II Training_original
CAESAR II Statics Training
CAESAR II Version 2011
Contents Introduction
6 Units
19 Axial
Theory and Development of Pipe Stress Requirements
25 Example
69 Analyse
CAESAR II Statics Training Introduction
228 B31
260 Jacket
264 B31
Introduction CAESAR II is pipe stress analysis software which uses beam theory to evaluate piping systems to numerous international standards
but instead uses a stick model built up of elements connected by nodes
This course will introduce CAESAR II and demonstrate various modelling and analysis methods in order to evaluate and correct piping systems
This is the window where all tasks are started from
reviewing results or accessing any auxiliary modules such as WRC 107/297 processor or the ISOGEN stress isometrics module
When opening a new file,
but you will return to the Main Window
You can then choose to go to the Input processor,
These modules (and other auxiliary modules) and their interfaces will be introduced as they occur throughout the training
Default Data Directory CAESAR II has the option to specify the default working directory – that is all files working with will be saved/opened from this default location
this setting is just the default location when selecting New/Open
Select File > Set Default Data Directory from the CAESAR II Main window
Click on the ellipsis button at the end of the text field and browse to E:\Training\CAESAR II\Exercises
units files are used by CAESAR II
These units files simply convert the internal CAESAR II English units to the user’s preferred unit
Each CAESAR II file (referred to as a “Job File”) uses a particular units file which is specified on creation of the job
FIL and are located in the CAESAR II System directory,
or in the same directory as the job file
we wish to use specific units for various parameters such as Pressure,
Density etc
This allows the creation of new units files,
or the review of existing units files,
useful if you receive a units file from a colleague and wish to check the units in use in the file
change the following units from the MM defaults: Stress Pressure Elastic Modulus Pipe Density Insul
which will be converted to actual diameters and wall thicknesses (e
enter 4 into the diameter field and CAESAR II will convert this to 114
it is easy to prove this using a simple cantilever example
This example will introduce the basic modelling methods in CAESAR II and introduce the Input Spread Sheet,
we can check the CAESAR II results against some simple hand calculations
Using the example below,
we will create a simple cantilever model,
and apply a displacement of 2mm at the other end
We can then calculate the force required to generate this 2mm displacement – and see this in the results
First we will create the model in CAESAR II
the units will be displayed to the user for confirmation
You will notice that the units file displayed here for our file is English (CAESAR II default units) not the units file we have just created
CAESAR II uses the units file set in the Configuration/Setup as the default file for new jobs (and also as the units to use to display the output results)
hover over any field in the input – the units used in this field will be displayed in the tooltips
we changed the pressure units to bars,
but the pressure field displays the units as lb
Close the input screen – we will change the units and return to the input with the correct units displayed
In the CAESAR II main window select Tools > Configure/Setup
select Database Definitions from the categories tree on the left
Now change the Units File Name setting to the units file just created
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Save and exit
the units file to be used will be displayed – this should now be your custom units file
Verify that the correct units are in use via the tooltips
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CAESAR II Statics Training Introduction Model Input We will now create the simple cantilever model and apply a 2mm displacement at the free end
The model will be as follows: One element 10m in length going from node 10 to node 20 in the X direction,
The input spread sheet will have defaulted to nodes 10 to 20,
so simply enter 10000 in the DX field
Enter the pipe diameter and wall thickness – this is 8” NS and STD wall thickness
simply type in 8 in the diameter and hit enter
simply type in “S” and press enter
Select A106 – B from the list of materials
you can simply type in the material number here
Selecting the material will fill in the Elastic modulus and Poisson ratio and various material allowables under the Allowable Stress area,
depending on the design code selected (B31
3 default)
CAESAR II Statics Training Introduction
We now need to anchor it at one end (node 10) and apply a displacement at the other end (node 20)
All the check boxes shown in the middle column on the spread sheet must be double clicked to check/uncheck
To define a restraint you must specify a minimum of the node that the restraint will be attached to,
