Seismic Response Analysis of Tower Crane Using SAP2000

Available online at www.sciencedirect.com

ScienceDirect Procedia Engineering 79 (2014) 513 – 522

37th National Conference on Theoretical and Applied Mechanics (37th NCTAM 2013) & The 1st International Conference on Mechanics (1st ICM)

Seismic Response Analysis of Tower Crane Using SAP2000 Huang Li-Jenga* and Syu Hong-Jieb 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. Threedimensional 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 2014 The Elsevier Ltd. This is an open access article © Authors. Published by Elsevier Ltd. 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 Selection and peer-review under responsibility of the National Tsing Hua University, Department of Power Mechanical Engineering. Engineering "Keywords: Seismic response analysis; Tower crane frame; SAP2000 ; Finite element method."

Nomenclature a(t) f f(t) K

ground acceleration natural frequencies (Hz) load vector stiffness matrix

* Corresponding author. Tel.:+886-7-3814526 ext 5230; fax:+886-7-3478019. E-mail address: [email protected]

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 Engineering doi:10.1016/j.proeng.2014.06.374

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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 ȷ natural frequencies (rad/sec) Subscripts n 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 for the 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-section with 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 M x(t ) K x(t )

(1)

f (t )

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: (Z 2 M K ) X

(2)

0

and the natural frequencies Z n and vibration modes Xn, n 1,2, " N can be obtained. When the loading is due to earthquake ground excitations, the equations of motion (1) can be rewritten to be [13] M x(t ) K x(t )

(3)

M a(t )

in which a(t) denotes the ground acceleration. In the dynamic response analysis the initial conditions x(0) x (0) 0 are prescribed. The dynamic responses can be solved by various numerical schemes such as WilsonĮȧġ ŮŦŵũŰťġ Űųġ ŏŦŸŮŢųŬĮȡġŮŦŵũŰťįġŊůġŔłőĳıııġŸŦġŤŢůġŤũŰŰŴŦġŵũŦġŴŰŭŶŵŪŰůġŴŤũŦŮŦġţźġŴŦŵŵŪůŨġŵũŦġťŪŢŭŰŨŶŦġŸŪůťŰŸġťŪųŦŤŵŭźįġ 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) 200 mm u 200 mm u 20 mm, (2) 90 mm u 90 mm u 7 mm, (3) 80 mm u 80 mm u 6 mm, and the cross-sectional properties (area and moments of inertia): (1) A 76 cm 2 , I x 2820 cm 4 , I y 2820 cm 4 , (2) A 12.2 cm 2 , I x 93 cm 4 , I y 93 cm 4 , (3) A 9.33 cm 2 , I x 56.4 cm 4 , I y 56.4 cm 4 , and the ASTM992 was employedˈthe Young’s modulus is E s U s 7800 kg / m 3 Ǆ

206 GPa ˈand the density is

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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. ġ ġ ġ ġ ġ ġ ġ ġ ġ ġ ġ ġ ġ ġ ġ ŇŪŨįġĲġġŔŤũŦŮŢŵŪŤġŰŧġŢġŵźűŪŤŢŭġŵŰŸŦųġŤųŢůŦġŧųŢŮŦġŶŴŪůŨġŔłőĳıııġ

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 =ġ ȷİĳȯ) 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 Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 Mode 6 Mode 7 Mode 8 Mode 9 Mode 10 Mode 11 Mode 12

Natural Frequencies f (Hz) 0.291 0.380 1.207 1.357 2.950 3.041 3.193 3.713 4.248 6.117 6.186 6.458

Natural Periods T (sec) 3.435 2.628 0.828 0.737 0.339 0.329 0.313 0.269 0.235 0.163 0.162 0.155

ġ ġ ġ ġ ġ ġ ġ ġ ġ ġ ĩŢĪġġġġġġġġġġġġġġġġġġġġġġġġġġġġġġġġġġġġġġġġġġġġġġġġġġġġġġġġġġġġġġġĩţĪġ ŇŪŨįġĳġŕũŦġŭŦŢťŪůŨġŵŸŰġŷŪţųŢŵŪŰůġŮŰťŦŴġĩŢĪġŧŪųŴŵġŮŰťŦġĩıįĳĺĲŉŻĪġĩţĪġŴŦŤŰůťġŮŰťŦġĩıįĴĹıġŉŻĪġ

Table 2. Maximal displacement, velocity and accelerations of the typical tower crane subjected to two typical seismic ground motions

Maximal Displacement (m) Maximal Velocity (m/s) Maximal Acceleration (m/s2)

1940 NS Component of El Centro ground motion 1.459 4.525 43.47

1995 Kobe ground motion 1.112 3.734 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 threedimensional 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 ŕũŦġŢŶŵũŰųŴġŸŰŶŭťġŭŪŬŦġŵŰġűŢźġŢŤŬůŰŸŭŦťŨŦŮŦůŵŴġŵŰġŵũŦġűŢųŵŪŢŭŭźġŧŪůŢůŤŪŢŭġŴŶűűŰųŵġŶůťŦųġŨųŢůŵġŰŧġŌŖłŔĮĲıĳĮŔńĮııĲį References [1] C. Chin, A. H. Nayfeh, E. M. Abdel-Rahman, Nonlinear Dynamics on a Boom Crane, J. Vib.Contr., 7 (2001), 199ȸ220. [2] E. M. Abdel-Rahman, A. H. Nayfeh, Z. N. Masoud, Dynamics and Control of Cranes: A Review, J. Vib. Contr., 9 (2003) 863ȸ908. [3] S-C Chu, N-L Lu, Vibration Analysis of Loading Arms and Level Arms of a Tower Crane, J. Transp. Mach., 2 (2003) 35 - 39 [4] Y-W, Li, Study on the Seismic-Resistance Requirements of Crane for Construction of High-Rise Buildings. Master Thesis, National Taipei University of Technology, 2005. [5] J-M Huang, Stability of Tower crane in Construction of High-Rise Buildings. Master Thesis, National Taipei University of Technology, 2005. [6] F. Ju, Y.S.Choo, Dynamic Analysis of Tower Cranes, ASCE J. Engng. Mech., 131 (2005) 88ȸ96. [7] F. Ju, Y.S. Choo, F.S. Cui, Dynamic Response of Tower Crane Induced by The Pendulum Motion of The Payload, Int. J. Solids and Struct., 43 (2006) 376-389. [8] I-C Tsai, Earthquake Response Analysis of High-Rise Building Assembled with Tower Canes and Apparatus. National Taiwan University, 2006. [9] C-Z Shen, Study on the Ultimate Load Capacity of Tower crane Structure. National Chao-Yang University of Technology, 2010. [10] L-X Hu, Y-F Li, Study on the Statics and Modal Shapes of Tower Crane, Trans. Ruo-Yang Tech. College, 20 (2010) 27 - 29. [11] L-J Huang, H-J Syu, ”Static Analysis of Tower Crane Frame Using SAP2000,” 2013 ACFA Conference, Kaohsiung, Taiwan, R.O.C., paper No. 7, 2013. [12] L-J Huang, H-J Syu, ”Free Vibration Analysis of Tower Crane Frame Using SAP2000,” 2013 ACFA Conference, Kaohsiung, Taiwan, R.O.C., paper No. 10, 2013. [13] G. C. Hart, K. Wong, Structural Dynamics for Structural Engineers. John-Wiley & Sons, Inc., 2000.

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Seismic Response Analysis of Tower Crane Using SAP2000

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