Proceedings. The 2 nd INDONESIAN STRUCTURAL ENGINEERING AND MATERIALS SYMPOSIUM. Bandung, 7 ~ 8 November Publisher:

The 2nd INDONESIAN STRUCTURAL ENGINEERING AND MATERIALS SYMPOSIUM Bandung, 7 ~ 8 November 2013

Proceedings

Publisher: Department of Civil Engineering – Faculty of Engineering Parahyangan Catholic University

Editor: Johannes Adhijoso Tjondro Helmy Hermawan Tjahjanto

Copyright © 2013 by Department of Civil Engineering – Faculty of Engineering, Parahyangan Catholic University All rights reserved. Printed in Indonesia. Published by: Department of Civil Engineering – Faculty of Engineering, Parahyangan Catholic University, Jalan Ciumbuleuit No. 94, Bandung. Phone: (022)2033691, Facs: (022)2033692

The 2nd INDONESIAN STRUCTURAL ENGINEERING AND MATERIALS SYMPOSIUM

KATA PENGANTAR

Pada kesempatan yang baik ini, perkenankan saya menyampaikan selamat datang kepada para peserta The 2nd Indonesian Structural Engineering and Materials Symposium (The 2nd ISEMS). Simposium dua tahunan ini merupakan kegiatan yang rutin diadakan oleh KBI Teknik Struktur, Jurusan Teknik Sipil Universitas Katolik Parahyangan. Pada penyelenggaraannya yang kedua, simposium dilaksanakan di kampus Unpar di wilayah Bandung Utara yang sejuk. Berkaitan dengan tanggung jawab untuk mewujudkan sarana/prasarana masa depan yang nyaman dan ramah lingkungan, para praktisi, akademisi maupun industri dituntut untuk terus berinovasi dalam desain struktur maupun pengembangan material. Simposium ini merupakan ajang diseminasi hasil penelitian akademik dan praktek desain dalam bidang teknik struktur dan material. Seiring dengan berkembangnya teknologi material, desain struktur dan tujuan di masa depan, simposium mengetengahkan smart and sustainable structures. Saya sangat berterima kasih kepada para penyaji, keynote speaker dan pemakalah, yang telah bersedia membagikan hasil penelitiannya pada forum ini. Terima kasih atas dukungan Fakultas Teknik Unpar dan para sponsor yang telah membantu terselenggaranya kegiatan ini. Dan tak lupa saya sampaikan penghargaan untuk panitia pelaksana yang telah bekerja keras mempersiapkan acara ini. Semoga kegiatan simposium ini dapat memberikan kontribusi nyata pada dunia teknik sipil demi masa depan yang lebih baik. Saatnya saya mengucapkan selamat bersimposium dan selamat menikmati kota Bandung.

Ketua Panitia

Dr.-Ing. Dina Rubiana Widarda.

Bandung, November 7-8, 2013

i



ii


DAFTAR ISI

Kata Pengantar............................................................................................................................................................................................ i Daftar Isi ......................................................................................................................................................................................................iii

Keynote Papers KAYU REKAYASA SEBAGAI MASA DEPAN STRUKTUR KAYU INDONESIA –Bambang Suryoatmono ..... K01–1 PENERAPAN PRINSIP SUSTAINABILITAS PADA KONSTRUKSI BETON – Iswandi Imran............................ K02–1 TANTANGAN KE DEPAN PENGGUNAAN KONTROL VIBRASI PADA STRUKTUR BANGUNAN SIPIL DI INDONESIA –Herlien D. Setio & Sangriyadi Setio ...................................................................................................... K03–1 STATE OF PRACTICE OF SEISMIC DESIGN AND CONSTRUCTION IN INDONESIA – Davy Sukamta .................................................................................................................................................................................. K04–1