so select ANC and locate it at node 10
Now we will apply the 2mm displacement at the opposite end
CAESAR II Statics Training Introduction Specify the displacement at node 20,
and specify a 2mm displacement downwards in the Y direction – i
Leave the remaining rows empty – do not specify 0
so just enter 21°C in T1 and 1bar in P1 fields
Before analysis the input must be error checked in order to identify any issues which may prevent the analysis running (such as specifying both an anchor and an applied displacement at the same point),
or anything which may provide incorrect results (such as Stress Intensification factors not present at a geometric intersection)
This can be useful for identifying problems such as incorrect densities applied – giving an incorrect weight for example
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CAESAR II Statics Training Introduction
review the model for any issues
A common error on this exercise is the following:
This indicates that the displacement and the anchor have been specified at the same location
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CAESAR II Statics Training Introduction Load Case Editor Once the error check is successful,
we can create load cases to analyse the system
Access the load case editor
This button is only available after a successful error check
as required by the design codes such as B31
Remove all these load cases,
as we are only concerned with the displacement
Add one new row
Into the load case we can add any of the loads defined in the input into the load case
drag in D1 – Displacement Case #1 into the L1 row
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CAESAR II Statics Training Introduction
The analysis will now take into account only the displacement reaction
let us first perform the hand calculation in order to check
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we can calculate this quite easily
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run the analysis by clicking on the “Running Man” icon from within the load case editor
You will see the following message explaining that certain loads have been defined in the model but are not included in any of the load cases to be analysed – this is OK in our case,
but can serve as a useful warning if you have may loads/load cases defined
Select OK as is…Continue and click OK to analyse
the Output Processor will be shown
We can view various results for any load case from here,
plus general model reports such as the Input Echo
or output to Word/Excel/Text or straight to a printer
In addition Custom report templates can be created,
and any available report can be selected and added to the Output viewer Wizard,
and exported/viewed to create/view a comprehensive report very quickly
and the force at node 20 to check against out hand calculation
view the Global Element Forces report
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CAESAR II Statics Training Introduction Axial We can repeat this exercise for axial forces
The analysis can be quickly re-run in cases where a change such as this has been made by using the Batch Run “Double Running Man” icon
This will run the error checker followed immediately by the analysis (providing there are no Errors)
The force should be as follows: We are still using F = Kx,
but we are using the Axial stiffness
The CAESAR II results,
Global Element forces report should verify this:
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CAESAR II Statics Training Introduction The forces calculated such as in the previous example produce bending moments throughout the piping system
Bending moment is produced when a Force is applied at a distance – MB = F x L'Once the bending moment has been calculated,
beam theory is used in order to calculate the stress at this point
rearranges to is the section modulus Z
So this reduces further to
The stresses are calculated using this basic theory and compared to the allowable stresses in the design codes
all of which have evolved separately over time,
thus the way the stresses are calculated for each specific code are slightly different
However,
looking at one of the most common piping codes – B31
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the equations essentially use bending stress M/Z
The equations are a little more complicated than the basic cantilever example for the following reasons:
To address piping systems in 3 dimensions To address areas in a piping system where particular geometry/components,
such as at a branch connection or a bend,
and therefore the likelihood of failure
the stress is increased by a Stress Intensification Factor (SIF) known as i
The design codes contain formulae to calculate these SIFs
Stresses can also be caused by Pressure and Axial Forces The Stresses are categorised into Sustained,
Sustained Stress: This is primary stresses caused by primary loadings such as the weight and pressure of the piping system
