International Journal of Advanced Engineering Research and Science (IJAERS)
httosJ/dx. doi. org/10.22161/iiaers.5.6.14

[Vol-5, Issue-6, Jun- 2018]
ISSN: 2349-6495(P) / 2456-1908(0)

Evaluation of the Stiffness Effect of Pipe
Supports in Relation to Static and Dynamic
Loads in a Flexibility Analysis

Pedro Americo Almeida Magalhaes Junior, Tiago Martins Portela

PPGEM/ PUCMINAS University - Brasil, Belo Horizonte/MG

Abstract — Piping flexibility analysis is done to ensure
structural integrity in all operating conditions that may
occur over the life of a system, whether static or dynamic.
In industrial designs generally the rigidity of the support is
neglected in the analysis of flexibility. The work presents
an evaluation of the loads transmitted the structures in
function of the rigidity of the pipe support. The evaluation
was done through computer simulation using finite
element techniques. The computational simulation made
possible the evaluation of the forces transmitted to the
support structures of an existing project of an orifice
station, when considering the rigidity of the support. The
work also shows that it is possible to refine projects when
taken into consideration the influence of the rigidity of the
supports, making a more adequate sizing the structure,
portraying more faithfully the behavior of the system. The
work also evaluates the influence, advantages and
disadvantages in the use of stiffness in the supports with
regard to the load transmitted to the support structures
(support, base and tube).

Keywords — Stiffness, Pipe, Dynamics, Flexibility
Analysis, Finite.

I. INTRODUCTION

Due to the disturbances that can occur during the
operational life of a pumping system, the project must take
into consideration besides the static loads to the dynamic
loads. Dynamic loads may occur due to flow disturbances
or due to the mode of excitation caused by positive
displacement pumps. These loads generate in the systems
abrupt changes of pressure, velocity and acceleration along
the pipe, thus generating the dynamic loads. With the
advancement in computational tools, it is common to
simulate structural elements to determine rigidity and as a
consequence to evaluate the dynamic behavior of the
system under various operating conditions. The work
shows that by considering the rigidity of the supports can
obtain economic gains due to reduction in the volume of
concrete to support the pipe.

The objective of the work is to evaluate the effect of the
forces transmitted to the support structures when using the
rigidity of the supports that was modeled by the finite
element method. Evaluate the advantages and
disadvantages of this use by means of a case study.

II. METHODOLOGY

All real systems are complex. The mathematical model
simplifies the physical system and allows it to be analyzed.
The finite element method is a technique that allows to
evaluate real systems through mathematical modeling.
With this technique physical arrangements can be studied
according to their behavior, evaluating the response of the
system to undergo the action of external and internal
efforts.

As one of the techniques used in this study, the linear
elastic analysis for static loading adopts the following
assumptions: static condition: all loads are applied slowly
and gradually to achieve their total magnitudes. After
reaching the total magnitude, the charges remain constant
(they do not vary with time); Linearity condition: the
relationship between loads and the induced responses are
linear. The linearity condition is met if all model materials
are in accordance with Hooke's law (Eq. 01), which states
that the stress is directly proportional to strain, if the
induced displacements are small enough to ignore the
change stiffness caused by loading, and whether the
boundary conditions do not vary during load application.
The loads must be constant in magnitude, direction and
distribution. They do not change while the model is being
deformed.

In industrial designs standards are used with guidelines
and considerations for the sizing of piping system.
Discharge pipe and pipeline projects are generally used as
standard ASME B31.4, this standard deals with stresses in
pipes but does not address the rigidity of supports. In this
way it is usual in industrial projects to consider rigid
supports in the analysis of flexibility as a conservative
condition of the modeling. However, the rigidity of the
supports changes the response of the system, which in

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International Journal of Advanced Engineering Research and Science (IJAERS) [Vol-5, Issue-6, Jun- 2018]

https://dx.doi.Org/10.22161/iiaers.5.6.14 ISSN: 2349-6495(P) / 2456-1908(0)

some cases can be detrimental to the dimensioning leading
to oversizing or undersizing of the structures.

The case study was done at an orifice station which carries
tailings to a dam. The orifice station functions as a charge -
loss station in order to control the rejection pressures. The
main transport tubing is 24 inches in diameter and a 14
inch shunt where the rupturing disc acts which is sized to
break to 52kgf / cm 2. The analysis was done for three
cases static (Hydrostatic testing, operation, solar
radiation), dynamic and three cases (Stop by power failure,
improper closure of the blocking valve and normal stop).
According to the hydraulic system report, the rupture disk
will rupture in the condition of improper closure of the
valve.

