Selecting the correct pipe support span is an important aspect of piping design. The maximum pipe support spacing is dependent on the maximum allowable deflection or sag in the piping and the maximum permissible longitudinal stress on account of the span.

## Criteria for determining the pipe support span

Allowable spans for horizontal lines are limited by the either the maximum allowable longitudinal stress in the pipe or maximum allowable deflection in the pipe so as to prevent excessive sag that can be detrimental to fluid flow. The maximum permissible sag or deflection is generally limited to between 1/4" to 1/2" (6.35mm to 12.5mm) though Owners may have other criteria which are more restrictive.

For example BP guidelines dictate that the maximum span between adjacent supports for horizontally run steel pipes are as follows:

- For DN25 to DN80 the pipe support span shall limit the maximum deflection due to total self weight to 7mm
- For DN100 and above the pipe support span shall be based on the lower of maximum deflection due to total self weight not to exceed 7mm or a stress limit of 40 N/mm
^{2}(5800 psi)

where total self weight includes any test water, contents and insulation.

Where the piping for a sloped line has to be run without pockets, the limitations on maximum pipe deflection or sag could be even lower. Pipe span may also be limited to avoid reasonant frequency in the piping system.

## Support Span based on limiting the Longitudinal Stress and maximum Deflection in pipe

As per para. 302.3.5 of ASME B31.3, the sum of the longitudinal stresses S_{L}, in any component in a piping system due to sustained loads such as pressure and weight, shall not exceed the product S_{h} x W where

S_{h} = basic allowable stress at maximum metal temperature expected during the displacement cycle under analysis and

W = Weld Joint Strength Reduction Factor.

For the sake of simplicity of this discussion, let us assume that the value of W = 1 so that as per ASME B31.3, the sum of longitudinal stress S_{L} < S_{h}.

### Hoop and Longitudinal Stresses

We know that for a pipe with outside diameter D and wall thickness t, subjected to design pressure P, the Hoop Stress is given by the equation:

Hoop Stress = \(\frac{PD}{2t}\)..........(1)

and Longitudinal stress is given by the equation:

Longitudinal Stress = \(\frac{PD}{4t}\)..........(2)

It is clear from equations (1) and (2) that longitudinal stress is half the hoop stress. Hence, if a pipe due to internal pressure is allowed to develop a hoop stress equal to basic allowable stress S_{h}, the associated longitudinal stress due this internal pressure will only be half of the basic allowable stress = S_{h}/2. Accordingly, it is reasonable to assume that for the design to be safe, the maximum value of longitudinal stress in the fully corroded condition due to internal pressure shall not exceed S_{h}/2 and the balance S_{h}/2 is available for accomodating longitudinal stress due to other sustained loads such as pipe deadweight due to material, contents, insulation and other applicable sustained loads. This value is referred to as S_{all} in equations (8) and (9) below.

To calculate the pipe support span it is common practice to limit the longitudinal stress due to deadweight effect to S_{h}/4 out of the available S_{h}/2. For Carbon steel pipe ASTM A106 Gr B pipe, this would mean limiting the longitudinal stress to a value of 20,000/4 = 5000psi (35N/mm^{2}).

### Bending Moment and Deflection in Pipe with uniformly distributed load

We start with the assumption that the pipe is a simply supported beam with a uniformly distributed load w, supported over a span of L and without any point loads. The support ends are considered as pinned and hence free to rotate.

The maximum bending moment is at the center of span is given by M_{max} = \(\frac{wL^2}{8}\)..........(3)

The maximum deflection is also at the center of span given by D_{max} = \(\frac{5wL^4}{384EI}\)..........(4)

However, if the pipe is anchored at both ends, then the rotation of the support points is restrained. In this case

The maximum bending moment is at the center of span is given by M_{max} = \(\frac{wL^2}{12}\)..........(5)

The maximum deflection is also at the center of span given by D_{max} = \(\frac{wL^4}{384EI}\)..........(6)

