Lecture on Horizontal Containers

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JB/T4731-2005 1. Scope of application: JB/T 4731—2005 \"Steel Horizontal Vessels\" incorporates certain revisions compared to Chapter 8 of the original GB l50—1989; for example, the use of ring seat supports has been eliminated, checks on the axial bending strength of saddle supports have been added, and Appendix A \"Strength Calculation of Horizontal Vessels under Additional Loads\" has been included. JB/T 4731 is applicable to atmospheric and pressurized horizontal vessels with a design pressure not exceeding 35 MPa, which are supported by two symmetric saddle supports under uniformly distributed loads. It is not applicable to: horizontal vessels subjected to direct flame heating or nuclear radiation ； ——Horizontal containers that are frequently moved around ； ——Horizontal vessel with jacket ； Horizontal vessels subjected to fatigue analysis: The design of horizontal vessels begins with determining the wall thickness based on the operating pressure (internal or external pressure), followed by evaluating axial, shear, circumferential stresses and stability considering the vessel’s own weight, wind, seismic forces, and other additional loads. The design also includes determining the location of supports as well as designing the supports themselves. 2. Terms and Definitions . Operating pressure . Design pressure . Calculated pressure . Test pressure Design temperature Operating temperature Test temperature Calculated thickness Design thickness Nominal thickness Effective thickness 3 General provisions for design 3.1 Determination of design pressure: (a) The design pressure value shall be not lower than the operating pressure ； (b) When equipped with an overpressure relief device, the design pressure shall be determined in accordance with Appendix B of GB150 ； (c) For horizontal containers of liquefied gases and liquefied petroleum gas, the design pressure shall be determined in accordance with the Container Regulations ； (d) The design pressure of the vacuum vessel is determined based on the external pressure it must withstand; when safety control devices are installed, the design pressure is taken as the lower of 1.25 times the maximum difference between internal and external pressures or 0.1 Mpa ； When there is no safety control device, the design pressure is taken as 0.1 Mpa. 3.2 Determination of design temperature: (a) The design temperature shall not be lower than the highest temperature that the metal of the component may reach during operation. For metal temperatures below 0 degrees, the design temperature should not be higher than the lowest temperature that the component’s metal may reach during operation. The design temperature should be indicated on the nameplate. (b) The design temperature of low-temperature horizontal vessels shall be determined in accordance with Appendix C of GB150. 3.3 Determination of component metal temperature (a) Heat transfer calculation ； (b) Determine on similar containers that have been used ； (C) During use, when the metal temperature is close to the medium temperature, it is determined based on the internal medium temperature. 3.4 For horizontal vessels operating under different conditions, they shall be designed for the most severe condition, and the operating pressure and temperature for each condition shall be specified in the drawings or technical documents. 3.5 Design Loads (a). Long-term load design pressure — internal pressure, external pressure ； hydrostatic pressure ； Container mass load – its own weight, the weight of the material contained within the container, and the weight of accessories such as insulation layers, ladder platforms, and piping. (b). Short-term loads: wind load, seismic load (seismic load is generally used), and the weight of water used for hydrostatic testing. (c). Additional loads: Appendix A of JB/T 4731 includes additional loads for horizontal vessels. This takes into account the presence of vertical equipment on a horizontal vessel, such as auxiliary devices like heat exchangers, distillation columns, deaeration heads, submersible pumps, agitators, etc. (all with a height of less than 10m), which exert additional bending moments on the vessel’s cylindrical shell as well as reactions at the supports. In essence, the attached load is also a type of long-term load. 3.6 Thickness addition amount C: C = C1 + C2, where C1 is the negative deviation of the steel thickness in mm, and C2 is the corrosion allowance in mm. The negative deviation of the thickness of steel plates or pipes is determined in accordance with the relevant steel standards. When the negative deviation of the steel thickness is not greater than 0.25 mm and does not exceed 0.6% of the nominal thickness, this negative deviation can be ignored in calculations. 