ultimate strength analysis

Ultimate Strength Analysis

Mark Cassidy

Platform, Pipeline and

Subsea Technology CIVL4171

• Offshore design codes such as API RP2A provide design rules for members (braces, legs etc.)

• They are less prescriptive about the structural performance of the overall platform

• Current “best practice” is to also determine the performance of the structure under extreme loads

• This is typically done by numerical analysis

Introduction

• Purpose written offshore structural design software such as SACS, StruCAD*3D & SESAM typically analyze structures using linear elastic theory

Linear Analysis

Linear elastic analysis can’t predict structural failure

Linear vs. Nonlinear Analysis

Load

Displacement

Linear analysis

Nonlinear analysis

P

Secondary Bending Moment = Pδ

δ

Nonlinearities

Nonlinearities in structural analysis come from a number of sources, including:

• Geometric nonlinearities (P-δ effect, buckling)

• Material nonlinearities (plastic failure, soil response)

• Contact between members

Why do linear analysis ?

• Design codes are often based on linear elastic results (particularly WSD versions)

– May include “amplification” factors to account for important nonlinear effects

• In designing for serviceability, we usually require the structure to remain linear elastic,

• If we trust the safety factors in the design code we may not need more complex analysis

Linear vs. Nonlinear Analysis

Why do nonlinear analysis ?

• To establish the ultimate strength and performance of the structure

• To determine the response of the structure to accidents (ship impact & blasts)

• Forms the basis for reliability analysis – i.e. to determine the Risk of Failure.

Linear vs. Nonlinear Analysis

Nonlinear Analysis

Software for offshore nonlinear analysis

• Some specialist offshore software has nonlinear modules:

– SACS

– StruCAD*3D

• Specialist software:

– USFOS

– ASAS

• A general FEA program, e.g. ABAQUS, ANSYS, LS/DYNA, NASTRAN

Incorporates wave loading

Nonlinear Analysis

Software for nonlinear analysis

• General packages are usually much more complex, but allow for less routine analyses to be performed

• The specialist packages automate may of the typical analysis tasks, and often have specialized features

Pushover Analysis

What is a pushover analysis ?

• The pushover analysis is the main (analytical) tool used to determine the ultimate limit state performance of an offshore jacket structure

• It is also sometimes used to calculate the reliability of the structure via the Reserve Strength Ratio (RSR)

Pushover Analysis

Steps in a Pushover Analysis:

1. Development of a detailed structural model

2. Application of an appropriate set of loads on the structure

3. Carrying out the analysis

4. Verification

5. Interpretation

Pushover Analysis

Step 1: Development of a detailed model

• The model used for design may not have enough detail for a pushover analysis

• Additional nodes may be required in the model, or more complex joint models

• Importantly, nonlinear material properties are needed, along with member imperfections

Braced Monotower

Ultimate Limit State

NWS Structural Failure

Pushover Analysis

Step 2: Application of appropriate loads

• The steps in applying the loads are generally straightforward

• But, The choice of actual loads to apply is more difficult and depends on the information that is to be extracted

• The combination of loads used may be important

Pushover Analysis

Step 3: Running the analysis

• For a well behaved structure, the nonlinear analyses are fairly straightforward

• Analyses can become more involved when failure is dominated by buckling response. Contact analysis can be particularly difficult.

• Parameters which control the analysis may need to be varied to obtain a consistent response

Pushover Analysis

Step 4: Verification

• Make sure that each of the steps in the analysis are verified against known results, if possible

• This may be particularly important for novel structural configurations

Pushover Analysis

Step 5: Interpretation

Do the results mean what you think they mean?

• Is the collapse mode sensible - do you understand why the particular failure mode occurred?

• Do the forces balance?

• Check failure values - are they reasonable?

• Is the result stable - if you change something by a small amount, do you get a similar answer (may not be the case, even for a correct analysis)

Pushover Analysis

Reserve Strength Ratio

• The RSR is a measure of the platform’s strength, when compared to the design strength

• The strength is measured in terms of the total load that is resisted

• The RSR should be an estimate of the true failure load - not a lower bound estimate

Load Design

Load CollapseRSR =

**

Pushover Analysis

Reserve Strength Ratio

• How do we measure the total load?

• Load is most commonly measured in terms of the total base shear acting on the structure

Pushover Analysis

Reserve Strength Ratio

Base Shear

Pushover Analysis

Pushover Analysis

Modelling

Pushover Analysis

Modelling

Pushover Analysis

Modelling

Pushover Analysis

Modelling

• There are often a few choices as to the method of modelling individual members

• The choice of model types has to be assessed on the basis of expected modes of failure, the sophistication of the required model and the available analysis tools

Member Modelling

Phenomenological elements:

• These elements represent the behaviour of tubular members by experimentally derived relationships between P-δ and M-θ

• Able to model buckling, and cyclic behaviour

• For example, can insert plastic hinges when required

Member Modelling

Member Modelling

Tension

Compression

Marshall Strut Element

Element is clever enough to model column buckling behaviour

Member Modelling

Plastic Section Capacity

Why not use phenomenological elements all the time?

