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Pipe Repair Using Wrapped Laminates per ISO 24817 Calculator

Pipe Repair Thickness Using Wrapped Laminate Stress Design Formulas and Calculator per. ISO 24817

These equations are for the design of pipe wrap material and thickness of composite material in situations for damages commonly encountered in oil, gas, utility pipe work systems and vessels. Calculations will determine the minimum thickness required in the wrap laminate.

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Design formulas limited by allowable stress in the substrate formulas

Equations (1) and (2) shall be used when it is assumed that the repair thickness is limited by the allowable stress in the substrate.

In the circumferential direction, the minimum repair laminate thickness, t_min (expressed in millimeters) , is given by

Eq. 1 Pipe Repair Using Wrapped Laminate Stress Design

${\displaystyle t_{min,c}=\frac{D}{2s}\cdot <!--\; \cdot \; -->\left(\frac{E_s}{E_c}\right)\cdot <!--\; \cdot \; -->(p_{eq}+\frac{2\mathrm{\nu <!--\; \nu \; -->}{F}_{eq}}{\mathrm{\pi <!--\; \pi \; -->}{D}^2}-<!--\; -\; -->p_s)}$

In the axial direction, the minimum repair laminate thickness, t_min (expressed in millimeters) , is given by

Equation 2

${\displaystyle t_{min,a}=\frac{D}{2s}\cdot <!--\; \cdot \; -->\left(\frac{E_s}{E_a}\right)\cdot <!--\; \cdot \; -->(\frac{2F_{eq}}{\mathrm{\pi <!--\; \pi \; -->}{D}^2}-<!--\; -\; -->\mathrm{\nu <!--\; \nu \; -->}\frac{E_a}{E_c}{p}_{eq}-<!--\; -\; -->p_s)}$

NOTE It is possible that when using Equation 2, that negative repair thickness values are calculated. This implies that the remaining wall thickness is sufficient to withstand the applied loads in the axial direction.

In Equation 2, the contribution of Feq shall be taken as positive.

p_eq is defined as:

Eq. 3a

${\displaystyle p_{eq}=p[1+\frac{16}{(\mathrm{\pi <!--\; \pi \; -->}{D}^{2}p{)}^2}{(f_{sh}+\frac{2}{D}{M}_{to})}^2]forp\ge <!--\; \ge \; -->\frac{4}{\mathrm{\pi <!--\; \pi \; -->}{D}^2}(F_{sh}+\frac{2}{D}{M}_{to})}$

Eq. 3b

${\displaystyle p_{eq}=p+\frac{4}{\mathrm{\pi <!--\; \pi \; -->}{D}^2}(f_{sh}+\frac{2}{D}{M}_{to})forp<<!--\; <\; -->\frac{4}{\mathrm{\pi <!--\; \pi \; -->}{D}^2}(F_{sh}+\frac{2}{D}{M}_{to})}$

F_eq is defined as:

Eq. 4

${\displaystyle F_{eq}=\frac{\mathrm{\pi <!--\; \pi \; -->}}{4}p{D}^2+\sqrt{F_{ax}^2+4F_{sh}^2}+\frac{4}{D}\sqrt{M_{ax}^2+M_{to}^2}}$

where

D is the original external diameter
MAWP is the Maximum Allowable Working Pressure
E_a is the axial tensile modulus of the repair laminate, expressed in megapascals;
E_c is the circumferential modulus of the repair laminate, expressed in megapascals;
E_s is the tensile modulus of substrate, expressed in megapascals;
D is the original external diameter, expressed in millimetres;
F_eq is the equivalent axial load, expressed in newtons [see Eq. 4] ;
ν is the Poisson’s ratio of the repair laminate (see Annex B for definition);
s is the allowable stress of the substrate material, expressed in megapascals;
p_eq is the equivalent internal pressure, expressed in megapascals [see Eq. (3)] ;
p_s is the MAWP, expressed in megapascals, which is defined according to the relevant defect assessment code;
t_s is the minimum remaining substrate wall thickness, expressed in millimetres.
p is the required internal design pressure, expressed in megapascals;
F_sh is the applied shear load, expressed in newtons;
M_to is the applied torsional moment, expressed in newton millimetres;
F_ax is the applied axial load, expressed in newtons;
M_ax is the applied axial moment, expressed in newton millimetres.

The design repair thickness, t_design (expressed in millimetres) , shall be the maximum value of t_min,c and t_min,a determined from Formulae (1) and (2) .

If the purpose of the repair system is to strengthen an undamaged section to carry additional bending or other axial loads, the value of F_eq shall be taken to be the increased total axial load requirement and the value of ps shall be the MAWP after the defect has been assessed.

Formulae (1) and (2) are valid for repair thickness

Eq. 5

${\displaystyle t_{design}=<<!--\; <\; -->\frac{D}{12}}$

The assumption made in deriving Formulae (1) and (2) is that the substrate is elastic.

Source:

• International Standard ISO 24817, Petroleum, petrochemical and natural gas industries - Composite repairs for pipework - Qualification and design, installation, testing and inspection

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