

Calculation Bases of EN 15911 method By Yann Guérout In design, the strength calculations corresponds to check that the applied loads are admissible : In the framework of the Pressure Equipment Directive PED 97/23/EC "New approach directive", the CEN Technical Committee TC74 "Flanges and their joints" prepared a new calculation standard : EN1591 : "Flanges and their joints  Design rules for gasketed circular flange connections  Part 1 : calculation method , Part 2 : gasket parameters". The aim of the EN 1591 calculation method is to verify both leaktightness and strength criteria. The method does not only consider basic calculation parameters such as :
but also :
Mechanical model In the calculation method of the EN15911, the behaviour of the whole Flangesboltsgasket system is considered in an axisymmetric mechanical model. The calculation is not only based on a forces balance, it also considers a deformation balance and rheological laws of the bolted flanged connection components. The calculation is organized in calculation conditions numbered with the letter I. The calculation is performed using the forces and deformations balances between the initial calculation condition : assembly condition (I=0), which is the reference state, and a subsequent condition I. The forces and deformations are determined at subsequent calculation conditions (typically : test condition (I=1), design condition (I=2), operating condition n°1 (I=3), ...). Flanges 3 different flange configurations are treated in the EN1591 : Integral flange Loose flange Blank flange For integral flanges and collar, the ring cross section is considered to be connected to an equivalent cylindrical shell. A tapered hub is treated as being an equivalent cylindrical shell whose thickness is calculated. For flanges without hub, the dimension of the equivalent cylindrical shell are those of the connected shell. Effective dimensions of the flanges : In the calculation of the width of the rectangular ring cross section, the bolts holes are partially subtracted : When the pitch between bolts is small, d5e is close to d5, when the pitch between bolts is high, d5e is close to 0. The effective thickness of the rectangular ring cross section can be obtained by dividing the cross section area of the ring AF or AL by the calculated radial width of this section. An effective bolt circle diameter is also considered in order to take into account the discrepancy between the arc of a circle and the string. The relation between the flange deformation and the load applied on the flange is :
where ΘF is the rotation angle of the flange, ZF is the flexibility modulus of the flange, EF is the Young modulus of the flange and MF is the rotational moment applied on the flange. In the case of loose flange : where ΘL is the rotation angle of the loose flange, ZL is the flexibility modulus of the loose flange, EL is the Young modulus of the loose flange and ML is the rotational moment applied on the loose flange. Bolts The relation between the bolt elongation and the bolt load is :
The relation between the gasket compression and the load on the gasket is :
The gasket contacts the flange faces over a calculated annular area. The effective gasket width varies with the flange rotation. This rotation also leads to a non homogenous radial gasket stress. The effective gasket width bGe is calculated for the assembly condition ( I=0) and is assumed to be unchanged for all subsequent load conditions. The calculation of bGe includes the elatic rotation of the flanges as well as the elastic and plastic deformations of the gasket. For gaskets with elastic behaviour, the evolution of the effective width of the gasket is a square root curve. For gaskets with plastic behaviour, the evolution of the effective width of the gasket is a straight line. The expression of the calculated gasket width is an approximation which enable to consider both elastic and plastic behaviour. 4 different types of gaskets are considered in the calculation of the effective dimensions :
Under compression and (or) at elevated temperature, the gasket may creep and gasket relaxation may occur. Loads
The following loads are considered in the calculation, in each condition I: Fluid pressure internal (PI < 0) or external (PI > 0) pressure, resulting in a force: Radial effect of the internal pressure The radial effect of the internal pressure is considered in the loading of the flange ring cross section with the term : where eP is the thickness of the flange ring cross section submitted to internal pressure. We find this effect in the expression of lever arms correction such as hP or hQ. External loads axial tensile (FAI>0) or compressive (FAI<0) forces, and bending moments MAI, resulting in a force:
