- Email: [email protected]
Effect of the moment transfer efficiency of a beam web on deformation capacity at box column-to-H beam connections
Journal of Constructional Steel Research 63 (2007) 24–36 www.elsevier.com/locate/jcsr
Effect of the moment transfer efficiency of a beam web on deformation capacity at box column-to-H beam connections Young-Ju Kim ∗ , Sang-Hoon Oh Research Institute of Industrial Science & Technology (RIST), 79, Youngcheon Dongtan, Hwasung, Kyoungkido, 445-810, Republic of Korea Received 7 November 2005; accepted 23 February 2006
Abstract This paper investigates the effect of moment transfer efficiency of a beam web on deformation capacity at beam-to-column connections. Non-linear finite element analysis of five connection models was conducted. Analytical results showed that the moment transfer efficiency of the connection with a box column was poor when compared to a connection with an H-column; this was due to the out-of-plane deformation of the column flange. Based on previous test data, analytical results were compared with experimental results. Analytical and experimental results showed that the deformation capacity of the connection with a box column decreased due to the poor moment transfer efficiency of a beam web, followed by strain concentration at the beam flange. c 2006 Elsevier Ltd. All rights reserved. Keywords: Box column; Moment transfer efficiency; Strain concentration; Deformation capacity
1. Introduction Typically, Japanese steel moment resisting frames have a square hollow section that is used for the columns, and an H-shaped section that is used for the beams. A square tube column has two webs at each side, but no web in the center where the beam web is connected. This is different from the US connection, which has a web at the center; this may cause an increase in the deformation of the column flange. Due to the column flanges’ out-of-plane deformation and the loss of web sections by the weld access hole in the vicinity of the connection, the web of the box column is significantly less effective in transferring flexural moment. Therefore, the actual transfer mechanism is completely different from the normally assumed mechanism in connection design. Generally, the features of the structural behavior of this type of connection are as follows: (1) due to the out-ofplane deformation of column flanges, as shown in Fig. 1, the contribution of the web moment is reduced in the vicinity of the connection; (2) the deformation capacity of the connection is considerably reduced due to the severe constraint and the inevitable geometrical notches [1]. ∗ Corresponding author. Tel.: +82 31 370 9558; fax: +82 31 370 9559.
E-mail address: [email protected] (Y.-J. Kim). c 2006 Elsevier Ltd. All rights reserved. 0143-974X/$ - see front matter doi:10.1016/j.jcsr.2006.02.009
It has been reported that the beam near the connection develops a reduced strength as compared to the beam located away from the connection, which is due to the decrease of the web moment transfer [2–5]. This research on steel moment connections with a box column has indicated that the classical beam theory cannot predict the force transfer mechanism. For the case of a severe seismic loaded structure, the moment transfer efficiency effects of a beam web on connection ductility have not been fully uncovered. The first objective of this paper was to investigate the relationships between the moment transfer efficiency of a beam web and the strain concentration at beam-to-column connections. The second objective was to evaluate the effect of the moment transfer efficiency at the beam-to-column connection on deformation capacity. These objectives were addressed through the non-linear finite element analysis using ANSYS [6] and previous test data. For convenience of analysis, this study was limited to monotonic loading and neglected the influence of inelastic loading cycles. 2. Analytical configurations A total of five models were adopted and analyzed in order to improve understanding of the moment transfer efficiency of a beam web and the local stress/strain behavior in the vicinity
Y.-J. Kim, S.-H. Oh / Journal of Constructional Steel Research 63 (2007) 24–36
25
Nomenclature D Fyc Fyj Fyw hc hd Sr Sw tc td tf ts Mw bM p b M tr
M tr wM p w M tr γw f
Eγw
γε ε ε0
Outer width of the square tube Yield stress of the column flange Yield stress of the fillet weld Yield stress of the beam web D − tc Inner distance between the upper and lower diaphragm Scallop (weld access hole) size Fillet weld size Column flange thickness Diaphragm thickness Beam flange thickness (td − t f )/2 Transfer moment of the beam web from the FEM result Plastic moment of the beam Total connection moment ( f M tr + w M tr ) Calculated flexural moment of the beam flange Plastic moment of the beam web Calculated flexural moment of the beam web Moment transfer efficiency of the beam web (Mw /w M p ) Predicted moment transfer efficiency of the beam web (w M tr /b M tr ) Strain concentration index (ε/ε0) Strain increment of each model, except for the HN model Strain increment of the HN model
of the beam-to-column connection. Key geometric parameters were: the column shape, the presence of a weld access hole, and the thickness of the column flange. The geometry and list of the analytical models utilized in this research are shown in Fig. 2 and Table 1. The following abbreviations were used for the specimen designation: H = H-column, B = box column, N = no weld access hole, S = weld access hole, T = thin column flange. HN consisted of a rolled H-shaped steel beam with the dimensions of H-612×202×13×23 connected to a column with the measurements of H-450 × 450 × 22 × 22; all dimensions are in mm and are for the beam depth, width, web thickness, and flange thickness, respectively. All models had the same beam size. In contrast to the pre-Northridge connection, there
Fig. 1. Deformation of box column flange.
Fig. 2. Analytical models.
was no weld access hole and the beam web was connected directly to the column flange. Except for the presence of the weld access hole (see Fig. 2), the HS model used the same size beam and column as those used for the HN model. The
Table 1 List of analytical specimens Specimen
Column
Panel zone
Weld access hole
Thickness of column flange welded beam web (mm)
HN HS BN BS BS-T
H-450 × 450 × 22 H-450 × 450 × 22 B-450 × 450 × 22 B-450 × 450 × 22 B-450 × 450 × 15
H-450 × 450 × 32 × 22 H-450 × 450 × 32 × 22 B-450 × 450 × 32 × 22 B-450 × 450 × 32 × 22 B-450 × 450 × 32 × 15
No Yes No Yes Yes
22 22 22 22 15
H: H-column, B: box column, N: no weld access hole, S: weld access hole, T: thin column flange.
26
Y.-J. Kim, S.-H. Oh / Journal of Constructional Steel Research 63 (2007) 24–36
Fig. 3. Finite element model (BS).