Technical Papers THE EFFECT OF AGGREGATE SHAPE AND CONFIGURATION TO THE CONCRETE BEHAVIOR – Yanuar Setiawan, Han Ay Lie, & Ilham Nurhuda ............................................................................................................. T01–1 UTILIZATION OF BAMBOO AS REINFORCEMENT IN PLASTERED BAMBOO MAT PANEL – Andriati Amir Husin, Fanji Sanjaya & Achmad Hidayat Effendi.............................................................................................................. T02–1 STUDI EKSPERIMENTAL APLIKASI MATERIAL NANO FLY ASH TERHADAP KUAT TEKAN MORTAR BETON – Purwanto, Arif Hidayat, Heri Sutanto, Endo Fathias, & Arini W............................................................................ T03–1 MECHANICAL PROPERTIES OF CONCRETE USING COARSE AND FINE RECYCLED CONCRETE AGGREGATES – Buen Sian, Johannes Adhijoso Tjondro, & Sisi Nova Rizkiani................................................... T04–1 SHEAR STRENGTH OF CNLT-SHEARWALL CONNECTIONS – Johannes Adhijoso Tjondro & Dina Rubiana Widarda.............................................................................................................................................................................................. T05–1 BEHAVIOUR OF LOW-RISE CROSS NAIL-LAMINATED TIMBER SHEARWALL WITH OPENINGS UNDER EARTHQUAKE LOADING – Dina Rubiana Widarda, Johannes Adhijoso Tjondro & Sumiawaty Purnama............................................................................................................................................................................................. T06–1 PENGARUH TONJOLAN PADA TULANGAN BAMBU TERHADAP KUAT LENTUR BALOK BETON BERTULANGAN BAMBU GOMBONG – Herry Suryadi & Eigya Bassita Bangun ................................................. T07–1 QUICK CONNECT MOMENT-ROTATION OF TIMBER BEAM-COLUMN JOINT USING LAG-SCREW BETWEEN BLOCK-SLEVEES AND MEMBERS – Pricillia Sofyan Tanuwijaya & Johannes Adhijoso Tjondro ............... T08–1 EFEK STYROFOAM BEKAS KOTAK MAKANAN SEBAGAI AGREGAT BETON – Cecilia G.S. Lauw & Laura A.N. Timotius ............................................................................................................................................................................................. T09–1 TESTING OF SHELL FINITE ELEMENTS USING CHALLENGING BENCHMARK PROBLEMS – F.T. Wong ........................................................................................................................................................................................... T10–1


iii

The 2nd INDONESIAN STRUCTURAL ENGINEERING AND MATERIALS SYMPOSIUM ANALISIS NUMERIK: PERILAKU HUBUNGAN PELAT-KOLOM DENGAN DETAIL TULANGAN GESER BARU TERHADAP KOMBINASI BEBAN LATERAL SIKLIK DAN BEBAN GRAVITASI – Riawan Gunadi, Bambang Budiono, Iswandi Imran & Ananta Sofwan ........................................................................................................................ T11–1 KAJIAN NUMERIK HUBUNGAN BALOK-KOLOM EKSTERIOR MENGGUNAKAN BETON BUBUK REAKTIF DI BAWAH BEBAN LATERAL SIKLIK – Pio Ranap Tua Naibaho, Bambang Budiono, Awal Surono & Ivindra Pane ..................................................................................................................................................................................................... T12–1 ELEMEN KUNCI DALAM DESAIN JEMBATAN PELENGKUNG BENTANG PANJANG – Lanneke Tristanto & Redrik Irawan.................................................................................................................................................................................. T13–1 TINJAUAN BALOK PERANGKAI KHUSUS (RC LINK BEAM) DENGAN GAYA GESER TINGGI PADA DINDING OUTRIGGER GEDUNG 50 LANTAI – Suryani Mettawana ............................................................................................. T14–1 DESAIN SUB-STRUCTURE PADA BANGUNAN GEDUNG DENGAN BESMEN DALAM YANG KOMPLEKS – Jessica N. Handoko ........................................................................................................................................................................ T15–1 PRYING ACTION IN SLIP-CRITICAL CONNECTIONS UNDER COMBINED SHEAR AND TENSION FORCES – Andrian H. Limongan & Bambang Suryoatmono............................................................................................................. T16–1 DIAGONAL STIFFENER EFFECT ON LATERAL-TORSIONAL BUCKLING OF STEEL BEAM: A NUMERICAL STUDY – Helmy H. Tjahjanto, Paulus Karta Wijaya & Victor H.L. Sibuea. ............................................................. T17–1 ELASTIC LATERAL TORSIONAL BUCKLING OF CANTILEVER I-BEAM – Paulus Karta Wijaya .................. T18–1 TEKUK TORSI LATERAL ELASTIS BALOK NON PRISMATIS DENGAN METODA BEDA HINGGA – Nenny Samudra ............................................................................................................................................................................................. T19–1 ANALISIS RESONANSI PADA JEMBATAN KERETA API BERKECEPATAN TINGGI – Dina R. Widarda, Irwan Setiadi, & Undagi Kausar A. ....................................................................................................................................................... T20–1 SIMULASI NUMERIK RESPON STRUKTUR GEDUNG BETON BERTULANG AKIBAT BEBAN LEDAKAN BOM – Elvira ................................................................................................................................................................................................... T21–1 EVALUASI KINERJA JEMBATAN PELENGKUNG BETON BERTULANG TERHADAP BEBAN GEMPA – Ida I Dewa G. Wijaya, Ariella Claresta, & Cinthya Ciptodewi ................................................................................................ T22–1 VERIFICATION OF IMPACT FACTOR FOR INDONESIAN HIGHWAY BRIDGE CODE – Abrar Husen & Krishna Mochtar .............................................................................................................................................................................................. T23–1 EKSPERIMEN STRUKTUR BETON UNTUK PENGEMBANGAN METODE PERENCANAAN TULANGAN GESER PADA BALOK LENTUR DENGAN BUKAAN - Antoni Halim ......................................................................................... T24–1

