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Investigation of secondary prying in thick built-up T-stub connections using nonlinear finite element modeling
Engineering Structures 36 (2012) 113–122
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Investigation of secondary prying in thick built-up T-stub connections using nonlinear finite element modeling Elie G. Hantouche a,⇑, Anant R. Kukreti b, Gian A. Rassati c a
Structural Engineering, Civil and Environmental Engineering Department, American University of Beirut, P.O. Box 11-0236, Riad El-Solh/Beirut 1107 2020, Lebanon Engineering Mechanics, School of Energy, Environmental, Biological and Medical Engineering, University of Cincinnati (ML-0021), P.O. Box 210012, Cincinnati, OH 452210071, USA c Structural Engineering, School of Advanced Structures, University of Cincinnati (ML-0071), P.O. Box 210071, Cincinnati, OH 452210071, USA b
a r t i c l e
i n f o
Article history: Received 11 March 2011 Revised 23 November 2011 Accepted 24 November 2011 Available online 29 December 2011 Keywords: Finite element Connection Secondary prying Continuity plates T-stub Thick-flange
a b s t r a c t This study investigates the prying behavior in thick-flange built-up T-stub/column systems that should be addressed in designing full-strength double tee connections for use in moment resisting frames which satisfy prequalification requirements. In particular, this study focuses on the phenomenon herein indicated as secondary prying, which is related to the additional forces that are introduced into the tension bolts due to significant bending of the column flange. Three-dimensional finite element models that incorporate pretension of fasteners, full contact interactions, and nonlinear material characteristics are used to investigate secondary prying effect in thickflange T-stub/column system with and without continuity plates. This study provides insight as to whether continuity plates are necessary in columns when designing and detailing full-scale T-stub connections for prequalification. The effect of secondary prying is incorporated into an existing prying strength model for thick T-stubs to quantify the amount of total prying encountered in thick built-up T-stub connections with and without continuity plates. Parameters that impact the secondary prying in thick flange T-stub/column systems were identified based on the geometric configuration that results from the design of full-strength double tee connections with deep girders. The results show that decreasing the effect of secondary prying is achieved through either increasing the column size, or adding continuity plates to the column. This study provides information for detailing columns without continuity plates as well as quantifying the amount of prying so engineers can design for the additional load by increasing the bolt diameter. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Continuity plates are often used in connections to stiffen the column flange and web in order to resist large forces transmitted by the beam flange. Continuity plates requirements in bolted/ welded connections are another consideration which may be important as greater ductility is required of moment frame connections. The state-of the-art report on connection performance by FEMA 350-D [1] discusses requirements for continuity plates to provide higher ductile connection performance. Continuity plates are designed consistent with Section J10.8 of ANSI/AISC 360-05 [2], and Section 9.5 or 10.5 of the AISC Seismic Provisions [3] for Special Moment Frames (SMF) systems or Intermediate Moment Frames (IMF) systems. The 2005 AISC seismic provisions classify a connection as prequalified if it is capable of sustaining an interstory drift of 4% with at least 80% of the beam plastic moment ⇑ Corresponding author. Tel.: +961 1 350000x3400; fax: +961 1 744462. E-mail addresses: [email protected] (E.G. Hantouche), [email protected] (A.R. Kukreti), [email protected] (G.A. Rassati). 0141-0296/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.engstruct.2011.11.030
for SMF, and an interstory drift of 2% for IMF. Connections used in SMF and IMF shall be prequalified by evaluating all yielding mechanism and failure modes [3]. Several experimental and analytical studies [4–7] have been conducted to investigate the behavior of bolted T-stub/column systems such as that shown in Fig. 1. One of the main characteristics of the behavior of such connections is the prying phenomenon (primary and secondary). Some of these studies [4–7] include experimental and analytical investigations on full-scale T-stub connections with and without continuity plates. Continuity plates were included in six full-scale tests on bolted T-stub connections conducted by Smallidge [5], Swanson [6], Popov and Takhirov [7]. Two tests conducted by Swanson [6] and Smallidge [5] did not include continuity plates. In most of these cases, no significant column flange yielding was reported. Four full-scale tests were performed by Larson [4] without continuity plates. For these tests it was reported that column flange bending displacements were relatively small compared to T-stub flange bending displacements, but Larson [4] reported that large bending displacements due to thinner column flanges may cause additional prying forces in the bolts.
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Fig. 1. Typical built-up T-stub moment connection [21].