BN and BS models had the same box column dimensions of B-450 × 450 × 22; all dimensions are in mm and are for the column depth, width, and thickness, respectively. The no-weld access hole design was adopted in the BN model, but not in the BS model. A conventional design was used for the weld access hole in the BS. The BS was derived from the geometry of specimen SP-1, which has been tested in previous research [7]. The sudden change in geometry at the toe of the weld access hole causes a stress/strain concentration at the flange–web junction of the beam. Furthermore, this junction is potentially low in fracture toughness due to the processes of hot-rolling, cooling, and rotary straightening [8]. The combination of high stress and low fracture toughness is believed to be a primary cause of the brittle fracture of the base metal; this initiates from the toe of the weld access hole. BS-T had a box column with the dimensions of B-450 × 450 × 15, and had a thinner flange plate. In the case of the box column with a thin plate, it was expected that the contribution of web moment would eventually be considerably reduced due to the severe out-ofplane deformation of the column flanges. As shown in Fig. 2, a relatively strong column was used to ensure that the beams could initiate the development of a plastic hinge mechanism during the loading, before damage developed in the column. Additionally, the incorporation of a rigid panel zone with a web thickness of 32 mm may significantly reduce the contribution of panel zone shear deformation to the mode of failure. 3. Analytical model An analytical model was used to investigate local behavior and local ductility demand near the weld access hole, where the fracture occurs. A three-dimensional finite element model was generated to represent a structural subassemblage. Fig. 3
shows the finite element model for a steel connection; due to symmetry, only half was modeled. Brick elements (SOLID45 element) with eight nodes, 24 nodal degrees of freedom, and three translational DOFs at each node, were used to model the steel shape using ANSYS commercial code [6]. For local behavior near the strain concentration, the mesh in the vicinity of the web access hole was finer than the mesh for other regions (Fig. 3). Based on previous research, it was possible to model the supports of the experimental setup [7]. Hinged boundary conditions were used to support the column top and bottom. Each subassemblage contained a column between the mid-height of the two adjacent floors and a half-span of the beam. The load was applied by imposing incremental vertical displacements, in a monotonic fashion, at the beam tip during the analysis. Based on the material test data of previous research, monotonic analyses were done using isotropic hardening for the steel beam and column [7]. The von Mises yield criterion was employed to define the plasticity. 4. Analytical results 4.1. Global behavior Fig. 4 plots the moment versus rotation relationship for the BS model and specimen SP-1. The curve for the BS model exhibited a slightly higher initial stiffness than the specimen SP-1; but, both connections had similar strengths. Nevertheless, it was speculated that the results were consistent with each other and that the ultimate moment and initial stiffness were well represented. Fig. 5 presents the moment versus rotation for all steel models to examine the global behavior of the connections, where b M p (=1404 kN m) was the plastic moment of the
Y.-J. Kim, S.-H. Oh / Journal of Constructional Steel Research 63 (2007) 24–36
27
all models: the out-of-plane deformation mode of the column flange, strain profiles, and von Mises stress distributions Fig. 6 show the deformed shapes of each connection and the von Mises stress distribution plot are shown in Fig. 7. The strain profiles of the beam web and beam flange near the connection are shown in Figs. 8 and 9, respectively. The locations for strain measurement were at three sections, A, B and C, and were at beam depth distances of 75 mm, 125 mm and 612 mm from the column face, respectively (Fig. 8). In particular, Section A was located in line with the toe of the weld access hole so that the stress/strain distributions could be investigated in more detail.
Fig. 4. Comparison between experimental and analytical global behavior.
beam with consideration of the full effective area. Fig. 5 shows that the curves for all connections had the same initial elastic stiffness; however, at the same rotation level after the elastic range they had different strength capacities. For example, at the rotation of 0.013 rad, the strength for HN had already reached 1406 kN m, which was the same as the plastic moment of the beam. Meanwhile, for HS, BN, BS, and BS-T, the strengths were 1336 kN m, 1336 kN m, 1256 kN m, and 1205 kN m, which are 95%, 95%, 89%, and 86% of the beam plastic moment, respectively. This meant that the HS, BN, BS, and BST connections reached the plastic range more rapidly than the HN model. Focusing on the strong column and panel zone, this result showed that the strength capacity of each model may be influenced by the moment transfer efficiency of the connection. This result also showed that a box column may be significantly less effective in transferring flexural moment due to the out-ofdeformation of the column flanges. 4.2. Influence of connection details on strain concentration To explicitly investigate the causes of the strain concentration and the effect of the moment transfer efficiency of a beam web at the connection, the following were observed for
4.2.1. Column shape As described above, when a rectangular hollow section was applied as a column, increased stress at the end of the beam was influenced by the efficiency in transmitting the stress in the web of the beam through the beam-to-column connection. Therefore, as compared to an H-section column, there was poor ductility capacity of the specimens using box columns [3–5]. As shown in Fig. 6(a) and (c), out-of- plane deformation of the column flange of BN was large. However, no part of the HN column flange deformed. Fig. 7 shows Von Mises stress contours for all models at a 4% rotation since AISC recommends a minimum 4% rad total rotation capacity of the connection at the moment resisting frames. In Fig. 7, the symbol “” represents the middle area of the beam web being virtually devoid of stress. It was believed that as the void range of stress increases, the moment transfer efficiency of the beam web may decrease. For example, the void range of stress of HN was significantly smaller than that of BN. Fig. 8 plots the flexural strain profiles along the beam height at sections A, B and C at a 4% rotation. As shown in Fig. 8(a), the strain profile of BN was poorly developed, while the strain of HN showed a symmetric balance for the tensile and compressive strain represented as a linear line at Section A. Based on these results, more effective moment transfer efficiency of a web could be expected in the severe lateral load for H-section column connections, as compared to box column connections. The tensile strain profiles of each specimen, along the width of the beam flange, are shown in Fig. 9. Fig. 9(a) shows that along line BBF, the tensile strain of HN was smaller than that
Fig. 5. Moment vs. rotation relationships.
28
Y.-J. Kim, S.-H. Oh / Journal of Constructional Steel Research 63 (2007) 24–36
Fig. 6. Deformed shapes at 4% rotation (5 times exaggerated): (a) HN; (b) HS; (c) BN; (d) BS; (e) BS-T.
of BN; this was similar along line TBF. The tensile profile of HS was also smaller than that of BS line BBF, as well as line TBF. This result showed that the H-column connections were more effective in decreasing the stress/strain concentration than the box column connections at the beam flange, which reveals that as the moment transfer efficiency increased, the strain concentration decreased. This means that a significant portion of the beam moment should be transferred through the beam flanges as moment transfer efficiency degrades.
Fig. 8(c) plots flexural strain profiles along the beam height (Section C). The measured strains were found to be linear. Fig. 9(c) shows tensile strain profiles along the beam width (Section C) of all models. As shown in Fig. 9(c), the strains remained primarily elastic and a strain concentration did not occur. This result shows that the classical beam theory provides a reliable load transfer mechanism in the beam which is away from the column flange as a beam depth.
Y.-J. Kim, S.-H. Oh / Journal of Constructional Steel Research 63 (2007) 24–36
29
Fig. 7. Von Mises stress contour: (a) HN; (b) HS; (c) BN; (d) BS; (e) BS-T.
4.2.2. Weld access hole The presence of the weld access hole would permit easier welding on the beam flange and possibly promote a higher weld quality. However, it was not clear how such a solution would impact inelastic behavior. Nakashima et al. [8] addressed this as follows:
the sudden change in geometry at the toe of weld access hole causes a stress (and strain) concentration at the flange-web junction of the beam. Further, this junction is potentially low in fracture toughness because of hot-rolling, cooling, and rotary straightening processes. The combination of high stress and low fracture toughness is believed to be a primary
30
Y.-J. Kim, S.-H. Oh / Journal of Constructional Steel Research 63 (2007) 24–36
Fig. 7. (continued)
Fig. 8. Flexural strain profiles along beam height: (a) section A; (b) section B; (c) section C.
Y.-J. Kim, S.-H. Oh / Journal of Constructional Steel Research 63 (2007) 24–36
31
Fig. 9. Tensile strain profiles along beam width at beam flange: (a) section A; (b) section B: (c) section C.
cause of the brittle fracture of the base metal initiating from the toe of the weld access hole. Test data suggest that the size and shape of an access hole can influence the cumulative inelastic rotation capacity of steel subassemblages [8]. In laboratory tests [9,10], the box type of connections with no weld access hole successfully prevented premature fracture and exhibited a large energy dissipation capacity. Because a fracture often initiates from the toe of the weld access hole, a no-weld access hole design was adopted in Japan [9,11]. In the United States, tests by Lee and Lu of composite joint subassemblages indicate that larger access holes may result in a premature fracture at the root of the access hole [12]. To investigate the effect of the presence of the weld access hole on moment transfer efficiency, four models were compared: HN and HS with a H-column, and BN and BS with a box column. Details of the access hole geometry are shown in Fig. 2. In Fig. 7(a) and (c) the beam flanges of HN and BN yielded near the column face and the maximum stress occurred at the beam flange side. As shown in Fig. 9, the strain concentration of the beam flange of HN and BN cannot be observed. However, as shown in Figs. 7(b), (d), and
9(a), localized stress/strain concentrations for HS and BS were observed in the weld access hole region; this was due to the abrupt change in geometry at the toe of the access hole. In addition, it was speculated that a loss of web section in the weld access hole region had an effect on the decrease of the moment transfer efficiency. For this reason, the presence of the weld access hole adversely affected the stress/strain condition at the beam-to-column interface. In other words, it could be predicted that a no-weld access hole design was effective in improving the connection ductility. 4.2.3. Thickness of the column flange As shown in Fig. 6(d) and (e), the out-of-plane deformation of the column flange of specimen BS-T was larger than that of BS. Consequently, Fig. 7(d) and (e) show that the void range of stress of BS was smaller than that of BS-T. Due to an increased lateral deformation of the column flange, this meant a thinner column flange was not very efficient in transferring the force from the beam to the column. In Fig. 8(a), the strain profile of BS was slightly larger than that of BS-T along the beam height at the beam web. The maximum strain value of BS-T was 29% larger than that of BS at Section A, as shown in Fig. 9(a).
