seismic response analysis of tower crane using sap2000
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Procedia Engineering 79 (2014) 513 – 522
Available online at www.sciencedirect.com
1877-7058 © 2014 Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/3.0/ ).
Selection and peer-review under responsibility of the National Tsing Hua University, Department of Power Mechanical Engineeringdoi:10.1016/j.proeng.2014.06.374
ScienceDirect
37th National Conference on Theoretical and Applied Mechanics (37th NCTAM 2013) & The 1stInternational Conference on Mechanics (1st ICM)
Seismic Response Analysis of Tower Crane Using SAP2000
Huang Li-Jenga* and Syu Hong-Jie b
a Associate Professor, Department of Civil Engineering, National Kaohsiung University of Applied Science, 80701, Taiwan, R.O.C.b Master Student, Institute of Civil Engineering, National Kaohsiung University of Applied Science, 80701, Taiwan, R.O.C.
Abstract
This paper presents a finite element seismic response simulation of a typical tower crane frame using SAP2000. Three-
dimensional beam elements and bar elements are employed for vertical and horizontal frames as well as the tie rods, respectively,
to build up the numerical model. Then numerical example is considered and two kinds of earthquake ground accelerations are
tested, i.e., 1940 NS component of the El Centro and 1995 Kobe accelerations. The dynamic responses of displacement, velocity
and accelerations of a typical node of the tower crane frame are illustrated and discussed. The numerical simulation results show
that the maximal displacements might be large to over 1 meter and the associated maximal velocity and acceleration can be
greater than 4 m/s and 40 m/s2, respectively at the highest position of tower crane.
© 2013 The Authors. Published by Elsevier Ltd.
Selection and peer-review under responsibility of the National Tsing Hua University, Department of Power Mechanical
Engineering.
"Keywords: Seismic response analysis; Tower crane frame; SAP2000 ; Finite element method."
Nomenclature
a(t) ground acceleration
f natural frequencies ( Hz)
f (t) load vector
K stiffness matrix
* Corresponding author. Tel.:+886-7-3814526 ext 5230; fax:+886-7-3478019.
E-mail address: [email protected]
© 2014 Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/3.0/ ).
Selection and peer-review under responsibility of the National Tsing Hua University, Department of Power Mechanical
Engineering
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514 Huang Li-Jeng and Syu Hong-Jie / Procedia Engineering 79 (2014) 513 – 522
M mass (inertia) matrix N total number of constrained degrees of freedom
T natural periods ( sec)
x(t) displacement vectors
Greek symbols
natural frequencies (rad/sec)
Subscriptsn sequential order of natural frequencies
1. Introduction
Tower cranes are widely employed in civil engineering for construction of high-rise buildings. During the period
of construction it becomes an additional structure aside of the constructed building and thus its structural stability
and safety is of the same importance with the major target building. In the past many preceding preliminary studies
on the static, stability and dynamic behaviors of the tower crane for high-rise buildings have been conducted [1-10].
Some disasters related to the tower cranes occurred in the past in Taiwan and other countries are due to different
causes: earthquake shaking-down, fracture of members, flexural failure, etc. [11]. The disasters caused from the
tower cranes include the destruction of the construction apparatus, people hit by the heavy falling-down components,induced failure of subordinate structures, etc.
The special features of tower crane structures are their relatively light weight and flexible as compared with the
major target building. When subjected to wind loading and earthquake excitation, giant displacements and internal
stresses of the structural members might be induced and lead to sudden failure and/or long-term fatigue. From the
points of view on structural mechanics, tower crane frame is a integrated three-dimensional truss or frame structure
made with a lot of bar elements, to form an integrated structures comprised with a major vertical supporting column,
a horizontal loading arm and some tensile tendons. However, analytical structural analysis of tower-type is difficult
due to its complicated and three-dimensional features and many trials are based on the matrix methods of structural
analysis and finite element methods [10-12].
This paper presents numerical modeling and structural dynamic analysis of a typical tower crane employed in
construction engineering. SAP2000 software was employed and finite element method is adopted. A typical
numerical example was considered, totally 516 three-dimensional beam elements with 207 nodes are employed forthe vertical and horizontal frame parts and bar elements are used for tensile tendons, respectively. Natural
frequencies and vibration modes were discussed and then the seismic responses due to 1940 NS component of El
Centro and 1995 Kobe ground accelerations are discussed in detail.
2. Dynamics Model of a Tower crane Frame
2.1. Problem Description
A typical tower crane is shown in Fig. 1. It comprises with basically three major parts: (1) a stretchable vertical
supporting column made of trusses and frames, (2) a horizontal cantilevered loading arms made of trusses and
frames, and (3) steel tensile tendons supporting the horizontal arms. The vertical column is with 54.9 m height and
in rectangular cross section with 1.5m x 1.5m , the horizontal arm is with length 50m and in triangular cross-sectionwith width 1.5m x 1.5m.
2.2. Basic Assumptions
For the structural analysis of the tower crane frame we employed the following hypotheses: (1) all the member in
the vertical column and horizontal arms are considered to be three-dimensional thin beams and only flexural and
stretching behaviors are included, Euler-Bernoulli assumptions are employed (2) the tensile tendons are considered
as pure tension members, (3) all the members are in small deformations, (4) all the stresses and strains of the
structural members are in linear elastic range and the Hookes law applied, and (5) damping effects are negligible.
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2.3. Finite Element Models
In this research we employ SAP2000 to build up the finite element model of the tower crane using the following
structural elements:
(1) Vertically supporting column: three-dimensional beam elements.
(2) Horizontally loading arm: three-dimensional beam elements.