Most of the earlier studies on T-stub connections have focused on issues related to classical prying action by neglecting column flange deformation [2,8–15]. Such classical prying action is caused by flexural deformations of the flange of a T-stub, which results in additional forces transferred to the bolts. Classical prying will be herein referred to as primary prying to distinguish it from a similar phenomenon caused by the flexural deformation of the column flange, which will be indicated as secondary prying. No prior studies in the literature dealt with the investigation of the effects of secondary prying in T-stub/column systems except for a pilot parametric analytical study conducted at the University of Cincinnati as a part of a NSF research experience for undergraduates summer program [16]. The study highlights the main parameters that influence the amount of secondary prying. In moment resisting frames, thick-flange built-up T-stub connections are needed with deep girders to resist the large moment expected. This may lead to a connection in which the T-stub flange is thicker than the column flange. In such cases, the column flange is subjected to bending, and may undergo significant deformations. This significant behavioral characteristic of the column flange causes the secondary prying phenomenon, in addition to the primary one. Secondary prying refers to the additional forces introduced in the tension bolts due to a significant deformation of the column flange. The column flange behaves similarly to the flange of the T-stub. The column flange deforms outwards at the connection (i.e., away from the T-flange), showing smaller deformations at the flange centerline, and larger toward the tips of the flange. This differential deformation causes secondary prying. This may lead to either column flange failure due to yield line mechanism, and/or tension bolt fracture due to secondary prying. Fig. 2 shows the deformation of the column flange and T-stub flange of a typical T-stub connection attached to a column.
Primary prying in thick flange T-stub connections has also been studied by various researchers [7,17,18] using experimental and finite element modeling to predict strength, stiffness, and ductility. This study is a part of a wider study that deals with the behavior of full strength thick flange T-stub connections for use in moment resisting frames. This included an experimental investigation on built-up thick flange T-stub connections including 24 connection component tests conducted to investigate the effect of connection variables and different fabrication and detailing practices used for welding and bolt holes fabrication. These physical test results were also used to develop and validate a finite element model of the thick flange T-stub connection which duplicates the test results within acceptable limits for load–deformation behavior and failure mechanism. The finite element results reported show excellent agreement with the experimental component tests [17,19]. Therefore, finite element modeling can be used as a reliable tool to study the significant behavioral characteristics occurring in thick T-stub/ column connections caused by the secondary prying phenomenon. The intent of this investigation is to study secondary prying in thick-flange T-stub/column systems with and without continuity plates using finite element modeling. The finite element study shows that the need for continuity plates is not only governed by panel zone shear strength, web yielding, and web crippling but also by the need to minimize the amount of secondary prying. Finite element results are also used to quantify the total prying by using the primary prying model developed and reported in [19], and incorporating the effect of secondary prying with and without continuity plates. The scope of this study is to investigate the amount of secondary prying encountered in thick T-stubs that are designed for fullscale connections having W24x76, W30x108, and W36x150 beams with different column sizes, with and without continuity plates. The 3 beam sizes selected for this study cover the range of deep girders
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Fig. 2. Two-dimensional top view of T-stub/column.
that may be used in SMF similar to the one tested for bolted flange plate steel moment connections [20]. The variation of the column flange thickness was selected to cover the practical range where the column considered as stiff (the column flange thickness is larger the T-stub flange thickness) or flexible (the T-stub flange thickness is larger the column flange thickness). A draft of the procedure for the design of full-strength T-stub connections has been developed [21,22], and submitted for ballot for incorporation into AISC/ANSI358 [23]. The design of the connections reported in this paper is based on the draft design procedure [21,22]. The connections considered in that design procedure are composed, respectively of W24x76, W30x108, and W36x150 beams connected to W14x257 columns. The design for a full-strength double tee connection between a W30x108 beam and a W14x257 column is presented in [19]. 2. Nonlinear finite element modeling The finite element analyses presented herein are intended to provide insight into the mechanisms of thick-flange T-stub/column flange behavior. Considering the T-stubs as three dimensional systems, twenty seven finite element models have been developed for T-stub connections using twenty-node quadratic brick elements available within the software package ABAQUS [24]. The finite element analyses presented herein are aimed at investigating the prying phenomenon (primary and secondary) using nonlinear material behavior, pretension of fasteners, and contact interactions. The same finite element technique was successfully used to reproduce component T-stubs tested experimentally as reported in [17,19]. 2.1. Mesh design of three-dimensional solid T-stub/column models Twenty-node quadratic brick elements with reduced integration (C3D20-R) are used to mesh the T-stub flange/column system.