32
Y.-J. Kim, S.-H. Oh / Journal of Constructional Steel Research 63 (2007) 24–36
obtained from FEM results. The moment transfer efficiency of a beam web, γw , could be defined by the following equation γw =
Fig. 10. Moment of beam web (w M P : plastic moment of beam web). Table 2 Moment transfer efficiency of beam web and strain concentration Specimen
Moment transfer efficiency (γw ) (%)
Strain concentration index (γε )
HN HS BN BS BS-T
104 88 86 57 42
1.00 1.32 1.08 1.43 2.00
5. Discussion 5.1. Evaluation of moment transfer efficiency All the foregoing observations implied that strain concentration of the beam flanges was related to the increased demand on the beam flanges due to the poor moment transfer efficiency of a beam web. To gain further insight into the moment transfer mechanism in the connection, the relationships between the transfer moment of a beam web (Mw ) versus the connection rotation (θ ) were plotted in Fig. 10. In Fig. 10, the plastic moment of the beam web was w M p (=378 kN m), which only considered the full effective area. The web transfer moment, Mw , could be acquired using the stress data of the beam web
Mw wMp
(1)
where Mw was the web moment at a 3% rotation. The 3% rotation was adopted since it had been speculated that, after yielding, the web moment was stable at a 3% rotation. Moment transfer efficiency, hereafter referred to as γw for simplicity, is given in Table 2 and Fig. 11(a). As expected, the γw of HN was the largest and exceeded 100%. This meant that the beam web of HN transferred 100% of the beam web moment. The γw of HS, BN, BS and BS-T were 88%, 86%, 57%, and 42%, respectively. This result showed that the primary factors influencing the γw were the shape of the column, the presence of the weld access hole, and in the case of the box column, the thickness of the column. γw of HN was 16% larger than that of HS, while γw of BN was 29% larger than BS. This inferred that the γw of the box column was more sensitive to the weld access hole than that of the H-column. Fig. 11(b) plots the moment transfer ratio of the beam flange and web to the total beam section. Fig. 11(b) implies that as γw degrades, a large amount of bending force was transferred through the beam flanges, thus leading to overstressed beam flanges. As described above, a web at the beam end welded to the H-column develops its full moment capacity. However, a web at the beam end connected to the box column transfers some amount of moment capacity to the column, which depends on lateral stiffness of the column flange. The mechanism of the moment transition based on the yield line analysis is shown in Fig. 12. Fig. 12(b) shows the comparison of the yield line mechanism in the column flange. In Fig. 12(b), the expected yield line mechanism and the stress contour for FEM analysis were consistent with each other. Fig. 12 also shows that the isosceles triangular web area connecting with the column center region was analyzed not carrying the web flexural moment. Therefore, the web flexural moment only develops in both of the upper and the lower X region (Fig. 12(a)). The transmission of the flexural moment by the beam web connection was given
Fig. 11. Moment transfer: (a) moment transfer efficiency of beam web; (b) moment transfer ratio of the beam flange and web to the total beam section.
Y.-J. Kim, S.-H. Oh / Journal of Constructional Steel Research 63 (2007) 24–36
33
Fig. 12. Mechanism of moment transition: (a) column deformation; (b) yield line mechanism.
by Eq. (2) for a welded connection w Mtr
= (X − Sr ) × (h w − X − Sr )Now
where, −C2 −
(2)
C22 − 4C1 C3
, (ts < X < h d /2) 2C1 C1 = −h d (16M0 + tw h c Fyw ) X=
C2 = 24h d (4ts + h d )M0 − 2h 2c M0 − h d h c tw Sr Fyw C3 = −8h d ts (2ts + h d )M0 + 4h 2c (ts + h d )M0 − h d h c tw Sr2 Fyw √ √ Now = min[tw · Fyw , 2Sw · Fyj / 6, 2tc Fyc / 3] Mo = tc2 · Fyc /4 and where Sr = weld access hole size; Sw = fillet weld size; tc = column flange thickness; Fyj = yield stress of the fillet weld; Fyc = yield stress of the column flange; Fyw = yield stress of the beam web; h c = D − tc ; D = outer width of the square tube; ts = (td − t f )/2; td = diaphragm thickness; t f = beam flange thickness; and h d = inner distance between the upper and lower diaphragm (refer to Fig. 12). To investigate the flexural moment of the beam web at the connection, model BS with a wide flange beam of dimensions H-612 × 202 × 13 × 23 and a box column with dimensions of B-450 ×450 ×22 was selected. Through use of Eq. (2), the web moments in terms of the column flange thickness and the weld access hole size were determined, as shown in Fig. 13. It can be seen from Fig. 13 that as the column thickness increases, the flexural moment of the beam web increases. On the contrary, as the weld access hole size increases, the flexural moment of the beam web decreases. This may be related to the test result of Lee and Lu regarding composite joint subassemblages, which was that larger access holes may result in a premature fracture at the root of the access hole [12]. Based on Eq. (2), Fig. 14 plots the relationships of the moment transfer efficiency ( E γ w ) predicted by Eq. (2) to the column flange thickness (tc ) and the weld access hole size (Sr ). Here, the moment transfer efficiency ( E γ ε ) was gained as the ratio of the web moment calculated by Eq. (2) to the plastic moment of the beam web. It can be seen from Fig. 14 that the column thickness and the scallop size affected the web flexural moment. Additionally, it
Fig. 13. Effects of column flange thickness and weld access hole size for web moment (“Sr = 0” means no weld access hole).
Fig. 14. Calculated moment transfer efficiency ( E γ ε ) in relation to column flange thickness (tc ) and weld access hole size (Sr ).
can be seen from Fig. 14 that the column flange thickness of both parameters played a more critical role on the web flexural capacity. Fig. 15 illustrates the ratio of the beam web flexural moment (w M tr ) to the total connection moment (b M tr ), in relation to the column flange thickness (tc ) and the weld access hole size (Sr ). The total connection moment (b M tr \) transferred from a
34
Y.-J. Kim, S.-H. Oh / Journal of Constructional Steel Research 63 (2007) 24–36
Fig. 15. Ratio of beam web flexural moment (w M tr ) to total connection moment (b M tr ) in relation to column flange thickness (tc ) and weld access hole size (Sr ).
Fig. 16. Comparison between equation and FEM or experiment for web moment transfer efficiency.
beam to a column can be calculated by Eq. (3), where f M tr and w M tr were the flexural moment of beam flange and beam web, respectively. The flexural moment of the beam web was already given by Eq. (2) b M tr
= f M tr + w M tr = Z p · Fyf + (X − Sr ) × (h w − X − Sr )Now .
