thermal analysis

1. INDRA CAHYONO
PIPING DEPARTMENT – PT. REKAYASA INDUSTRI
07/03/2014

2. 1. Introduction
2. Thermal Expansion Force and Stress
3. Methods of Providing Flexibility
4. Self-Limiting Stress
5. Stress Intensification and Flexibility Factors
6. Cold Spring
7. Pressure Effects on Piping Flexibility
8. General Procedure of Piping Flexibility Analysis
9. Problems With Excessive Flexibility
OUTLINE

3. 1. INTRODUCTION

4. Source “http://65.57.255.42/”
1. INTRODUCTION
THIS IS
ONE REASON..
WHY WE MUST LEARN…
THERMAL EXPANSION
AND PIPING FLEXIBILITY..

5.  Sebuah sistem perpipaan dikatakan mempunyai fleksibilitas yang cukup atau
baik, bila sistem perpipaan tersebut
 dapat mengalami perubahan panjang akibat ekspansi atau kontraksi
termal
 gerak titik tumpu sistem perpipaan tanpa mengalami kerusakan-
kerusakan :
 kegagalan sistem perpipaan atau titik-titik tumpunya akibat
tegangan berlebih atau akibat lelah
 kebocor pada sambungan
 tegangan yang merusak atau distorsi yang dialami sistem
perpipaan, valve atau peralatan yang tersambung dengan sistem
perpipaan akibat beban atau momen yang berlebih pada sistem
perpipaan tersebut.
1. INTRODUCTION

6.  When a pipe expands it causes the entire piping system to make room for its
movement. This creates forces and stresses in the pipe and on its connecting
equipment. If the piping system does not have enough flexibility to absorb this
expansion, force and stress generated can be large enough to damage the
piping and the connecting equipment. In the real world, however, the stiffness
of the anchor is limited. A stiffness of 106 lb/in is very difficult to achieve due
to the flexibility of the structure/foundation. Depending on pipe size, the
practical anchor stiffness more likely ranges from 104-107 lb/in. The real
anchor will absorb part of the pipe expansion.
2. THERMAL EXPANSION FORCE AND
STRESS
Figure 3.1(a)(2) shows that when one end of the pipe
is loose, the pipe has a free expansion equal to Δ = aL
(T 2 - T 1 ), where “a” is the thermal expansion rate of
the pipe and (T 2 - T 1 ) is temperature change.
E : modulus of elasticity of the pipe material
A : cross-section area of the pipe
F : anchor force
S : axial stress

7.  There are two main categories of methods for providing piping flexibility: the
flexible joint method and the pipe loop method.
3. METHODS OF PROVIDING
FLEXIBILITY
 Expansion loops
 Expansion joints
Universal Expansions joints

8.  Estimating Leg Length Required
The required leg length can be estimated via the guided cantilever approach. The
method is explained by using the L-bend given in Fig. 3.3 as an example:
 
ft
length,
input
as
OD
use
for
equation
that the
note
inches
diameter,
nominal
inches
loop,
by the
absorbed
be
to
expansions
)
400
at
steel
carbon
elasticity
(modulus
10
29
)
400
at
steel
carbon
for
stress
(allowable
psi
20.000
o
6
o







L
L
D
F
psi
E
F
S

9. Nomograph untuk
menghitung loop size

10. Contoh 1 :
Tentukan ukuran dari expansion loop yang mampu menyerap expansi yang
terjadi pada sistem pipa berdiameter 12 in sepanjang 200 ft. Material pipa adalah
baja karbon dan beroperasi pada temperatur 400oF. Asumsikan rasio antara tinggi
dan lebar loop.
Jawab :
Total expansi yang terjadi = (200)(0.027) = 5,4 in.
Dengan menggunakan nomograph dan menarik satu garis lurus dengan titik awal
pada diameter nominal 12 in dan melalui expansi termal mendekati 6 in ( 5.4 in) akan
memotong garis bend length kira-kira pada angkan 50 ft. Jika diasumsikan H = W,
maka dari rumus bend length L = W + 2H, maka diperoleh H = W = 17 ft yang
menghasilkan L= 17 + 2(17) = 51 in.

11. Perhitungan expansion loop menggunakan nomograph
Dengan perhitungan diperoleh
ft
24
,
44
)
000
.
20
(
144
)
4
,
5
(
12
)
10
29
(
3
144
3 6





S
D
E
L
Jika dibandingkan dengan perkiraan menggunakan nomograph, terjadi
kesalahan sebesar 16 %
S
D
E
S
D
E
L




3
12
/
1
3

12.  Dalam tahun 1984, penggunaan expansion joints mulai diijinkan dalam
nuclear piping design kecuali untuk ASME Section III, Nuclear Class 1 Code
Subsection NB-3671.2 yang menyatakan bahwa expansion joint tidak
diijinkan dalam Class 1 nuclear components.
 Expansion joints digunakan untuk menyerap kompresi arah aksial atau
perpanjangan offset arah lateral dan rotasi sudut.
• Expansion joints umumnya dapat diklasifikasikan ke dalam kelas jenis sliding
atau flexible.
• Pada jenis sliding dimungkinkan adanya gerakan relatif antara bagian yang
berdekatan. Termasuk ke dalam jenis ini adalah : slip joints, swivel joints, dan
ball joints. Dresser coupling dan Victaulic coupling adalah contoh nama
komersial dari joints jenis sliding. Nama lain dari sliding joints adalah packed
joints.
• Jenis flexible joints dapat dibagi lagi menjadi bellows joints, metal hose, dan
corrugated pipe.