Unpresented Papers STUDI PENEMPATAN DINDING GESER PADA GEDUNG TINGGI – Lidya Fransisca Tjong & Noegraha Laksana............................................................................................................................................................................................... U01–1 SAMBUNGAN KAKU BALOK-KOLOM UNTUK GEDUNG BAJA STRUKTURAL TAHAN GEMPA MENURUT SNI 1729-20xx – Suradjin Sutjipto ................................................................................................................................................ U02–1


iv


ELASTIC LATERAL TORSIONAL BUCKLING OF CANTILEVER I BEAM Paulus Karta Wijaya 1

Lecturer of Civil Engineering Department Parahyangan Catholic University

ABSTRACT Lateral torsional buckling is one of the limite states in beam design. For cantilever beam, Guide to Stability Design Criterion for Metal Structures gives some equations to calculate elastic critical moment of the beam. The equations are used to calculte elastic critical moments for load applied at shear center or at top flange. For load applied below the shear center, the critical moment is taken as the same as critical moment applied at shear center. Two kind of loading are considered, point load applied at the free end of the beam and uniformly distributed load. This paper present the results of an evaluation of the equations. Critical moment of some cantilever beams are analyzed. The parameters that are considered are section properties and length of beams. The method of analysis is finite element method. As a result of this evaluation, new equations are made to calculate the critical moment of a cantilever beam. Also a new equation is made for the load applied at the bottom flange. Key Words: lateral torsional buckling, critical moment.

1.

Introduction

Lateral torsional buckling is one of the limit states in steel beam design. Lateral torsional buckling is a phenomenon, when a beam is loaded by transverse load, suddenly displaced laterally outside the plane of bending after its bending moment reaches a certain level of moment. The bending moment at which the beam buckled laterally is called critical moment. The value of critical moment is used as a limit state of the beam. When the stresses in the beam is below yield stress everywhere, it is called elastic critical moment, otherwise it is called inelastic critical moment. In design practice, the inelastic critical moment is computed using elastic critical moment which is mapped into inelastic critical moment. Therefore usually the study of lateral torsional buckling is done using assumption that the material is elastic and the result is used by mapping it into inelastic lateral torsional buckling. There have been many researchers that study the lateral torsional buckling of beam and at the first place it must be mentioned that Timoshenko (1963) is the first that gives solution for critical moment of simply supported beam due to uniform bending moment. Timoshenko solution is based on the assumption that at the ends of the beam, torsional rotation is prevented but warping is allowed. Timoshenko’s formula is adopted in AISC Specification for Structural Steel Building. For non uniform bending moment, AISC developed modification factor for nonuniform moment diagram C b . For cantilever beam the specification states that the value of C b is taken 1. In other words, AISC use the same equation as for simply supported beam. Actually the boundary conditions of cantilever beam are not the same as simply supported beam. Both ends of simply supported beam are prevented for torsional rotation and free to warp. But for cantilever, at fixed end torsional rotation and warping are prevented but at free end torsional rotation and warping are free. Guide to Stability Design Criteria (Ziemian, 2010) gives some equation to calculate elastic critical moment of cantilever beam for point load at free end and uniformly distributed load. Two different location of loading are considered, at shear center, at top flange. This paper presents an evaluation of the equation and added equations for load at bottom at free end.