(3)
Fig. 15 showed that having a thicker column flange and no weld access hole, Sr = 0, was very efficient in attracting the flexural moment of a beam web due to the larger lateral stiffness of the column flange. The result suggests that it was important to use a small access hole, as well as no-weld access hole, to develop a larger beam flexural capacity. As shown in Fig. 15, when the column thickness was 22 mm and the weld access hole size was 35 mm, w M tr / b M tr was approximately 13%. This meant that the beam web only transferred 13% of the applied beam flexural moment; therefore, 87% of the beam bending should be transferred through the beam flanges. In the case of the wide flange beam used in this analysis, H-612 × 202 × 13 × 23, the plastic moment ratio of the beam flange to the entire beam section could be easily calculated; the ratio was approximately 78%. This infers that the connection with the box column may not provide sufficient strength for the plastic moment capacity of the connected beam to be reached. This also indicates that a significant portion of the beam should be transferred through the beam flanges, which results in the higher potential of a fracture. Therefore, it was speculated that when the box column was applied as a column, this trend was detrimental to the seismic behavior of the connection, and the moment transfer efficiency of a beam web should be considered in the design. To verify the validation of Eq. (2), the predictions were compared with the FEM and experimental results [2,4] in terms of the moment transfer efficiency of the beam web. Fig. 16 plots the comparison between the web moment transfer efficiency, E γ w , predicted by Eq. (2) and the FEM or experimental, γw . The experimental results are addressed by Akiyama et al. [2]
Fig. 17. Average tensile strain vs. rotation relationships at section A.
and by Okada et al. [4]. The results were nearly consistent with each other. According to Fig. 16, the web moment transfer efficiency of the connection with a box column can be reasonably predicted with Eq. (2). Based on these observations, it was speculated that Eqs. (2) and (3) could be used to predict the moment capacity and to design the connection that accounts for the effect of the lateral stiffness of the column flange for a box column. 5.2. Strain concentration Fig. 17 plots the relationships of the gross sectional average tensile strain of the beam flange versus the rotation at Section A (refer to Fig. 8(a)). In Fig. 17, at the same rotation, average flange strains at Section A were different for each model. A general trend was that the presence of the weld access hole, the box column as a column, and the thinner column flange affected the increase of the strain value at beam flanges; that is, it affected the increase of the local demand at the connections. To explicitly evaluate the strain concentration, the
Y.-J. Kim, S.-H. Oh / Journal of Constructional Steel Research 63 (2007) 24–36
Fig. 18. Moment transfer efficiency of beam web vs. strain concentration index relationship.
strain concentration index, γε , could be defined as in Eq. (4) ε γε = ε0
(4)
where ε0 was the strain increment per unit rotation of model HN and ε was the strain increment of each model. The strain increment of HN was adopted as a denominator because the moment transfer efficiency of HN developed 100%. Note that the increment was calculated after yielding. Table 2 shows the strain concentration index, γε . In Table 2, the γε of BS is 1.08, which means that strain concentration at the beam flange of BN did not occur. The γε of HS, BS, and BS-T were 1.32, 1.43, and 2.00, respectively. These results also showed that the strain concentration index was influenced by the weld access hole and the thin flange of a box column. Fig. 18 plots the relationship between the moment transfer efficiency of a beam web (γw ) and strain concentration index (γε ) from FEM analysis and experimental [4] results. It was observed that the strain concentration index decreased rapidly with the moment transfer efficiency. As shown in Fig. 18, the following formula was fitted for the strain concentration index: γε = −c1 · ln(γw ) + c2
(5)
where c1 and c2 were coefficients. This equation indicates that the strain concentration index was inversely proportional to the moment transfer efficiency. This relationship rule was very limited and further experimental and analytical studies had to be performed to determine the values of the coefficients in Eq. (5). Fig. 19 plots the relationship of the strain concentration index versus maximum rotation based on previous test data [4, 5,7] and [13]. In research conducted by Okada et al. [4], steel beam connections were tested by a monotonic loading pattern, while in researches conducted by Okada et al. [5], Kim et al. [7], and Oh et al. [13], composite beam connections were tested by a cyclic loading pattern. In Fig. 19, the vertical axis shows the maximum connection rotation, and the horizontal axis shows the strain concentration index. Irrespective of loading pattern, Fig. 19 indicates that the maximum rotation was
35
Fig. 19. Strain concentration index vs. maximum rotation relationship.
inversely proportional to the strain concentration index. These results indirectly implied that the deformation capacity of the connection was proportional to the moment transfer efficiency of the connections. Previous research [4,5] indicated that the deformation capacity of the connection with a box column decreases as their moment transfer efficiency diminishes. 6. Summary and conclusion Based on both analytical and previous test results, the following conclusions can be drawn concerning the effect of the moment transfer efficiency on deformation capacity at steel moment connections. 1. Due to the out-of-plane deformation of the column flange, the connection with a box column had poor moment transfer efficiency as compared to the connection with an H-column. Additionally, the presence of scallop and thin plates of the box column causes a decrease in moment transfer efficiency. 2. Strain concentration at the end of the beam was influenced by the efficiency in transmitting the moment in the web of the beam through the beam-to-column connection. The strain concentration index was inversely proportional to moment transfer efficiency. 3. The deformation capacity of the connection was poor as moment transfer efficiency degrades. The deformation capacity of the connection was proportional to the moment transfer efficiency of connections, while it was inversely proportional to the strain concentration index. Acknowledgements This research (03R&D C04-01) was financially supported by the Ministry of Construction & Transportation of South Korea and Korea Institute of Construction and Transportation Technology Evaluation and Planning, and the authors are grateful to the authorities for their support. References [1] Teraoka M et al. Effect of details on structural behavior for square tubular steel column-to-H shaped steel beam with mixed connection (1, 2). In: Annual assembly of AIJ. 1994. p. 1473–6.
36
Y.-J. Kim, S.-H. Oh / Journal of Constructional Steel Research 63 (2007) 24–36
[2] Akiyama H, Yamada S, Matsumoto Y, Matsuoka S, Ogura K, Kitamura H. Study on fracture of beam-to-column connections by means of full scale shaking table test. J Struct Constr Eng, AIJ 1998;512 (10):165–72. [3] Matsumoto Y, Akiyama H, Yamada S. Relationship between deformation capacity of beam at steel beam-to-column connection and joint efficiency. J Struct Constr Eng, AIJ 1999;523(9):117–24. [4] Okada K, Matsumoto Y, Yamada S. Evaluation of effect of joint efficiency at beam-to-column connection on ductility capacity of steel beams. J Struct Constr Eng, AIJ 2003;568(6):131–8. [5] Okada K, Oh SH, Yamada S. Effect of joint efficiency at beam-to-column connection on ductility capacity of composite beams. J Struct Constr Eng, AIJ 2003;573(11):185–92. [6] ANSYS user manual. Swanson Analysis Systems, Inc.; 2001. [7] Kim YJ, Oh SH, Moon TS. Seismic behavior and retrofit of steel moment connections considering slab effects. Eng Struct 2004;26:1993–2005. [8] Nakashima M, Suita K, Morisako K, Maruoka Y. Tests of welded
[9]
[10]
[11] [12] [13]
beam-column subassemblies. I: Global behavior. J Struct Eng, ASCE 1998;124(11):1236–44. Suita K, Tamura T, Morita S, Nakashima M, Engelhardt MD. Plastic rotation capacity of steel beam to column connections using a reduced beam section and no weld access hole design-full scale tests for improved steel beam to column subassemblies-part 1. J Struct Const Eng AIJ 1999; 526(12):177–84. Okada K. Experimental study on deformation capacity of the composite beams. In: Proceeding of 6th Pacific structural steel conference. 2001. p. 233–8. FEMA. Connection performance state of art report. FEMA-355D. Washington (DC): Federal Emergency Management Agency; 2000. Lee SJ, Lu WL. Cyclic tests of full-scale composite joint subassemblages. J Struct Eng, ASCE 1989;115(8):1977–98. Oh SH, Kim YJ, Moon TS. Experimental study on seismic retrofit of steel moment connections considering constraint effect of the floor slab. J Korean Society of Steel Construction, KSSC 2004;16(2):247–55.
