ISOPLUS

Isoplus® Static Calculation
Program Installation
This program needs at least the following configuration to work properly:
Hardware configuration: PC 486 66Mhz with 8 MBytes of RAM, 3 MBytes of free disk space,
SVGA video card.
Software configuration: Windows 95 / NT.
To install the program, insert the disk number 1 in the floppy disk drive; within Windows, select
'Execute/Run'. A blank prompt will appear asking the command line; write a:\setup.exe and then press
enter on the keyboard. The program will automatically create the icons and the group in the program
menu list.
Please note: this software is provided with two languages, German and English, and the images found in
this manual are taken from the English version only. The contents are the same for both languages.
Starting Isoplus® Static Calculation
The first window you will see is the following:
It informs the user that upon the field experience some limits should be observed during the pipe design,
the first in the dilatation and the second in the deflection. So when using compressible dilatation zones
with PUR or PE cushions the suggested limits are the following, which depend themselves upon the
diameter of the pipes involved in the calculation: for a pipe between DN 20 and 200 dilatation and
deflection should not exceed 40.0 mm; for a pipe between DN 225 and 300 the limit is set to 50.0 mm
and finally over DN 300 the limits are 60.0 mm. With a deflection greater than 65.0 mm the use of a
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
corresponding text field. Every time these limits will be exceeded an appropriate warning message will
be displayed (see after). It is also possible to disable all the warnings simply checking the "Ignore these
limits" button. Pressing the OK button will let you to proceed with the next window:
With this window you will set the default ground type that will be used in the next calculations. Please
note that the you will be able to change the ground type anytime during the work. After having selected
the default ground type (and having pressed the button) the main program window will be displayed.

The selectable menus are the following
Exit:
the exit menu lets you close the application.
Language: With this menu it is possible to switch between german and english language. All the
changes are simultaneous and will affect also the output (i.e.: the printed sheets will be in the selected
language.) The selected language will be maintained in the next program run.
View detailed static calculations: a windows with in-depth static calculations will be showed.
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
this button, a window with all the data will be displayed. The window shows roughly the data as they
will be printed on the paper sheet. In the left-upperside window corner another 'Print' menu will be
prompted: clicking on this menu another window will appear (the contents reflect the window's
language):
Using this window you'll be able to select how many copies, the kind of printer you are going to use and
so on.
Compensations: four kind of compensations are actually available:
Selecting L, Z or U compensation simply change the data in the compensation window (see below);
selecting the axial compensation will force the program to take the data set out in the main window
'Pipes laying with L-Z-U compensation' and to transfer them in the 'Axial Compensation' window. So
switching from L-Z-U compensation to axial compensation will take the main values present in the L-
Z-U window (Norm, Stress, DN, Steel Type, Design Pressure and Temperature and so on) and will
use them for the calculations in the axial window. Switching from the axial window back to the L-Z-
U the values will be maintained.

Settings: with this menu, it will be possible to select the 'Limits' window
This window is responsible for setting/resetting the dilatation and/or deflection limits for different pipe
dimensions. When the 'Ignore this limits' flag is set, the program won't inform the user about the
limits exceeding.
There are other windows on the screen, depending from which kind of compensation is used. In the
following sections each window type will be discussed. When a L-Z-U compensation is used, on the
screen the following windows are visible:
Header Data:
data sheet general informations
Ground Samples: basis settings for different kinds of ground
T-pieces: calculates the dilatation values for a side derivation (*)
Further Calculations: global static values in the pipe - normally hidden
Expansion/Deflection: find the pipe lenghts for a specified expansion or deflection (*)
L/Z/U compensator: displays the values for the specified compensator type (*)
Main comp. window: set the environmental variables for L/Z/U compensation
(*) These windows are not visible when axial compensation is used
In the next section the detailed explanation for the single windows will follow.