Expansion Stress: Expansion stresses are secondary stresses caused by secondary loadings such as the thermal expansion and applied displacements
Occasional Stress: Combines sustained stresses with those produced by an occasional loading such as earthquake of relief valve operation
the allowable can be increased by a scalability factor,
k is usually dependant of the duration or frequency of the occasional load
Theory and Development of Pipe Stress Requirements Basic Stress Concepts Normal Stresses: Normal stresses are those acting in a direction normal to the face of the crystal structure of the material,
and may either be tensile or compressive in nature
normal stresses tend more to be in tension due to the predominant nature of internal pressure as a load case
and may develop from a number of different types of loads
For a piping system these are: Longitudinal Stress: Longitudinal or axial stress is the normal stress acting along the axis of the pipe
This may be caused by an internal force acting axially in the pipe
Where: Longitudinal Stress Internal axial force acting on cross section Cross sectional area of pipe (
) Outer diameter Inner diameter
CAESAR II Statics Training Theory and Development of Pipe Stress Requirements A specific instance of longitudinal stress is that due to internal pressure:
⁄ Design pressure Internal area of pipe ⁄ Replacing the terms for the internal and metal areas of the pipe,
the previous equation may be written as ⁄
⁄ For convenience the longitudinal pressure stress is often conservatively approximated as
Bending Stress: Another component of axial normal stress is bending stress
Bending stress is zero at the neutral axis of the pipe and varies linearly across the cross-section from the maximum compressive outer fibre to the maximum tensile outer fibre
Calculating the stress as linearly proportional to the distance from the neutral axis:
⁄ Where: Bending moment acting on cross section Distance of point of interest from neutral axis of cross section Moment of inertial of cross section
CAESAR II Statics Training Theory and Development of Pipe Stress Requirements The maximum bending stress occurs where c'is highest – the maximum value c'can be is equal to the radius of the pipe
Where: Outer radius of pipe
Section modulus of pipe
Hoop Stress: Hoop stress is another of the normal stresses present in the pipe and is caused by internal pressure
The magnitude of the hoop stress varies through the pipe wall and can be calculated by Lame’s equation as: (
Where: Hoop stress due to pressure Inner radius of pipe Outer Radius of pipe Radial position where stress is being considered The hoop stress can be approximated conservatively for thin-wall cylinders by assuming that the pressure force applied over an arbitrary length of pipe,
l is resisted uniformly by the pipe wall over that same arbitrary length
CAESAR II Statics Training Theory and Development of Pipe Stress Requirements
Radial stress is caused by internal pressure and varies between a stress equal to the internal pressure at the pipe’s inner surface,
and a stress equal the atmospheric pressure at the pipe’s external surface
radial stress is calculated as:
Where Radial stress due to pressure Note that radial stress is zero at the outer radius of the pipe,
where the bending stresses are maximised
For this reason,
this stress component has traditionally been ignored during the stress calculations
Shear Stresses: Shear Stresses are applied in a direction parallel to the face of the plane of the crystal structure of the material and tend to cause adjacent planes of the crystal to slip against each other
For example,
shear stress may be caused by shear forces acting on the cross section
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Where: Maximum shear stress shear force shear form factor
Since this is the opposite of the case with bending stresses and since these Shear stresses are usually small,
shear stresses due to forces are traditionally neglected during pipe stress analysis
⁄ Where: Internal torsional moment acting on cross-section distance of point of interest from torsional centre (intersection of neutral axes) or cross section torsional resistance of cross section
Maximum torsional stress occurs where c'is maximised
Again at the outer radius
⁄ Summing the individual components of the shear stress,
the maximum shear stress acting on the pipe cross section is:
a number of the stress components described above have been neglected for convenience during calculation of pipe stresses
Most piping codes require stresses to be calculated using some form of the following equations: Longitudinal Stress: Shear Stress: Hoop Stress: Example This example calculation illustrates for a 6” nominal diameter,
standard schedule pipe (assuming the piping loads are known): Cross sectional properties Outside diameter Mean thickness Inside diameter 154
CAESAR II Statics Training Theory and Development of Pipe Stress Requirements Piping loads Bending Moment Axial Force Internal Pressure Torsional Moment
