Introduction

The need to reduce the cost of the enclosure material for direct fired heaters or power boilers prompted this study, whose purpose was to determine whether significant cost savings could be achieved if the structural enclosures of such heaters employed steel-reinforced concrete construction rather than steel plate and structural steel construction. The article indicates the manner in which mechanical and thermal stresses in such internally heated structures can be determined and provides a proposed design for structures of this type. Material costs are provided, assuming the use of standard reinforcing steel wire mesh with a maximum wire size of ¼ inch diameter, 4-inch by 4-inch mesh openings, and conventional concrete with a design compressive strength of 4000 to 5000 PSIG. The tensile strength of the mesh wires is assumed to be 20,000 to 30,000 PSI, and the transverse or structural strength of the concrete is assumed to be 10% of its compressive strength, or 500 PSIG for 5000-PSIG concrete.

Design of a Direct Fired Process Heater or Power Boiler Enclosure

Figure 1 shows the general arrangement of a tubular direct fired process heater or power boiler enclosure, and Figure 2 shows a vertical longitudinal section at the center line of the heater. Both drawings provide details of the heater components. The figures do not show the details of the internal hardware, which consists of banks of horizontal or vertical tubular heat transfer elements on two diameter centers situated at either sidewall, supported by alloy steel tube supports fastened to the outer concrete walls. A sufficient thickness of insulation—about 12 inches behind the tubes and attached to the concrete wall—is provided so that the hot and cold surfaces of the concrete outer wall are exposed to acceptable temperatures. Because of the void space between the tubes, the hot face of the refractory insulation can reach high temperatures: about 1200°F in the case of the process heater and 550°F in the case of the power boiler. In both cases it is assumed that heat is generated by burners firing upward, with the burners situated in the closure plate at the bottom of the lowermost enclosure. That enclosure, which is referred to as the radiant section, consists of an internally insulated cavity bounded by the side and end walls, a top closure plate with a central rectangular opening, a bottom closure plate with openings to accommodate the burners, and tubular heat transfer elements at either sidewall within the cavity. The uppermost enclosure, which is referred to as the convection section, consists of an internally insulated cavity bounded by side and end walls, the closure plate at the top of the radiant section, a closure plate with a rectangular opening at the top of the cavity, and closely spaced horizontal and vertical rows of tubular heat transfer elements contained within the cavity. A stack for venting flue gas is located above the top opening in the top closure plate of the convection section.

The average temperature of the combustion product flowing from top to bottom of the radiant section is approximately 1500°F. Flue gas passing through the convection section is at a somewhat lower temperature than that in the radiant section, averaging approximately 800°F, and the combustion product gases leaving the convection section and entering the stack are at an even lower temperature: usually less than 1000°F. Because of the variation in combustion product gas temperature in these sections, horizontal and vertical expansion joints must be provided to accommodate the differences in movement between sections to avoid excessive stress to and damage of the enclosure.

For further details, refer to Figures 1 and 2; the numbered items in those figures are defined in Table 1.

Figure 1: General Arrangement of a Tubular Direct Fired Process Heater or Power Boiler Enclosure

Figure 2: Vertical Longitudinal Section at the Heater Center Line.

Table 1
Mechanical Design Data

1. Bottom support, 40 feet long × 8 feet high × 12 feet wide × 8 inches thick
2. Radiant section, 40 feet long long × 24 feet high × 12 feet wide × 8 inches thick, fabricated from five shop-assembled panels that are 8 feet wide × 12 feet high
3. Convection section, 40 feet long ×16 feet high × 6 feet wide × 8 inches thick
4. Stack, cross-section 6 feet long × 60 feet high × 8 inches thick
5. Three peripheral platforms with tread 2.5 feet wide and rail 3.5 feet high × 8 inches thick
6. Platform supports
7. 2 feet wide × 24 feet high radiant section tube access openings
8. 3 feet wide × 5 feet high radiant section access openings at each end
9. 3 feet wide × 5 feet high peripheral support access openings at each end
10. [not labeled]
11. Horizontal field joint for the bottom of the vertical shop-fabricated panels, consisting of alternating projections and spaces, with the spaces providing for clearance between vertical mesh projections at the bottom of the upper panels and the top of the lower panels. As in all field joints, wire mesh plates are provided at either side of the wire mesh projections to maintain mesh continuity at the joints before concrete is applied to fill the joints
12. Lower closure plate for bottom of radiant section, with openings for burner installation
13. Upper closure plate for radiant section, 40 feet long × 12 feet wide × 8 inches thick with an opening 8 feet wide × 36 feet long
14. Horizontal, peripheral expansion joints consisting of a continuous double layer of friction-lowering slide plates provided between bottom support section and radiant section, the radiant section and convection section, and the convection section and the stack
15. Vertical field joint (see item 11)
16. Four corner posts, 3 feet long × 3 feet wide × 8 inches thick
17. T bracket
18. Radiant section end panel, 12 feet wide × 24 feet high
19. Radiant section side panel, 40 feet wide × 24 feet high
20. Flexible expansion joints
21. Horizontal field joint

Calculation of Thermal Stress for a Process Heater or Power Boiler

Thermal stress can increase the stress in the reinforcing steel and concrete composite wall of a direct fired process heater or power boiler significantly because of the relatively high temperatures to which the inner surface of the concrete wall is exposed and the temperature difference between the inner and outer surfaces of the wall.
The power boiler is assumed to have the same general configuration as the process heater but differs in that the power boiler has so-called membrane-type vertical tubular surfaces, or surfaces with closed spaces between tubes, so that the temperature of the membrane wall and the hot insulation surface behind it can be assumed to be equal to that of the steam-water mixture inside the tubes: about 550°F, corresponding to a steam pressure of 1000 PSIA. It will be shown that this significantly reduces the thermal stress in the outer concrete wall if free expansion has not been provided for.

