Free Vibration and Modal Analysis of Tower Crane Using SAP2000 and ANSYS

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1 Free Vibration and Modal Analysis of Tower Crane Using SAP2000 and ANSYS Huang, Li-Jeng 1, Syu, Hung-Jie 2 1 Associate Professor, Department of Civil Engineering, National Kaohsiung University of Applied Science, 80701, Taiwan, R.O.C. 2 Master Student, Institute of Civil Engineering, National Kaohsiung University of Applied Science, 80701, Taiwan, R.O.C. Abstract This paper presents finite element free vibration and modal analysis of a typical tower crane frame using SAP2000 and ANSYS. 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 the first leading twelve fundamental frequencies and periods of the tower crane obtained by SAP2000 and ANSYS, respectively, are obtained. The associated modes obtained from these two softwares are also resented and discussed. The discrepancies between these free vibration characteristics of the first nine modes calculated from different analysis programs are small than 10 %, and thus can be accepted in the sense of engineering application. There exist additional vibration modes with high frequency predicted by different software. Keywords ANSYS, Free Vibration, Modal Analysis, Tower Crane, SAP2000. I. 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 threedimensional 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 and ANSYS software was employed, respectively, 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 in detail. This document is template. We ask that authors follow some simple guidelines. In essence, we ask you to make your paper look exactly like this document. The easiest way to do this is simply to download the template, and replace(copy-paste) the content with your own material. II. DYNAMICS MODEL OF A TOWER CRANE FRAME A. 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 5.9 m height and in rectangular cross section with 1.5m x 1.5m, the horizontal arm is with length 50m and in triangular crosssection with width 1.5m x 1.5m. 26

2 B. 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, () 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. An easy way to comply with the conference paper formatting requirements is to use this document as a template and simply type your text into it. C. 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) f( t) (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: ( 2 M K) X 0 (2) and the natural frequencies 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] 27 M x ( t) K x( t) M a( t) (3) 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 Wilson-θ method or Newmark- β method. In SAP2000 we can choose the solution scheme by setting the dialogue window directly. A. Case Description III. NUMERICAL EXAMPLE In the preliminary numerical study we consider a typical tower crane frame with totally height of supporting column 5.9 m and length of loading arm 50m, made of the following L-shape structural steel members with the sizes: (1) 200 mm 200 mm 20 mm, (2) 90 mm 90 mm 7 mm, (3) 80 mm 80 mm 6 mm, and the cross-sectional properties (area and moments of inertia): (1) A 76 cm 2, I 2820 cm, I 2820 cm x y, (2) A 12.2 cm 2, I 93 cm, I 93 cm x y, (3) A 9.33 cm 2, I 56. cm, I 56. cm x y, and the ASTM992 was employed,the Young s modulus is Es 206 GPa,and the density is 7800 kg / m 3 s The finite element mesh using SAP2000 is summarized as follows: 1. Vertically supporting column: 26 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: 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. B. Free Vibration Analysis The natural frequencies and corresponding vibration modes of the finite element model of typical tower crane can be obtained using SAP2000.

3 The first leading 12 natural frequencies (f = ω/2π) and natural periods (T=1/f) are summarized in Table 1. The first leading 12 various vibration modes obtained from SAP2000 and ANSYS are shown in Fig. 2 to Fig. 13. 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 0.05 Hz to 5.6 Hz. There appear a lot of interesting different vibration mode shapes considering of pitching, rotation and yawing of horizontal arm, vertical column and horizontal tail (short arm) as well as some combined modes, as shown in the figures 2 to 13 [12]. These mode shapes can be itemized following the nomenclature employed in airplane dynamics since it is also can be considered as a dynamic system with 6 degrees of freedom (but tower crane is an elastic deformable structure). Defining the rotation with respect to x-axis to be pitching, the rotation with respect to y-axis to be rotation, and the rotation with respect to z-axis to be yawing, respectively, we can summarize the leading 12 natural modes of a typical tower crane to be as follows: (1) 1st-yawing of horizontal arm; (2) 1st-pitching of total tower; (3) 1st-rotating of total tower; () 1st-pitching of horizontal arm; (5) 2nd-yawing of horizontal arm; (6) 2nd-pitching of horizontal arm; (7) 2nd-rotating of column; (8) 1st-pitching of column; (9) 1st-rotating of horizontal arm; (10) combined rotating of column and yawing of arm; (11) 1st-pitching of tail; (12) Combined tail-pitching and column-pulsating. IV. CONCLUSION The famous structural analysis software SAP2000 and ANSYS has been successfully applied to analyze the free vibration 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 0.05 Hz to 6.0 Hz. Various vibration modal shapes can be observed from these two different kinds of structural analysis programs and compared with each other for correctness. Acknowledgements The authors would like to pay acknowledgements to the partially financial support under grant of KUAS-102-SC REFERENCES [1] Chin, C., Nayfeh, A. H. and Abdel-Rahman, E. M Nonlinear Dynamics on a Boom Crane, J. Vib.Contr., 7, [2] Abdel-Rahman, E. M., Nayfeh, A. H. and Masoud, Z. N Dynamics and Control of Cranes: A Review, J. Vib. Contr., 9, [3] S.C. Chu and N.L. Lu, Vibration Analysis of Loading Arms and Level Arms of a Tower Crane, J. Transp. Mach., 2, [] Y.W. Li, Study on the Seismic-Resistance Requirements of Crane for Construction of High-Rise Buildings. Master Thesis, National Taipei University of Technology. [5] J. M. Huang, Stability of Tower crane in Construction of High-Rise Buildings. Master Thesis, National Taipei University of Technology. [6] F. Ju and Y.S.Choo, Dynamic Analysis of Tower Cranes, ASCE J. Engng. Mech., 131, [7] F. Ju, Y.S. Choo and F.S. Cui, Dynamic Response of Tower Crane Induced by The Pendulum Motion of The Payload, Int. J. Solids and Struct., 3, [8] I. C. Tsai, Earthquake Response Analysis of High-Rise Building Assembled with Tower Canes and Apparatus. National Taiwan University. [9] C. Z. Shen, Study on the Ultimate Load Capacity of Tower crane Structure. National Chao-Yang University of Technology. [10] L. X Hu and Y. F. Li, Study on the Statics and Modal Shapes of Tower Crane, Trans. Ruo-Yang Tech. College, 20, [11] L. J. Huang and H. J. Syu, Static Analysis of Tower Crane Frame Using SAP2000, 2013 ACFA Conference, Kaohsiung, Taiwan, R.O.C., paper No. 7. [12] L. J Huang and H. J. Syu, Free Vibration Analysis of Tower Crane Frame Using SAP2000, 2013 ACFA Conference, Kaohsiung, Taiwan, R.O.C., paper No