(3) Steel tensile tendons: bar elements.After assemblage of the element mass and stiffness matrices and loading vectors, we obtain the global systematic
matrices and vectors and then enforce the prescribed boundary conditions (e.g. the fixed ends at the bottom of the
vertical supporting column) we can express the equations of motion of the finite element model of the tower crane
as
)()()( t t t f xK xM (1)
where M and K denotes the inertia and stiffness matrix, respectively; x (t) and x(t) denotes the acceleration vector
and displacement vector, respectively, and f (t ) denotes the external loading vector.
When free vibration is considered, f (t ) = 0, and under the assumption of sinusoidal motion, we can obtain the
eigen-value system:
0)2( XK M (2)
and the natural frequencies n and vibration modes Xn, N n ,2,1 can be obtained.
When the loading is due to earthquake ground excitations, the equations of motion (1) can be rewritten to be [13]
)()()( t t t aMxK xM (3)
in which a(t ) denotes the ground acceleration. In the dynamic response analysis the initial conditions 0xx (0)(0)
are prescribed. The dynamic responses can be solved by various numerical schemes such as Wilson
3. Numerical Example
3.1. Case Description
In the preliminary numerical study we consider a typical tower crane frame with totally height of supporting
column 54.9 m and length of loading arm 50m, made of the following L-shape structural steel members with the
sizes:
(1) ,20200200 mmmmmm
(2) ,79090 mmmmmm
(3) ,68080 mmmmmm
and the cross-sectional properties (area and moments of inertia):
(1) ,42820,42820,276 cm y I cm x I cm A
(2) ,493,493,22.12 cm y I cm x I cm A
(3) ,44.56,44.56,233.9 cm y I cm x I cm A
and the ASTM992 was employedthe Young’s modulus is GPa s E 206 and the density is
3/7800 mkg s
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The finite element mesh using SAP2000 is summarized as follows:
(1) Vertically supporting column: 264 three-dimensional beam elements with totally 92 nodes.
(2) Horizontally loading arm: 270 three-dimensional beam elements with totally 117 nodes.
(3) Steel tensile tendons: 4 bar elements with totally 5 nodes.
The overall numerical model of a space frame structure comprises of 207 nodes (each on e has 6 degrees of
freedom), 516 elements and is fixed at the bottom of the vertical supporting column onto ground.
3.2. Free Vibration Analysis
The natural frequencies and corresponding vibration modes of the finite element model of typical tower crane can
be obtained using SAP2000. The first leading 12 natural frequencies ( f = ) and natural periods (T=1/f ) are
summarized in Table 1 and the leading 2 major vibration modes are shown in Fig. 2. (The first leading 12 various
vibration modes can be referred to [8]). It can be clearly found that the fundamental natural frequencies of the
typical tower crane are generally lower than those of major RC buildings. The leading 12 natural frequencies range
from 0.3 Hz to 6.5 Hz . While the first 2 fundamental vibration modes are bending modes in x and z directions, there
exists complicated torsional, twisting and combined modes corresponding to higher frequencies [12].
3.3. Seismic Response Analysis
Time-domain history of tower crane subjected to typical earthquake ground motion is interesting to structural
engineers. We consider two typical earthquake acceleration records for the dynamic response analysis of the
numerical model of tower crane: (1) 1940 NS component of El Centro ground motion, (2) 1995 Kobe ground
motion. The maximal displacement, velocity and accelerations obtained from the nodal point located at the highest
position (i.e. the nodal no. 105 with coordinates [75, 0, 5490]) of tower crane due to two typical seismic excitations
are summarized in Table 2. The corresponding simulated results of time history of seismic responses in x-direction
(transversal to the horizontal loading arm) are shown in Fig. 3a to Fig 3d for El Centro, and Fig. 4a to Fig. 4d for
Kobe earthquake excitation, respectively. It an be depicted that the maximal displacements of the typical tower
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crane due to earthquake excitations can be large to more than 1 meter and the associated maximal velocity and
acceleration can be greater than 4 m/s and 40 m/s2, respectively.
Table 1.Natural frequencies and periods for a typical tower crane frame
Natural Frequencies f ( Hz ) Natural Periods T (sec) Mode 1 0.291 3.435
Mode 2 0.380 2.628
Mode 3 1.207 0.828
Mode 4 1.357 0.737
Mode 5 2.950 0.339
Mode 6 3.041 0.329
Mode 7 3.193 0.313
Mode 8 3.713 0.269
Mode 9 4.248 0.235
Mode 10 6.117 0.163
Mode 11 6.186 0.162
Mode 12 6.458 0.155
Table 2. Maximal displacement, velocity and accelerations of the typical tower crane subjected to two typicalseismic ground motions
1940 NS Component of El Centro
ground motion
1995 Kobe ground motion
Maximal Displacement (m) 1.459 1.112
Maximal Velocity (m/s) 4.525 3.734
Maximal Acceleration (m/s2) 43.47 40.51
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4. Concluding Remarks
The famous structural analysis software SAP2000 has been successfully applied to analyze the free vibration and
seismic responses of a typical tower crane frame structure. Finite element model is first built up using three-
dimensional beam elements for the vertical supporting column and the horizontal cantilever loading arm as well as
bar elements for the tensile steel tendons. It is found that the fundamental natural frequencies of the typical tower
crane are generally lower than those of major RC buildings and the leading 12 natural frequencies range from 0.3 Hz to 6.5 Hz . After tested by 1940 NS component of El Centro and 1995 Kobe ground motions, the seismic response
analysis depicted that the maximal displacements of the typical tower crane due to earthquake excitations can be
large to more than 1 meter and the associated maximal velocity and acceleration can be greater than 4 m/s and 40
m/s2, respectively.
Acknowledgements
References
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earthquake
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