13.  Single Expansion Joint : Merupakan bentuk yang paling sederhana dari expansion
joint untuk jenis kontruksi bellow tunggal. Bellow ini dirancang untuk menyerap
semua gerakan dari sistem pipa di mana joint tersebut dipasang.
 Double Expansion Joint : terdiri dari dua bellows disambung oleh satu penghubung
yang dipegang oleh tumpuan yang dipasangkan pada dasar anchor. DEJ tidak sama
dengan universial expansion joints.
 Internally Guided Expansion Joint : Tipe ini dirancang untuk dapat memberikan axial
guiding pada expansion joint dengan memasang sebuah heavy telescoping internal
guide sleeve .
 Universal Expansion Joint : terdiri dari dua bellows yang disambungkan dengan
sebuah penghubung dan digunakan untuk menyerap setiap kombinasi dari tiga
gerakan dasar, yaitu : gerakan aksial, defleksi lateral, dan rotasi sudut. Jenis ini
biasanya dilengkapi dengan batang-batang pembatas (limit rods) untuk
mendistribusikan gerakan diantara kedua bellows dan menstabilkan penghubung
kedua belows. Definisi ini tidak berarti bahwa hanya double expansion bellows joint
yang dapat menyerap gerakan universal.
Beberapa Tipe Expansion Joints

14.  Hinged Expansion Joint : terdiri dari satu bellows dan dirancang untuk tumpuan yang
mengijinkan adanya rotasi sudut pada satu bidang hanya menggunakan sepasang pin
melalui hinge plate yang dikaitkan dengan ujung-ujung expansion joint. Hinge pins dan hinge
harus dirancang agar masih kuat menahan gaya dorong akibat tekanan internal. HEJ harus
digunakan berpasangan dua atau tiga agar dapat berfungsi dengan baik .
Swing Expansion Joint : tipe ini dirancang untuk menyerap defleksi lateral dan/atau rotasi
sudut pada satu bidang. Gaya akibat tekanan internal dan gaya lainnya ditahan dengan
menggunakan sepasang swing bar yang masing-masingnya disambung dengan pin pada
ujung-ujung expansion joint.
 Internally Guided Expansion Joint : Tipe ini dirancang untuk dapat memberikan axial guiding
pada expansion joint dengan memasang sebuah heavy telescoping internal guide sleeve .
 Universal Expansion Joint : terdiri dari dua bellows yang disambungkan dengan sebuah
penghubung dan digunakan untuk menyerap setiap kombinasi dari tiga gerakan dasar, yaitu :
gerakan aksial, defleksi lateral, dan rotasi sudut. Jenis ini biasanya dilengkapi dengan
batang-batang pembatas (limit rods) untuk mendistribusikan gerakan diantara kedua bellows
dan menstabilkan penghubung kedua belows. Definisi ini tidak berarti bahwa hanya double
expansion bellows joint yang dapat menyerap gerakan universal.

15. Various types of expansion joints

17.  Inherent Flexibility
English units:
SI units:
D = nominal pipe size, in (mm)
Y = resultant of movement to be absorbed by piping system, in (mm)
L = developed length of piping system between two anchors, ft (m)
U = anchor distance (length of straight line joining anchors), ft (m)
o Sistem perpipaan yang tidak memerlukan analisis fleksibilitas:
o sistem perpipaan yang merupakan duplikat sistem perpipaan yang sudah ada, yang
dalam operasi menunjukan kinerja yang memuaskan
o sistem perpipaan yang dengan mudah dapat dinilai mempunyai fleksibilitas yang cukup
bila dibandingkan dengan sistem perpipaan yang fleksibilitasnya telah dianalisis
sebelumnya
o sistem perpipaan dengan ukuran seragam, yang ditumpu dengan hanya dua titik tumpu
tanpa ada titik restraint diantara keduanya, dan yang memenuhi ketentuan berikut :

18.  CONTOH SOAL
Sistem perpipaan dengan dua buah anchor seperti ditunjukkan pada gambar,
memiliki diameter luar OD = 8.625 in dan schedule 40, terbuat dari baja
carbon. Temperature rancang adalah 200o F, sedangkan temperature instalasi
adalah 70oF. Diketahui e = 0.99 in./100 ft pada 2000 F. Tentukanlah apakah
sistem perpipaan dengan dua anchor ini memerlukan analisis fleksibilitas.

