10icce English Full Paper Format

10th International Congress on Civil Engineering, 5-7 May 2015 University of Tabriz, Tabriz, Iran

Analytical study on gusset plate behavior of braced frames through finite element method Javad Amiri1, Soheil Salimi2,*, Ali Akbar Hekmatzadeh3, Hamed Roohbakhsh4 , Mohammad Darvishi 5 1,5- Department of Engineering, Loghman Hakim Institute of Higher Education 2,4- Department of Civil & Environmental Engineering, Shiraz University 3- Department of Civil & Environmental Engineering, Shiraz University of Technology * Corresponding Author’s E-mail: [email protected] Abstract Nowadays, it’s common place to use concentrically braced frames (CBFs) for lateral-load resisting systems in steel structures sporadically. Gusset plate connections play an outstanding role to connect the beams and columns in CBFs systems, so need to be taken into center of attention in designing of CBFs. This analytical study has illustrated that buckling capacity of CBFs under a monotonic loading can be improved by considering the behavior of gusset plate connection through designing its thickness and size. In this paper, experiment results and finite element model have been verified, in addition, it indicates that CBFs performance depend upon gusset plate connections, consequently.

Keywords: Concentrically braced frame (CBF), Finite element method, Gusset plate connections, Buckling capacity

1.

INTRODUCTION

Concentrically braced frames (CBFs) are frequently used in steel structural buildings, as shown schematically in Fig. 1 [1]. Lateral-load resisting has been controlling by these frames, which are also transferred to the beams and columns by gusset plate connections [2]. Mostly steel frames with concentrically systems are preferred to use in comparison to moment frames, since the ability of braced members to control the lateralload resisting of frame has more efficiency than that had no braced members. Moreover, steel sections used in the beams and columns of braced frames are significantly lighter than required ones for moment frames. That is why, structural engineers widely choose braced frames since it’s much more beneficially [3]. There are two usual ways to connect gusset plate connections to the diagonal bracing members and main framing members encompass welding and bolting, however, the gusset plates of considered model at this paper bolted to the braced member.

Figure 1. Typical concentrically braced steel frames [1]

This paper presents that buckling capacity of CBFs depend on gusset plate thickness and size, which was derived by verifying experimental investigation of CBF model developed at University of Alberta [1] and inelastic finite element model through the commercial finite element program Abaqus 6.13-1 [4]. 1. MSc. Student Structural Engineering [email protected] 2. MSc. Student of Environmental Engineering, [email protected] 3. Assistant Professor, [email protected] 4. MSc. Student Structural Engineering [email protected] 5. MSc. Student Structural Engineering [email protected]

1


2.

LITERATURE REVIEW

Concentrically braced frames (CBFs) provide required characteristics needed for seismic design [5]. Stress distribution at the two gusset plates was studied by Richard E. Whitmore in 1952 [6], which modeled a connection from a Warren Truss shown in Fig. 2. The commonly known Whitmore section is found by multiplying effective width by the plate thickness, in turn found by extending two lines from the first row of fasteners in a connection at 30o degrees away from the line of action to where they intersect a line extended through the final row of bolts [7], as shown in Fig. 3 [6].

Figure 2. Connection geometry of Whitmore’s model, 1952 [6]

Whitmore found that for predicting the normal and shear stresses across the section identified in Fig. 2, beam theory doesn’t work accurately. He also did find that the thirty degree method conservatively predicted the experimental maximum principal stress. [7] Irvan (1957) conducted some tests on a model of a Pratt Truss joint with double gusset plates. Although, the method he proposed was similar to the Whitmore’s for calculating the normal stress at the end of the truss members, but the difference was that the 30° lines should project from the center of gravity of the rivet group instead of the outside fasteners on the first row [8]. He came to a conclusion that was similar to Whitmore’s with respect to the calculation of stresses at the critical sections, then more studies by Hardin in 1958 on the gusset plates of Pratt Truss verified previous efforts as well [9]. Besides that, finite element method was used for investigating the elastic stress distribution by Lavis in 1967 [10]. Vasarhelyi (1971) conducted an experimental model of Warren Truss joint with double gusset plates, and plotted the stress distribution. He concluded that maximums of stress found in a gusset plate are slightly different; while the major deviations occurred in the location of those maximums [11]. In 1972, Struik’s analysis of gusset plates by using an elastic-plastic finite element program indicated that current design procedures which utilize the beam equations produced substantial variations in the factor of safety [12]. In 1984, Thornton proposed that buckling load of a gusset plate is considered as the compressive strength of a column with both ends fixed, then suggested an equation to account the restraint provided against buckling in compression condition as following [13]: k=0.65

