposed allowable peak pressure on the RC wall intended to be designed while subjected to boiler blast load. A RC wall with a chosen unit resistance from the previous charts (Figure 4.21, Figure 4.22 and Figure 4.23) will withstand the corresponding allowable peak pressure as obtained from these charts (Figure 4.24, Figure 4.25 and Figure 4.26). These charts are developed for a ductility demand of 0.96 ± 1.0% which will ensure the sustainability of the wall under these pressures. It is to be noted that, just like the charts developed earlier for the unit resistance of the walls, these three charts are only applicable for a concrete strength of 27.6 MPa (4 ksi) and 415 MPa (60 ksi).
By observing the graphs, it can be seen that the shape of the graph is convex. The degree of curvature of the graphs is higher for lower wall thicknesses and as soon as the thickness increases, the degree of curvature also decreases.
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0 8 16 24 32 40 48
0 1 2 3 4
0.00 6.89 13.79 20.68 27.58
Allowable Peak Pressure of Wall (KPa)
Allowable Peak Pressure of Wall (psi)
Unit Resistance of Wall, Ru (kPa) 10 ft span
12 ft span 15 ft span
Figure 4.24: Proposed allowable peak pressure on wall vs. unit resistance of wall curve for a wall thickness of 152.4 mm (6 inch).
8 16 24 32 40 48 56 64
1 2 3 4 5 6 7
6.89 13.79 20.68 27.58 34.47 41.37 48.26
Allowable Peak Pressure of Wall (KPa)
Allowable Peak Pressure of Wall (psi)
Unit Resistance of Wall, Ru (kPa) 10 ft span
12 ft span 15 ft span
Figure 4.25: Proposed allowable peak pressure on wall vs. unit resistance of wall curve for a wall thickness of 203.2 mm (8 inch).
59
0 8 16 24 32 40 48 56 64 72 80
2 3 4 5 6 7 8 9 10
13.79 20.68 27.58 34.47 41.37 48.26 55.16 62.05 68.95
Allowable Peak Pressure of Wall (KPa)
Allowable Peak Pressure of Wall (psi)
Unit Resistance of Wall, Ru (kPa) 10 ft span
12 ft span 15 ft span
Figure 4.26: Proposed allowable peak pressure on wall vs. unit resistance of wall curve for a wall thickness of 254.0 mm (10 inch).
A detailed example of the design of RC walls subjected to boiler blast pressure is presented at the end of appendix C using the design charts shown here.
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