• Limited to modelling members with well known properties

• Cannot be extended to different geometries or materials without physical tests to establish the member behaviour

Member Modelling

Plastic hinge beam-column models:

• Based on beam-column theory

• Model the typical behaviour of beams in combined bending and compression

• Plastic failure of the member is modelled by formation of a “plastic hinge” in the member

Member Modelling

Plastic hinge beam-column models:

• Element formulation may include local buckling, denting and modelling of hydrostatic pressure effects

• But this needs to be confirmed for each different program

Member Modelling

General beam models:

• Model the member behaviour from first principles

• To model column buckling behaviour, a number of elements are required along the beam member (this can add a lot of complexity to the model)

Member Modelling

General beam models:

• More detailed material properties may be required than for the other element types

• Other element types usually include “default”properties and only require an input of yield stress

• However, for most pushover analysis, member strains are restricted to the yield plateau

Member Modelling

General beam models:

Member Modelling

Elastic - Perfectly Plastic material behaviour

END Lecture 1

Imperfections:

• Regardless of the type of element used to model members, initial imperfections play an important part in the collapse load of compression members

• Member collapse may drive failure of the frame, and hence imperfections need to be modelled appropriately

Member Modelling

Imperfections:

Imperfections in real members are due to:

1. Geometric imperfections (member “out of shape”)

2. Residual stresses due to fabrication

• Imperfections are generally modelled as “equivalent imperfections”

• These are geometric imperfections with account for both sources of imperfections

• Therefore, not quite the same as the geometric imperfections

Member Modelling

Effect of Imperfections

Member Modelling

Imperfections

• In specialized pushover software, imperfections may be included by the analysis program automatically

• In general FE software, imperfections usually need to be modelled in a separate step

Member Modelling

Imperfections

Member Modelling

Hybrid Beam – Shell model in ABAQUSImperfections modelled using a separate Eigenvalue analysis

Material properties:

• If the pushover analysis is being conducted for a reliability analysis, then the best estimate material properties should be used

• Young’s modulus is usually well known (210 GPa), but yield stress may be specified as a minimum, or characteristic value

• If a probability of failure is to be calculated, then the best estimate (or true) yield should be used. These should be available from the mill certificates. Typically about 10% greater than the specified minimum yield stress

Member Modelling

Joints:

• Joints may be modelled in a number of ways

• The easiest is to model them simply as rigid connections. That is, there is no rotational flexibility at the connection

• This assumption is required for a linear elastic analysis, as design codes (conservatively) correct for this (e.g. member effective length)

Pushover Analysis

Modelling - Joints

Pushover Analysis

Modelling - Joints

Pushover Analysis

Modelling - Joints

Pushover Analysis

Modelling - Joints

Pushover Analysis

Loading

Two theories to how to load the structure

1. Apply the design wave, and increase that

or

2. Apply waves with kinematics corresponding to increasing return period

Pushover Analysis

Pushover Analysis

Pushover Analysis

Pushover Analysis

Loading

• First method is simple

• Second method better as

– Allows for deck inundation to be checked

– More accurately represents the loading on the structure with increasing return period (very important for moment dominated structures)

Pushover Analysis

Effect of Structural Configuration

Pushover Analysis

100 year wave Wave

corresponding to failure

Platform

type

RSR Return

Period

RSR Return

Period

Monopod 1.48 350 1.29 210

Hybrid 1.71 590 1.51 310

Jack-up 2.17 1450 1.97 1100

Jacket 2.30 1800 2.28 1600

Ratio

1.66

1.90

1.32

1.12

Effect of Structural Configuration

Pushover Analysis

Finding the Return Period from the RSR

Pushover Analysis

• Will have wave height as a function of return period, or frequency of occurrence

• This may be plotted as a function of the critical action (base shear or moment), by running two return period waves past the structure, and then extrapolating

• If environmental variability is the dominant source of uncertainty, this provides a first pass estimate of the reliability of the structure

Finding the Return Period from the RSR

Pushover Analysis

Finding the Return Period from the RSR

Pushover Analysis

Finding the RP from the RSR

-1.5

-1

-0.5

0

0.5

1

0 0.2 0.4 0.6 0.8 1 1.2

Log(Ln(N ))

Log(E/Ed)

NWS

GoM

CNS

Questions

?