The T-stub flange and the column flange consist of three layers of elements, and the continuity plates consist of two layers of elements. A full three dimensional finite element model of the T-stub/column assemblage considered is shown in Fig. 3. A finer mesh was used in the T-flange, tension bolts and column region surrounding the T-stub. A length of the column equal to 120 in. (305 cm) is used in the analysis. The model is subdivided into T-stem, T-flange, eight tension bolts, continuity plates, and a column. The continuity plates are placed using tie constraints representing the welds connecting them to the faces of column flange and column web. In order to allow for a full transfer of loads, surface based tie constraints were used between the T-stem and the T-flange for the built-up T-stub with Complete Joint Penetration (CJP) welds. A tie constraint allows fusing together two surfaces even though the meshes on both surfaces are not similar. Nodes on both surfaces have the same deformation. The interaction between plates, bolt head and plate, and bolt nut and plate are modeled using finite sliding with a coefficient of friction value of 0.3. 2.2. Material properties The von Mises yield criterion is used in the analysis to model yielding; isotropic hardening is used to model plastic behavior. Bolt tests were performed at the University of Cincinnati as a part of research experience for undergraduate summer project [25]. They revealed an average ultimate load of 100 kips (445 kN) for 1 in. (25.4 mm) A-490 bolts with 8 threads. The bolts were modeled in ABAQUS using their gross area, rather than their effective area. An idealized bilinear model with isotropic hardening for the bolt material was used in the finite element analysis. The bolt material properties used in the analysis are yield stress = 117,530 psi (811 MPa), ultimate stress = 126,500 psi (872 MPa), having a yield strain (ey) of 0.00405 and ultimate plastic strain of 0.03084 (=8ey), respectively. The stresses and strains are obtained from the bolt tests using gross
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load the T-stub stem. The bolt pretensioning is simulated by applying a temperature change to the restrained bolt shanks. The applied temperature change corresponds to the pretension which is equal to the minimum bolt pretension defined in Table J3.1 of the AISC specification [2]. A temperature change of 350 °C is applied for the following bolt diameters of 1–1/8 in. (28.6 mm), 1–1/ 4 in. (31.8 mm), and 1–1/2 in. (38.1 mm). The temperature change, DTemp, is calculated using the following expression:
DTemp ¼ Bo =aAE
ð1Þ
where Bo is the minimum bolt pretension (kip), A is the nominal gross area of the bolts (kips), a is the coefficient of thermal expansion, and E is the Young’s modulus of elasticity = 29,000,000 psi (203,000 MPa). The temperature change causes the heads and the nuts of the bolts to come into contact with the T-stub and column base material surrounding the bolt holes. The temperature change was applied by increasing it by 10% incrementally and in each load step nonlinear material behavior was modeled using an isotropic hardening rule and the von Mises yield criterion. The second load step was used to incrementally apply monotonic load acting on the T-stem by increasing it by 10% in each load increment. For design purposes, and since the initial stiffness and ultimate load are needed, force control was used in this step. The solution method used in the analysis was the Newton–Raphson (Full-Newton as designated in ABAQUS). The convergence criterion for residual force for this nonlinear problem is assumed to be 5 103 lb. 2.4. Boundary conditions
Fig. 3. Three-dimensional T-stub/column model.
area, so that the failure load of the bolts is the same as obtained in the experiment. This approach is used since no coupon test was performed for the bolt material. The material properties of the bolts used in finite element modeling are similar to the ones used by Takhirov and Popov [18], where 1–1/4 in. (31.75 mm) A490 bolts were used in the finite element model of bolted T-stub connections. Since there was no coupon test performed for the base material, and according to the AISC seismic provisions [3], the stress–strain behavior for A572 Gr. 50 steel can be increased by an amount of 10%; so, RyFyt, the expected yield stress, and RtFut, the expected tensile strength with Ry = 1.1 and Rt = 1.1 were used. Note that Ry and Rt are the ratios of expected yield stress to the specified minimum yield stress, and the expected tensile strength to the specified minimum yield strength, respectively. Here Fyt and Fut are the specified minimum yield stress of 50,000 psi (350 MPa) and tensile stress of 65,000 psi (455 MPa), respectively. The yield strain (ey) used for the base material is 0.00189, and the plastic strain is 0.09827 (=50ey). The yield and ultimate stress used for the base material are 55,000 psi (385 MPa) and 71,500 psi (500 MPa), respectively. For all members of the connection, Young’s modulus was assumed as E = 29,000,000 psi (203,000 MPa), and Poisson’s ratio as t = 0.30. In summary, a bilinear model with isotropic hardening for both base and bolt material was used in the analysis [19]. 2.3. Loadings The model is loaded in two steps. The first step is used to pretension the bolts, and the second step is used to monotonically
Boundary conditions are applied through bolt pretensioning and static monotonic load applied to the T-stem. In the pretension loading step, the degrees-of-freedom of the column edge are constrained against any translation and rotation. The degrees-offreedom on all sides of the T-stub flange are constrained against translation along all directions, except in the X-direction, as shown in Fig. 3. The nodes on the tension bolt heads are fixed against translation in all directions and the bolt nuts are kept free, so that pretension can be applied. In the static monotonic loading step, all bolt and T-flange nodes are free to deform along all directions. In order to compute the net secondary prying force, QS, three model types with different boundary conditions are used: (1) the column flange is assumed fully rigid to compute the net primary prying force, QP; (2) the column edges are assumed to be pinned to compute the total prying force, QT/NO–CP, without continuity plates; and (3) the column edges are also assumed to be pinned to compute the net total prying force, QT/CP, with continuity plates. 