ISOPLUS
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
Isoplus® Static Calculation<br />
Program Installation<br />
This program needs at least the following configuration to work properly:<br />
Hardware configuration: PC 486 66Mhz with 8 MBytes of RAM, 3 MBytes of free disk space,<br />
SVGA video card.<br />
Software configuration: Windows 95 / NT.<br />
To install the program, insert the disk number 1 in the floppy disk drive; within Windows, select<br />
'Execute/Run'. A blank prompt will appear asking the command line; write a:\setup.exe and then press<br />
enter on the keyboard. The program will automatically create the icons and the group in the program<br />
menu list.<br />
Please note: this software is provided with two languages, German and English, and the images found in<br />
this manual are taken from the English version only. The contents are the same for both languages.<br />
Starting Isoplus® Static Calculation<br />
The first window you will see is the following:<br />
It informs the user that upon the field experience some limits should be observed during the pipe design,<br />
the first in the dilatation and the second in the deflection. So when using compressible dilatation zones<br />
with PUR or PE cushions the suggested limits are the following, which depend themselves upon the<br />
diameter of the pipes involved in the calculation: for a pipe between DN 20 and 200 dilatation and<br />
deflection should not exceed 40.0 mm; for a pipe between DN 225 and 300 the limit is set to 50.0 mm<br />
and finally over DN 300 the limits are 60.0 mm. With a deflection greater than 65.0 mm the use of a<br />
stonework trench is recommended. These limits are, however, changeable every time and they will
emain in the program memory: it is possible to change every limit simply inserting the new value in the<br />
corresponding text field. Every time these limits will be exceeded an appropriate warning message will<br />
be displayed (see after). It is also possible to disable all the warnings simply checking the "Ignore these<br />
limits" button. Pressing the OK button will let you to proceed with the next window:<br />
With this window you will set the default ground type that will be used in the next calculations. Please<br />
note that the you will be able to change the ground type anytime during the work. After having selected<br />
the default ground type (and having pressed the button) the main program window will be displayed.
The selectable menus are the following<br />
Exit:<br />
the exit menu lets you close the application.<br />
Language: With this menu it is possible to switch between german and english language. All the<br />
changes are simultaneous and will affect also the output (i.e.: the printed sheets will be in the selected<br />
language.) The selected language will be maintained in the next program run.<br />
View detailed static calculations: a windows with in-depth static calculations will be showed.<br />
Normally this window is hidden and is detailed in the "Further Calculations Window" section.
Print: the print menu lets you examine, print and export the data sheet. The first time you push<br />
this button, a window with all the data will be displayed. The window shows roughly the data as they<br />
will be printed on the paper sheet. In the left-upperside window corner another 'Print' menu will be<br />
prompted: clicking on this menu another window will appear (the contents reflect the window's<br />
language):<br />
Using this window you'll be able to select how many copies, the kind of printer you are going to use and<br />
so on.<br />
Compensations: four kind of compensations are actually available:<br />
Selecting L, Z or U compensation simply change the data in the compensation window (see below);<br />
selecting the axial compensation will force the program to take the data set out in the main window<br />
'Pipes laying with L-Z-U compensation' and to transfer them in the 'Axial Compensation' window. So<br />
switching from L-Z-U compensation to axial compensation will take the main values present in the L-<br />
Z-U window (Norm, Stress, DN, Steel Type, Design Pressure and Temperature and so on) and will<br />
use them for the calculations in the axial window. Switching from the axial window back to the L-Z-<br />
U the values will be maintained.