The program used for the flexibility analysis was
CAESAR II which considers infinite stiffness equal to
1012 N / cm. As a conservative practice of projects, the
supports are considered as rigid in the modeling of piping
systems, believing that in this condition the dimensioning
would be more conservative. In special cases where they
are subject to severe loads, such as long-distance pumping,
this consideration can generate significant errors in both
the dynamic behavior of the system and the load results.
Flexibility analyzes were performed using CAESARII
software modifying only the rigidity of a specific support.
This program evaluates the dynamic behavior of the
system by means of solution matrices of the dynamics
equation (Eq.03). The stiffness of the support was
determined by the finite element method, applying a load
in the three directions (x, y and z), and obtaining the
displacements of the structure using Newton's second law
and Hooke's law for the determination of rigidity of the
support.

Hooke's law F = k.x [A] (Eq.01)

2° Lei de Newton £ F = m. a [A] (Eq.02)

Dynamic equation F(t) =

M.X + C.X + Ax [A] (Eq.03)

Where: F - applied force [N]; K-Stiffness matrix [N / m];

C - Damping Matrix [-]; M-mass matrix [kg]; a -
acceleration [m / s 2 ]; x - displacement [m]; x' - Speed [m /
s]; x" acceleration [ml s 2 ].

III. RESULTS AND ANALYSIS

The support evaluated and modeled was a support type
guide which restricts the 2 movements, the translation in Y
and Z. In the model was considered a friction factor of 0.3
(usual for steel / steel contact). The generated physical
model can be seen in Fig. 1.

Fig. 1: 3D model of the orifice station elaborated in
CAESARII software.

The orifice station was evaluated under the conditions
shown in table 1

Table. 1: Operating conditions of the system for static and

dynamic loads.

Carga Estatica

Carga Dinamica

El - Teste

Hidrostatico

T=21°C,

P=30,0Kgf/cm 2 ;

p=1000kg/m 3 .

D1 -

Parada

normal do

sistema

T=35°C,

AP=32,0Kgf/cm 2 ;
Tempo de
manobra 120s.

E2-

Condi£ao
de opera£ao

T=35°C,

P=30,0Kgf/cm 2 ;

p=1420kg/m 3 .

D2-

Parada por
queda de
energia

T=35°C,

AP=42,0Kgf/cm 2 ;
Tempo de
manobra 10s.

E3-

Insola£ao

T=60°C,

P=NA;

p=NA.

D3 -

Parada

devido a

fechamento

indevido

da valvula

de

bloqueio

T=35°C,

AP=52,0Kgf/cm 2 ;
Tempo de
manobra 60s.

The carrier selected for analysis was the carrier inserted
into the 14-inch rupture disk line. In the region of this
support a significant pressure variation occurs when the
rupture disk ruptures caused by the transient overpressure
in the event of improper closing of the blocking valve
(accidental case D3). The propagation of the shock wave
due to improper closure of the valve causes an
overpressure of the order of 52 kgf / cm2 and can be seen
in the graph shown in figure 2, the transient analysis was
developed using the AFT impulse software. The hydraulic
transient data calculated in the AFT are presented in the
time domain, these data are transformed to the frequency
domain for evaluation of the flexibility by means of the
Fourier transform. This transformation is done by
CAESAR II itself.

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International Journal of Advanced Engineering Research and Science (IJAERS)
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Fig. 2: Hydraulic transient upstream of the orifice station
closing valve.

The study support was evaluated using the Ansys 16.0
software for structural analysis. The support model and the
mesh test are shown in Fig 3.

right mesh test.

The mesh test showed that the mesh used is not
influencing the result for a mesh density greater than zero,

[Vol-5, Issue-6, Jun- 2018]
ISSN: 2349-6495(9) / 2456-1908(0)

obtaining a deviation of less than 0.1% in relation to the
Von Misses voltage. With this model a support rigidity
was obtained in the X, Y and Z directions as shown in
table 2. The displacements were obtained in the center of
the pipe.

Table. 2: Stiffness obtained by the finite element model.

Rigidez [N/cm]

X

Y

Z

8,7E+06

l,4E+06

6,5E+06

With the rigidity obtained for the designed support,
simulation with and without stiffness was done in order to
verify the response of the system loading. The study
presented reduction of static and dynamic loads with the
reduction of stiffness as shown in table 3. Taking into
account the rigidity of the designed support, the load
showed a decrease of the transmitted load of up to 8% in
the static load and of approximately 5% for the load,
dynamic loading. An even more refined study can be
developed for each system support in order to determine
the optimal rigidity for that loading without impairing
system operation.

Table. 3: Result of static and dynamic loading with and without support rigidity.