Stresses Longitudinal Stress
Bending Component of Longitudinal stress is the radius where the stress is being considered
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CAESAR II Statics Training Theory and Development of Pipe Stress Requirements
pipes are subject to all these types of stresses
Examining a small cube of metal form the most highly stressed point of the pipe wall,
the stresses are distributed as so:
each with a different combination of normal and shear stresses on the faces
there is one orientation of the orthogonal stress axes for which one normal stress is maximised and another for which one normal stress is minimised – in both cases
all shear stress components are zero
the resulting normal components of the stress are termed the principal stresses
there are three of them and they are designated S1 (the maximum),
the sum of the orthogonal stress components is always equal,
The converse of these orientations is that in which the shear stress component is maximised (there is also an orientation in which the shear stress is minimised,
but this is ignored since the magnitudes of the minimum and maximum shear stresses are the same)
this is appropriately called the orientation of maximum shear stress
The maximum shear stress in a three dimensional state of stress is equal to ½ the difference between the largest and smallest of the principal stresses (S1 and S3)
The values of the principal and maximum shear stress can be determined through the use of Mohr’s circle
therefore considering a less complex (i
A Mohr’s circle can be developed by plotting the normal vs
shear stresses for the two known orientations (i
and constructing a circle through the two points
The infinite combinations of normal and shear stresses around the circle represent the combinations present in the infinite number of possible orientations of the local stress axes
A differential element at the outer radius of the pipe (where bending and torsional stresses are maximised and the radial normal and force-induced shear stresses are usually zero) is subject to 2D plane stress and thus the principal stress terms can be computed from the following Mohr’s circle:
CAESAR II Statics Training Theory and Development of Pipe Stress Requirements
The centre of the circle is at
Therefore
the principal stresses S1 and S2 are equal to the centre of the circle,
plus or minus the radius respectively
The principal stresses are calculated as: *(
As noted above,
the maximum shear stress present in any orientation is equal to
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CAESAR II Statics Training Theory and Development of Pipe Stress Requirements Maximum Principal Stress S1 √(
Or from the Mohr’s circle above,
07 + 50
59 = 128
Or from the Mohr’s circle,
07 – 50
59 = 27
Failure Theories The calculated stresses are not much use on their own,
until they are compared to material allowables
therefore calculated stresses must also be related to the uniaxial tensile test
This relationship can be developed by looking at available failure theories
There are three generally accepted failure theories which may be used to predict the onset of yielding in a material:
Octahedral Shear or Von Mises theory Maximum Shear or Tresca Theory Maximum Stress or Rankine Theory
These theories relate failure in an arbitrary 3D stress state in a material to failure in the stress state found in a uniaxial tensile test specimen,
since it is that test that is most commonly used to determine the allowable strength of commonly used materials
release of the load does not result in the specimen returning to its original state
The three failure theories state: Von Mises:
“Failure occurs when the octahedral shear stress in a body is equal to the octahedral shear stress at yield in a uniaxial tension test”
The octahedral shear stress is calculated as: √ In a uniaxial tensile test specimen at the point of yield:
CAESAR II Statics Training Theory and Development of Pipe Stress Requirements Therefore the octahedral shear stress in a uniaxial tensile test specimen at failure is calculated as: √(
√ Therefore under the Von Mises theory: Plastic deformation occurs in a 3-Dimensional stress state whenever the octahedral shear stress
“Failure occurs when the maximum shear stress in a body is equal to the maximum shear stress at yield in a uniaxial tension test
Therefore
Therefore,
under Tresca theory Plastic deformation occurs in a 3-Dimensional stress state whenever the maximum shear stress exceeds
“Failure occurs when the maximum tensile stress in a body is equal to the maximum tensile stress at yield in a uniaxial tension test”
S1 is always the largest of the principal stresses
) In a uniaxial tensile test specimen at the point of yield:
Therefore,
under Rankine theory: Plastic deformation occurs in a 3-Dimensional stress state whenever the maximum shear stress exceeds