Effect of the moment transfer efficiency of a beam web on deformation capacity at box column-to-H beam connections Young-Ju Kim ∗ , Sang-Hoon Oh Research Institute of Industrial Science & Technology (RIST), 79, Youngcheon Dongtan, Hwasung, Kyoungkido, 445-810, Republic of Korea Received 7 November 2005; accepted 23 February 2006
Abstract This paper investigates the effect of moment transfer efficiency of a beam web on deformation capacity at beam-to-column connections. Non-linear finite element analysis of five connection models was conducted. Analytical results showed that the moment transfer efficiency of the connection with a box column was poor when compared to a connection with an H-column; this was due to the out-of-plane deformation of the column flange. Based on previous test data, analytical results were compared with experimental results. Analytical and experimental results showed that the deformation capacity of the connection with a box column decreased due to the poor moment transfer efficiency of a beam web, followed by strain concentration at the beam flange. c 2006 Elsevier Ltd. All rights reserved. Keywords: Box column; Moment transfer efficiency; Strain concentration; Deformation capacity
1. Introduction Typically, Japanese steel moment resisting frames have a square hollow section that is used for the columns, and an H-shaped section that is used for the beams. A square tube column has two webs at each side, but no web in the center where the beam web is connected. This is different from the US connection, which has a web at the center; this may cause an increase in the deformation of the column flange. Due to the column flanges’ out-of-plane deformation and the loss of web sections by the weld access hole in the vicinity of the connection, the web of the box column is significantly less effective in transferring flexural moment. Therefore, the actual transfer mechanism is completely different from the normally assumed mechanism in connection design. Generally, the features of the structural behavior of this type of connection are as follows: (1) due to the out-ofplane deformation of column flanges, as shown in Fig. 1, the contribution of the web moment is reduced in the vicinity of the connection; (2) the deformation capacity of the connection is considerably reduced due to the severe constraint and the inevitable geometrical notches [1]. ∗ Corresponding author. Tel.: +82 31 370 9558; fax: +82 31 370 9559.
E-mail address: [email protected] (Y.-J. Kim). c 2006 Elsevier Ltd. All rights reserved. 0143-974X/$ - see front matter doi:10.1016/j.jcsr.2006.02.009
It has been reported that the beam near the connection develops a reduced strength as compared to the beam located away from the connection, which is due to the decrease of the web moment transfer [2–5]. This research on steel moment connections with a box column has indicated that the classical beam theory cannot predict the force transfer mechanism. For the case of a severe seismic loaded structure, the moment transfer efficiency effects of a beam web on connection ductility have not been fully uncovered. The first objective of this paper was to investigate the relationships between the moment transfer efficiency of a beam web and the strain concentration at beam-to-column connections. The second objective was to evaluate the effect of the moment transfer efficiency at the beam-to-column connection on deformation capacity. These objectives were addressed through the non-linear finite element analysis using ANSYS [6] and previous test data. For convenience of analysis, this study was limited to monotonic loading and neglected the influence of inelastic loading cycles. 2. Analytical configurations A total of five models were adopted and analyzed in order to improve understanding of the moment transfer efficiency of a beam web and the local stress/strain behavior in the vicinity
Y.-J. Kim, S.-H. Oh / Journal of Constructional Steel Research 63 (2007) 24–36
25
Nomenclature D Fyc Fyj Fyw hc hd Sr Sw tc td tf ts Mw bM p b M tr
M tr wM p w M tr γw f
Eγw
γε ε ε0
Outer width of the square tube Yield stress of the column flange Yield stress of the fillet weld Yield stress of the beam web D − tc Inner distance between the upper and lower diaphragm Scallop (weld access hole) size Fillet weld size Column flange thickness Diaphragm thickness Beam flange thickness (td − t f )/2 Transfer moment of the beam web from the FEM result Plastic moment of the beam Total connection moment ( f M tr + w M tr ) Calculated flexural moment of the beam flange Plastic moment of the beam web Calculated flexural moment of the beam web Moment transfer efficiency of the beam web (Mw /w M p ) Predicted moment transfer efficiency of the beam web (w M tr /b M tr ) Strain concentration index (ε/ε0) Strain increment of each model, except for the HN model Strain increment of the HN model
of the beam-to-column connection. Key geometric parameters were: the column shape, the presence of a weld access hole, and the thickness of the column flange. The geometry and list of the analytical models utilized in this research are shown in Fig. 2 and Table 1. The following abbreviations were used for the specimen designation: H = H-column, B = box column, N = no weld access hole, S = weld access hole, T = thin column flange. HN consisted of a rolled H-shaped steel beam with the dimensions of H-612×202×13×23 connected to a column with the measurements of H-450 × 450 × 22 × 22; all dimensions are in mm and are for the beam depth, width, web thickness, and flange thickness, respectively. All models had the same beam size. In contrast to the pre-Northridge connection, there
Fig. 1. Deformation of box column flange.
Fig. 2. Analytical models.
was no weld access hole and the beam web was connected directly to the column flange. Except for the presence of the weld access hole (see Fig. 2), the HS model used the same size beam and column as those used for the HN model. The
Table 1 List of analytical specimens Specimen
Column
Panel zone
Weld access hole
Thickness of column flange welded beam web (mm)
HN HS BN BS BS-T
H-450 × 450 × 22 H-450 × 450 × 22 B-450 × 450 × 22 B-450 × 450 × 22 B-450 × 450 × 15
H-450 × 450 × 32 × 22 H-450 × 450 × 32 × 22 B-450 × 450 × 32 × 22 B-450 × 450 × 32 × 22 B-450 × 450 × 32 × 15
No Yes No Yes Yes
22 22 22 22 15
H: H-column, B: box column, N: no weld access hole, S: weld access hole, T: thin column flange.
26
Y.-J. Kim, S.-H. Oh / Journal of Constructional Steel Research 63 (2007) 24–36
Fig. 3. Finite element model (BS).
BN and BS models had the same box column dimensions of B-450 × 450 × 22; all dimensions are in mm and are for the column depth, width, and thickness, respectively. The no-weld access hole design was adopted in the BN model, but not in the BS model. A conventional design was used for the weld access hole in the BS. The BS was derived from the geometry of specimen SP-1, which has been tested in previous research [7]. The sudden change in geometry at the toe of the weld access hole causes a stress/strain concentration at the flange–web junction of the beam. Furthermore, this junction is potentially low in fracture toughness due to the processes of hot-rolling, cooling, and rotary straightening [8]. The combination of high stress and low fracture toughness is believed to be a primary cause of the brittle fracture of the base metal; this initiates from the toe of the weld access hole. BS-T had a box column with the dimensions of B-450 × 450 × 15, and had a thinner flange plate. In the case of the box column with a thin plate, it was expected that the contribution of web moment would eventually be considerably reduced due to the severe out-ofplane deformation of the column flanges. As shown in Fig. 2, a relatively strong column was used to ensure that the beams could initiate the development of a plastic hinge mechanism during the loading, before damage developed in the column. Additionally, the incorporation of a rigid panel zone with a web thickness of 32 mm may significantly reduce the contribution of panel zone shear deformation to the mode of failure. 3. Analytical model An analytical model was used to investigate local behavior and local ductility demand near the weld access hole, where the fracture occurs. A three-dimensional finite element model was generated to represent a structural subassemblage. Fig. 3
shows the finite element model for a steel connection; due to symmetry, only half was modeled. Brick elements (SOLID45 element) with eight nodes, 24 nodal degrees of freedom, and three translational DOFs at each node, were used to model the steel shape using ANSYS commercial code [6]. For local behavior near the strain concentration, the mesh in the vicinity of the web access hole was finer than the mesh for other regions (Fig. 3). Based on previous research, it was possible to model the supports of the experimental setup [7]. Hinged boundary conditions were used to support the column top and bottom. Each subassemblage contained a column between the mid-height of the two adjacent floors and a half-span of the beam. The load was applied by imposing incremental vertical displacements, in a monotonic fashion, at the beam tip during the analysis. Based on the material test data of previous research, monotonic analyses were done using isotropic hardening for the steel beam and column [7]. The von Mises yield criterion was employed to define the plasticity. 4. Analytical results 4.1. Global behavior Fig. 4 plots the moment versus rotation relationship for the BS model and specimen SP-1. The curve for the BS model exhibited a slightly higher initial stiffness than the specimen SP-1; but, both connections had similar strengths. Nevertheless, it was speculated that the results were consistent with each other and that the ultimate moment and initial stiffness were well represented. Fig. 5 presents the moment versus rotation for all steel models to examine the global behavior of the connections, where b M p (=1404 kN m) was the plastic moment of the
Y.-J. Kim, S.-H. Oh / Journal of Constructional Steel Research 63 (2007) 24–36
27
all models: the out-of-plane deformation mode of the column flange, strain profiles, and von Mises stress distributions Fig. 6 show the deformed shapes of each connection and the von Mises stress distribution plot are shown in Fig. 7. The strain profiles of the beam web and beam flange near the connection are shown in Figs. 8 and 9, respectively. The locations for strain measurement were at three sections, A, B and C, and were at beam depth distances of 75 mm, 125 mm and 612 mm from the column face, respectively (Fig. 8). In particular, Section A was located in line with the toe of the weld access hole so that the stress/strain distributions could be investigated in more detail.