Settings: with this menu, it will be possible to select the 'Limits' window<br />
This window is responsible for setting/resetting the dilatation and/or deflection limits for different pipe<br />
dimensions. When the 'Ignore this limits' flag is set, the program won't inform the user about the<br />
limits exceeding.<br />
There are other windows on the screen, depending from which kind of compensation is used. In the<br />
following sections each window type will be discussed. When a L-Z-U compensation is used, on the<br />
screen the following windows are visible:<br />
Header Data:<br />
data sheet general informations<br />
Ground Samples: basis settings for different kinds of ground<br />
T-pieces: calculates the dilatation values for a side derivation (*)<br />
Further Calculations: global static values in the pipe - normally hidden<br />
Expansion/Deflection: find the pipe lenghts for a specified expansion or deflection (*)<br />
L/Z/U compensator: displays the values for the specified compensator type (*)<br />
Main comp. window: set the environmental variables for L/Z/U compensation<br />
(*) These windows are not visible when axial compensation is used<br />
In the next section the detailed explanation for the single windows will follow.
The Header Data Window<br />
The L-Z-U or Axial compensation windows share a common part which defines the data sheet general<br />
informations:<br />
These informations (Customer, Order, Plan n° and so on) will be always printed on the top of the data<br />
sheet. It isn't compulsory to fill all the data: blank fields won't be printed.<br />
The Ground Samples Window<br />
This window is simply a list of different materials, and it is possible to insert the correspondent values in<br />
the main window by clicking anywhere in the correspondent row.<br />
Clicking, for example, in the fourth row will set in the main window Kd = 0.7, re = 1800 and m = 0.45.<br />
The last entry in the list is the "standard ground setting", which is the default one for all the calculations.
The T-Pieces Dilatation Window<br />
It is possible to calculate the T-pieces dilatation by putting the distance (in m.) from the beginning of the<br />
selected section (one or two, pushing the grayed button) and choosing the T-piece DN.<br />
To calculate the necessary cushion and the piece dilatation, the program will work this way: first, it will<br />
set the other section length to 0.0 m.; then it calculates the T-piece distance from the pipe's middle<br />
section (Neutral Point) and will use that length doubled for all the successive calculations.<br />
This length will give thus the T-piece dilatation: please note that this dilatation will be calculated using<br />
the main pipe's DN. To calculate the branch arm cushion the program will use the T-piece DN with the<br />
found dilatation giving thus the closest approximation possible.<br />
Thus:<br />
ls1 m total length section 1<br />
tls1 m T-piece position from the beginning of sect. 1<br />
dl1 mm dilatation of sect. 1<br />
tdl help 1 mm dilatation calc for help<br />
tdl1 mm dilatation at T-piece position<br />
If tls1 > ls1/2 then tls1 = ls1 – tls1; that means we always have to take the shortest way from one end to<br />
the T-piece:<br />
Example:<br />
ls1 = 300m<br />
if tls1 = 25m then we don’t make any calculation, else if tls1 = 270m let tls1= 300 – 270 = 30m, so we<br />
calculate with 30m. Please note that tls1 never can be negative or longer than ls1, that always is<br />
incorrect.<br />
Dilatation calc.:<br />
Dilatation for the total length<br />
DN100<br />
90°C<br />
10°C<br />
ls1 = 300mm<br />
dl1 = 25.909mm
Dilatation for a fictitious length of (2* tls1)<br />
DN100<br />
90°C<br />
10°C<br />
tls1 = 25m (dilatation of 50m)<br />
tdl help 1 = 18.343mm<br />
Dilatation at T-piece<br />
tdl1 = dl1 - tdl help 1 = 25.909 – 18.343 = 7.566mm the dilatation at the T-piece is 7.566mm<br />
The 'Further Calculations' Window<br />
The L-Z-U or Axial compensation windows share another window, the 'Further Calculations' window in<br />
which there is an entire set of data concerning dilatations and stresses in the two pipe sections:<br />
The meaning of these variables will be explained in the next pages. It is important to notice that every<br />
change in the main window will force the recalculation of the entire data sheet; hence, the values present<br />
on the screen are always the most up-to-date ones. Please note that normally this window is hidden and<br />
will be displayed only by selecting the entry "view detailed static calculation" in the "Program" menu.