(1)

where k, E, t, bE are respectively effective length factor, Young's modulus, gusset plate thickness, Whitmore effective width presented in Fig. 3, and LC is the length of the column, the average of three lengths extending in the direction of framing member from the middle and the ends of the last rows of bolts to the edges of the gusset plate or adjacent group of bolts (L1, L2 and L3 in Fig. 3)

2


Figure 3. Concept for Whitmore effective width method and Thornton method

Yamamoto, Akiyama, and Okumura (1985) calculated the stresses at the critical sections of the plates and found that the maximum elastic shear stress in the plates can be closely approximated using the beam equations [14]. Hardash and Bjorhovde’s 1985 experiment expanded the basic understanding of gusset plate behaviors as well, and identified the need for a capacity method that takes into account the failure mechanism of a connection [15]. Astaneh conducted three experiments on gusset plate specimens in 1992, and recommended that the plastic stress distribution be used to calculate the horizontal shear capacity, and also modified effective length factor in Thornton’s equation from k=0.65 to k=1.2 [16]. Yam and Cheng (2002) proposed the modified Thornton method based on a 45 dispersion angle instead of a 30 angle to reevaluate the Whitmore width [1]. Important role of gusset plate connections was highlighted specially after collapsing of the I-35W Bridge in Minneapolis, Minnesota-USA in 2007, which caused further studies on load rating requirements for gusset plates, thereafter. [17] To date, enormous amount of research works and studies have tried to understand the behavior of gusset plate connections, and many experimental and/or analytical programs have been focused to develop this subject all over the world.

3.

THE VERIFICATION OF FINITE ELEMENT MODEL

This analytical study has been based on an experimental program conducted by Yam and Cheng [1] to investigate compression behavior of gusset plate connections includes thickness and size, then, compressive strength and stability of gusset plate connections achieved from finite element program, Abaqus 6.13-1, compared with experimental results. Hence, computer simulation models have been verified through experimental model GP1 fabricated at University of Alberta, with details and properties as following, shown in Table 1 and Fig. 4:

Specimen Designation GP1

Table 1. Details of experimental model GP1 fabricated at University of Alberta [1] Plate size, mm2 Plate thickness, mm Brace angle (o) Ultimate load, kN 500×400

13.3

45o

1956

Note that, this experimental model had been already tested by Sheng et al. [18] as well, to investigate inelastic compressive behavior and strength of gusset plate connections.

3


Figure 4. Further details of GP1 [1] was also modeled through Abaqus program by Sheng et al. [17]

As illustrated in Fig. 5, the ultimate load of both experimental results and analytical model of this paper is much closed to each other, which is 1960.81 kN in numerical model, with an acceptable error, 0.2459 per cent, furthermore, a mesh size of 50 mm by 50 mm is used at Abaqus program. Hence, the finite element model has been verified subsequently.

Figure 5. Load versus deflection curves for the specimen GP1 [1]

4.

