Variable and Constant Spring Selection in START-PROF

Read about START-PROF pipe stress analysis software

Variable Spring Supports and Hangers

The main element of such supports are springs or spring chains. They are used to allow thermal expansion and control piping stress by spring compression forces. Variable spring supports are usually placed under the piping (fig. 1a), while variable spring hangers are usually above (fig. 1c).

Fig. 1

A variable spring support can contain one or more vertical spring chain (rod), see fig. 2. Spring chain (rod) number must be selected based on placement conditions. Each chain (rod) can contain one or more spring, placed on top of each other.

Fig. 2

If the effects of hanger displacement from the vertical position and friction force are ignored, the model is the same in both cases (fig. 1b and 1d). For the following, the number of springs is not significant, so we will assume the presence of one spring.

A support is a linear vertical spring restraint. Restraint reaction is always vertically upward and consists of two terms

,

where

P_з - vertical force created by forced spring compression during installation (pre-stretch force),

r_z - spring reaction to piping displacement in point C, equal to spring stiffness multiplied by its displacement r_z = l ·Δ.

The spring is assumed to always be in a compressed state. Due to this, a variable spring support works as a double-acting restraint. If during analysis the spring is stretched, the corresponding  message is displayed.

Pre-compression Force P_з

Pre-compression force  P_з is a concentrated force created by compressing variable spring support springs outside the piping. P_з force physical properties can be determined by looking at  variable spring support pre-stretch methods.

The operating and cold loads on spring (R_op and R_cold) are changed in different operating modes. But pre-compression value always remains constant. This allows you to keep the selected springs, but at the same time change the piping design. Hence, while analyzing a different piping design conditions of the same model like Equipment Alignment Check, transportation stage etc. we should convert the springs into the custom restraints.

Spring Chain Structure and Variable Spring Support Flexibility

All springs can be divided into two categories: class 1 with allowable subsidence (operation deformation) of 70mm and class 2 with allowable subsidence of 140mm. "1+2+2" indicates that a spring chain contains one spring with 70mm allowable subsidence and two springs with 140mm allowable subsidence each.

In this example, the chain structure is 1+2+2=5, and the total allowable subsidence of the whole spring chain is 5*70 = 350mm. Spring code is set according to the corresponding value in  standards, indicated in Project Settings.

Flexibility is the elastic operation properties of a variable spring support or hanger, containing one or more spring chains. Total subsidence of a variable spring support or hanger  l depends on the number of springs and the flexibility value of individual springs in the variable spring support. In the above example, total flexibility is

l= l₇₀ + l₁₄₀ + l₁₄₀

Flexibility of springs with allowable subsidence of 140mm (l₁₄₀) is twice as big as that of springs with allowable subsidence of 70mm (l₇₀). l₁₄₀ = 2·l₇₀. Therefore, total subsidence equals:

l=5·l₇₀

Stiffness K is the opposite value of flexibility

K=1/l

Automatic Variable Spring Hanger Selection

Ideally, a piping should function in response to thermal expansion as a weightless spring. Based on this, variable spring support compression is determined so as to remove weight from a heated piping. In other words, in every restraint point variable spring support reactions should be such that vertical displacement from weight is 0 [1].

When springs are selected correctly, the following conditions must be met:

1. Load difference between operation and cold mode should not exceed 25%

Ratio=(R_op-R_cold)/R_op*100%≤25%

This done by selecting appropriate variable spring support stiffness λ. The lower the variable spring support stiffness λ, the easier it is to meet this condition. With a high visible displacement  Δ_vis, the condition may not always be met and spring should be replaced by a constant spring support. There are 2 types of visible displacements:

Inst-Ope: Δ_vis = Δ_inst - Δ_op = (R_inst - R_op)·l·n

Ope-Cold: Δ_vis = Δ_op - Δ_cold = (R_op - R_cold)·l·n

2. Variable spring support allowable load must be greater than R_op and R_cold.

n - number of ties

When selecting springs in cold mode, the cold and operating mode loads are switched in formula denominations.