The L-Z-U Compensation Window<br />
This window presents all the environmental variables the user can change:<br />
These are the variables' meanings and their possible range of values:<br />
Pipe Norm (P Norm ):<br />
It is the pipes' set from the list ranging from 1 to 3.<br />
Default: 1<br />
Pre Stress (P Stress )<br />
With this box it is possible to force the pipes' pre-stressing: this affects the laying temperature as<br />
explained later.<br />
Default: No<br />
Ground Cover ( h o )<br />
It is the depth of soil covering, ranging from 0.60 to 2.50 m.<br />
Default: 1.0 m.<br />
Steel Type ( S Type )<br />
The pipe steel types implemented in this version are: steel 37, steel 44 and steel 52.<br />
Default: Steel 37
Design Temperature (T d )<br />
The design temperature (or working temperature) ranges from 0°C to 150°C with 5°C step.<br />
Default: 90°C<br />
Alternative Temperature (T alt )<br />
It is possible to define the value for the laying temperature (T l ) by changing the Talt value. The<br />
installation could be set with or without prestressing: this affects the laying temperature in this way:<br />
Without pre-stressing: T l = T alt or, if this one is 0, T l = 10 °C<br />
With pre-stressing: T l = T alt or, if this one is 0, T l = (T d +T min )/2+5 °C<br />
Default: 20°C<br />
Minimum Temperature ( T min )<br />
This is the ground temperature, ranging from 0°C to 20°C with a 5°C step.<br />
Default: 10°C<br />
Design Pressure (P d )<br />
This is the maximum working pressure, ranging from 0 bar to 40 bar.<br />
Default: 14 bar<br />
DN<br />
The pipe's DN ranges from 20 to 800 as written in the standard Isoplus list.<br />
Default: 100<br />
r e<br />
It is the ground density ranging from 1700 to 2200 kg/m³ with a 50 kg/m³ step in the possible values.<br />
Default: 1900 kg/m³<br />
K d<br />
This is the compressive pressure coefficient whom values range from 0.4 to 0.95 with a 0.05 step.<br />
Default: 0.75<br />
m<br />
It is the friction factor, with values ranging from 0.2 to 0.95 with a 0.05 step in the values.<br />
Default: 0.4<br />
Please note that, as explained before, r e , K d and m are function of the first ground selection. The<br />
above values are true on ly if "Standard Ground" was selected in the "Select ground types" window. (Or<br />
enter was pressed)<br />
Deflection Angle (d)<br />
The deflection angle affects the maximum deflection for the pipe sections, and its possible values range<br />
from 5° to 90° with a 5° step.<br />
Default: 90°
Length of the Sections (L s1 and L s2 )<br />
This value represents the length of the two pipe sections (1 and 2): the value is free, but it cannot be<br />
bigger than the maximum installation length: in this case the lenght(s) in excess will be displayed in red<br />
and a question mark will appear on the left of the text box. If the user pushes the question mark, there<br />
will be the possibility to enter the axial compensation or to correct the lenghts.<br />
Default: 80.0 m for Section 1 and 20.0 m for Section 2<br />
Wall thickness of steel pipe (wt)<br />
It is possible to change the default value for the pipe ' s wall thickness. This value will be reset to the<br />
default every time the user changes the pipe's DN.<br />
Permissible Stress (s perm )<br />
The permissible reference stress for the pipe is based upon the steel type employed, and if a greater<br />
safety factor is wanted in the net design, it is possibe to change this value. If the user presses the 'R'<br />
button on the right side of the text cell, the value will be reset to the default.<br />
Algorithms used for the L-Z-U Compensation<br />
The following section explains which formulas where used for the L-Z-U calculations.<br />
Given:<br />
de = external diameter of steel pipe [mm]<br />
DE = external diameter of jacket pipe [mm]<br />