The Header Data Window
The L-Z-U or Axial compensation windows share a common part which defines the data sheet general
informations:
These informations (Customer, Order, Plan n° and so on) will be always printed on the top of the data
sheet. It isn't compulsory to fill all the data: blank fields won't be printed.
The Ground Samples Window
This window is simply a list of different materials, and it is possible to insert the correspondent values in
the main window by clicking anywhere in the correspondent row.
Clicking, for example, in the fourth row will set in the main window Kd = 0.7, re = 1800 and m = 0.45.
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
It is possible to calculate the T-pieces dilatation by putting the distance (in m.) from the beginning of the
selected section (one or two, pushing the grayed button) and choosing the T-piece DN.
To calculate the necessary cushion and the piece dilatation, the program will work this way: first, it will
set the other section length to 0.0 m.; then it calculates the T-piece distance from the pipe's middle
section (Neutral Point) and will use that length doubled for all the successive calculations.
This length will give thus the T-piece dilatation: please note that this dilatation will be calculated using
the main pipe's DN. To calculate the branch arm cushion the program will use the T-piece DN with the
found dilatation giving thus the closest approximation possible.
Thus:
ls1 m total length section 1
tls1 m T-piece position from the beginning of sect. 1
dl1 mm dilatation of sect. 1
tdl help 1 mm dilatation calc for help
tdl1 mm dilatation at T-piece position
If tls1 > ls1/2 then tls1 = ls1 – tls1; that means we always have to take the shortest way from one end to
the T-piece:
Example:
ls1 = 300m
if tls1 = 25m then we don’t make any calculation, else if tls1 = 270m let tls1= 300 – 270 = 30m, so we
calculate with 30m. Please note that tls1 never can be negative or longer than ls1, that always is
incorrect.
Dilatation calc.:
Dilatation for the total length
DN100
90°C
10°C
ls1 = 300mm
dl1 = 25.909mm

Dilatation for a fictitious length of (2* tls1)
DN100
90°C
10°C
tls1 = 25m (dilatation of 50m)
tdl help 1 = 18.343mm
Dilatation at T-piece
tdl1 = dl1 - tdl help 1 = 25.909 – 18.343 = 7.566mm the dilatation at the T-piece is 7.566mm
The 'Further Calculations' Window
The L-Z-U or Axial compensation windows share another window, the 'Further Calculations' window in
which there is an entire set of data concerning dilatations and stresses in the two pipe sections:
The meaning of these variables will be explained in the next pages. It is important to notice that every
change in the main window will force the recalculation of the entire data sheet; hence, the values present
on the screen are always the most up-to-date ones. Please note that normally this window is hidden and
will be displayed only by selecting the entry "view detailed static calculation" in the "Program" menu.

The L-Z-U Compensation Window
This window presents all the environmental variables the user can change:
These are the variables' meanings and their possible range of values:
Pipe Norm (P Norm ):
It is the pipes' set from the list ranging from 1 to 3.
Default: 1
Pre Stress (P Stress )
With this box it is possible to force the pipes' pre-stressing: this affects the laying temperature as
explained later.
Default: No
Ground Cover ( h o )
It is the depth of soil covering, ranging from 0.60 to 2.50 m.
Default: 1.0 m.
Steel Type ( S Type )
The pipe steel types implemented in this version are: steel 37, steel 44 and steel 52.
Default: Steel 37

Design Temperature (T d )
The design temperature (or working temperature) ranges from 0°C to 150°C with 5°C step.
Default: 90°C
Alternative Temperature (T alt )
It is possible to define the value for the laying temperature (T l ) by changing the Talt value. The
installation could be set with or without prestressing: this affects the laying temperature in this way:
Without pre-stressing: T l = T alt or, if this one is 0, T l = 10 °C
With pre-stressing: T l = T alt or, if this one is 0, T l = (T d +T min )/2+5 °C
Default: 20°C
Minimum Temperature ( T min )
This is the ground temperature, ranging from 0°C to 20°C with a 5°C step.
Default: 10°C
Design Pressure (P d )
This is the maximum working pressure, ranging from 0 bar to 40 bar.
Default: 14 bar
DN
The pipe's DN ranges from 20 to 800 as written in the standard Isoplus list.
Default: 100
r e
It is the ground density ranging from 1700 to 2200 kg/m³ with a 50 kg/m³ step in the possible values.
Default: 1900 kg/m³
K d
This is the compressive pressure coefficient whom values range from 0.4 to 0.95 with a 0.05 step.
Default: 0.75
m
It is the friction factor, with values ranging from 0.2 to 0.95 with a 0.05 step in the values.
Default: 0.4
Please note that, as explained before, r e , K d and m are function of the first ground selection. The
above values are true on ly if "Standard Ground" was selected in the "Select ground types" window. (Or
enter was pressed)
Deflection Angle (d)
The deflection angle affects the maximum deflection for the pipe sections, and its possible values range
from 5° to 90° with a 5° step.
Default: 90°