2.5. Data analysis After the completion of the finite element analysis, two output files are obtained consisting of the average stress and average strain for a cluster of nodes centered at the neutral axis where the bending effect is minimum. An interior bolt is selected as it is subjected to higher prying forces. The axial force in these interior bolts, Bi, is determined by multiplying the calculated stress by the gross section area of the bolt shank. The primary prying force (QP) or total prying force (QT) in the bolt is computed by subtracting the interior bolt force from the applied load. The deformation of the bolts, illustrated in [19], show that the interior bolts experience greater deformation and thus the higher bolt force. The first model used for calculating the net primary prying force, QP, assumes no deformation of the column flange, and the flange of the column is fixed against displacement, resulting in a T-stub connected to a column whose all nodes on its flange are restrained against rotation and translation. The second model is the
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same as the first one but with continuity plates, but the column edges are assumed to be pinned (with no translation but free to rotate) to be able to compute the total net prying, QT, with continuity plates. The third model corresponds to the case without continuity plates and assuming the same boundary conditions as the one analyzed with continuity plates. The total net prying, QT, with no continuity plates is obtained from the model. Therefore, the secondary prying, QS, is obtained by subtracting the total prying with/without continuity plates from the primary prying. Fig. 4 shows the deformed shape and stress distribution of a three-dimensional (3D) finite element model of a T-stub/column system. It is seen that the column flange is fully yielded and its cross-section has reached the ultimate stress and ultimate plastic strain. Figs. 5 and 6 show the deformed shape and stress distribution due to secondary prying force that occurs due to column flange bending with and without continuity plates, respectively. 3. Selection of cases and methodology Full-strength T-stub connections composed of W24x76, W30x108, and W36x150 beams all connected to W14x257 columns have been designed as a part of this research. The design procedure outlined by Swanson [26], and Swanson and Rassati [21] is used. Connection details obtained for the specimens are presented in Table 1. Using ABAQUS, three-dimensional finite element models are developed for the T-stub connections similar to the ones described in [19]. T-stubs are
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designed with W24x76, W30x108, W36x150 beams and W14x257 columns having a constant length. This is accomplished in the following steps: Using ABAQUS, finite element models of thick-flange T-stub connections, designed for W24x76, W30x108, and W36x150 beams and assuming a fully rigid (all nodes on the column flange are restrained against rotation and translation) W14x257 column of constant length, are analyzed to determine the primary prying force encountered for each connection, for a total of 3 models. Using ABAQUS, finite element models of thick-flange T-stub connections, designed for W24x76, W30x108, and W36x150 beams with 4 different column flange thickness (one corresponding to a W14x257 column) having a constant length, are analyzed within a T-stub/column system without continuity plates to determine the net total prying, for a total of 12 models. Using ABAQUS, finite element models of thick-flange T-stub connections, designed for W24x76, W30x108, and W36x150 beams with 4 different column flange thickness (one corresponding to a W14x257 column) having a constant length, are analyzed within a T-stub/column system with continuity plates to determine the net total prying, for a total of 12 models. For each of the 24 cases considered above (12 each for with/ without continuity plates), secondary prying is computed by subtracting the total prying from the primary prying. The primary, secondary and total prying are quantified for each T-stub/column flange system considered with/without continuity plates. Table 1 shows the test matrix that identifies the main geometric parameters of the T-stub connections designed for W24x76, W30x108, and W36x150 beams. It also shows the 4 different column flange thicknesses considered in this study, ranging from thin to thick flange columns for the T-stub connections for W24x76, W30x108, and W36x150 beams. The bolt gage arrangement or column gage distance, gc, for the connections resulting from W24x76, W30x108, and W36x150 beams are 6 in. (15.24 cm), 6–1/4 in. (15.87 cm), and 6–3/4 in. (17.15 cm), respectively (see Fig. 2). This column gage distance, gc, is not considered as a parameter that influences the amount of secondary prying, and is calculated according to the clearance needed for bolt tightening.
4. Results 4.1. Effect of continuity plates on secondary prying
Fig. 4. Deformed shape of a three-dimensional finite element model of T-stub/ column system.
The total, primary, and secondary prying with and without continuity plates were obtained as a function of geometrical parameters and material properties. To study the effect of secondary prying with and without continuity plates, first the percentage of total prying force at failure is obtained for a T-stub/column system without continuity plates for each case analyzed. The failure load of the cases without continuity plates is used as a datum to find the corresponding primary prying, and total prying with continuity plates. The results obtained are presented in Table 2. In this table, column (1) shows the dimensionless ratio of the column flange to T-stub flange (tcf/tTf) without and with continuity plates; columns (2) and (5) show the percentage of total prying encountered in the column/T-stub system without and with continuity plates, respectively; column (3) represents the percentage of primary prying encountered in the T-stub assuming a fully rigid column; columns (4) and (6) show the percentage of secondary prying encountered in the T-stub/column system without and with continuity plates, respectively.
