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Pipe Repair Limited by Allowable Strain in the Repair Calculator

Pipe Repair Limited by Allowable Strain in the Repair Laminate Formulas and Calculator per. ISO 24817

Formulae (1) and (2) shall be used when it is assumed that the repair is limited by the allowable strain of the repair laminate. In the circumferential direction, laminate thickness, t_min (expressed in millimetres) is given by Equation (2)

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Preview Pipe Repair Thickness Using Wrapped Laminate Calculator

NOTE It is possible that when using Equation(1) , that negative repair thickness values are calculated. This implies that the remaining wall thickness is sufficient to withstand the applied loads.

Design formulas limited by allowable stress in the substrate formulas by

Eq. 1

${\displaystyle {\mathrm{ϵ<!--\; ϵ\; -->}}_c=\frac{1}{E_c{t}_{min}}(\frac{p_{eq}D}{2}+v\frac{F_{eq}}{\mathrm{\pi <!--\; \pi \; -->}D})-<!--\; -\; -->\frac{p_{s}D}{2E_c{t}_{min}}-<!--\; -\; -->\frac{p_{live}D}{2(E_c{t}_{min}+E_s{t}_s)}}$

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

Eq. 2:

${\displaystyle t_{min,a}=\frac{1}{{\mathrm{ϵ<!--\; ϵ\; -->}}_a}(\frac{F_{eq}}{\mathrm{\pi <!--\; \pi \; -->}D}\frac{1}{E_a}-<!--\; -\; -->\frac{P_{eq}D}{2}\frac{v}{E_c})}$

If the repair is applied at zero internal pressure, i.e. plive = 0, and axial loads can be neglected, i.e. buried pipelines, then Eq. 2 can be rearranged to give:

Eq. 3

${\displaystyle t_{min}=\frac{D}{2{\mathrm{ϵ<!--\; ϵ\; -->}}_c{E}_c}(p_{eq}-<!--\; -\; -->p_s)}$

The design repair thickness, tdesign, shall be taken as the maximum value determined from either Equation (1) or (2) .

Equation (1) to (3) are valid for repair thickness

Eq. 4

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

The assumptions made in deriving Equations (1) to (3) are that the substrate is elastic and only contributes to the load-sharing up to the allowable stress (of the substrate) .

In Equation 6, the contribution of F_eq shall be taken as positive.

p_eq is defined as:

Eq. 5a

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

Eq. 5b

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

F_eq is defined as:

Eq. 6

${\displaystyle F_{eq}=\frac{\pi }{4}p{D}^2+\sqrt{F_{ax}^2+4F_{sh}^2}+\frac{4}{D}\sqrt{M_{ax}^2+M_{to}^2}}$

where

p_live is the internal pressure during repair installation, expressed in megapascals;
ε_c is the repair laminate circumferential strain, expressed in millimetres per millimetre;
ε_a is the repair laminate axial strain, expressed in millimetres per millimetre
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_m 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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