COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE
EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China
©2006 Tsinghua University Press & Springer
Elasto-Plastic Finite Element Analysis of a Tapered Steel Silo
C.L. Xu *, Y. F. Luo, H. J. Song
College of Civil Engineering, Tongji University, 1239 Sipping Road, Shanghai, 200092 China
E-mail: [email protected]
Abstract The large displacement elasto-plastic behavior of tapered steel silos is analyzed. The finite element method
(FEM) is used for the simulation of the structure. ANSYS program is used for numerical computation. The spatial
mechanical model of the silo is created and presented. Main static characters of the silos including the Mises stress
distribution of beams and shells and the loading capacity of silos have been obtained. On the basis of numerical results,
the specific problems such as section choice of the silo beams and loading capacity are solved and a reasonable design
scheme of the silos is proposed.
Keywords: tapered silo, easto-plastic, finite element analysis, loading capacity
INTRODUCTION
The tapered steel silos are used in storage and accumulation of bulk granular materials. Their usage in different
branches of industry is numbered about one hundred already, but they are one of the weaker studied building
constructions. The reason is that steel silo design is a very complicated subject covered by the thin shells and stiffened
plate structures. The load distribution of the steel silos is uncertain. The stresses of the beams and shells are difficult to
be accurately calculated under the design load. In addition, there are no special analysis techniques and assessing
methods for the design of the tapered steel silos in current national design codes of our country, which results in
creating uneconomic and unreliable silos and supporting systems. The cases of accidents and damages of the steel silos
are well known in engineering practice. It is necessary to carry on the large displacement elasto-plastic finite element
analysis for the tapered steel silo structure to obtain the loading capacity of the beams and shells during design.
According to the design command, the large displacement elasto-plastic analysis of the tapered steel silo structure of
Taiyuan Mining Vertical Preheater is conducted in the paper. The silo structure is divided into beam and shell elements
and calculations are carried out by means of ANSYS software [1]. The reliable numerical data are provided to the
design. The valuable ideas about the loading behavior of the tapered silo are concluded. It is a useful reference for
design of similar silo structures.
THE MODEL OF THE TAPERED SILO
1. Construction of the Tapered Steel Silo The vertical cross-sections of the tapered steel silo used for Taiyuan Mining
Vertical Preheater are shown in Fig. 1.
A typically tapered silo consists of an inner taper and an outer taper. The ring beams are placed on the top of the tapers
of the steel silo. Outer silo walls are directly supported on eighteen columns. All the walls of two tapers are made of
thin steel sheets (10 mm). To be able to grasp pressure of the granular material or other technological loads, the walls
are strengthened by sloping beams being situated slopingly every 20 degree in a circle. The stiffening plates were used
in junctions where sloping beams intersect silo walls. The structure steel is Q235. The section dimensions of the main
members are listed in Table 1.
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(a) Vertical Cross-section of Original Scheme
(b) Vertical Cross-section of Modified Scheme
Fig.1. Vertical Cross-Sections of Tapered Steel Silos
1: top ring beam of outer taper; 2: sloping beam of outer taper; 3: stiffening plate in junction; 4: silo wall
5: supporting column; 6: floor stiffening plate; 7: floor beam; 8-sloping beam of inner taper; 9: top ring beam of inner taper
Table 1 Sectional Dimensions of Main Members
Item No
1
2
3
4
5
Sectional
Dimensions
C360×96×9×16
(2C360×96×9×16)
H233×95×199×8×6×12
Plate12
Plate 10
H350×350×12×19
Item No
6
7
8
9
———
Sectional
Dimensions
Plate 10
H700×300×13×24
H700×300×13×24 C1150×128×12×20
———
2.2 Finite Element Model for Numerical Analysis It is well known that the silo design is a complicated subject
covering the analysis of thin shells and stiffened plate structure with uncertain load distribution. That’s why for the
presented research the finite element ideology and methodology allow for using of it for static analysis of the silo work.
The computation is done by means of ANSYS software.
In the process of the investigations, the system of numerical experiments is use for optimal design. Two constructive
schemes of the taper steel silo are analyzed. The first model (Fig. 1(a)) represents the original structure design. The
second model (Fig. 1(b)) is the modified structure scheme after optimal design. The shapes and the dimensions of top
beams of outer taper and stiffening plates in junction are changed in the second model.
1
ELEMENTS
JAN 18 2006
10:21:53
Y
Z
X
Fig.2 Finite Element Model of the Tapered Steel Silo
The finite element model of the spatial shell structure of the silo is shown in Fig. 2. The shell element shell43 and beam
element beam188 with 6 degrees of freedom in each node are used. The whole numbers of the degrees of freedom of the
two models are 71544 and 66048 respectively. The two models are completely fixed at the foot of supporting columns.