Length of the Sections (L s1 and L s2 )
This value represents the length of the two pipe sections (1 and 2): the value is free, but it cannot be
bigger than the maximum installation length: in this case the lenght(s) in excess will be displayed in red
and a question mark will appear on the left of the text box. If the user pushes the question mark, there
will be the possibility to enter the axial compensation or to correct the lenghts.
Default: 80.0 m for Section 1 and 20.0 m for Section 2
Wall thickness of steel pipe (wt)
It is possible to change the default value for the pipe ' s wall thickness. This value will be reset to the
default every time the user changes the pipe's DN.
Permissible Stress (s perm )
The permissible reference stress for the pipe is based upon the steel type employed, and if a greater
safety factor is wanted in the net design, it is possibe to change this value. If the user presses the 'R'
button on the right side of the text cell, the value will be reset to the default.
Algorithms used for the L-Z-U Compensation
The following section explains which formulas where used for the L-Z-U calculations.
Given:
de = external diameter of steel pipe [mm]
DE = external diameter of jacket pipe [mm]
wt = wall thickness of steel pipe [mm]
se = wall thickness of jacket pipe [mm]
r e = ground density [kg/m³]
g = acceleration due to gravity [m/s²]
h o = depth of soil covering
K d = compressive pressure coefficient
m = friction factor
P v = r e * g * h o vertical ground press. on the superior / inferior pipe surface
P h = K d * r e * g * (h o +DE/2) horizontal ground pression on the lateral pipe surface
Fixed as:
D list = de -2*wt internal steel pipe diameter [mm]
A list = D list ² * p/4 internal steel pipe area [mm²]
As = de²*p/4-Alist overall steel pipe cross sectional area [mm²]
D lim = DE-2*se internal jacket pipe diameter [mm]
A lim = D lim ²*p/4-de²*p/4 overall internal jacket pipe cross sectional area [mm²]
Am = DE²*p/4-D lim ²*p/4 overall external jacket pipe cross sectional area [mm²]
Being:
r w
= water density [kg/m³]

st
r m
r lim
= steel density [kg/m³]
= external jacket pipe density [kg/m³]
= internal jacket pipe density [kg/m³]
The overall pipe weight per meter is:
mv = A list *r w +As*r st +A lim *r lim +A m *r m [kg/m]
And the frictional force is derived from:
F c = m*g* [DE²*p/4*K d * r e + mv] frictional force due to the pipe
F h = m*g* [DE*p/2* r e *(1+K d )] frictional factor per ground meter
So the frictional force per pipe meter is:
Fr' = F c + h o *F h frictional force per pipe meter [N/m]
Other variables of interest are the following:
T d = design or operating temperature [°C]
T l = laying temperature [°C]
T alt = alternative temperature, which defines Tl (see after) [°C]
T min = the pipes ' minimum temperature (ground temp.) [°C]
P d
= design water pressure [bar]
The permissible reference stress for the pipe is based upon the steel type employed, and the following
formula uses a safety factor of 1.225 as written in the Tab. A.1. for the DIN 1626 for steels 37,44 and
52:
Steel 37: If Td

where DT is the max abs. value between ( T d - T l ) and ( T l - T min )
The average peripheral stress due to the internal pressure is:
s up = (de/wt-1)*P d /2 = (D list *P d )/(2*wt) [N/mm²]
While the longitudenal stress due to internal pressure is:
s lp = A list *P d /As [N/mm²]
The internal pressure generates an elastic radial dilatation in the pipe and a similar contraction in the
longitudenal sense (e) but opposite in sign. The real dilatation is:
e = (0.5-n)*s up /E
n = steel trasversal contraction factor (0.3)
The length of the sliding section at repeating temperature changes is:
I ob = (a*E*(T d -T min )+t)*As/Fr' [m]
t = s lp -0.3*s up [N/mm²]
And the change of the length of the sliding zone due to the differential temperature is:
DI ob = (a*(T d -T min )+t/E)*I ob /2
[mm]
When expansion is taken up in natural expansion bends, the longitudenal stress at the free end of the
pipe is 0.5*s up ; hence, the length of the sliding section at T max is:
I ow = (a*E*(T d -T l )+t)*As/Fr' [m]
Consequently the change of the length of the sliding zone at T max is:
DI ow = (a*(T d -T l )+t/E)*I ow /2
[mm]
When the pipe is cooled from T l to T min under atmospheric pressure, the length (and the change in
lenght) of the sliding section at T min is:
I ok = a*E*(T l -T min )*As/*Fr' [m]
DI ok = -a*(T l -T min )*I ok /2
[mm]
For the following formulas it is important to consider Ix, the semi-length of the pipe section 1 (I 1 ) and
section 2 (I 2 ) to the natural reference point: the object is to calculate the following:
DI w = change of length at T max [mm]
DI b = change of length due to the differential temperature [mm]
DI k = change of length at T min [mm]
s lw = longitudenal stress at T max [N/mm²]
s lk = longitudenal stress at T min [N/mm²]
There are two main cases and three sub-cases:
1) the length of the sliding zone at T max (I ow ) is greater than the length of the sliding section at
repeating temperature changes (I ob ):