The actual situation for a pipe which is continuously supported with multiple support spans is between the above two scenarios i.e. simply supported and fully restrained pipe. Hence an approximation can be made to select a value between the above two values as follows:

The maximum bending moment is at the center of span is given by M_{max} = \(\frac{wL^2}{10}\)..........(6)

The maximum deflection is also at the center of span given by D_{max} = \(\frac{3.9wL^4}{384EI}\)..........(7)

The bending moment is related to section modulus (Z) of the pipe and allowable stress for dead weight effect (S_{all}) by the formula

M_{max} = S_{all} x Z = \(\frac{wL^2}{10}\)..........(8)

### Allowable Support Span based on Stress

Rearranging equation (8) gives allowable support span based on limiting stress to

Allowable Support Span L ≤ \(\sqrt{\frac{10S_{all} Z}{w}}\)..........(9)

### Allowable Support Span based on Deflection

Rearranging equation (7) gives allowable support span based on limiting the maximum deflection D_{max} to a specified value.

Allowable Support Span L ≤ \(\sqrt[4]{\frac{98EID_{max}}{w}}\)..........(10)

**Example Problem**

Calculate the maximum allowable pipe support span given the following:

6" Pipe material ASTM A106 Gr. B, wall thickness = 7.11 mm (0.28 inches) with design temperature of 400°F in water service and provided with insulation 14.9 kg/m (10 lb/ft).

Maximum allowable deflection D_{max} = 0.25 inches (6.35 mm)

**Solution**

Refer to Table C-6 of ASME B31.3 to get value of E = 27.7 x 10^{6} psi at 400°F.

OD of 6" pipe = 6.625 in and ID = 6.625-2*0.28 = 6.065 in

Calculate I = π\(\frac{(OD^4 - ID^4)}{64}\) = 28.14 in^{4}

Value of section modulus Z = 28.14/3.3125 = 8.495 in^{3}

From this page we get value of empty pipe weight = 28.26 kg/m = 19.2 lb/ft

The weight of water is calculated as 18.6 kg/m = 12.5 lb/ft

The weight of insulation is given as 10 lb/ft

Hence total w = 19.2 + 12.5 + 10 = 41.7 lb/ft = 3.475 lb/in

Substituting the values in equation (10) above for **allowable span based on maximum deflection** of 0.25 inches gives us

Allowable Support Span L ≤ \(\sqrt[4]{\frac{98 * 27.7 * 10^6 * 28.14 * 0.25}{3.475}}\) = 272 in = 22.7 ft = 6.9 m

From ASME B31.3 Sh = 20,000 psi. S_{all} = S_{h}/4 = 5000 psi

Substituting the values in equation (9) above for **allowable span based on maximum allowable stress** of 5000 psi gives us

Allowable Support Span L ≤ \(\sqrt{\frac{10 * 5000 * 8.495}{3.475}}\) = 349 in = 29 ft = 8.9 m

Comparing the above it is noted that allowable pipe support span based on maximum deflection gives us a value of 6.9m and based on maximum allowable stress gives us a value of 8.9m. Hence the governing case is maximum deflection and the pipe support span shall be limited to 6.9m.

## Support spacing as per MSS SP 58

Table 4 of MSS SP 58 - Pipe Hangers and supports, provides support spacing for carbon steel standard weight pipe in water and vapor service for temperatures not exceeding 343°C. The standard also provides support spacing for Copper tubes, PVC pipe, CPVC pipe, Stainless steel, Ductile Iron and Cast Iron pipe. However, the standard does not provide any criteria or basis for deriving the support spacings.

As per Table-4 of MSS SP 58, the support span for 6" sch40 pipe in water service is 5.2m. Using the online support span calculation tool this would translate to a maximum permissible deflection or sag of 2mm for piping considering insulation weight as per example above and sag of 1.5mm without taking into consideration any insulation weight. If allowable stress was used as a criteria this would translate to an allowable stress of about 1300psi. Thus the support spacing values defined in Table-4 of MSS SP 58 can be deemed to be conservative for use in piping design.