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The 2nd INDONESIAN STRUCTURAL ENGINEERING AND MATERIALS SYMPOSIUM Critical moment of cantilever beam Guide to Stability Design Criterion (Ziemian, 2010) gives some equation to calculate elastic critical moment of cantilever beam. The equation is as follows,

M cr  C L C H C B

E I yG J L

1

With, E is modulus of elasticity, I y is moment of inertia of the cross section about weak axis, G is shear modulus, J is torsional constant and L is the length of the beam.

C L is a coefficient to account for moment distribution along the length of the beam. For beams with a point load at the free end

C L  3.95  3.52 W

2

For beams with a uniformly distributed load

C L  5.83  8.71 W

3

W is the non-dimensional parameter computed using the following equation,

W

 L

EC w GJ

4

C w is warping constant of the cross section. The influence of section properties are taken into account by using this non-dimensional parameter. The coefficient C H accounts for the effect of load height. If the load is applied at or below the level of the shear center, C H  1 . When the load is applied at top flange, the value of C H is as follows. For beams with a point load at the free end

C H  0.76  0.51 W  0.13 W 2

5

For beams with uniformly distributed load.

C H  0.76  0.51 W  0.13 W 2

6

The coefficient C B accounts the effect of bracing. If the beam is not braced C B  1 . For beams with the load at the shear center,

C B  1.42  0.88W  0.26W 2 .

7

For beams with the loads at the top of flange or conservatively for loads above shear center,

C B  1.48  0.16W

8

The equations are based on the work of Bo Dowswell (Dowswell, 2004). Dowswell calculate the critical moment of several I beam with various lengths using finite element method. He used Buckling Analysis of Stiffened Plates program. In this study, an evaluation of those equations is done using finite element method. Critical moment of several I beams are analyzed using SAP v.14. The study is only for C B  1 (Beams without lateral bracing). The purpose of the study is to make an evaluation of the accuracy of the equation and also to obtain an equation for C H if the load acts at the bottom flange.


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The 2nd INDONESIAN STRUCTURAL ENGINEERING AND MATERIALS SYMPOSIUM 2.

The finite element model

The buckling analysis is based on bifurcation theory. The critical moment is a bending moment at which the beam can be in equilibrium in more than one configuration. The first configuration is a configuration without lateral and torsional displacement. The beam is displaced in the plane of bending. The other configuration is a configuration that the beam displaced laterally accompanied by torsional rotation. The theory leads to an Eigen Value problem. The critical moment is the Eigen Value of the equation and the Eigen Vector is the mode shape of buckling. With this theory, the equation of buckling analysis is (Cook, 1989)

K   K     0

9

With K is the stiffness matrix of the system, K  is the geometric stiffness,  is the Eigen value and  is Eigen vector. The beams to be analyzed are from WF600x200x11x17 and WF500x200x10x16. Shell elements are used in this analysis. Every node has six degree of freedom, three translations and three rotations. One end of the beams is fixed and the other end is free. It means, at the fixed end, all degree of freedom are restrained and at free ends all degree of freedom are free. The length of the beams end is 4 meter, 5 meter, 6 meter, 7 meter, 8 meter and 9 meter. Analysis is done using buckling analysis facility in SAP program. The model is shown in Figure 1. First, critical moment for load at the shear center is computed ( C H  1 ) and then the

C L values is computed. In second and third analysis, the critical moment for load at top flange and at bottom flange is computed and then C H values are computed. Analysis is done for point load at the free end and for uniformly distributed load. For every beam with certain length, there is a value of W. Based on the discrete values of C L and C H , equations are developed. After the equations are developed, they are tested by analyzing some other beams, which are beams of WF400x200x8x13 and WF300x150x6.5x9.

Figure 1.

3.

Finite element model for buckling analysis of beam

Result of analysis.

The result of the analysis is presented in form some equations and in Figure 2 – Figure 7. For point load at the shear center, the difference between critical moment computed using equation 2 and critical moment using finite element is very small. Figure 2 show the curve of equation 2 compared to the result of the finite element. No new equation is created for this condition.


T18-3


CL

Finite element

Equation 2

W

Figure 2.

The Curve of C L for point load at free end

For distributed load at the shear center, there is little difference between equation 3 and finite element. New equation for uniform distributed load at shear center is as follows,

C L  8.00  6.29W

10

Figure 3 present the curve for equation 10 compared to equation 3 and finite element result. For small value of W, the difference between eq 3 and equation 10 is small. For higher value of W, the difference is higher.

Finite element Equation 3

CL

Equation 10

W Figure 3.