START-PROF select springs in two steps:

Step 1: All springs are replaced by single-directional rigid supports. Only weight loads are applied. The operation spring loads R_max=R_op/n are determined from this analysis. The springs with allowable load greater than R_max are selected form the table.

Step 2: Added stiffness of springs selected on previous step. Only temperature and displacement loads are applied. The operation displacements Δ_op are determined from this analysis. Now calculated the maximum spring load R_max=R_op/n if Δ_op≤0 and R_max=(1+Ratio/100%)·R_op/n if Δ_op>0. Spring minimum stiffness l = (Ratio/100%)·R_op/(Δ_op·n). Now the springs are selected from the table with allowable load greater than R_max and stiffness less than l.

Ratio=(R_op-R_cold)/R_op*100% - the load difference between cold an operating mode.

The step 2 is repeated several times until the same springs are selected on two iterations in a row.

See the table below:

START-PROF can carry out selection of:

1. Variable spring support flexibility  l  and corresponding spring chain properties: spring types, spring number and spring chain (rod) number. Spring chain composition selection is done if flexibility (stiffness) in variable spring support and variable spring hanger properties is equal to 0. Spring chain (rod) number calculated through START-PROF analysis will be no less than that indicated in input data, but can be more if allowable load conditions require more than two chains. Springs are automatically selected with sufficient carry capacity to support forces  R_op and R_cold.
2. Variable spring support or hanger supporting forces  R_op, R_cold, R_assembly, P_з. Automatically supporting force selection is done if supporting forces in variable spring support and variable spring hanger properties are equal to 0. Values aside from 0 are set to regulate piping forces and stress manually.

Automatically variable spring support properties selection is done according to  [1]. To control forces and stress manually, supporting forces and variable spring support flexibility can be input. Manual adjustments can produce more economic results than automatic selection with  [1]. In addition, manual adjustment of supporting forces in variable spring supports is often necessary to remove load from equipment connections. To transfer automatically calculated spring properties to input data for further manual editing, a special function exists.

Spring selection can be done from the following two conditions (input in Project Settings):

1. Displacement from weight loads in operation state is equal to 0 (i.e., weight load balancing in operation state). Used when springs are compressed in two steps or pre-stretched.
2. Displacement from weight loads in cold state is equal to 0 (i.e., weight load balancing in cold state). Used when springs are compressed in one step (separation method).

For high-temperature pipelines (Т_op>350⁰), spring selection and adjustments in operating mode are recommended (spring selection should be in two steps or through pre-stretch). For cold-temperature pipelines (Т_op≤350⁰), installation can be done in one step, and spring selection should be done for cold mode.

Note: spring selection is done in START-PROF according to  [1] assuming an absence of non-linear effects (friction, pendulum effect, etc.), and then analyzes the piping considering non-linear effects. As such, calculated load difference can be greater than that input during selection. In this case, less than required load difference should be input and analysis should be restarted.

Input and calculated variable spring support loads depending on piping state when spring selection is done are given in the table below.

Allowable Load Conditions

Variable spring support loads in all states should not exceed variable spring support allowable load R_max with a specific allowance  m [1].

m∙R_op ≤ R_max
m∙R_cold ≤ R_max

m - allowance set in  spring properties.

Springs are automatically selected so that loads  R_op and R_cold will not exceed allowable load R_max. If supporting forces are input manually, an automatic check is done and corresponding messages are displayed. If springs are modeled with custom restraints, allowable load conditions are not checked automatically and must be checked manually.

If  support pre-stretch is done, the following condition must be met:

m∙P_з ≤ R_max

This condition is not automatically checked!

If compression is done in two steps or with the separation method, "pre-stretch" state does not exist, so allowable load in this state need not be checked.