wt = wall thickness of steel pipe [mm]<br />
se = wall thickness of jacket pipe [mm]<br />
r e = ground density [kg/m³]<br />
g = acceleration due to gravity [m/s²]<br />
h o = depth of soil covering<br />
K d = compressive pressure coefficient<br />
m = friction factor<br />
P v = r e * g * h o vertical ground press. on the superior / inferior pipe surface<br />
P h = K d * r e * g * (h o +DE/2) horizontal ground pression on the lateral pipe surface<br />
Fixed as:<br />
D list = de -2*wt internal steel pipe diameter [mm]<br />
A list = D list ² * p/4 internal steel pipe area [mm²]<br />
As = de²*p/4-Alist overall steel pipe cross sectional area [mm²]<br />
D lim = DE-2*se internal jacket pipe diameter [mm]<br />
A lim = D lim ²*p/4-de²*p/4 overall internal jacket pipe cross sectional area [mm²]<br />
Am = DE²*p/4-D lim ²*p/4 overall external jacket pipe cross sectional area [mm²]<br />
Being:<br />
r w<br />
= water density [kg/m³]
st<br />
r m<br />
r lim<br />
= steel density [kg/m³]<br />
= external jacket pipe density [kg/m³]<br />
= internal jacket pipe density [kg/m³]<br />
The overall pipe weight per meter is:<br />
mv = A list *r w +As*r st +A lim *r lim +A m *r m [kg/m]<br />
And the frictional force is derived from:<br />
F c = m*g* [DE²*p/4*K d * r e + mv] frictional force due to the pipe<br />
F h = m*g* [DE*p/2* r e *(1+K d )] frictional factor per ground meter<br />
So the frictional force per pipe meter is:<br />
Fr' = F c + h o *F h frictional force per pipe meter [N/m]<br />
Other variables of interest are the following:<br />
T d = design or operating temperature [°C]<br />
T l = laying temperature [°C]<br />
T alt = alternative temperature, which defines Tl (see after) [°C]<br />
T min = the pipes ' minimum temperature (ground temp.) [°C]<br />
P d<br />
= design water pressure [bar]<br />
The permissible reference stress for the pipe is based upon the steel type employed, and the following<br />
formula uses a safety factor of 1.225 as written in the Tab. A.1. for the DIN 1626 for steels 37,44 and<br />
52:<br />
Steel 37: If Td
where DT is the max abs. value between ( T d - T l ) and ( T l - T min )<br />
The average peripheral stress due to the internal pressure is:<br />
s up = (de/wt-1)*P d /2 = (D list *P d )/(2*wt) [N/mm²]<br />
While the longitudenal stress due to internal pressure is:<br />
s lp = A list *P d /As [N/mm²]<br />
The internal pressure generates an elastic radial dilatation in the pipe and a similar contraction in the<br />
longitudenal sense (e) but opposite in sign. The real dilatation is:<br />
e = (0.5-n)*s up /E<br />
n = steel trasversal contraction factor (0.3)<br />
The length of the sliding section at repeating temperature changes is:<br />
I ob = (a*E*(T d -T min )+t)*As/Fr' [m]<br />
t = s lp -0.3*s up [N/mm²]<br />
And the change of the length of the sliding zone due to the differential temperature is:<br />
DI ob = (a*(T d -T min )+t/E)*I ob /2<br />
[mm]<br />
When expansion is taken up in natural expansion bends, the longitudenal stress at the free end of the<br />
pipe is 0.5*s up ; hence, the length of the sliding section at T max is:<br />
I ow = (a*E*(T d -T l )+t)*As/Fr' [m]<br />
Consequently the change of the length of the sliding zone at T max is:<br />
DI ow = (a*(T d -T l )+t/E)*I ow /2<br />
[mm]<br />
When the pipe is cooled from T l to T min under atmospheric pressure, the length (and the change in<br />
lenght) of the sliding section at T min is:<br />
I ok = a*E*(T l -T min )*As/*Fr' [m]<br />
DI ok = -a*(T l -T min )*I ok /2<br />
[mm]<br />
For the following formulas it is important to consider Ix, the semi-length of the pipe section 1 (I 1 ) and<br />
section 2 (I 2 ) to the natural reference point: the object is to calculate the following:<br />
DI w = change of length at T max [mm]<br />