Maximum Stress Intensity Criterion Most of the piping codes use a slight modification of the maximum shear stress theory for flexibility related failures
Repeating,
the maximum shear stress theory predicts that failure occurs when the maximum shear stress in a body equals
the maximum shear stress existing at failure during
the maximum shear stress in a body is given by:
For a differential element at the outer surface of the pipe,
the principal stresses were computed earlier as: √(
the maximum shear stress theory states that during the uniaxial tensile test the maximum shear stress at failure is equal to one-half of the yield stress,
so the following requirement is necessary: √
CAESAR II Statics Training Theory and Development of Pipe Stress Requirements Multiplying both sides by 2 creates the stress intensity,
which is an artificial parameter defined simply as twice the maximum shear stress
Therefore the Maximum Stress Intensity Criterion,
as adopted by most piping codes,
dictates the following requirement: √ Note that when calculating only the varying stresses for fatigue evaluation purposes,
the pressure components drop out of the equation
the Maximum Stress Intensity criterion yields an expression very similar to that specified by the B31
shear and hoop stresses were calculated:
Assuming that the yield stress of the pipe material is 206 MPa (30,000 psi) at operating temperature,
and a factor of safely of 2/3 is to be used,
the following calculations must be made: √ √
the pipe would appear to be safely loaded under these conditions
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Code Stress Equations The piping code stress equations are a direct outgrowth of the theoretical and investigative work discussed above,
with specific limitations established by Markl in his 1955 paper
1 and B31
combined the bending and torsional stress terms,
It should be noted that the piping codes calculate exactly the stress intensity (twice the maximum shear stress) only for the expansion stress,
since this load case contains no hoop or radial components and thus becomes an easy calculation
Including hoop and radial stresses (present in sustained loadings only) in the stress intensity calculation makes the calculation much more difficult
it is no longer clear which of the principal stresses is largest and which is the smallest
Additionally the subtraction of S1 – S3 does not produce a simple expression for the stress intensity
As it turns out the inclusion of the pressure term can be simplified by adding only the longitudinal component of the pressure stress directly to the stress intensity produced moment loading only
This provides an equally easy to use equation and sacrifices little as far as accuracy is concerned
Note that most codes allow for the exact expression for pressure stress
the sustained stress calculations
Note also that there are many additional piping codes addressed by CAESAR II
expansion and occasional stresses,
exactly defined as below: Sustained
Where: = sustained stress = intensification factor = resultant moment due to sustained (primary) loads √ = basic allowable material stress at the hot (operating) temperature,
Sh is roughly defined as the minimum of: 1
¼ of the ultimate tensile strength of the material at operating temperature 2
CAESAR II Statics Training Theory and Development of Pipe Stress Requirements Expansion
Where: = expansion stress range = resultant range of moments due to expansion (secondary) loads =√ = Allowable expansion stress = basic allowable material stress at the cold (installation) temperature,
Where: = Occasional Stresses = resultant moment due to occasional loads =√ = occasional load factor = 1
and introduce alternative editing tools which may increase productivity in creating models
We will also investigate and review the results to see what to look for and see how the piping system is behaving,
and how to correct any issues which may arise during the design
The first stage of this exercise is to input the model
you will also have the same isometric printed on a separate hand-out in a larger format
As before with the cantilever example,
the model will be input using the node numbering system
node 10 to node 20 are linked together by an element,
referred to by ‘element 10 to 20’
it can be very useful and is a good idea to mark up the isometric drawing with the intended node number sequence
We will use a slightly different method of inputting the data,
which will allow us to maximise the graphics area during input
notice the “>>” symbol in the top right corner:
CAESAR II Statics Training Pipe 1 Double click this symbol to “tear off” the particular section of the input spread sheet
As the material temperatures and pressures do not change throughout the model we can enter these on the first element and then we will not need them again
The rest of the information we will need to enter for our model can be done via the three windows we have “torn off”
along with the densities and corrosion allowance,
CAESAR II Statics Training Pipe 1