Fig. 4. Comparison between experimental and analytical global behavior.
beam with consideration of the full effective area. Fig. 5 shows that the curves for all connections had the same initial elastic stiffness; however, at the same rotation level after the elastic range they had different strength capacities. For example, at the rotation of 0.013 rad, the strength for HN had already reached 1406 kN m, which was the same as the plastic moment of the beam. Meanwhile, for HS, BN, BS, and BS-T, the strengths were 1336 kN m, 1336 kN m, 1256 kN m, and 1205 kN m, which are 95%, 95%, 89%, and 86% of the beam plastic moment, respectively. This meant that the HS, BN, BS, and BST connections reached the plastic range more rapidly than the HN model. Focusing on the strong column and panel zone, this result showed that the strength capacity of each model may be influenced by the moment transfer efficiency of the connection. This result also showed that a box column may be significantly less effective in transferring flexural moment due to the out-ofdeformation of the column flanges. 4.2. Influence of connection details on strain concentration To explicitly investigate the causes of the strain concentration and the effect of the moment transfer efficiency of a beam web at the connection, the following were observed for
4.2.1. Column shape As described above, when a rectangular hollow section was applied as a column, increased stress at the end of the beam was influenced by the efficiency in transmitting the stress in the web of the beam through the beam-to-column connection. Therefore, as compared to an H-section column, there was poor ductility capacity of the specimens using box columns [3–5]. As shown in Fig. 6(a) and (c), out-of- plane deformation of the column flange of BN was large. However, no part of the HN column flange deformed. Fig. 7 shows Von Mises stress contours for all models at a 4% rotation since AISC recommends a minimum 4% rad total rotation capacity of the connection at the moment resisting frames. In Fig. 7, the symbol “” represents the middle area of the beam web being virtually devoid of stress. It was believed that as the void range of stress increases, the moment transfer efficiency of the beam web may decrease. For example, the void range of stress of HN was significantly smaller than that of BN. Fig. 8 plots the flexural strain profiles along the beam height at sections A, B and C at a 4% rotation. As shown in Fig. 8(a), the strain profile of BN was poorly developed, while the strain of HN showed a symmetric balance for the tensile and compressive strain represented as a linear line at Section A. Based on these results, more effective moment transfer efficiency of a web could be expected in the severe lateral load for H-section column connections, as compared to box column connections. The tensile strain profiles of each specimen, along the width of the beam flange, are shown in Fig. 9. Fig. 9(a) shows that along line BBF, the tensile strain of HN was smaller than that
Fig. 5. Moment vs. rotation relationships.
28
Y.-J. Kim, S.-H. Oh / Journal of Constructional Steel Research 63 (2007) 24–36
Fig. 6. Deformed shapes at 4% rotation (5 times exaggerated): (a) HN; (b) HS; (c) BN; (d) BS; (e) BS-T.
of BN; this was similar along line TBF. The tensile profile of HS was also smaller than that of BS line BBF, as well as line TBF. This result showed that the H-column connections were more effective in decreasing the stress/strain concentration than the box column connections at the beam flange, which reveals that as the moment transfer efficiency increased, the strain concentration decreased. This means that a significant portion of the beam moment should be transferred through the beam flanges as moment transfer efficiency degrades.
Fig. 8(c) plots flexural strain profiles along the beam height (Section C). The measured strains were found to be linear. Fig. 9(c) shows tensile strain profiles along the beam width (Section C) of all models. As shown in Fig. 9(c), the strains remained primarily elastic and a strain concentration did not occur. This result shows that the classical beam theory provides a reliable load transfer mechanism in the beam which is away from the column flange as a beam depth.
Y.-J. Kim, S.-H. Oh / Journal of Constructional Steel Research 63 (2007) 24–36
29
Fig. 7. Von Mises stress contour: (a) HN; (b) HS; (c) BN; (d) BS; (e) BS-T.
4.2.2. Weld access hole The presence of the weld access hole would permit easier welding on the beam flange and possibly promote a higher weld quality. However, it was not clear how such a solution would impact inelastic behavior. Nakashima et al. [8] addressed this as follows:
the sudden change in geometry at the toe of weld access hole causes a stress (and strain) concentration at the flange-web junction of the beam. Further, this junction is potentially low in fracture toughness because of hot-rolling, cooling, and rotary straightening processes. The combination of high stress and low fracture toughness is believed to be a primary
30
Y.-J. Kim, S.-H. Oh / Journal of Constructional Steel Research 63 (2007) 24–36
Fig. 7. (continued)
Fig. 8. Flexural strain profiles along beam height: (a) section A; (b) section B; (c) section C.
Y.-J. Kim, S.-H. Oh / Journal of Constructional Steel Research 63 (2007) 24–36
31
Fig. 9. Tensile strain profiles along beam width at beam flange: (a) section A; (b) section B: (c) section C.
cause of the brittle fracture of the base metal initiating from the toe of the weld access hole. Test data suggest that the size and shape of an access hole can influence the cumulative inelastic rotation capacity of steel subassemblages [8]. In laboratory tests [9,10], the box type of connections with no weld access hole successfully prevented premature fracture and exhibited a large energy dissipation capacity. Because a fracture often initiates from the toe of the weld access hole, a no-weld access hole design was adopted in Japan [9,11]. In the United States, tests by Lee and Lu of composite joint subassemblages indicate that larger access holes may result in a premature fracture at the root of the access hole [12]. To investigate the effect of the presence of the weld access hole on moment transfer efficiency, four models were compared: HN and HS with a H-column, and BN and BS with a box column. Details of the access hole geometry are shown in Fig. 2. In Fig. 7(a) and (c) the beam flanges of HN and BN yielded near the column face and the maximum stress occurred at the beam flange side. As shown in Fig. 9, the strain concentration of the beam flange of HN and BN cannot be observed. However, as shown in Figs. 7(b), (d), and
9(a), localized stress/strain concentrations for HS and BS were observed in the weld access hole region; this was due to the abrupt change in geometry at the toe of the access hole. In addition, it was speculated that a loss of web section in the weld access hole region had an effect on the decrease of the moment transfer efficiency. For this reason, the presence of the weld access hole adversely affected the stress/strain condition at the beam-to-column interface. In other words, it could be predicted that a no-weld access hole design was effective in improving the connection ductility. 4.2.3. Thickness of the column flange As shown in Fig. 6(d) and (e), the out-of-plane deformation of the column flange of specimen BS-T was larger than that of BS. Consequently, Fig. 7(d) and (e) show that the void range of stress of BS was smaller than that of BS-T. Due to an increased lateral deformation of the column flange, this meant a thinner column flange was not very efficient in transferring the force from the beam to the column. In Fig. 8(a), the strain profile of BS was slightly larger than that of BS-T along the beam height at the beam web. The maximum strain value of BS-T was 29% larger than that of BS at Section A, as shown in Fig. 9(a).