⎯ 346 ⎯
The ideal elasto-plastic stress-strain model of steel is adopted to study structural bearing behavior of taper steel silo
considering material plasticity. The material parameters of steel are f=235MPa (design strength), fy=235MPa (yield
strength), E=206GPa (Young’s modulus) andν=0.3 (Poisson ratio)[2].
The plane figure of the concentrated loads is shown in Fig. 3. Three concentrated forces are applied on the top ring
beam of outer taper. The loads are 370kN, 234kN and 20 KN respectively. The design values of load are used in design
calculations. The load factor is 1.2.
Figure 3: Plane Figure of Concentrated Loads
NUMERICAL RESULTS
The loading capacity of a structure is very important for design. Sometimes even an expected imperfection in the
structures will result in the overall damage or collapse of the structure. Therefore the influence of any change in the
structure on its loading capacity should be well studied to ensure the structure safety. From this point of view, the large
displacement elasto-plastic analysis is conducted to obtain the loading capacity of the tapered steel silo.
1. The Stress Distribution under Concentrated Loads From the numerical results of the large displacement
elasto-plastic finite element analysis, the maximal Von Mises stresses of taper steel silo under concentrated loads are
shown in Table 2.
Table 2 Maximal Stresses under Primary Load
Item No
Shell elements
Top beam elements
Plate12
Original Scheme
235 MPa
235 MPa
118 MPa
Modified Scheme
55 MPa
193 MPa
33 MPa
For the original scheme, the maximal stresses of top ring beam and shell elements reach the yield stress of 235 MPa in
the loading point of the concentrated force (F = 370 kN). The stresses of the ring beam and shell of the original scheme
is greater than the design strength (f = 215 MPa) of the steel. The original scheme will not satisfy the structure safety.
The section dimension of the top ring beam must be enlarged. Two channel steels are adopted in the modified scheme
for strengthening the top ring beam properly. For the modified scheme, the maximal stresses of top ring beam and shell
elements are reduced to 193 MPa and 55 MPa in the loading point of the concentrated force (F = 370 kN) respectively.
The maximal stress of ring beam is less than the design strength of the steel. The stresses of shell elements are greatly
reduced because top ring beams is strong enough to bear the concentrated loads. The modified scheme can satisfy
structure safety requirement. The stress diagram of top ring beams is shown in Fig. 4.
From the stress distribution of stiffening plate in junction shown in Fig. 5, the maximal stress of the stiffening plates is
118 MPa in the original scheme and only 33 MPa in the modified scheme. The high stress concentration appears easily
in the original scheme. The stiffening plate with sharp angles is harmful and dangerous in structure. The sharp angle
often makes stress concentration when the structure bears loads, which may result in collapse of the structure. The
sharp angles are cut down in the modified model for improving the plate with a reasonable sharp. Therefore, the
⎯ 347 ⎯
1
1
NODAL SOLUTION
NODAL SOLUTION
MAR 15 2006
21:57:43
STEP=1
SUB =15
TIME=.511177
SEQV
(AVG)
DMX =.02532
SMN =794940
SMX =.235E+09
MAR
STEP=1
SUB =8
TIME=.272741
SEQV
(AVG)
DMX =.0071
SMN =375009
SMX =.209E+09
1 2006
15:21:54
MN
MN
MX
794940
.528E+08
.268E+08
.105E+09
.789E+08
.157E+09
.131E+09
MX
.209E+09
.183E+09
375009
.235E+09
.468E+08
.236E+08
(a) Stress Distribution of Original Schemes
.932E+08
.700E+08
.140E+09
.116E+09
.186E+09
.163E+09
.209E+09
(b) Stress Distribution of Modified Schemes
Figure 4: Stress Distribution of Top Ring Beams
1
1
NODAL SOLUTION
NODAL SOLUTION
MAR 15 2006
22:08:08
STEP=1
SUB =15
TIME=.511177
SEQV
(AVG)
DMX =.003593
SMN =.172E+07
SMX =.118E+09
MAR
STEP=1
SUB =8
TIME=.272741
SEQV
(AVG)
DMX =.001927
SMN =395152
SMX =.331E+08
MN
1 2006
15:34:01
MN
Stress concentration point
MX
.172E+07
.276E+08
.147E+08
.535E+08
.406E+08
.794E+08
.665E+08
MX
.105E+09
.923E+08
395152
.118E+09
.766E+07
.403E+07
(a) Stress Distribution of Original Scheme
.149E+08
.113E+08
.222E+08
.186E+08
.295E+08
.258E+08
.331E+08
(b) Stress Distribution of Modified scheme
Figure 5: Stress Distribution of Stiffening Plates in Junction
stresses of stiffening plates in the modified scheme become less than the one of original scheme and the stress
distribution is more reasonable.