Variable Spring Support and Hanger Compression Methods

Three methods exist  [1], [2]:

1. Pre-compression

2. Separation method

3. Compression in two-steps

Support Pre-compression

Done for spring selection in both  cold and operation state.

1. Spring height in free state is  H_free, spring compression force at this point is  R_free=0.

2. Spring is pre-compressed outside the piping (for example, on the floor) using a jack. Compression value must be such that compression force corresponds to P_з. Corresponding height will be H_з. Spring compression is fixed with temporary ties welded to spring shell. The spring is then installed in the piping placed on technical (temporary) rigid supports, and all gaps are removed (by regulating rod length, shims, etc.). Support load will be R_з=0, spring compression force will be P_з and spring height will be H_з. This state is called installation prior to spring adjustment.

3. Then, temporary tightening is cut. The piping will immediately react with corresponding displacement Δ_assembly, i.e. will shift to installation state after spring adjustment. From this point, two springs start functioning - variable spring support and the piping itself. Support load in installation mode will be  R_assembly, and spring height H_assembly.

R_assembly= P_з - Δ_assembly/l
H_assembly = H_з + Δ_assembly

4. After filling the piping with the product and heating up to transported product temperature, displacement relative to "original" state will be Δ_op, support load will be  R_op and height will be H_op.

R_op= P_з - Δ_op/l
H_op = H_з + Δ_op

5. After piping cooling and removal of pressure, displacement from "original" state will be  Δ_cold, support load will be R_cold, and spring height will be H_cold.

R_cold= P_з - Δ_cold/l
H_cold = H_з + Δ_cold

Negative signs are due to the fact that positive directions for concentrated force and linear displacement correspond in START-PROF.

R_op and R_cold - supporting forces (reactions), created by the variable spring support in operation and cold states, respectively. Knowing these forces and support flexibility  l, visible piping displacement during the shift from cold to operating mode and vice versa can be calculated:

Δ_vis = |Δ_op - Δ_cold| = |H_op - H_cold| = | l (R_op - R_cold)|

Compression in One Step ("separation method")

Done for spring selection in  cold state.

A piping placed on technical (temporary) rigid supports is gradually separated from these support using spring compression. The resulting spring compression will create supporting forces balancing piping weight loads.

For low-temperature pipelines, variable spring support thermal displacement is minor compared with high-temperature ones; therefore, further spring compression is not necessary.

Spring height  H_assembly for various values need not be selected. As soon as the piping is separated from technical supports, compression can be stopped. In addition, this method eliminates all height  H_assembly analysis inaccuracies.

For this type of piping analysis, spring selection must be done in cold mode. Actual supporting forces  R_assembly and displacements H_assembly in springs should theoretically match design values selected from the condition of displacement from weight loads in  cold state equalling to 0 (i.e. weight load balancing in  cold state). However, in reality differences will appear due to analysis inaccuracies (difference in model and real structure).

Compression in Two Steps

Done for spring selection in operation state.

A piping placed on technical (temporary) rigid supports is gradually separated from these support using spring compression. Technical supports are then removed and spring compression is continued until spring height is equal to the design value of H_assembly and supporting forces to R_assembly.

In this case, piping springs in installation mode are "over-compressed". However, after piping heating, an additional thermal displacement of the spring position will occur, supporting force will equal R_op, and height will equal  H_op. Pipeline weight in operation state will be removed, since spring selection is done based on the condition that displacement from weight loads in operation state is equal to 0 (i.e. weight load balance in operation state).

References

1. RTM 24.038.12-72 Variable spring hanger selection for nuclear or power plants piping. Ministry of heavy, power and transport engineering. Moscow 1973

2. D. Kostovetsky, B. Tokarski. On variable spring hanger selection. CKTI journal. Design and calculation of pipelines of power plants. 67 release, Saint-Petersburg, 1966

3. V. Nahalov. Variable spring hanger adjusting for power plants, Moscow 1975