32
Y.-J. Kim, S.-H. Oh / Journal of Constructional Steel Research 63 (2007) 24–36
obtained from FEM results. The moment transfer efficiency of a beam web, γw , could be defined by the following equation γw =
Fig. 10. Moment of beam web (w M P : plastic moment of beam web). Table 2 Moment transfer efficiency of beam web and strain concentration Specimen
Moment transfer efficiency (γw ) (%)
Strain concentration index (γε )
HN HS BN BS BS-T
104 88 86 57 42
1.00 1.32 1.08 1.43 2.00
5. Discussion 5.1. Evaluation of moment transfer efficiency All the foregoing observations implied that strain concentration of the beam flanges was related to the increased demand on the beam flanges due to the poor moment transfer efficiency of a beam web. To gain further insight into the moment transfer mechanism in the connection, the relationships between the transfer moment of a beam web (Mw ) versus the connection rotation (θ ) were plotted in Fig. 10. In Fig. 10, the plastic moment of the beam web was w M p (=378 kN m), which only considered the full effective area. The web transfer moment, Mw , could be acquired using the stress data of the beam web
Mw wMp
(1)
where Mw was the web moment at a 3% rotation. The 3% rotation was adopted since it had been speculated that, after yielding, the web moment was stable at a 3% rotation. Moment transfer efficiency, hereafter referred to as γw for simplicity, is given in Table 2 and Fig. 11(a). As expected, the γw of HN was the largest and exceeded 100%. This meant that the beam web of HN transferred 100% of the beam web moment. The γw of HS, BN, BS and BS-T were 88%, 86%, 57%, and 42%, respectively. This result showed that the primary factors influencing the γw were the shape of the column, the presence of the weld access hole, and in the case of the box column, the thickness of the column. γw of HN was 16% larger than that of HS, while γw of BN was 29% larger than BS. This inferred that the γw of the box column was more sensitive to the weld access hole than that of the H-column. Fig. 11(b) plots the moment transfer ratio of the beam flange and web to the total beam section. Fig. 11(b) implies that as γw degrades, a large amount of bending force was transferred through the beam flanges, thus leading to overstressed beam flanges. As described above, a web at the beam end welded to the H-column develops its full moment capacity. However, a web at the beam end connected to the box column transfers some amount of moment capacity to the column, which depends on lateral stiffness of the column flange. The mechanism of the moment transition based on the yield line analysis is shown in Fig. 12. Fig. 12(b) shows the comparison of the yield line mechanism in the column flange. In Fig. 12(b), the expected yield line mechanism and the stress contour for FEM analysis were consistent with each other. Fig. 12 also shows that the isosceles triangular web area connecting with the column center region was analyzed not carrying the web flexural moment. Therefore, the web flexural moment only develops in both of the upper and the lower X region (Fig. 12(a)). The transmission of the flexural moment by the beam web connection was given
Fig. 11. Moment transfer: (a) moment transfer efficiency of beam web; (b) moment transfer ratio of the beam flange and web to the total beam section.
Y.-J. Kim, S.-H. Oh / Journal of Constructional Steel Research 63 (2007) 24–36
33
Fig. 12. Mechanism of moment transition: (a) column deformation; (b) yield line mechanism.
by Eq. (2) for a welded connection w Mtr
= (X − Sr ) × (h w − X − Sr )Now
where, −C2 −
(2)
C22 − 4C1 C3
, (ts < X < h d /2) 2C1 C1 = −h d (16M0 + tw h c Fyw ) X=
C2 = 24h d (4ts + h d )M0 − 2h 2c M0 − h d h c tw Sr Fyw C3 = −8h d ts (2ts + h d )M0 + 4h 2c (ts + h d )M0 − h d h c tw Sr2 Fyw √ √ Now = min[tw · Fyw , 2Sw · Fyj / 6, 2tc Fyc / 3] Mo = tc2 · Fyc /4 and where Sr = weld access hole size; Sw = fillet weld size; tc = column flange thickness; Fyj = yield stress of the fillet weld; Fyc = yield stress of the column flange; Fyw = yield stress of the beam web; h c = D − tc ; D = outer width of the square tube; ts = (td − t f )/2; td = diaphragm thickness; t f = beam flange thickness; and h d = inner distance between the upper and lower diaphragm (refer to Fig. 12). To investigate the flexural moment of the beam web at the connection, model BS with a wide flange beam of dimensions H-612 × 202 × 13 × 23 and a box column with dimensions of B-450 ×450 ×22 was selected. Through use of Eq. (2), the web moments in terms of the column flange thickness and the weld access hole size were determined, as shown in Fig. 13. It can be seen from Fig. 13 that as the column thickness increases, the flexural moment of the beam web increases. On the contrary, as the weld access hole size increases, the flexural moment of the beam web decreases. This may be related to the test result of Lee and Lu regarding composite joint subassemblages, which was that larger access holes may result in a premature fracture at the root of the access hole [12]. Based on Eq. (2), Fig. 14 plots the relationships of the moment transfer efficiency ( E γ w ) predicted by Eq. (2) to the column flange thickness (tc ) and the weld access hole size (Sr ). Here, the moment transfer efficiency ( E γ ε ) was gained as the ratio of the web moment calculated by Eq. (2) to the plastic moment of the beam web. It can be seen from Fig. 14 that the column thickness and the scallop size affected the web flexural moment. Additionally, it
Fig. 13. Effects of column flange thickness and weld access hole size for web moment (“Sr = 0” means no weld access hole).
Fig. 14. Calculated moment transfer efficiency ( E γ ε ) in relation to column flange thickness (tc ) and weld access hole size (Sr ).
can be seen from Fig. 14 that the column flange thickness of both parameters played a more critical role on the web flexural capacity. Fig. 15 illustrates the ratio of the beam web flexural moment (w M tr ) to the total connection moment (b M tr ), in relation to the column flange thickness (tc ) and the weld access hole size (Sr ). The total connection moment (b M tr \) transferred from a
34
Y.-J. Kim, S.-H. Oh / Journal of Constructional Steel Research 63 (2007) 24–36
Fig. 15. Ratio of beam web flexural moment (w M tr ) to total connection moment (b M tr ) in relation to column flange thickness (tc ) and weld access hole size (Sr ).
Fig. 16. Comparison between equation and FEM or experiment for web moment transfer efficiency.
beam to a column can be calculated by Eq. (3), where f M tr and w M tr were the flexural moment of beam flange and beam web, respectively. The flexural moment of the beam web was already given by Eq. (2) b M tr
= f M tr + w M tr = Z p · Fyf + (X − Sr ) × (h w − X − Sr )Now .