a) the semi-length of the section (Ix) is greater than I ow and I ob :
DI b = DI ob
DI w = DI ow
DI k = DI w - DI b
s lw = -(I ow *Fr'/As-s lp )
s lk = I ob *Fr'/As
b) the semi-length of the section (Ix) is smaller than I ow and I ob :
DI b = DI ob * Ix/I ob *(2-Ix/I ob )
DI w = DI ow * Ix/I ow *(2-Ix/I ow )
DI k = DI w - DI b
s lw = -(Ix*Fr'/As-s lp )
s lk = Ix*Fr'/As
c) the semi-length of the section (Ix) is smaller than I ow but greater than I ob :
DI b = DI ob
DI w = DI ow * Ix/I ow *(2-Ix/I ow )
DI k = DI w - DI b
s lw = -(Ix*Fr'/As-s lp )
s lk = I ob *Fr'/As
2) the length of the sliding zone at Tmax (I ow ) is smaller than the length of the sliding section at
repeating temperature changes (I ob ):
a) the semi-length of the section (Ix) is greater than I ok and I ob :
DI b = DI ob
DI k = DI ok
DI w = DI b +DI k
s lw = -(I ob *Fr'/As-s lp )
s lk = I ok *Fr'/As
b) the semi-length of the section (Ix) is smaller than I ok and I ob :
DI b = DI ob * Ix/I ob *(2-Ix/I ob )
DI k = DI ok * Ix/I ok *(2-Ix/I ok )
DI w = DI b + DI k
s lw = -(Ix*Fr'/As-s lp )
s lk = Ix*Fr'/As
c) the semi-length of the section (Ix) is smaller than I ok but greater than I ob :
DI b = DI ob
DI k = DI ok * Ix/I ok *(2-Ix/I ok )
DI w = DI b + DI k

s lw = -(I ob *Fr'/As-s lp )
s lk = Ix*Fr'/As
The expansion Dlx of the section is equal to the greater value between the change of length at T max
(DI w ) and the change of length at T min (DI k ).
The permissible longitudenal stress is based upon s st and the peripheral stress s up :
_____________
s lzul = s up - Ö s st ² - 0.75*s up ² [N/mm²]
The semi permissible length without prestressing is then:
I lzul = (s lp - s lzul )*As/Fr' [m]
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
permissible installation length is unlimited; else it corresponds to 2*I lzul .
The correspondent reference stress for the section is:
_________________
s v = Ö s lw ² + s up ² - s lw * s up [N/mm²]
And the max deflection for the pipe sections is based upon the deflection angle d °:
W 1 = Dl 1 /sind + Dl 2 / tand [mm]
W 2 = Dl 2 /sind + Dl 1 / tand [mm]
For the cushion thickness we have to consider the deflection angle and the expansion of both sections:
__________________
Wd = Ö (Dl 1 /sind)²+(Dl 2 / tand)²
The cushion thickness is calculated is calculated as follows:
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
W 1 , the cushion is proportional to W 2 , else the cushion is proportional to Wd. The cushion cannot be
greater than 150 mm. Let it be W X the quantity derived from the aforementioned calculation (being it,
W 1 , W 2 or Wd ):
If it is W X

The 'Set the Expansion or Deflection Amount' window
This window is displayed under the main one and his purpose is to help the net design trying to find the
best section lengths with a given expansion or deflection. Actually it is possible to enter the wanted
deflection (or deflection) for a certain section and after a while the program will display the best value
for the corresponding section. Clicking on the "Insert these Values" button will force the program to
use the found values in the main window. This is also useful when dealing with deflection or deflection
limits: whenever limits are used (unckecking the "Ignore these limits" square in the 'Set limits' window)
the program will display a small button with a triangle inset everytime deflection or deflection for a
section exceeds a certain pipe limit. These limits are set within the 'Set limits' window which appears
everytime the program is run or by clicking the 'settings' menu in the main window. When limits are
surpassed the main window will look as below:
In this case both dilatation and deflection exceed the limits: clicking on the corresponding button the
following request will be displayed:
Clicking on the 'Yes' button will force the program to accept the suggested values for the dilatation. The
same is for the deflection:

Z - Compensation
When Z-Compensation is used, the following window will appear:
The length of the sliding section at T max is based upon an average value (T max -T min )/2 :
I ow = (a*E*(T d -T min )/2+t)*As/Fr' [m]
Consequently the change of the length of the sliding zone at T max is:
DI ow = (a*(T d -T min )/2+t/E)*I ow /2
And DI w , change of length at T max ,
is:
[mm]
DI w = DI ow * Ix/I ow *(2-Ix/I ow ) if the semi-length of the section (Ix) is less than I ow
DI w = DI ow
if the semi-length of the section (Ix) is greater than or equal to
I ow
The deflection is based upon DI w , as follows:
W L1 = DI w1 /sind + DI w2 / tand
W L2 = DI w2 /sind + DI w1 / tand
[mm]
[mm]
Take note that the W L1 and W L2 values are not W 1 and W 2 , but they represent the maximum
deflection possible, that is, the deflection coming from the greatest DT possible, T max -T min . We’ll use
the W L1 and W L2 values instead of the W 1 and W 2 values.
The expansion leg length DZ 1 for the compensator is function of the deflection: DZ 1 = ¦(W 1 +W 2 );
hence DZ 2 is calculated as follows:
DZ 2
_______
= 44.0 * de * W
Where:
de = external diameter of steel pipe [mm]

W
= max between the W 1 and W 2 values
The tests showed that the better approximation of the "real" world is given using the "stress"
calculation, which involves the evaluation of values W L1 and W L2 . Thus for all the compensations the
"stress" option is used, but for the clarity of calculations also the "normal" way is presented.
L - Compensation
When L-Compensation is used, the following window will appear:
The length of the sliding section at T max is based upon an average value (T max -T min )/2 :
I ow = (a*E*(T d -T min )/2+t)*As/Fr' [m]
Consequently the change of the length of the sliding zone at T max is:
DI ow = (a*(T d -T min )/2+t/E)*I ow /2
And DI w , change of length at T max ,
is:
[mm]
DI w = DI ow * Ix/I ow *(2-Ix/I ow ) if the semi-length of the section (Ix) is less than I ow
DI w = DI ow
if the semi-length of the section (Ix) is greater than or equal to
I ow
The deflection is based upon DI w , as follows:
W L1 = DI w1 /sind + DI w2 / tand
W L2 = DI w2 /sind + DI w1 / tand
[mm]
[mm]
The expansion leg length DL x for the compensator is function of the deflection: DL x = ¦(W x ).
_______
DL x = 55.0 * de * W x

Where:
de = external diameter of steel pipe [mm]
W x = W 1 and W 2
U - Compensation
When U-Compensation is used, the following window will appear:
The length of the sliding section at T max is based upon an average value (T max -T min )/2 :
I ow = (a*E*(T d -T min )/2+t)*As/Fr' [m]
Consequently the change of the length of the sliding zone at T max is:
DI ow = (a*(T d -T min )/2+t/E)*I ow /2
And DI w , change of length at T max ,
is:
[mm]
DI w = DI ow * Ix/I ow *(2-Ix/I ow ) if the semi-length of the section (Ix) is less than I ow
DI w = DI ow
if the semi-length of the section (Ix) is greater than or equal to
I ow
The deflection is based upon DI w , as follows:
W L1 = DI w1 /sind + DI w2 / tand
W L2 = DI w2 /sind + DI w1 / tand
[mm]
[mm]
Take note that the W L1 and W L2 values are not W 1 and W 2 , but they represent the maximum
deflection possible, that is, the deflection coming from the greatest DT possible, T max -T min . We will
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
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
have relatively little effect on the permissible amount of expansion; so the Dilatation Zone Length DU 1
is function of the deflection: DU 1 = ¦(W 1 +W 2 ), length DU 3 is calculated as follows:
_______
DU 3 = 31.0 * de * W 2
where de = external diameter of steel pipe [mm]