TABLE I NATURAL FREQUENCIES AND PERIODS FOR A TYPICAL TOWER CRANE Frequencies (Hz) SAP2000 Frequencies (Hz) ANSYS Periods (sec) SAP2000 Periods (sec) ANSYS Discrepancies (%) (SAP-ANSYS)/ANSYS *100%

4 TABLE I NATURAL FREQUENCIES AND PERIODS FOR A TYPICAL TOWER CRANE Frequencies (Hz) SAP2000 Frequencies (Hz) ANSYS Periods (sec) SAP2000 Periods (sec) ANSYS Discrepancies (%) (SAP-ANSYS)/ANSYS *100% Mode Mode Mode Mode Mode Mode Mode Mode Mode Mode Mode ANSYS additional Mode Fig. 1 Schematic of a typical tower crane frame using SAP2000 and ANSYS 29

5 1 st mode from SAP2000 ( Hz) 1st mode from ANSYS (0.059 Hz) Fig. 2 The first modes obtained from SAP2000 and ANSYS (1st-yawing of horizontal arm) 2nd mode from SAP2000 ( Hz) 2nd mode from ANSYS (0.206 Hz) Fig. 3 The second modes obtained from SAP2000 and ANSYS (1st-pitching of total tower) 30

6 3rd mode from SAP2000 ( Hz) 3rd mode from ANSYS (0.360 Hz) Fig. The third modes obtained from SAP2000 and ANSYS (1st-rotaing of total tower) th mode from SAP2000 ( Hz) th mode from ANSYS (0.535 Hz) Fig. 5 The fourth modes obtained from SAP2000 and ANSYS (1st-pitching of horizontal arm) 31

7 5th mode from SAP2000 ( Hz) 5th mode from ANSYS (1.661 Hz) Fig. 6 The fifth modes obtained from SAP2000 and ANSYS (2nd-yawing mode of horizontal arm) 6th mode from SAP2000 ( Hz) 6th mode from ANSYS (2.19 Hz) Fig. 7 The sixth modes obtained from SAP2000 and ANSYS (2nd-pitching of horizontal arm) 32

8 7th mode from SAP2000 ( Hz) 7th mode from ANSYS (2.80 Hz) Fig. 8 The seventh modes obtained from SAP2000 and ANSYS (2nd-rotating of column) 8th mode from SAP2000 (3.607 Hz) 8th mode from ANSYS (3.535 Hz) Fig. 9 The eighth modes obtained from SAP2000 and ANSYS (1st-pitching of column) 33

9 9th mode from SAP2000 ( Hz) 9th mode from ANSYS(3.58 Hz) Fig. 10 The nineth modes obtained from SAP2000 and ANSYS (1st-rotating of horizontal arm) 10th mode from SAP2000 (3.889 Hz) 10th mode from ANSYS(.75 Hz) Fig. 11 The tenth modes obtained from SAP2000 and ANSYS (combined rotating of column and yawing of arm) 3

10 11th mode from SAP2000 (.989 Hz) 11th mode from ANSYS(.757 Hz) Fig. 12 The 11th modes obtained from SAP2000 and ANSYS (1st-pitching of tail) 12th mode from SAP2000 ( Hz) 13 th mode from ANSYS( Hz) Fig. 13 The 12th modes obtained from SAP2000 and ANSYS (Combined tail-pitching and column-pulsating) 35

Passive Vibration Control Synthesis of Power Transmission Tower Using ANSYS: Part II - Control of Seismic Response

Passive Vibration Control Synthesis of Power Transmission Tower Using ANSYS: Part II - Control of Seismic Response Huang Li-Jeng 1, Lin Yi-Jun 1 Associate Professor, Department of Civil Engineering, National