19. Solusi :
 diameter luar, D = 8.625 in.
 regangan akibat perpindahan
 panjang pipa, L = 12 + 25 = 37 ft.
 jarak antara kedua anchor, U = (122 +252)1/2 = 27.73 ft.
 hitung :
DY/(L-U)2 = 8.625 X 0.2745/(37 - 27.72)2 = 0.0275 < 0.03
Dari analisis di atas dapat dilihat bahwa sistem perpipaan dengan dua
anchor ini tidak memerlukan analisis fleksisbilitas.

20.  Figure 3.4(a) is a pipe subject to weight load, thus generating sustained stress in
the pipe. By increasing the weight gradually, the stress and the accompanying
displacement also increase accordingly.
 Figure 3.4(b) shows the case for self -limiting stress. When the pipe is subject to
thermal expansion or other displacement load, the mechanism of balance shifts to
the strain — that is, the strain always corresponds with the amount of expansion or
displacement. The stress due to thermal expansion is self -limiting stress.
4. SELF-LIMITING STRESS
SE: Expansion Stress
Sy: Yield strength
ew: Strain (W)
eE: Stain (expansion)

21.  A piping system consists of many different components such as bends, elbows,
reducers, tees, valves,and flanges. However, in the analysis we normally idealize
these various components into two types of elements: the straight pipe beam
element and the curved pipe beam element .
5. STRESS INTENSIFICATION AND
FLEXIBILITY FACTORS

22. To show the function of these
tables, we use ASME B31.3 tables
as shown in Tables 3.1 and 3.2 as
an example. The B31.3 table is
somewhat morecomplicated than
the others. It shows in-plane and
out-plane categories of SIFs for
each type of component.

23. No cold spring and no stress relaxation. As shown in Fig. 3.7(a), this piping system
heats up from the zero stress, zero strain point, 0, expanding gradually to reach the
yield point at hot condition, a, and continues on to the final point, b. Figure 3.7(b)
shows a non-cold-sprung system with a stress relaxation at operating condition.

24. 6. COLD SPRING
 Cold spring, pre-spring, and cold pull all refer to the process that pre-
stresses the piping at installation or cold condition in order to reduce the
force and stress under the operating or hot condition. Cold spring is often
applied to a piping system to: (1) reduce the hot stress to mitigate the
creep damage [14]; (2) reduce the hot reaction load on connecting
equipment; and (3) control the movement space.

25. In actual installations, more analyses are required. In general,
the following three analyses regarding thermal expansion are
required:
 Under operating temperature, but no cold spring gap. This is
used to check the thermal expansion stress range to compare
with the code allowable stress range.
 Under operating temperature with 2/3 of the cold spring gap.
This is used to find the credible anchor reaction at operating
condition. The 2/3 factor is the fraction of the cold spring
effect allowed by the code.
 Under ambient temperature with full cold spring gap. This is
used to find the anchor reaction at the cold condition after
the cold spring. This analysis is also used to provide
displacement guides for executing the cold spring process.

26. 7. PRESSURE EFFECTS ON PIPING
FLEXIBILITY
 Potential Twisting at Bends
Equations have been developed for this opening rotation and are implemented in
some computer programs. This opening effect is often misquoted as the Bourdon tube
effect. It has artificially generated, on paper, much bigger twisting effects on the
piping than was experienced in the field. Actually, a Bourdon tube is an arc shape
tube with an oval cross-section. This oval cross-section is the key for the opening
rotation.

27.  Pressure Effect on Bend Flexibility and SIFs
The flexibility factor and SIF at a bend are mainly caused by the ovalization of
the bend cross-section. Internal pressure tends to reduce ovalization, thus
reducing flexibility and stress intensifica tion. The pressure effect on bend
flexibility and SIFs has been well investigated. One of the most recognized
treatments is the use of modification factors established by Rodabaugh and
George [17]. These factors have been adopted by the ASME piping codes, and
are summarized bellow.In large-diameter, thin-wall elbows and bends, pressure
can significantly affect the magnitudes of the flexibility factor, k, and the SIF, i.
Under pressurized conditions, the value of k calculated from Eq. (3.5) should be
adjusted by dividing it with:

28. 8. GENERAL PROCEDURE OF PIPING
FLEXIBILITY ANALYSIS
 The system may have several different operating modes. Although it is
possible to select one mode that represents the most critical situation,
normally more than one operating mode has to be considered. In this
sample system, there are three possible operating modes: (1) both heat
exchanger loops are operating; (2) only HX-1 heat exchanger is operating;
and (3) only HX-2 heat exchanger is operating. The analyst decides which
of these three modes needs to be analyzed. At first sight, it may appear

29.  Because everyone is aware of the importance of piping flexibility,
engineers have a tendency to provide more flexibility than required in a
piping system. Indeed, it is widely believed that the more flexibility that is
provided, the more conservative is the design. This is actually a very
serious misconception. Today, it is pretty accurate to say that more piping
problems have been created by excessive flexibility than by insufficient
flexibility.
9. PROBLEMS WITH EXCESSIVE
FLEXIBILITY