2. The Loading Capacity and Load-Displacement Curve For ideal elasto-plastic steel, the members will get into
plastic stage when the member stress reaches their yield strength. The stress will no longer rise, but the strain continues
to go up. Therefore the stress distribution of shell and beam elements in plastic stage must be different from the one in
elastic stage [4]. When concentrated forces reach the ultimate loading, the plastic zone become more and more larger
gradually until the taper steel silo collapses. The major plastic zones of two models appear near concentrated loading
points. The load factors and stresses of the steel silo are listed in Table 3. The stress diagrams of top ring beam and shell
elements at the ultimate loading are shown in Fig. 6.
Table 3 Load Factors and Maximal Stresses under Ultimate Loads
Item No
Load factor Shell element
Top beam element
Plate12
Original scheme
1.51
235 MPa
235 MPa
235 MPa
Modified scheme
3.43
235 MPa
235 MPa
235 MPa
From the load-displacement curves of two schemes shown in Fig. 7, the linear behavior is obvious in early stage. With
increment of loading, step by step, the load-displacement curves appear yield platform clearly. The plastic zones are
formed in the top ring beams and the shells of the structure. The plastic zones and displacements become large
obviously at the stage of yield platform. The loads on the structure will not rise any more. At last the structure
generated the plastic damage and collapse. The ultimate loading capacity of original scheme is 1.51 times as design
load, that is the load factor n = 1.51. The load factor of modified scheme is n = 3.43. The structure of the original
scheme appears plastic before the load factor reaches 1.0. The structure of the modified scheme appears plastic when
the load factor reaches to 2.0. Therefore the modified scheme has enough safety and can satisfy the design requirement
of the structure.
⎯ 348 ⎯
1
1
NODAL SOLUTION
NODAL SOLUTION
MAR
STEP=1
SUB =42
TIME=.752742
SEQV
(AVG)
DMX =.091246
SMN =.212E+07
SMX =.235E+09
1 2006
14:32:41
MAR
STEP=1
SUB =42
TIME=.752742
SEQV
(AVG)
DMX =.086511
SMN =110756
SMX =.307E+09
1 2006
14:40:07
Y
MN
MN
Z
X
MX
MX
.212E+07
.539E+08
.280E+08
.106E+09
.797E+08
.157E+09
.131E+09
110756
.209E+09
.183E+09
.682E+08
.342E+08
.235E+09
.136E+09
.102E+09
.204E+09
.170E+09
.273E+09
.239E+09
.307E+09
(a) Stress distribution of original Scheme
1
1
NODAL SOLUTION
NODAL SOLUTION
MAR
STEP=1
SUB =48
TIME=.857529
SEQV
(AVG)
DMX =.080027
SMN =.173E+07
SMX =.235E+09
1 2006
10:04:28
MAR
STEP=1
SUB =48
TIME=.857529
SEQV
(AVG)
DMX =.078676
SMN =229660
SMX =.283E+09
1 2006
10:06:47
Y
MN
Z
X
MX
MN
MX
.173E+07
.536E+08
.277E+08
.105E+09
.795E+08
.157E+09
.131E+09
229660
.209E+09
.183E+09
.631E+08
.316E+08
.235E+09
.126E+09
.945E+08
.189E+09
.157E+09
.252E+09
.220E+09
.283E+09
(b) Stress distribution of modified scheme
Figure 6: Stress distribution of top ring beam and shell elements
(a) Load-displacement curves of original schemes
(b) Load-displacement curve of modified schemes
Figure 7: Load-displacement curves of taper steel silos
CONCLUSIONS
Presented data give the idea about the large displacement elasto-plastic finite element analysis of tapered steel silos
which is useful in the process of static analysis. The Mises stress distribution of beams and shells and the loading
capacity of silos have been obtained. A reasonable design scheme of the silos is proposed in the paper. Therefore the
large displacement elasto-plastic finite element analysis can help to ensure the safety of structures and solve some
specific problems such as section choice of silo beams, weak region of silo structure.
⎯ 349 ⎯
REFERENCES
1.
Hao WH. ANSYS 7.0 Analysis and Application Examples. Tsinghua University Press, Beijing, China, 1995 (in
Chinese).
2.
The Ministry of Construction of P. R. China. Code for Design of Steel Structures (GBJ50017-2003). China
Planning Press, Beijing, Chna, 2003 (in Chinese).
3.
Wang XC, Shao M. Basic Principle and Numerical Methods of the Finite Element Method. Tsinghua University
Press, Beijing, China, 1995 (in Chinese).
4.
Xu BY, Liu XS. Applied Elasto-Plastic Mechanics. Tsinghua University Press, Beijing, China, 2003 (in
Chinese).
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