SPECIMEN DESCRIPTION AND ANALYTICAL PARAMETER STUDY

Due to understanding of gusset plate behavior under monotonic loading in compression condition, a CBF model was developed by Abaqus with the input material properties and type of steel listed in Table 2 and Table 3, below. Type

Density, Kg/m3

W300

7850

Section

Type

Beam Column Brace Gusset plate Splice plate

W310×129 W310×129 W250×67 500×400 WT125×22.5

Table 2. Type of steel Yield stress, Ultimate stress, MPa MPa 345 450

Table 3. Material properties Web Flange thickness, thickness, mm mm 13.1 20.6 13.1 20.6 8.9 15.7 13.3 13.3 7.62 13

4

Poisson ratio

Failure strain, %

0.3

18

of test specimen Type of Type of steel element W300 W300 W300 W300 W300

S4R S4R S4R S4R S4R

Modulus of elasticity, Kg/cm2 2.1E6 2.1E6 2.1E6 2.1E6 2.1E6


4.1.

ANALYSIS OF INFLUENCE OF GUSSET PLATE SIZE

Another parameter was studied is the size of plate; for each thickness three sizes of 500×400 mm2, 600×500 mm2 and 800×700 mm2 considered, and then, the ultimate load was calculated as shown in Table 4 and Fig. 6. According to the table below, the ultimate load decreases in bigger plate sizes. Table 4. Influence of gusset plate thickness and size on the ultimate load of CBF Thickness, 8 mm Thickness, 12 mm Thickness, 16 mm Thickness, 20 mm size, mm2

Ultimate load, kN

size, mm2

Ultimate load, kN

size, mm2

Ultimate load, kN

size, mm2

Ultimate load, kN

500×400 600×500 800×700

950 800 650

500×400 600×500 800×700

1600 1500 1300

500×400 600×500 800×700

2200 1950 1800

500×400 600×500 800×700

2500 2300 2100

(a)

(b)

(c)

(d)

Figure 6. Load versus size of gusset plate connection with different thicknesses: (a) t=8 mm, (b) t=12 mm, (c) t=16 mm, (d) t=20 mm

5


4.2.

ANALYSIS OF INFLUENCE OF GUSSET PLATE THICKNESS

Totally four different thicknesses include 8 mm, 12 mm, 16 mm and 20 mm considered for these plate sizes, 500×400 mm2, 600×500 mm2 and 800×700 mm2, to see the influence of gusset plate thickness on the performance of CBFs. As presented in Table 4 and Fig. 7 the ultimate load of models rise by increasing the thickness of plates, led to higher buckling capacity of gusset plate.

Figure 7. Ultimate load versus gusset plate thickness

4.3.

ANALYSIS OF LENGTH OF STIFFENER

Moreover, there is another important parameter was also studied in this analytical effort, the length of stiffener, with the same thickness of the plate; located in braced member direction, as shown in Fig. 8.

Figure 8. Three-demensional model of gusset plate connection with stiffener in CBF, modeled by Abaqus 13.6-1

A significant change in ultimate load of CBF was observed, due to using of stiffeners with three various lengths of 7.5 cm, 15 cm, 20 cm, respectively caused 2100 kN, 2514 kN, 2708 kN; compared with 1960 kN when that had no stiffener, shown in Fig 9. Note that, the middle plate is 400×500 mm2 with the thickness of 13.3 mm.

6


Figure 9. Ultimate load calculated with different length of stiffeners

5.

CONCLUSIONS

In this paper, the gusset plate connection from experimental results of Yam and Cheng [1] was modeled in the finite element program Abaqus, and validated with the original data reported. The buckling capacity and CBFs performance were studied through considering three parameters to analyze namely, gusset plate size, thickness and length of stiffener. To sum up, the conclusions can be summarized as following: 1. Buckling capacity decreased in bigger gusset plate sizes, so the dimension of gusset plate is a crucial parameter for buckling capacity. 2. The ultimate load rose almost linearly proportional to the gusset plate thickness, which presets the importance role of thickness in gusset plate behavior. 3. A better CBF performance was observed by increasing length of stiffener. Hence, it can be concluded that size and thickness of gusset plates, and length of stiffeners are significantly important and need to be center of attention in designing of CBFs.

6.

ACKNOWLEDGMENT

The authors would like to appreciate Dr. Jung-Han Yoo, who encouraged the team to complete this analytical study by sending some details of his experimental results at University of Washington.

7.