DI b = change of length due to the differential temperature [mm]<br />
DI k = change of length at T min [mm]<br />
s lw = longitudenal stress at T max [N/mm²]<br />
s lk = longitudenal stress at T min [N/mm²]<br />
There are two main cases and three sub-cases:<br />
1) the length of the sliding zone at T max (I ow ) is greater than the length of the sliding section at<br />
repeating temperature changes (I ob ):
a) the semi-length of the section (Ix) is greater than I ow and I ob :<br />
DI b = DI ob<br />
DI w = DI ow<br />
DI k = DI w - DI b<br />
s lw = -(I ow *Fr'/As-s lp )<br />
s lk = I ob *Fr'/As<br />
b) the semi-length of the section (Ix) is smaller than I ow and I ob :<br />
DI b = DI ob * Ix/I ob *(2-Ix/I ob )<br />
DI w = DI ow * Ix/I ow *(2-Ix/I ow )<br />
DI k = DI w - DI b<br />
s lw = -(Ix*Fr'/As-s lp )<br />
s lk = Ix*Fr'/As<br />
c) the semi-length of the section (Ix) is smaller than I ow but greater than I ob :<br />
DI b = DI ob<br />
DI w = DI ow * Ix/I ow *(2-Ix/I ow )<br />
DI k = DI w - DI b<br />
s lw = -(Ix*Fr'/As-s lp )<br />
s lk = I ob *Fr'/As<br />
2) the length of the sliding zone at Tmax (I ow ) is smaller than the length of the sliding section at<br />
repeating temperature changes (I ob ):<br />
a) the semi-length of the section (Ix) is greater than I ok and I ob :<br />
DI b = DI ob<br />
DI k = DI ok<br />
DI w = DI b +DI k<br />
s lw = -(I ob *Fr'/As-s lp )<br />
s lk = I ok *Fr'/As<br />
b) the semi-length of the section (Ix) is smaller than I ok and I ob :<br />
DI b = DI ob * Ix/I ob *(2-Ix/I ob )<br />
DI k = DI ok * Ix/I ok *(2-Ix/I ok )<br />
DI w = DI b + DI k<br />
s lw = -(Ix*Fr'/As-s lp )<br />
s lk = Ix*Fr'/As<br />
c) the semi-length of the section (Ix) is smaller than I ok but greater than I ob :<br />
DI b = DI ob<br />
DI k = DI ok * Ix/I ok *(2-Ix/I ok )<br />
DI w = DI b + DI k
s lw = -(I ob *Fr'/As-s lp )<br />
s lk = Ix*Fr'/As<br />
The expansion Dlx of the section is equal to the greater value between the change of length at T max<br />
(DI w ) and the change of length at T min (DI k ).<br />
The permissible longitudenal stress is based upon s st and the peripheral stress s up :<br />
_____________<br />
s lzul = s up - Ö s st ² - 0.75*s up ² [N/mm²]<br />
The semi permissible length without prestressing is then:<br />
I lzul = (s lp - s lzul )*As/Fr' [m]<br />
If I lzul is greater than the length of the sliding zone at T max (I ow ) or (s lw and s lk ) < s lzul the<br />
permissible installation length is unlimited; else it corresponds to 2*I lzul .<br />
The correspondent reference stress for the section is:<br />
_________________<br />
s v = Ö s lw ² + s up ² - s lw * s up [N/mm²]<br />
And the max deflection for the pipe sections is based upon the deflection angle d °:<br />
W 1 = Dl 1 /sind + Dl 2 / tand [mm]<br />
W 2 = Dl 2 /sind + Dl 1 / tand [mm]<br />
For the cushion thickness we have to consider the deflection angle and the expansion of both sections:<br />
__________________<br />
Wd = Ö (Dl 1 /sind)²+(Dl 2 / tand)²<br />
The cushion thickness is calculated is calculated as follows:<br />
If W 1 is greater than Wd and W 2 , the cushion is proportional to W 1 ; if W 2 is greater than Wd and<br />
W 1 , the cushion is proportional to W 2 , else the cushion is proportional to Wd. The cushion cannot be<br />
greater than 150 mm. Let it be W X the quantity derived from the aforementioned calculation (being it,<br />
W 1 , W 2 or Wd ):<br />
If it is W X
The 'Set the Expansion or Deflection Amount' window<br />
This window is displayed under the main one and his purpose is to help the net design trying to find the<br />
best section lengths with a given expansion or deflection. Actually it is possible to enter the wanted<br />
deflection (or deflection) for a certain section and after a while the program will display the best value<br />