3.6.1 Corrosion margin C2: To prevent container components from having their thickness reduced due to corrosion or mechanical wear, a corrosion margin must be taken into account. The specific requirements are as follows: a) For components that are subject to corrosion or wear, the corrosion margin shall be determined based on the expected design life and the rate at which the medium corrodes the metal material ； b) When the corrosion levels experienced by various components of a horizontal vessel vary, different corrosion margins can be used ； c) Horizontal vessels made of carbon steel or low-alloy steel, with a corrosion margin of not less than 1 mm. 3.7 The minimum thickness of the horizontal vessel shell, after processing, excluding the corrosion allowance, shall be as follows: a) For horizontal vessels made of carbon steel or low-alloy steel, it shall be not less than 3 mm ； b) For horizontal vessels made of high-alloy steel, not less than 2 mm. 3. Allowable stress of 3.8 stainless steel composite plates: (a) For composite plates whose bonding degree between the clad layer and the base layer meets level B2 or above as specified in JB4733, if it is necessary to take into account the strength of the clad material in the design calculations, the allowable stress at the design temperature is as follows: (b) For corrosion-resistant linings that are not integrated with the wall of horizontal vessel shells, the strength of such corrosion-resistant linings is not considered in the design calculations. 3.9 When seismic loads are combined with other loads, the allowable stress in the shell wall shall not exceed 1.2 times the allowable stress. 3.10 For horizontal vessels, if steel materials other than those specified in GB150 are to be used, they shall meet the requirements specified in Appendix A of GB150. 3.11 Weld joint factor For horizontal vessels, the weld joint factor shall be determined based on the welding process characteristics of the weld joints in the pressure-bearing elements (single-sided welding or double-sided welding, with or without gussets), as well as the proportion of length subject to non-destructive testing. 3.12 Pressure testing: In line with GB150-1998. 3.13 Materials: (a) The materials for horizontal pressure vessels shall comply with the provisions of GB150 ； The materials for horizontal atmospheric-pressure vessels shall comply with JB/T4735. (b) For saddles, important internal components welded to the pressure-bearing shell, and non-pressure-bearing elements such as reinforcement rings, the steel used shall meet the requirements specified below: Depending on the operating temperature in °C, the allowable stress σ]sa in MPa is as follows: 0–250°C: Q235-B; 147–200°C: Q345; ≥200°C: 16MnR. (c) The material of the saddle gasket shall be the same as that of the shell ； (d) The anchor bolts should preferably be made of Q235 in accordance with GB/T700, or Q345 in accordance with GB/T1591. If other carbon steels are used, ns=1.6; if other low-alloy steels are used, ns≥2.0. 3.14 Saddle Supports: When saddle supports for horizontal tanks are in accordance with the JB/T4712 standard, the strength verification of such saddles can be omitted provided that the conditions specified in JB/T4712 are met ； Otherwise, strength verification shall be carried out in accordance with JB/T4731－7.4. 4 Structure 4.1 Support types: Most supports for horizontal containers are saddle-type supports, with three saddles; ring supports are rarely used. JB/T 4731 mainly specifies the symmetric arrangement of double saddles. When saddle supports are used for horizontal vessels, whether there are two, three, or more saddles, only one of them must be a fixed support while the rest should be sliding supports, in order to reduce the additional loads on the supports caused by thermal expansion and contraction of the cylinder, as well as by the mass of the cylinder and the material contained within it. For double saddles, the fixed end is usually chosen on the side where the container nozzles are larger in number and size. For the three-saddle configuration, the fixed end is chosen to be at the middle saddle in order to reduce the displacement of the sliding end. A steel plate should be embedded in the foundation surface beneath the sliding end support; for those with a higher expansion frequency, rolling columns can be installed between the saddle base plate and the foundation surface plate. When concrete saddles are used, a lining plate should be welded in the container support area, and positioning plates should be used to prevent the container from rotating. When welding the lining plate or saddle reinforcement plate in the container support area to the cylindrical shell, continuous welding should be employed; however, at the lowest point, 50 mm of unwelded area should be left on each side of the plate. 4.2 Support Arrangement Figure 4-1 It is very difficult to conduct an accurate theoretical analysis of the stresses in horizontal vessels supported by double saddles. Currently, relevant vessel design codes both at home and abroad adopt the approximate analysis and calculation methods proposed by Zick in 1951 based on experimental research. According to Zick’s assumptions and analysis, a horizontal vessel placed on saddles can be simplified as an overhanging beam with double hinges, subjected to a uniformly distributed load and exhibiting symmetric stress distribution. According to mechanics of materials, for a simply supported beam with two equal outward extensions and a total length of L, when it is subjected only to a uniformly distributed transverse load and the outward extension A equals 0.207L, the absolute values of the bending moments at the supports as well as at the midpoint between them are equal; this