Differential axial thermal expansion between the bolts and the flanges The differential axial thermal expansion between the bolts and the flanges is given by the following expression : where TB,G,F,L and αB,G,F,L are respectively the temperature and the thermal expansion factor of the corresponding elements. Forces and Deformation balances At every calculation condition I a forces balance is established between the bolt load, the gasket reaction, the resulting force due to the external loads, the resulting force due to the internal pressure : At assembly condition as well as for all the subsequent calculation conditions, the bolted flange connection components are joint together by the internal forces. It leads to the following geometrical relation between the component displacements : From these 2 balances, the fundamental equation which links the forces variation in a bolted flange connection is obtained : Required tightening force : FB0 req The EN 1591 calculation is based on integrity criteria. A minimum tightening force is determined by considering both seating and leaktightness criteria. If leaktightness test results are not available, QI can be determined with PI and the m value. From the Qmin and QI values, we determine the required tightening force FB0 req. Load rates Generally speaking, several types of damage can affect components : excessive deformations, creep, erosion/corrosion, fatigue… In the EN 1591 the strength criteria are based on the limitation of excessive deformations. The creep of flanges and bolts as well as fatigue proof (usually not taken into account in such code) are not considered in EN1591. In pressure equipment and static structures, deformation becomes excessive when the equipment dimensions increase much more rapidly than the load does. It leads to the definition of an excessive deformation threshold. Limit analysis theory defines a mathematical approach of the excessive deformation threshold. In this view, the material is considered elastic – perfectly plastic. The material is assumed to have an elastic behaviour until it reaches yield stress Sy. Then the stress remains constant at Sy regardless of the strain imposed. In the EN1591, the strength criteria correspond to the verification that load rates are acceptable. Load rate in EN1591 can be defined as the ratio between the load applied on the considered component and the strength of the component. Since the load influences the strength of the component, there is no exact proportionality following : Allowable load = (applied load) / (load rate) At tightening the load rates are calculated with FB0max which is the tightening force taking into account the scattering due to the bolting up method. For the subsequent calculation conditions, the forces to consider in the calculation of load rates are obtained from an assembly gasket force FG0d which guarantee that the required gasket surface pressure is applied at all the calculation conditions. In the case of frequent reassembly, accumulation of plastic deformations is limited. Gasket load rate The strength criterion on the gasket corresponds to a limitation of the gasket compression. The condition on the load rate given below must be verified : Bolts load rate The strength criterion on the bolts corresponds to a limitation of the bolts traction. The limit load equation for the bolts is the following : The condition on the load rate given below must be verified : The value C = 1 is based on a plastic limit criterion. Due to this criterion, some limited plastic strains may occur at periphery of the bolts in assembly condition. Flanges load rates The strength criterion on the flanges corresponds to a limitation of the flanges rotation. The radial cross section of the flange ring is considered undeformed. Only circumferential stresses and strains in the ring are treated; radial and axial stresses and strains are neglected. For the flanges, the load ratios are calculated for the section of the flange ring or collar, of the loose flange (if there is one), and in some cases, for particularly critical sections. Example of determination of flange with connected shell load rate : If we consider ST : circumferential stress in the ring and SF the yield stress or the nominal design stress for the flange ring. From the elasticity theory : we determine the resulting force and moment in the flange ring due to the deformation.
At the limit load :
For a rectangular cross section :
The limit load equation for the flange ring is then : We use the expression of RF and MF determined with the elasticity theory applied to the flange ring. We also use the force and moment expressions applied on the flange ring by the connected shell and we obtain the load rate expression of the flange with a connected shell. Each load rate shall be less than or equal to unity for all calculation conditions. For wide flanges, a more stringent requirement applies to integral flanges and loose flanges : the load rate shall be less than or equal to F max < 1. Tightening recommendation The bolting up method generates some degree of inaccuracy. That is why the targeted tightening force must be higher than the required tightening force. The EN 1591 considers the negative e  and positive e + scattering due to the bolting up method. As a consequence, the actual bolt tightening force FB0 is limited as follow : with: The nominal bolt assembly force must verify the following condition : In the same way, the load rates at assembly condition are calculated with the following bolting up force. Tightening torque To obtain the target bolt assembly force FB0nom, the value of the torque to apply at tightening is given by the expression below : nB: number of bolts  Last update : 19 Feb. 2002


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