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Fig. 5. Deformed shape causing secondary prying in a column (column/T-stub top view), (a) with no continuity plates; (b) with continuity plates.
stiffness of the column flange to the T-stub flange described by the dimensionless ratio (tcf/tTf) has a major impact on the secondary prying. When the dimensionless ratio (tcf/tTf) is greater than 1.00, continuity plates can be omitted since the amount of secondary prying is negligible. The secondary prying with and without continuity plates is obtained by subtracting the total from the primary prying as follows:
Applied Load vs. Bolt Force
Bolt Force (kips)
89
178
267
160
356
445
534
623
712 712
140
623
120
534
100
445
80
356
60
267 Prying-No Continuity Plates
40
Bolt Force (kN)
Applied Load (kN) 0
178
Prying-With Continuity Plates Prying-Rigid Column
20
89
No Prying
0 0
20
40
60
80
100
120
140
0 160
Applied Load (kips) Fig. 6. Prying in T-stub resulting from a W30x108 beam with a W14x257 column.
As can be seen from column (7) in Table 2, the secondary prying decreases when continuity plates are provided in the columns with thin flanges. The percentage decrease of secondary prying is 100% for the T-stub associated with the W30x108 beam with a dimensionless ratio of tcf/tTf = 0.60. The analysis shows that the relative
ðQ =TÞS=NO—CP ¼ ðQ =TÞT=NO—CP ðQ =TÞP
ð2Þ
ðQ =TÞS=CP ¼ ðQ =TÞT=CP ðQ =TÞP
ð3Þ
where (Q/T)S/NO–CP is the percentage of secondary prying with no continuity plates; (Q/T)S/CP is percentage of secondary prying with continuity plates; (Q/T)T/NO–CP is percentage of total prying with no continuity plates; (Q/T)T/CP is percentage of total prying with continuity plates; (Q/T)P is percentage of primary prying. Fig. 7 shows the prediction of the bolt prying forces in the Tstub/column associated with W30x108 beam and W14x257 column, with and without continuity plates. The 45° line in this figure represents a bolt force with zero pretension and no prying. At the same load level, the total prying is large when no continuity plates exist in the column. The total prying at tension bolt failure is estimated to be around 17.49%, whereas when continuity plates are available, the total prying is estimated to be 11.98%, as presented in Table 2 (Row (6) - columns (2) and (5)). Figs. 8 and 9 show the amount of secondary prying with and without continuity plates in a thick T-stub associated with W24x76, W30x108, and W36x150 beams with different column thicknesses (1.50 in. (3.81 cm) 6 tcf 6 3.00 in. (7.62 cm)). It can be seen that the secondary prying decreases as the dimensionless ra-
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E.G. Hantouche et al. / Engineering Structures 36 (2012) 113–122 Table 1 Secondary prying test matrix. Column flange thickness, tcf
Continuity plates thickness, tcp
T-stub flange thickness, ttf
Tension bolt diameter, db
Connection details resulting from beam W24x76 1.500 in. (3.81 cm) 3/4 in. (1.91 cm) 2.250 in. (5.72 cm) 1.890 in. (4.80 cm) 3/4 in. (1.91 cm) 2.250 in. (W14x257) (5.72 cm) 2.250 in. (5.72 cm) 3/4 in. (1.91 cm) 2.250 in. (5.72 cm) 3.000 in. (7.62 cm) 3/4 in. (1.91 cm) 2.250 in. (5.72 cm) Connection resulting from beam W30x108 1.500 in. (3.81 cm) 7/8 in. (2.22 cm) 1.890 in. (4.80 cm) (W14x257) 2.250 in. (5.72 cm)
7/8 in. (2.22 cm) 7/8 in. (2.22 cm)
3.000 in. (7.62 cm)
7/8 in. (2.22 cm)
Connection resulting from beam W36x150 1.500 in. (3.81 cm) 1.000 in. (2.54 cm) 1.890 in. (4.80 cm) (W14x257) 2.250 in. (5.72 cm)
1.000 in. (2.54 cm) 1.000 in. (2.54 cm)
3.000 in. (7.62 cm)
1.000 in. (2.54 cm)
1–1/8 in. (28.6 mm) 1–1/8 in. (28.6 mm) 1–1/8 in. (28.6 mm) 1-1/8 in. (28.6 mm)
2.500 in. (6.35 cm) 6.35 cm (2.500 in.) 6.35 cm (2.500 in.) 6.35 cm (2.500 in.)