results in the minimum absolute value of the axial bending stress caused by the uniformly distributed load. However, for large-diameter, thin-walled horizontal containers, the stresses that play a controlling role are often those at the saddle points. Therefore, A should be kept as low as possible, at or below 0.5Ra, in order to make effective use of the reinforcement provided by the end caps to the cylinder. For horizontal vessels with a large L/Di ratio – that is, a ratio greater than 15 and thin wall thicknesses – it is advisable to use three or more supports in order to prevent severe deformation of the cylinder and excessive stress resulting from overly large support spans. However, using more than three supports may result in additional bending moments and reaction forces at those supports due to variations in support height and uneven settlement of the foundation; therefore, it is advisable to use as few as possible. 4.3 Installation of reinforcing rings (1) The reinforcing ring should be a complete ring or have a structure equivalent to that of a complete ring; the connection between the reinforcing ring and the shell shall comply with the provisions of GB150 ； (2) When considering the local stresses at the supports of horizontal containers, reinforcement rings can be installed on or near the saddle plane, as shown in the following figures: Figure 4-2, Figure 4-3. (3) When considering external pressure instability of horizontal containers, the installation and calculation of reinforcement rings shall comply with the provisions of GB150. 5 Load analysis and internal force analysis: The external forces acting on a horizontal container supported on symmetrically arranged saddles include the applied loads and the reaction forces from the supports. In addition to the operating internal or external pressure (vacuum), the load is mainly composed of the weight of the container (including its own weight, the weight of attachments, and the insulation layer), as well as the weight of the materials inside or the water used for hydrostatic testing. When subjected to gravity, a double-saddle horizontal container can be approximated as a cantilever beam supported at two hinge points and subjected to a uniformly distributed load. The beam is subjected to the external forces shown in Figure (5-1). 5.1 Uniform load q and support reactions F: It is assumed that the weight of the container itself and the weight of the material inside it is mg, which is distributed uniformly along the length of the container. Under normal circumstances, the ends of a container have convex end caps; therefore, when determining the length over which the load is distributed, these end caps must first be converted into equivalent cylinders with the same diameter as the container. For convex end caps such as hemispherical ellipsoids and dish shapes, based on the principle of equal volume, they can be converted into cylinders with a diameter equal to that of the container and a length of (the depth of the convex end cap); thus, the length over which the weight load acts is the distance between the tangents of the two end caps. The total weight of the container in mg should be equal to the reaction force at each of the two supports, 2F. Therefore, the uniform load per unit length acting on the cantilever beam is: (1) According to the conditions of static equilibrium, the reaction force at each of the two symmetrically arranged supports is F; this can also be expressed as: (2) 5.2 Vertical shear force V and moment M: The weight of the head itself and the material contained within it is , and this gravity acts at the center of gravity of the head (including the material). For a hemispherical head, the position of the center of gravity can be calculated as the distance from the center of gravity of the head to the tangent to the head, where Ri is the inner radius of the cylinder. This relationship is also approximately applicable to other forms of convex end caps, namely . According to the rule of force line translation, this gravity can be replaced by a transverse shear force V acting at the end of the beam and an additional couple m1, namely equations (3) and (4). Furthermore, when the head is filled with liquid, the hydrostatic pressure exerts a horizontal outward thrust on the head. Since the hydrostatic pressure of the liquid column varies linearly along the diameter of the container, the horizontal thrust deviates from the container’s axis, creating a couple m2 at the ends of the beam. By integrating the hydrostatic pressure, the following result is obtained: In equation (5), Ra represents the average radius of the cylinder, and it is defined as . The two couple forces, m1 in equation (4) and m2 in equation (5), are combined into a single couple M, as shown in equation (6). Thus, the mechanics of a horizontal container with double saddles can be simplified to that of a simply supported beam subjected to a uniformly distributed load; moreover, the two ends of this beam are subject to transverse shear force V and couple force M, as illustrated in the figure and shown in Table 5-1. 