The Curve of C L for uniformly distributed load

For point load at free end and at top flange, there is quite large difference bewteen equation 5 and finite element result. New equation for coefficient C H for point load at the free end at top flange is as follows,

C H  1.076  0.806 W  0.221 W 2

11

Figure 4 shows the curve for equation 11 compared to equation 5 and result of the finite element. It can be seen that the new equation is higher than equation 5.


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Finite element

CH

Equation 11 Equation 5

W Figure 4.

The curve of C H for point load at free end at top flange

For distributed load at top flange, a new equation for coefficient of C H ias as follows,

C H  0.924  0.652 W  0.18 W 2

12

The curve of equation 12 compared to equation 6 and finite element result is presented in Figure 5. The equation 12 gives considerably higher than equation 5. Coefficient C H for point load at the free end at the bottom of the flange,

C H  0.993  0.351 W

13

The curve of equation 13 compared to finite element result is presented in Figure 6. The equation is coincidence with finite element result. Coefficient C H for distributed load at the free end at the bottom of the flange,

C H  1.293  0.211 W

14

Finite element

CH

Equation 12

Equation 5

W

Figure 5.

The curve of C H for distributed load at free end at top flange


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CH

Equation 13 Finite element

W Figure 6.

The curve of C H for point load at free end at bottom flange

CH

The curve of equation 14 compared to the result of finite element is presented in Figure 7.

W Figure 7.

The curve of C H for uniformly distributed load at bottom flange

After the new equations are created, they are tested using some other section. WF400x200x8x13 with length 8000 mm and 6000 mm and WF300x150x6,5x9 with length 4000 mm will be used. The result is presented in Table 1. From this comparison, it can be concluded that the new equations are accurate compared to the result of finite element method.


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The 2nd INDONESIAN STRUCTURAL ENGINEERING AND MATERIALS SYMPOSIUM Table 1.

The value of coefficient for WF400x200 and WF300x150

From Finite Element Method compared to the new equations

WF400x200-a

P

q

WF400x200-b

P

q

WF300x150

P

q

FEM

New equation

Difference (%)

CHa

0,546

0,5493

0,5

CHb

1,294

1,2375

4,4

CL

13.824

13.366

3.3

CHa

0.495

0.499

3.3

CHb

1.477

1.473

0.2

CHa

0.4444

0.4452

0.1

CHb

1.347

1.339

0.5

CL

16.086

15.154

5.8

CHa

0.4144

0.4153

0.08

CHb

1.58

1.533

2.99

CHa

0.407

0.398

2.2

CHb

1.4477

1.4029

3.1

CL

17.51

16.28

7.03%

CHa

0.3828

0.3776

1.34

CHb

1.6368

1.5708

4.0

4.

Conclusions

1.

For point load at the free end, the value of C L from Stability Design Guide gives acurate result compared to the result of SAP program. No new equation is developed from this condisiton.

2.

For distributed load, the value of C L from Stability Design Guide is a little higher compared to the result of SAP program. A new equation is developed for this condition (equation 10).

3.

For point load at free end at top flange and for distributed load at top flange, the value of C H from Stability Design Guide is considerably lower than the result of SAP program. A new equation is developed for this condition (equation 11 and equation 12).

4.

For point load at free end at bottom flange and for distributed load at bottom flange, equations are developed (equation 13 and equation 14).

5.

The new equation is accurate for some other cross section.

5. Acknowledgement The author thanks to Parahyangan Catholic University for his support by giving permision to use SAP v14 program.

6.

Reference

1)

AISC (2010). Specification For StructuralSteelBuilding, Chicago: AISC.

2)

Cook,R.D., Malkus,D.S., Plesha,M.E., Concept and Application of Finite Element Analysis, New York, John Wiley and Sons.

3)

Dowswell,B. (2004), Lateral Torsional Buckling of Wide Flange Cantilever Beams, Engineering Journal.


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The 2nd INDONESIAN STRUCTURAL ENGINEERING AND MATERIALS SYMPOSIUM 4)

Timoshenko, Gere, A. (1963). Theory of Elastic Stability, 2nd ed., London: McGraw Hill.

5)

Ziemian,R.D., (2010), “Guide To Stability Design Criteria for Metal Structures” ,6 th Ed, John Wiley and Son.


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Proceedings. The 2 nd INDONESIAN STRUCTURAL ENGINEERING AND MATERIALS SYMPOSIUM. Bandung, 7 ~ 8 November Publisher:

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