1–1/4 in. (31.8 mm) 1–1/4 in. (31.8 mm) 1–1/4 in. (31.8 mm) 1–1/4 in. (31.8 mm)
2.625 in. (6.67 cm) 2.625 in. (6.67 cm) 2.625 in. (6.67 cm) 2.625 in. (6.67 cm)
1–1/2 in. (38.1 mm) 1–1/2 in. (38.1 mm) 1–1/2 in. (38.1 mm) 1–1/2 in. (38.1 mm)
that impact the amount of primary prying which was found to be the slenderness ratio (gt/tf), the selected cases were analyzed using finite element modeling. The cases cover most of the actual practical cases and they vary within acceptable current steel fabrication and current design practices. Since sufficient number of cases are considered within the practical range of variation gt/tf, the empirical equation obtained from the best fit of the finite element results for these cases, is expected to represent other cases which fall within the range of variation. This model represents the results of the finite element analysis that was used to determine the prying action in the flange-bolt system for thick flange T-stub connections built-up with CJP welds with various flange thicknesses and gage distances (3.00 6 gt/tf 6 4.00). The primary pring (Q/T)P–M is found at the failure of the bolts. A linear relationship was fitted to the finite element results to obtain an analytical model for predicting the prying force when partial yielding occurs in the flange followed by bolt fracture. The von Mises stress contours for the selected cases show that no full plastification of the flange at the K-zone is formed. Thus, the problem is statically indeterminate and an additional relationship that relates the prying force to the applied load is needed to solve the problem. More details about the model and its validation is available in Hantouche [19]. The primary prying in the thick-flange T-stubs is computed using the proposed equation below:
ðQ =TÞPM ¼ ð23:1ðg t =tf Þ 66:2Þð3=pÞ
The width of the T-stub tributary to a pair of tension bolts is computed using the following equation:
p ¼ 2W Tstub =n tio, tcf/tTf, increases for both T-flange/column flanges with/without continuity plates. It can be seen that the continuity plates can be omitted when using a column flange thickness equal to the T-stub flange thickness. Also, providing continuity plates in the column does not entirely eliminate the secondary prying when the thickness of the column flange (tcf) is less than the thickness of the T-stub flange (tTf). 4.2. Analytical investigation of secondary, primary, and total prying An equation is developed as a part of this study and described in Hantouche’s dissertation [19] to predict the primary prying force for thick built-up T-stub connections with CJP welds corresponding to the failure mode due to partial yielding of the flange followed by bolt fracture. After identifying the major geometric parameters
ð5Þ
In Eqs. (4) and (5), gt is the gage between the rows of the tension bolts in the T-stub, tf is the flange thickness of the T-stub, WT-stub is the overall width of the T-stub, and n is the number of bolts. It is necessary to know the amount of total prying force encountered in the T-stub/column system in order to be able to account for it in the design. To be able to use the primary prying strength model developed by Hantouche [19], the level of prying force needs to be normalized. The normalized values were presented in Table 2 and are retabulated in Table 3 along with the dimensionless thickness factor, tcf/tTf, and a normalizing factor b that relates the primary prying strength model to the primary prying finite element model. The factor, b, is expressed as follows:
b ¼ ðQ=TÞP—FE =ðQ =TÞP—M
ð6Þ
Table 2 Secondary prying in thick T-stub connections with/without continuity plates. Beam
a b c d e f
tcf/tTfa (1)
Column without continuity plates
Column with continuity plates
(Q/T)T/NO–CPb (2)
(Q/T)S/NO–CPd (4)
(Q/T)T/CPe (5)
(Q/T)S/CPf (6)
(Q/T)P–FEc (3)
ð4Þ
% Decrease in secondary prying due to continuity plates (7)
W24x76
0.67 0.84 1.00 1.33
19.85 14.18 12.38 11.48
3.33 3.33 3.33 3.33
16.52 10.85 9.05 8.15
11.87 11.52 11.40 11.21
8.54 8.19 8.07 7.88
48.31 24.52 10.83 3.31
W30x108
0.60 0.76 1.00 1.20
41.68 17.49 6.32 1.59
31.32 10.74 6.24 10.74
10.36 6.75 0.08 0.00
31.68 11.98 6.24 1.84
0.00 1.24 0.00 0.00
100.00 81.63 0.00 0.00
W36x150
0.57 0.72 1.00 1.14
45.31 39.63 22.57 4.89
35.47 21.93 16.25 3.97
9.84 17.70 6.32 0.92
36.84 22.09 16.73 3.37
1.37 0.16 0.48 0.00
86.08 33.62 92.41 100.00
Dimensionless ratio of column flange thickness to T-stub flange thickness. Total prying without continuity plates. Primary prying from finite element models. Secondary prying without continuity plates. Total prying with continuity plates. Secondary prying with continuity plates.