(3)
Fig. 15 showed that having a thicker column flange and no weld access hole, Sr = 0, was very efficient in attracting the flexural moment of a beam web due to the larger lateral stiffness of the column flange. The result suggests that it was important to use a small access hole, as well as no-weld access hole, to develop a larger beam flexural capacity. As shown in Fig. 15, when the column thickness was 22 mm and the weld access hole size was 35 mm, w M tr / b M tr was approximately 13%. This meant that the beam web only transferred 13% of the applied beam flexural moment; therefore, 87% of the beam bending should be transferred through the beam flanges. In the case of the wide flange beam used in this analysis, H-612 × 202 × 13 × 23, the plastic moment ratio of the beam flange to the entire beam section could be easily calculated; the ratio was approximately 78%. This infers that the connection with the box column may not provide sufficient strength for the plastic moment capacity of the connected beam to be reached. This also indicates that a significant portion of the beam should be transferred through the beam flanges, which results in the higher potential of a fracture. Therefore, it was speculated that when the box column was applied as a column, this trend was detrimental to the seismic behavior of the connection, and the moment transfer efficiency of a beam web should be considered in the design. To verify the validation of Eq. (2), the predictions were compared with the FEM and experimental results [2,4] in terms of the moment transfer efficiency of the beam web. Fig. 16 plots the comparison between the web moment transfer efficiency, E γ w , predicted by Eq. (2) and the FEM or experimental, γw . The experimental results are addressed by Akiyama et al. [2]
Fig. 17. Average tensile strain vs. rotation relationships at section A.
and by Okada et al. [4]. The results were nearly consistent with each other. According to Fig. 16, the web moment transfer efficiency of the connection with a box column can be reasonably predicted with Eq. (2). Based on these observations, it was speculated that Eqs. (2) and (3) could be used to predict the moment capacity and to design the connection that accounts for the effect of the lateral stiffness of the column flange for a box column. 5.2. Strain concentration Fig. 17 plots the relationships of the gross sectional average tensile strain of the beam flange versus the rotation at Section A (refer to Fig. 8(a)). In Fig. 17, at the same rotation, average flange strains at Section A were different for each model. A general trend was that the presence of the weld access hole, the box column as a column, and the thinner column flange affected the increase of the strain value at beam flanges; that is, it affected the increase of the local demand at the connections. To explicitly evaluate the strain concentration, the
Y.-J. Kim, S.-H. Oh / Journal of Constructional Steel Research 63 (2007) 24–36
Fig. 18. Moment transfer efficiency of beam web vs. strain concentration index relationship.
strain concentration index, γε , could be defined as in Eq. (4) ε γε = ε0
(4)
where ε0 was the strain increment per unit rotation of model HN and ε was the strain increment of each model. The strain increment of HN was adopted as a denominator because the moment transfer efficiency of HN developed 100%. Note that the increment was calculated after yielding. Table 2 shows the strain concentration index, γε . In Table 2, the γε of BS is 1.08, which means that strain concentration at the beam flange of BN did not occur. The γε of HS, BS, and BS-T were 1.32, 1.43, and 2.00, respectively. These results also showed that the strain concentration index was influenced by the weld access hole and the thin flange of a box column. Fig. 18 plots the relationship between the moment transfer efficiency of a beam web (γw ) and strain concentration index (γε ) from FEM analysis and experimental [4] results. It was observed that the strain concentration index decreased rapidly with the moment transfer efficiency. As shown in Fig. 18, the following formula was fitted for the strain concentration index: γε = −c1 · ln(γw ) + c2
(5)
where c1 and c2 were coefficients. This equation indicates that the strain concentration index was inversely proportional to the moment transfer efficiency. This relationship rule was very limited and further experimental and analytical studies had to be performed to determine the values of the coefficients in Eq. (5). Fig. 19 plots the relationship of the strain concentration index versus maximum rotation based on previous test data [4, 5,7] and [13]. In research conducted by Okada et al. [4], steel beam connections were tested by a monotonic loading pattern, while in researches conducted by Okada et al. [5], Kim et al. [7], and Oh et al. [13], composite beam connections were tested by a cyclic loading pattern. In Fig. 19, the vertical axis shows the maximum connection rotation, and the horizontal axis shows the strain concentration index. Irrespective of loading pattern, Fig. 19 indicates that the maximum rotation was
35
Fig. 19. Strain concentration index vs. maximum rotation relationship.
inversely proportional to the strain concentration index. These results indirectly implied that the deformation capacity of the connection was proportional to the moment transfer efficiency of the connections. Previous research [4,5] indicated that the deformation capacity of the connection with a box column decreases as their moment transfer efficiency diminishes. 6. Summary and conclusion Based on both analytical and previous test results, the following conclusions can be drawn concerning the effect of the moment transfer efficiency on deformation capacity at steel moment connections. 1. Due to the out-of-plane deformation of the column flange, the connection with a box column had poor moment transfer efficiency as compared to the connection with an H-column. Additionally, the presence of scallop and thin plates of the box column causes a decrease in moment transfer efficiency. 2. Strain concentration at the end of the beam was influenced by the efficiency in transmitting the moment in the web of the beam through the beam-to-column connection. The strain concentration index was inversely proportional to moment transfer efficiency. 3. The deformation capacity of the connection was poor as moment transfer efficiency degrades. The deformation capacity of the connection was proportional to the moment transfer efficiency of connections, while it was inversely proportional to the strain concentration index. Acknowledgements This research (03R&D C04-01) was financially supported by the Ministry of Construction & Transportation of South Korea and Korea Institute of Construction and Transportation Technology Evaluation and Planning, and the authors are grateful to the authorities for their support. References [1] Teraoka M et al. Effect of details on structural behavior for square tubular steel column-to-H shaped steel beam with mixed connection (1, 2). In: Annual assembly of AIJ. 1994. p. 1473–6.
36
Y.-J. Kim, S.-H. Oh / Journal of Constructional Steel Research 63 (2007) 24–36
[2] Akiyama H, Yamada S, Matsumoto Y, Matsuoka S, Ogura K, Kitamura H. Study on fracture of beam-to-column connections by means of full scale shaking table test. J Struct Constr Eng, AIJ 1998;512 (10):165–72. [3] Matsumoto Y, Akiyama H, Yamada S. Relationship between deformation capacity of beam at steel beam-to-column connection and joint efficiency. J Struct Constr Eng, AIJ 1999;523(9):117–24. [4] Okada K, Matsumoto Y, Yamada S. Evaluation of effect of joint efficiency at beam-to-column connection on ductility capacity of steel beams. J Struct Constr Eng, AIJ 2003;568(6):131–8. [5] Okada K, Oh SH, Yamada S. Effect of joint efficiency at beam-to-column connection on ductility capacity of composite beams. J Struct Constr Eng, AIJ 2003;573(11):185–92. [6] ANSYS user manual. Swanson Analysis Systems, Inc.; 2001. [7] Kim YJ, Oh SH, Moon TS. Seismic behavior and retrofit of steel moment connections considering slab effects. Eng Struct 2004;26:1993–2005. [8] Nakashima M, Suita K, Morisako K, Maruoka Y. Tests of welded
[9]
[10]
[11] [12] [13]
beam-column subassemblies. I: Global behavior. J Struct Eng, ASCE 1998;124(11):1236–44. Suita K, Tamura T, Morita S, Nakashima M, Engelhardt MD. Plastic rotation capacity of steel beam to column connections using a reduced beam section and no weld access hole design-full scale tests for improved steel beam to column subassemblies-part 1. J Struct Const Eng AIJ 1999; 526(12):177–84. Okada K. Experimental study on deformation capacity of the composite beams. In: Proceeding of 6th Pacific structural steel conference. 2001. p. 233–8. FEMA. Connection performance state of art report. FEMA-355D. Washington (DC): Federal Emergency Management Agency; 2000. Lee SJ, Lu WL. Cyclic tests of full-scale composite joint subassemblages. J Struct Eng, ASCE 1989;115(8):1977–98. Oh SH, Kim YJ, Moon TS. Experimental study on seismic retrofit of steel moment connections considering constraint effect of the floor slab. J Korean Society of Steel Construction, KSSC 2004;16(2):247–55.