5.3 Bending Moments and Shear Forces Similar to the analysis of beams under bending in material mechanics, under the action of weight loads, bending moments and shear forces exist at the cross-section of the aforementioned cantilever beam; its bending moment diagram and shear force diagram are shown in the figures. As can be seen from Figure 5-1, the maximum bending moment occurs at the sections located at the center of the beam span and at the support sections, while the maximum shear force occurs at the support sections; these values can be calculated using the methods described below. 1. Bending moment: The bending moment at the mid-span section of the cylinder, as determined from the equilibrium conditions of the beam shown in the diagram. (7) By substitution, we obtain: (8) M1 is usually positive, indicating that the upper part of the cylinder is under compression while the lower part is under tension. The bending moment at the support section of the cylinder is (9) M2, which is generally negative, indicating that the upper half of the cylinder is in tension while the lower half is in compression. Table 5-1 Directions of V, M, and bending moment M2 at the ends of different end caps. For container end caps, the end cap depth is hi; the lateral shear force at the end is V, the end couple is M, and the bending moment at the support section is M2. For flat end caps, when Ra = 0.5Ra, the bending resistance cross-section decreases, which results in an increase in V and M. For long horizontal containers with a large L/D ratio, using A ≤ 0.5Ra may lead to an excessive value of M1; in such cases, A should be adjusted so that 0.2L > A > 0.5Ra, ensuring that V and M meet the required values first, before checking other stresses. 2. Relationship with tangential shear stress: When A > 0.5Ra or the reinforcement ring is close to the saddle plane, the value in equation (16) depends on A; as A increases, this value decreases. Furthermore, the value of K3 for this formula is 0.319 when there is a reinforcement ring; without such a ring, it is 1.171, 0.958, and 00.799 respectively for wrap angles of 120°, 135°, and 150°. When the head is reinforced, K3 is only 0.88, 0.645, and 0.485 respectively. 3. Relationship with circumferential stress: The second term in the formula for a cylindrical shell without reinforcing rings represents the circumferential stress generated by the circumferential bending moment. The coefficient K6 is highly dependent on whether the end cap provides reinforcement to the cylinder; when A ≤ 0.5Ra, K6 = K7/4 ； When Ra>A≥0.5Ra, K6=(1.5A/Ra-0.5)K7 ； When A>0.5Ra, K6=K7. It can be seen that when A≤0.5Ra, K6 is only 1/4 of K6 when A≥Ra. It can be seen that A should be kept as low as possible, ≤0.5Ra. 8.2 Dimensions of the saddle structure: During design, efforts should be made to ensure that the shims serve a reinforcing role; that is, the width b4 of the shims should not be less than b2, their thickness should be at least 0.6 times the thickness of the cylinder, and the angle between the shims and the cylindrical surface should be sufficient. At this point, the backing plate can be referred to as a reinforcement plate. (1) The saddle pad has an impact on ,, and , especially . It should be noted, however, that due to the reinforcing effect of the shims, the controlling circumferential stress may be transferred to the cylindrical surface at the outer edge of the reinforcement plate. Increasing the thickness can cause a decrease, but it will not decrease. Regarding the reinforcing effect of shims, there is an term in the denominator of the formula representing the horizontal force on the web that is carried by the shims (see Section 22.5). (2) Under normal conditions, the wrap angle of the saddle should not be less than 120°; increasing this wrap angle, when A>0.5Ra, changes due to the increase in K1 and K2. An increase in the wrap angle will cause all values from K3 to K8 to decrease, thereby reducing the respective stress components as well. (3) Regarding the wrap angle of the cylinder gasket: as specified, it should be less than a certain value; in such cases the gasket is considered to have no reinforcing effect. But what if it is greater than that value? Is that acceptable? What is its effect on the circumferential stress? According to Zick’s analysis, increasing the wrap angle of the shimming plate to a value greater than a certain threshold is beneficial for reducing the circumferential stress on the outer cylindrical surface of the saddle shimming plate; however, current standards require only the stress in that specific area to be checked. 8.3 Installation of reinforcement rings: Reinforcement rings can effectively reduce the stress levels at the saddle area, especially in large thin-walled horizontal vessels, where stress control at the saddle area is typically important. Installing reinforcement rings is often an effective way to adjust circumferential stress; there are inner reinforcement rings and outer reinforcement rings. It is assumed that the reinforcement ring in the saddle plane should be the most efficient and material-saving solution. If the required moment of inertia for the reinforcement rings in the saddle plane is too large, two inner or outer reinforcement rings can be placed near the saddle plane; in this case, and should be checked. Note: When calculating the combined cross-section of the reinforcement ring and the cylinder, the effective width of the cylinder is , as shown in Figure 4-2 ； 4‑3.