The thermal stresses can be calculated in the manner described below, and the stress that is calculated can be added to the mechanical stress caused by wind loads and weight loads to arrive at a figure for total stress, which must be sufficient to avoid permanent damage to the concrete or steel that constitutes the enclosure.

Of importance is the finding that the stress in the steel and concrete outer wall caused by the temperature gradient across the wall can be reduced very significantly and perhaps eliminated by accommodating thermal expansion of the wall through the use of properly placed and designed expansion joints. A conservative design would be one that assumes maximum design stresses in steel and concrete that are based on the sum of both the mechanical stress and the thermal stress. A much less conservative design would be one that considers maximum design stress equal to the thermal or mechanical design stress only.

The equations in Table 2 were used to calculate the tensile stresses that are developed in the composite wall of the enclosure as a result of the temperature gradient across the wall when allowance has not been made to allow for free expansion.

Table 2
Equations for Calculating Thermal Stress in an Internally Heated Steel-Reinforced Concrete Enclosure

Calculated and physical property data for the process heater and power boiler based on these equations are summarized in Table 3.

Table 3
Data for Calculating Thermal Stress in a Concrete Wall Reinforced with Steel Wire Mesh

Calculation of Combined Thermal and Mechanical Stress

Based on the preceding equations and data, the maximum calculated strain, e/L, at 110°F, the temperature differential at the hot face of the wall, is 0.000759 inch/inch. The strain decreases linearly from the hot face to the cold face so that the concrete and steel strain and the thermal stress at any point in the wall from hot face to cold face stress are determinable.

The net mechanical stress generated in the steel and concrete of the enclosure wall can be said to be equal to the thermal stress, as calculated by the Equations and Data of Tables 2 and 3, when used in combination with the Equations and Data of Table 4. The mechanical stress is based on a maximum wind pressure of 30 PSF acting in a horizontal direction at the radiant wall. The wind pressure and the thermally generated stresses generated by the temperature differential in the walls causes transverse bending of the wall and tensile and compressive stress in the steel and concrete at either face of the wall. The distance separating the steel wire mesh planes is 6 inches. With such an arrangement the wall can resist wind – propagating tensile and compressive stress regardless of whether the wind impinges at right angles to one wall or the wall opposite. The Equations of Tables 2 and 4 are based on the configuration of the radiant wall, but comparable calculations can be used to evaluate stresses in the convection section and stack.

Table 4
Equations for Calculating Thermal and Mechanical Stress

Mm = mechanical moment caused by 30-PSF wind pressure, lb.-inch
Lw = height of radiant wall, inches.
Wp = wind pressure, lbs./square foot
Rstl. = center-to-center distance between wire mesh plane and neutral axis, inches
Rconc. = center-to-center distance between concrete area and neutral axis, inches
Aw = radiant wall area, square feet
Astl. = area of wires in steel wire mesh planes, square inches
Aconc. = area of concrete, square inches
(Stl) = Ss = stress in steel, PSI
(Sconc) = Sc = stress in concrete, PSI
St-t = thermal stress in wires of mesh under tension, PSI
St-c = thermal tensile stress in wires of mesh under compression, PSI
Es = steel modulus of elasticity = 30 million PSI
Ce = thermal coefficient of expansion = (6.9)(10)^-6 , inches/inch-deg. F
(Deg.F)h = 96.3°F = temperature difference of steel and concrete at hot face
(Deg.F)c = 13.7°F = temperature difference of steel and concrete at cold face

Table 5 provides a summary of the calculations of tensile and compressive stress in steel and concrete.

Table 5
Summary of Calculated Tensile and Compressive Stresses in Steel and Concrete, thousand PSI

Conclusions

Because of the wall temperature differential defined and shown in this article, the hot face of any wall in the heated enclosure will increase in length by an amount greater than the cold face, causing the wall to bow inward. If there were no restraints on the wall, there would be no stress in the wall as a result of the bowing that occurs. However, the weight of the structure above and below the wall creates end moments that oppose wall bowing. Initially, the net result is that the steel and concrete are stressed in tension at both the hot and cold faces, whereas at the end, the steel and concrete are stressed in tension at the hot face and in compression at the cold face. The initial concrete stress in tension is high enough to cause cracking at both the hot and cold faces since the tensile stress at these locations exceeds the tensile strength of concrete, which is about 500 PSI. Cracking resulting from tensile stress failure of concrete is not uncommon in concrete beams used in steel-reinforced concrete structures, but this does not interfere with their use in their intended load-bearing service. The same could be said about the use of reinforced concrete for internally heated structures.

Despite the fact that cracking occurs at both the inner and outer surfaces of the internally heated enclosures, air infiltration should be minimal because once cracking occurs, further widening of the cracks will not occur. Coating of the external surfaces with a commercially available elastic compound such as one that would be used for the expansion joints therefore would be desirable.

The steel-reinforced concrete structure provides a material cost advantage relative to a conventional structural steel structure, as follows:

References

1. American Institute of Steel Construction. Steel Construction Manual, 5th ed. New York: AISC, 1949.
2. Seely, F. B. Resistance of Materials, 3d ed. New York: Wiley, 1952.

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