REFERENCES

1.

Yam, M.C.H, Cheng, J.J.R. (2002), “Behavior and Design of Gusset Plate Connections in Compression,” Journal of Constructional Steel Research, 58, pp. 1143-1159

2.

Rabinovitch, J.S., and Cheng, J.J.R. (1993), “Cyclic Behavior of Steel Gusset Plate Connections”, Report No.191, Department of Civil and Environmental Engineering, University of Alberta, Edmonton, Canada.

3.

Burkholder, M. (2012), “Performance Based Analysis of a Steel Braced Frame Building with Buckling Restrained Braces”, In Partial Fulfillment of the Requirements for the Degree Master of Science, A Thesis presented to the Faculty of California Polytechnic State University, San Luis Obispo, California.

4.

.‫ س‬،‫ سروش نیا‬، .‫ هـ‬،‫ نجفیان‬، .‫ م‬،‫ مهروند‬،.‫ م‬،‫ ممقانی‬، )1392( "‫"کاملترین مرجع کاربردی آباکوس‬، ‫انتشارات نگارنده ی دانش‬

5.

Yoo, J. H., Lehman, D. E., Roeder, C. W., (2008), “Influence of Connection Design Parameters on the Seismic Performance of Braced Frames,” Journal of Construction Steel Research, 64, pp. 607-623

7


6.

Whitmore R.E., (1952), “Experimental Investigation of Stresses in Gusset Plates”, Bulletin No. 16. Engineering Experiment Station, University of Tennessee, Knoxville.

7.

Rosenstrauch, P. L., Sanayei, M., Brenner, B. R. (2013), “Capacity Analysis of Gusset Plate Connections Using the Whitmore, Block Shear, Global Section Shear, and Finite Element Methods,” Journal of Engineering Structures, 48, pp. 543-557

8.

Irvan, W.G., (1957). “Experimental Study of Primary Stresses in Gusset Plates of Double Plane Pratt Truss,’’ Bulletin No. 46, University of Kentucky Engineering Experiment Station

9.

Hardin, B. O. (1958), “Experimental Investigation of the Primary Stress Distribution in Gusset Plates of a Double Plane Pratt Truss Joint with Chord Splice at the Joint,” Bulletin No. 49, University of Kentucky Engineering Experiment Station.

10. Lavis, C. S. (1967), “Computer Analysis of the Stresses in a Gusset Plate,” Masters Thesis, University of Washington. 11. Vasarhelyi, D. D. (1971), “Tests of Gusset Plate Models,” Journal of the Structural Division, Proceedings of the American Society of Civil Engineers, 97, No. ST2, pp. 665-679 12. Struik, J. H. A. (1972), “Applications of Finite Element Analysis to Non-linear Plane Stress Problems,” Ph.D. Dissertation, Lehigh University 13. Thornton, W.A., (1984),“Bracing Connections for Heavy Construction,” AISC, Third Quarter, pp. 13948 14. Yamamoto, K., Akiyama, N., and Okumara, T. (1985), “Elastic Analysis of Gusseted Truss Joints,” Journal of Structural Engineering, ASCE, 111, No. 12, pp. 2545-2564 15. Hardash S.G., Bjorhovde R. (1985), “New Design Criteria for Gusset Plates in Tension,” AISC, 22(2), pp. 77–94 16. Astaneh, A. (1992), “Cyclic Behavior of Gusset Plate Connections in V-Braced Steel Frames,” Stability and Ductility of Steel Structures under Cyclic Loading, Fukomoto, Y. and Lee, G. C., eds., CRC Press, Ann Arbor, pp. 63-84 17. Crosti, C. , Duthinh, D., (2014), “A Nonlinear Model for Gusset Plate Connections,” Journal of Engineering Structures, 62, pp. 135-147 18. Sheng, N., Yam, C.H. and Iu, V.P. , (2002), “Analytical Investigation and Design of the Compression Strength of Steel Gusset Plate Connections,” Journal of Construction Steel Research, 58, pp. 1437-1493

8