The Axial Compensation Window
When the axial compensation is used only these windows are used: the 'Further Calculation' window, the
'Axial Compensator' window and the 'Select Ground Type' window.
All the controls are the same as in the L-Z-U window, with the exception of the pre stress box which is
not used. The alternative temperature is now effectively the laying temperature wanted and there is the
pre heating temperature box in which the pre heating temperature is calculated. It is also possible to
change the wall thickness and the permissible reference stress. The main changes are in the lower part of
the window: in the total line length box it is possible to enter the installation length. The program will
calculate (as detailed below) the maximum sections' lenghts, then it will reduce the Section 2 until the
total line length is reached. For example, in the page before a total line length of 800 m. was entered.
The program defines the maximum values for the sections, S 1max = Section B + Section A = 103.16 m,
while S 2max = 2 * Section A = 99.32 m.
The Ideal Lengths of Section A and B represent the maximum extent possible for these single sections
in an ideal condition ( with a pipe of infinite length), meanwhile the Real Length is the one in a pipe of
finite extent (in this example, the 1000 m. in the total line length box).
The pipes will be placed as for the following figure:

So for a total line lengh of 1000 m., we will have:
Sect 1 (103.16 m) + 8 * Sect 2 (99.32) + Sect 1 (103.16 m) = 1000.88 m
Please note that all the values for dilatation, reference stress, etc are referred to the real sections
length, not to the ideal ones.
section 1
section 2
B
A A A A
h
p
preheat
Kompensator
B
hot
zul
p
cold
zul
L B
L
A
To calculate the dilatation, stresses and section lengths the first step is the mean permissible stress:
s st mean = (s st (T ins ) + s st (T max ))/2
Where:
s st mean = mean permissible stress [N/mm²]
s st (T ins ) = permissible stress at T ins [N/mm²]
s st (T max )
= permissible stress at T max [N/mm²]
Secondly the preheating temperature (T pre ) is the lower between:

T pre = T ins + s st mean /(a*E) (rounded down) and
T pre = (T max )* 0.9
Where:
T pre = preheating temperature [°C]
T ins = temperature at installation [°C]
s st mean = mean permissible stress [N/mm²]
Formula for section B
L b =( s st mean * As)/Fr´
Length of Section B [m]
Where:
As = de²*p/4-Alist Overall steel pipe cross sectional area [mm²]
Fr' = F c + h o *F h Frictional force per pipe meter [N/m]
s st mean
Formula for section A
Mean permissible stress [N/mm²]
L a =( 2 * s st mean - a * E * ( T max - T ins ))* As/F
Length of Section A [m]
Where:
As = de²*p/4-Alist Overall steel pipe cross sectional area [mm²]
Fr' = F c + h o *F h Frictional force per pipe meter [N/m]
a = (11.4 + Td/129)* 10 -6 Expansion coefficient [1/°C]
E = (21.4 - Td/175)* 10 +4 Young's modulus [N/mm²]
s st mean
mean permissible stress [N/mm²]
And then the correspondent max length for the sections A and B is
I 1 = L b + L a [m]
I 2 = L a + L a [m]
At this point, all the calculations are made at design temperature Td with a laying temperature T pre (i.e.
all the calculations are made with T l = T pre ): as a result we'll find the dilatations DL 1 and DL 2 . When
axial compensation is used, the sand on the B-side will compensate for a »20% of the total expansion:
the residual 80% will be reduced by the axial compensator, so that the expansion joint range will be:
DZ 1 = DL 1 * .8 + DL 2 + DL 2 For the first section
DZ 2 = DL 2 + DL 2 For the other sections

Index
Isoplus® Static Calculation ................................................................................................................... 1
Program Installation ........................................................................................................................... 1
Starting Isoplus® Static Calculation ................................................................................................... 1
The Header Data Window .................................................................................................................. 6
The Ground Samples Window ............................................................................................................ 6
The T-Pieces Dilatation Window ........................................................................................................ 7
The 'Further Calculations' Window ..................................................................................................... 8
The L-Z-U Compensation Window .................................................................................................... 9
Algorithms used for the L-Z-U Compensation .................................................................................. 11
The 'Set the Expansion or Deflection Amount' window..................................................................... 16
Z - Compensation ............................................................................................................................. 17
L - Compensation ............................................................................................................................. 18
U - Compensation ............................................................................................................................ 19
The Axial Compensation Window .................................................................................................... 21
Index ................................................................................................................................................... 24