Introduction to Offshore Structures

Module 3

Contents

PalmGren-Miner Rule Design Methodology Simple joint calculation Fatigue Life Improvement

PalmGren-Miner Rule

Suppose a body can tolerate only a certain amount of damage, D. If that body experiences damages Di (i=1,2,n) from N sources, then we might expect that failure will occur if

= =1

PalmGren-Miner Rule

Equivalently,

= 1=1

where Di/D is the fractional damage received from the ith source.

PalmGren-Miner Rule

We can use this linear damage concept in a fatigue setting by considering the situation where a component is subjected to n1 cycles at alternating stress 1 , n2 cycles at stress 2 , , Nn cycles at N . From the S-N curve for this material, then we can find the number of cycles to failure, N1 at 1 ,N2 at 2 , , NN at N .

Example

Assume we are interested in the cycles to failure of a paper clip. As illustrated in the following figure, a cycle is defined as opening and closing a clip. It is known that the angle of the two arms of the paper clip affects the number of cycles to failure. So here the angle is treated as the stress.

PalmGren-Miner Rule -Advantages

For tests with random loading histories at several stress levels, correlation with the Palmgren-Miner rule is generally very good.

The Palmgren-Miner rule can be interpreted graphically as a "shift" of the S-N curve.

PalmGren-Miner Rule - Limitations

1. It does not consider sequence effects, i.e. the order of the loading makes no difference in this rule. Sequence effects are definitely observed in many cases.

2. Palmgren-Miner rule says that the damage accumulation is independent of stress level. This can be seen from the modified S-N diagram above where the entire curve is shifted the same amount, regardless of stress amplitude.

Design Methodology

1. Develop a parametric equation empirical method for each of the plane frame and basically looking similar to either T, Y, K or X.

2. Analyses will be done plane by plane. Of course, the three-dimensional effect is taken into account in terms of empirical multiplications.

3. If the design of one side is done, the effect of other side is already taken into account.

4. Repeat the procedure for all frames in one junction and look at whichever is producing maximum requirement

Design Methodology

Tubular Joint

PresenterPresentation NotesThe gap for simple K-joints should be largerthan 50 mm and less than D. Minimum distances for chord cans and brace stubs should not includethickness tapers.

PresenterPresentation Notesbrace planes within 15 of each other may be considered as being in a commonPlane.For a brace to be considered as K joint classification, the axial force in the brace should be balanced to within 10 % by forces in other braces in the same plane and on the same side of the joint. For Y-joint classification, the axial force in the brace is reacted as beam shear in the chord. For X-joint classification, the axial force in the brace is carried through the chord to braces on the opposite side.

Simple joint calculation API RP2A

Simple-joint calculation

This is valid based on the following criteria: 0.2 1.0 10 50 30 90 Fy 72 ksi (500 Mpa) g/D>0.6 (for K joints)

Simple-joint calculation

Tubular joints without overlap of principal braces and having no gussets, diaphragms, grout or stiffeners should be designed using the following guidelines (plus increase in both cases where applicable).

where Pa = allowable capacity for brace axial load; Ma = allowable capacity for brace bending moment, Fyc = the yield stress of the chord member at the joint(or 0.8 of the tensile strength, if less), in ksi (MPa); FS = safety factor = 1.60.

Strength Factor Qu

Chord Load Factor Qf The chord load factor Qf accounts for the presence of nominal loads in the chord and is calculated from the following equation.

PresenterPresentation Noteswhere Pc and Mc are the nominal axial load and bending resultant in the chord;Py is the yield axial capacity of the chord; and Mp is the plastic moment capacity

Chord Load Factor Qf

Strength Check

The interaction ratio JIR for the joint with applied axial loads and bending moments in the brace should be calculated using the expression:

Joint detailing- In plane

PresenterPresentation NotesThe minimum nominal gap between adjacent braces, whether in-plane orout-of-plane, is 2 inches (50 mm). Care should be taken to ensure that overlapof welds at the toes of the joint is avoided.

Joint detailing- Out of plane

Fatigue Life Improvement

The fatigue life can be improved by one of the following methods. Profile grinding the weld Weld Toe grinding Hammer peeling of the weld toe Smoothening Weld caps in butt welds. Post weld Heat treatment Adding Internal rings

Profiling the Weld surface

Involves smoothening

of weld caps at the butt weld

It improves fatigue life by reducing the stress concentration due to under cut or crack like features

Smoothening weld caps

In this process, fatigue life is improved by reducing the stress concentration due to undercut or crack like features

Thank You

Introduction to Offshore StructuresContentsPalmGren-Miner RulePalmGren-Miner RulePalmGren-Miner RuleExamplePalmGren-Miner Rule -AdvantagesPalmGren-Miner Rule - LimitationsDesign MethodologyDesign MethodologyTubular JointSlide Number 12Simple joint calculation API RP2ASimple-joint calculation Simple-joint calculation Slide Number 16Slide Number 17Strength Factor QuChord Load Factor QfChord Load Factor QfStrength CheckJoint detailing- In planeJoint detailing- Out of planeFatigue Life ImprovementProfiling the Weld surfaceSmoothening weld capsSlide Number 27