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20
Percentage of Secondary Prying
18 16 14 Column with CP 12
Column without CP
10 8 6 4 2 0 0.40
0.50
0.60
0.70
0.80
0.90
1.00
1.10
1.20
1.30
1.40
Column Flange to T-flange Thickness Ratio Fig. 7. Secondary prying in thick T-stubs resulting from W24x76 beam with different column flange thicknesses.
20
Percentage of Secondary Prying
18 16 14 12 10
Column with CP Column without CP
8 6 4 2 0 0.40
0.50
0.60
0.70
0.80
0.90
1.00
1.10
1.20
1.30
Column Flange to T-flange Thickness Ratio Fig. 8. Secondary prying in thick T-stubs resulting from a W30x108 beam with different column flange thicknesses.
20
Percentage of Secondary Prying
18 16 14 12 Column with CP
10
Column without CP
8 6 4 2 0 0.40
0.50
0.60
0.70
0.80
0.90
1.00
1.10
1.20
1.30
Column Flange to T-flange Thickness Ratio Fig. 9. Secondary prying in thick T-stubs resulting from a W36x150 beam with different column flange thicknesses.
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a
(Q/T)P–FE
a
Beam
tcf/tTf
(Q/T)P–M
b = (Q/T)P–FE/(Q/T)P–M
W24x76
0.67 0.84 1.00 1.33
3.33 3.33 3.33 3.33
4.25 4.25 4.25 4.25
0.78 0.78 0.78 0.78
W30x108
0.60 0.76 1.00 1.20
31.32 10.74 6.24 10.74
2.33 2.33 2.33 2.33
13.44 4.61 2.68 4.61
W36x150
0.57 0.72 1.00 1.14
35.47 21.93 16.25 3.97
2.46 2.46 2.46 2.46
14.42 8.91 6.61 1.61
Ratio of primary prying from finite element to primary prying from model.
Table 4 Results of total, primary, and secondary prying without continuity plates in a thick T-stub/column system. Beam
a b
Column without continuity plates a 0
b
0.78 0.78 0.78 0.78
4.96 3.26 2.72 2.45
5.96 4.26 3.72 3.45
3.33 3.33 3.33 3.33
19.85 14.18 12.38 11.48
2.33 2.33 2.33 2.33
13.44 4.61 2.68 4.61
0.30 1.05 0.01 0.00
1.30 2.05 1.01 1.00
31.32 10.74 6.24 10.74
40.70 21.99 6.32 10.74
2.46 2.46 2.46 2.46
14.42 8.91 6.61 1.61
0.50 0.81 0.39 0.23
1.50 1.81 1.39 1.23
35.47 21.93 16.25 3.97
53.27 39.63 22.57 4.89
tcf/tTf
(Q/T)P–M
W24x76
0.67 0.84 1.00 1.33
4.25 4.25 4.25 4.25
W30x108
0.60 0.76 1.00 1.20
W36x150
0.57 0.72 1.00 1.14
K = 1 + k0
k = (Q/T)S/NO–CP/a(Q/T)P–M
b
b(Q/T)P–M
(Q/T)T = Kb(Q/T)P–M
Ratio of secondary prying to the primary prying from finite element. Ratio of total prying to primary prying from finite element.
Table 5 Results of total, primary, and secondary prying with continuity plates in a thick T-stub/column system. Beam
a b
Column with continuity plates a 0
b
0.78 0.78 0.78 0.78
2.56 2.46 2.42 2.37
3.56 3.46 3.42 3.37
3.33 3.33 3.33 3.33
11.87 11.52 11.40 11.21
2.33 2.33 2.33 2.33
13.44 4.61 2.68 4.61
0.00 0.12 0.00 0.00
1.00 1.12 1.00 1.00
31.32 10.74 6.24 10.74
31.32 11.98 6.24 10.74
2.46 2.46 2.46 2.46
14.42 8.91 6.61 1.61
0.04 0.01 0.03 0.00
1.04 1.01 1.03 1.00
35.47 21.93 16.25 3.97
36.84 22.09 16.73 3.97
tcf/tTf
(Q/T)P–M
W24x76
0.67 0.84 1.00 1.33
4.25 4.25 4.25 4.25
W30x108
0.60 0.76 1.00 1.20
W36x150
0.57 0.72 1.00 1.14
k = (Q/T)S/CP/a(Q/T)P–M
b
K = 1 + k0
b(Q/T)
P–M
(Q/T)T = Kb(Q/T)P–M
Ratio of secondary prying to the primary prying from finite element. Ratio of total prying to primary prying from finite element.