Modelo

Condigdes

Operacionais

Avalia?ao Carregamento Estatico

Condi?oes

Operacionais

Avalia?ao Carregamento Dinamico

FX [N] FY [N] FZ [INI]

Modulo

[N]

FX [N] FY [N] FZ [N]

Modulo

[N]

Rigid Z; Rigid GUI

Rigid Z; Rigid GUI

Projetado

El

-256

-1752

-13713

13827

D1

7747

6799

17153

20012

E2

39907

13032

-3532

42129

D2

244469

216941

234060

402011

E3

40144

14582

6805

43249

D3

256589

34377

66526

267293

MAX

40144

14582

-15130

45311

MAX

256589

216941

234060

402011

Modificado
com Rigidez
doSuporte

El

-165

-1579

-13134

13230

D1

7156

4290

18965

20719

E2

36451

11988

-3610

38541

D2

218036

223558

220484

382271

E3

36617

13406

6291

39498

D3

230404

32965

80524

246286

MAX

36617

13406

-14495

41601

MAX

230404

223558

220484

382271

Redu?ao de Carga

8,8%

8,1%

4,2%

8,2%

10,2%

-3,1%

5,8%

4,9%

An extrapolation of the stiffness of the support was done
through computer simulation to evaluate the impact of the
same in static and dynamic loads. The study showed that
by acting on the stiffness of the support there can be a
significant gain in the reduction of static and dynamic
loads. However, the dynamic load presented smaller gains
in relation to the static load, this can be explained by the
change in the mode of vibration of the system, because
making the system more flexible also becomes more
subject to greater amplitudes of vibration, changing the
response of the system .

Figure 4 shows the decrease in modulus of the transmitted
forces in relation to the decrease in the stiffness of the
support. It is observed that the decrease in stiffness shows

significant gains for the static loading, while the dynamic
loading there are more moderate gains as the stiffness
decreases.

In this way in industrial projects submitted to great efforts,
the system must be designed for a reduction of stiffness
that guarantees the operation without that the same enters
resonance or has great amplitudes. A suitable working
range for the case under study would be a stiffness greater
than IE + 5 N / cm, as very low stiffness can lead to
excessive vibrations and damage to structures.

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1.00E+04 1.00E+05 1.00E+06 l.OOE+07 1,00E+{B 1.00E+09

Stiffness [N/cm]

» Modulo Estatico Maximo ■ Modulo Dinamico Maximo ■ Ganho Estatico [X] ■■ Ganho Dinamico [X]

Fig. 4: Fall of the transmitted efforts with the decrease of
the rigidity of the support and its respective percentage in
relation to the projected effort.

IV. CONCLUSION

The study showed that using the stiffness of the designed
support, a reduction in modulus of the loads transmitted to
structures of approximately 5% with respect to the load
anticipated in the initial design corresponding to a
reduction of effort of 2 tons transmitted the structures is
possible;

Special attention should be given to the vibration modes of
the system to avoid amplitude increase when decreasing
stiffness;

The study of the stiffness of the support can contribute
significantly to the reduction of the load transmitted the
support structures, and in the case studied could be
reduced by up to 50%, if the support was suitable for a
rigidity in the order of 1.0E + 5N / cm.

As a suggestion of refinement and continuity of this study
it is suggested an evaluation of the loading considering the
non-linearity of the material under conditions of dynamic
loading (short interval of time), and to evaluate the effects
of the loads by allowing in sporadic events that the support
works in the region of plasticity.

ACKNOWLEDGEMENTS

To Puc Minas University for the support and incentive to
this research

[Vol-5, Issue-6, Jun- 2018]
ISSN: 2349-6495(P) / 2456-1908(0)

[6] Williams, J. G., Anley, R. E., Nash, D. H., & Gray, T.
G. F. (2009). Analysis of externally loaded bolted
joints: analytical, computational and experimental
study. International Journal of Pressure Vessels and
Piping , 86(7), 420-427.

REFERENCES

[1] ASME B31.4 (2012). Pipeline Transportation Systems
for Liquidsand Slurries. New York: American Society
of Mechanical Engineers.

[2] Fish, J., Belytschko T. (2007) - A First Course In
Finite Elements. England: John Wiley & Sons Ltd.

[3] Hibbeler, R. C. (2009) Vibragoes. In: Dinamica:
Mecanica para engenharia. 10° Ed. Sao Paulo: Person
Education do Brasil.

[4] Sadd, M. H. (2009), Elasticity: Theory, Applications,
and Numerics, Academic Press, (2nd ed.). Burlington:
Elsevier Inc.

[5] Timoshenko, S.P. e Goodier, J.N. (1970), Theory of
Elasticity (3nd Ed.). New York: McGraw-Hill.

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