for the corresponding section. Clicking on the "Insert these Values" button will force the program to<br />
use the found values in the main window. This is also useful when dealing with deflection or deflection<br />
limits: whenever limits are used (unckecking the "Ignore these limits" square in the 'Set limits' window)<br />
the program will display a small button with a triangle inset everytime deflection or deflection for a<br />
section exceeds a certain pipe limit. These limits are set within the 'Set limits' window which appears<br />
everytime the program is run or by clicking the 'settings' menu in the main window. When limits are<br />
surpassed the main window will look as below:<br />
In this case both dilatation and deflection exceed the limits: clicking on the corresponding button the<br />
following request will be displayed:<br />
Clicking on the 'Yes' button will force the program to accept the suggested values for the dilatation. The<br />
same is for the deflection:
Z - Compensation<br />
When Z-Compensation is used, the following window will appear:<br />
The length of the sliding section at T max is based upon an average value (T max -T min )/2 :<br />
I ow = (a*E*(T d -T min )/2+t)*As/Fr' [m]<br />
Consequently the change of the length of the sliding zone at T max is:<br />
DI ow = (a*(T d -T min )/2+t/E)*I ow /2<br />
And DI w , change of length at T max ,<br />
is:<br />
[mm]<br />
DI w = DI ow * Ix/I ow *(2-Ix/I ow ) if the semi-length of the section (Ix) is less than I ow<br />
DI w = DI ow<br />
if the semi-length of the section (Ix) is greater than or equal to<br />
I ow<br />
The deflection is based upon DI w , as follows:<br />
W L1 = DI w1 /sind + DI w2 / tand<br />
W L2 = DI w2 /sind + DI w1 / tand<br />
[mm]<br />
[mm]<br />
Take note that the W L1 and W L2 values are not W 1 and W 2 , but they represent the maximum<br />
deflection possible, that is, the deflection coming from the greatest DT possible, T max -T min . We’ll use<br />
the W L1 and W L2 values instead of the W 1 and W 2 values.<br />
The expansion leg length DZ 1 for the compensator is function of the deflection: DZ 1 = ¦(W 1 +W 2 );<br />
hence DZ 2 is calculated as follows:<br />
DZ 2<br />
_______<br />
= 44.0 * de * W<br />
Where:<br />
de = external diameter of steel pipe [mm]
W<br />
= max between the W 1 and W 2 values<br />
The tests showed that the better approximation of the "real" world is given using the "stress"<br />
calculation, which involves the evaluation of values W L1 and W L2 . Thus for all the compensations the<br />
"stress" option is used, but for the clarity of calculations also the "normal" way is presented.<br />
L - Compensation<br />
When L-Compensation is used, the following window will appear:<br />
The length of the sliding section at T max is based upon an average value (T max -T min )/2 :<br />
I ow = (a*E*(T d -T min )/2+t)*As/Fr' [m]<br />
Consequently the change of the length of the sliding zone at T max is:<br />
DI ow = (a*(T d -T min )/2+t/E)*I ow /2<br />
And DI w , change of length at T max ,<br />
is:<br />
[mm]<br />
DI w = DI ow * Ix/I ow *(2-Ix/I ow ) if the semi-length of the section (Ix) is less than I ow<br />
DI w = DI ow<br />
if the semi-length of the section (Ix) is greater than or equal to<br />
I ow<br />
The deflection is based upon DI w , as follows:<br />
W L1 = DI w1 /sind + DI w2 / tand<br />
W L2 = DI w2 /sind + DI w1 / tand<br />
[mm]<br />
[mm]<br />
The expansion leg length DL x for the compensator is function of the deflection: DL x = ¦(W x ).<br />
_______<br />
DL x = 55.0 * de * W x
Where:<br />
de = external diameter of steel pipe [mm]<br />
W x = W 1 and W 2<br />
U - Compensation<br />
When U-Compensation is used, the following window will appear:<br />
The length of the sliding section at T max is based upon an average value (T max -T min )/2 :<br />
