ultimate strength analysis
DESCRIPTION
Ultimate Strength AnalysisTRANSCRIPT
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
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