We will begin at the bottom “right” pipe where it is connected to a pump
Enter DZ as
Node 10 is also fixed so we need to specify an anchor
Use the toolbar on the left hand side of the graphics window (default location) to specify a restraint
The Auxiliary Data – Restraints window will appear
Specify that the anchor is at node 10
The auxiliary data window can now be closed
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and should look like the one below:
We could enter this in a number of ways
so must be specified as a “rigid element” with a weight
This can be done either as 3 separate elements (flange – valve – flange),
or as one overall element with the total length and combined weight specified
This can be done manually or by using the valve flange database to obtain the length/weight automatically from CAESAR II’s catalogue,
Select the Valve flange database button and select a gate valve with flanged ends,
The Flange – Valve – Flange check box can be used to split the component into 3 elements ifrequired
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The correct length will be inserted (and the element will continue in the same direction as the previous element)
Also note that the Rigid check box is checked and the rigid weight has been entered with the relevant weight for a 300# gate valve and flanges
(Hover briefly over the Classic piping input where it is docked)
Enter the DZ as
so press the Bend button on the right hand toolbar
If using the classic piping input we could check the bend check box to achieve the same result
alternatively any radius required can simply be typed in here
further data can also be entered such as if the bend is flanged or mitred etc
as there is no following element
This element is a 10”x12” concentric reducer and is 203mm in length
The Reducer Auxiliary will appear and we can specify further data,
entering a nominal size in here will be converted to the actual OD
which will be converted to the actual values
note the node numbers in the image:
CAESAR II Statics Training Pipe 1 We can now take advantage of the fact that the model is symmetrical and use the functions in CAESAR II to mirror the piping to create the opposite leg
Use the Select group function to activate the graphical selection mode and draw a window around the model
All elements will turn yellow to indicate that they are currently selected
If we increase the node numbers by 70,
so the piping will not actually be connected
This can easily be fixed by chaging node 140 (the centre of the tee on the second leg) to become node 70 (the node at the centre of the tee on the first leg)
This will connect up the piping at the common node,
but as already stated there is no common node so CAESAR II does not know where to place the pipe
As such it locates it at the origin
The resulting model looks like the following
There are various ways of doing this – either double click in the graphics area,
or user the navigation buttons to navigate to the correct element (as this is the last element the end button will quickly take you to the correct element)
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CAESAR II Statics Training Pipe 1 The Edit Node numbers window should now read 13 to 140 and the element will be highlighted in the model
Simply change the “To” node from 140 to 70
We can now complete the model by adding the vertical leg and connection to the vessel
Skip to the last element
This can be done by again using the Last Element navigation button or using the Ctrl + End buttons on the keyboard
Click “Continue” to move to the next element need to change this to 70 to 140
The node numbers will default to 70 to 80
CAESAR II Statics Training Pipe 1 This element is the vertical leg,
This also leads into a bend so select the Bend icon as well
so we will place an anchor at this point
Click the retsraint button and specify an anchor at node 150 Notice in the isometric that at the vessel connection,
there are DY and DZ displacements
Select the Displacements button and enter in the required values 3mm in DZ and 12mm in DY
We must correct the errors before we can analyse the model
The warnings may be acceptable but we should check to confirm that the input is as intended
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CAESAR II Statics Training Pipe 1 So our error is mentioning that we have both an anchor and displacements speciified at node 150
but the displacements move the same point
Remove the anchor and edit the displacements
Double click the error message to go straight to the area of concern
Now click the restraints button to remove restraints
so now our node is fixed in all directions,
except for DY and DZ where the relevant displacements are applied
Re run the error checker and investigate the warnings
The second two warnings are regarding the reducer alpha angle which is not specified
The first warning is stating that there is a geom
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