I ow = (a*E*(T d -T min )/2+t)*As/Fr' [m]<br />
Consequently the change of the length of the sliding zone at T max is:<br />
DI ow = (a*(T d -T min )/2+t/E)*I ow /2<br />
And DI w , change of length at T max ,<br />
is:<br />
[mm]<br />
DI w = DI ow * Ix/I ow *(2-Ix/I ow ) if the semi-length of the section (Ix) is less than I ow<br />
DI w = DI ow<br />
if the semi-length of the section (Ix) is greater than or equal to<br />
I ow<br />
The deflection is based upon DI w , as follows:<br />
W L1 = DI w1 /sind + DI w2 / tand<br />
W L2 = DI w2 /sind + DI w1 / tand<br />
[mm]<br />
[mm]<br />
Take note that the W L1 and W L2 values are not W 1 and W 2 , but they represent the maximum<br />
deflection possible, that is, the deflection coming from the greatest DT possible, T max -T min . We will<br />
use the W L1 and W L2 values instead of the W 1 and W 2 values: i.e. the program will show the resulting<br />
dilatation zone length for both the dilatation and deflection components.
The crown length DU 2 is equal to twice the leg length of the standard 1x1 bends, while the lengths DU 3<br />
have relatively little effect on the permissible amount of expansion; so the Dilatation Zone Length DU 1<br />
is function of the deflection: DU 1 = ¦(W 1 +W 2 ), length DU 3 is calculated as follows:<br />
_______<br />
DU 3 = 31.0 * de * W 2<br />
where de = external diameter of steel pipe [mm]
The Axial Compensation Window<br />
When the axial compensation is used only these windows are used: the 'Further Calculation' window, the<br />
'Axial Compensator' window and the 'Select Ground Type' window.<br />
All the controls are the same as in the L-Z-U window, with the exception of the pre stress box which is<br />
not used. The alternative temperature is now effectively the laying temperature wanted and there is the<br />
pre heating temperature box in which the pre heating temperature is calculated. It is also possible to<br />
change the wall thickness and the permissible reference stress. The main changes are in the lower part of<br />
the window: in the total line length box it is possible to enter the installation length. The program will<br />
calculate (as detailed below) the maximum sections' lenghts, then it will reduce the Section 2 until the<br />
total line length is reached. For example, in the page before a total line length of 800 m. was entered.<br />
The program defines the maximum values for the sections, S 1max = Section B + Section A = 103.16 m,<br />
while S 2max = 2 * Section A = 99.32 m.<br />
The Ideal Lengths of Section A and B represent the maximum extent possible for these single sections<br />
in an ideal condition ( with a pipe of infinite length), meanwhile the Real Length is the one in a pipe of<br />
finite extent (in this example, the 1000 m. in the total line length box).<br />
The pipes will be placed as for the following figure:
So for a total line lengh of 1000 m., we will have:<br />
Sect 1 (103.16 m) + 8 * Sect 2 (99.32) + Sect 1 (103.16 m) = 1000.88 m<br />
Please note that all the values for dilatation, reference stress, etc are referred to the real sections<br />
length, not to the ideal ones.<br />
section 1<br />
section 2<br />
<br />
B<br />
A A A A<br />
h<br />
<br />
p<br />
<br />
preheat<br />
Kompensator<br />
B<br />
hot<br />
zul<br />
<br />
p<br />
<br />
cold<br />
zul<br />
<br />
L B<br />
L<br />
A<br />
To calculate the dilatation, stresses and section lengths the first step is the mean permissible stress:<br />
s st mean = (s st (T ins ) + s st (T max ))/2<br />
Where:<br />
s st mean = mean permissible stress [N/mm²]<br />
s st (T ins ) = permissible stress at T ins [N/mm²]<br />
s st (T max )<br />
= permissible stress at T max [N/mm²]<br />
Secondly the preheating temperature (T pre ) is the lower between:
T pre = T ins + s st mean /(a*E) (rounded down) and<br />
T pre = (T max )* 0.9<br />
Where:<br />
T pre = preheating temperature [°C]<br />
T ins = temperature at installation [°C]<br />
s st mean = mean permissible stress [N/mm²]<br />
Formula for section B<br />
L b =( s st mean * As)/Fr´<br />
Length of Section B [m]<br />
Where:<br />
As = de²*p/4-Alist Overall steel pipe cross sectional area [mm²]<br />
Fr' = F c + h o *F h Frictional force per pipe meter [N/m]<br />
s st mean<br />
Formula for section A<br />
Mean permissible stress [N/mm²]<br />
L a =( 2 * s st mean - a * E * ( T max - T ins ))* As/F<br />
Length of Section A [m]<br />
Where:<br />
As = de²*p/4-Alist Overall steel pipe cross sectional area [mm²]<br />
Fr' = F c + h o *F h Frictional force per pipe meter [N/m]<br />
a = (11.4 + Td/129)* 10 -6 Expansion coefficient [1/°C]<br />
E = (21.4 - Td/175)* 10 +4 Young's modulus [N/mm²]<br />
s st mean<br />
mean permissible stress [N/mm²]<br />
And then the correspondent max length for the sections A and B is<br />
I 1 = L b + L a [m]<br />
I 2 = L a + L a [m]<br />
At this point, all the calculations are made at design temperature Td with a laying temperature T pre (i.e.<br />
all the calculations are made with T l = T pre ): as a result we'll find the dilatations DL 1 and DL 2 . When<br />
axial compensation is used, the sand on the B-side will compensate for a »20% of the total expansion:<br />
the residual 80% will be reduced by the axial compensator, so that the expansion joint range will be:<br />
DZ 1 = DL 1 * .8 + DL 2 + DL 2 For the first section<br />
DZ 2 = DL 2 + DL 2 For the other sections
Index<br />
Isoplus® Static Calculation ................................................................................................................... 1<br />
Program Installation ........................................................................................................................... 1<br />
Starting Isoplus® Static Calculation ................................................................................................... 1<br />
The Header Data Window .................................................................................................................. 6<br />
The Ground Samples Window ............................................................................................................ 6<br />
The T-Pieces Dilatation Window ........................................................................................................ 7<br />
The 'Further Calculations' Window ..................................................................................................... 8<br />
The L-Z-U Compensation Window .................................................................................................... 9<br />
Algorithms used for the L-Z-U Compensation .................................................................................. 11<br />
The 'Set the Expansion or Deflection Amount' window..................................................................... 16<br />
Z - Compensation ............................................................................................................................. 17<br />
L - Compensation ............................................................................................................................. 18<br />
U - Compensation ............................................................................................................................ 19<br />
The Axial Compensation Window .................................................................................................... 21<br />
Index ................................................................................................................................................... 24