The total prying (Q/T)T, can be determined by multiplying a factor K to the normalized primary prying b(Q/T)P–M. This representation incorporates the effect of secondary prying (Q/T)S, and can be written as follows:
K ¼ ðQ=TÞT =bðQ=TÞP—M
ð7Þ
where
ðQ=TÞT ¼ bðQ =TÞP—M þ ðQ =TÞS
ð8Þ
Another form of the factor, K, can be written as follows:
K ¼ 1 þ ððQ =TÞS =bðQ =TÞP—M Þ ¼ 1 þ k
0
ð9Þ
where k0 is the ratio of secondary prying to the normalized primary prying, b(Q/T)P–M. The results of the total, primary, and secondary prying are compiled in Tables 4 and 5 using the above equations. The total prying is computed using Eq. (8) by adding the secondary prying to the normalized primary prying model, b(Q/T)P–M. For columns without continuity plates, the results in
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Table 4 show that total prying is significant in thick flange T-stub connections when the dimensionless ratio (tcf/tTf) is less than 1.00 (W14x157 column). Total prying is significant and should be accounted for in design when the dimensionless ratio (tcf/tTf) is less than 1.00. The total prying is considered significant when it is greater than 10% of the applied load. Taking into account this increase in the bolt force and by recalculating the bolt diameter, the design requires a larger bolt diameter. The bolt diameter is recalculated to carry the additional force introduced to the bolts due to primary and secondary prying effect. This is achieved by increasing the applied load by the amount of total prying (Q/T)T, as given by Eq. (8). Therefore, the minimum bolt diameter can be computed [2,21,27]:
db ¼
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4F=npF nt
ð10Þ
where F is the total applied load (kip or kN) incorporating the prying effect, and Fnt is the tensile stress of the bolt (ksi or MPa). It should be noted that F = T [1 + (1/100) (Q/T)T]. By supplying continuity plates, the results in Table 5 show that total prying decreases. However, it is still considered significant for a dimensionless ratio (tcf/tTf) less than 0.72, as shown in Table 5. For W14x257 columns used with W24x76, W30x108, and W36x150 beams where the dimensionless ratio (tcf/tTf) is 0.84, 0.76, and 0.72, respectively, continuity plates should be provided unless larger column with thicker flange are used instead of the W14x257 column. 5. Conclusions An investigation using finite element modeling has been performed on the secondary prying encountered in thick T-stub connections with W24x76, W30x108, and W36x150 beams having different column sizes. In designing full-strength connections, all yielding mechanism and failure modes are needed to be identified including the secondary prying phenomenon which can be a potential failure mode that might happen especially when the thickness of the T-flange is larger than the column flange. In the cases considered in this study, the percentage of prying was quantified and showed whether it is significant or not, and whether continuity plates are needed to be supplied or not. Also by quantifying the amount of prying, the designer can check whether the bolt diameter is needed to be increased to carry the additional load that comes from the primary and secondary prying. It is concluded that the secondary prying force decreases by either adding continuity plates to the column, or by using larger column flange thicknesses as compared to the T-stub flange thickness. This is found to be true for T-stub/column systems in which tcf/tTf is greater or equal 1.00. Adding continuity plates to columns with thin flanges is not enough to solve the secondary prying force encountered in thickflange T-stub/column systems. However, increasing the thickness of the column flange decreases the amount of secondary prying force, so full T-stub connections can be detailed without continuity plates if other requirements are satisfied (column flange yielding, web yielding, and web crippling). Secondary prying forces are incorporated in the thick flange T-stub primary prying model to predict the total prying force encountered in thick flange T-stub/ column flange system. Continuity plates in W14x257 columns used with W24x76, W30x108, and W36x150 beams should be provided, unless larger columns with thicker flanges are used instead. This study provides the fabricator information for detailing columns without continuity plates as well as quantifying the amount of prying so engineers can design for the additional load by increasing the bolt diameter.
Acknowledgment Special thanks are due to Dr. James A. Swanson at the University of Cincinnati for providing the design procedure draft and his detailed review and comments on the design of the full-scale builtup T-stub connection cases considered in the study reported. References [1] Federal Emergency Management Agency FEMA. Recommended seismic design criteria for new steel moment-frame buildings. FEMA-350; 2000. [2] American Institute of Steel Construction AISC. ANSI/AISC 360-05 load and resistance factor design specification for structural steel buildings. Chicago (IL): AISC; 2005. [3] American Institute of Steel Construction AISC. ANSI/AISC 341-05 seismic provisions for structural steel buildings. Chicago (IL): AISC; 2005. [4] Larson PC. The design and behavior of bolted beam-column frame connections under cyclical loading, M.S. thesis. Austin (TX): University of Texas Austin; 1996. [5] Smallidge JM. Behavior of bolted beam-to-column T-stub connections under cyclic loading, M.S. thesis. Atlanta (GA): Georgia Institute of Technology; 1999. [6] Swanson JA. Characterization of the strength, stiffness, and ductility behavior of T-stub connections, Ph.D. thesis. Atlanta (GA): Georgia Institute of Technology; 1999. [7] Popov EP, Takhirov SM. Bolted large seismic steel beam to column connections Part 1: experimental study. J Eng Struct 2002;24:1523–34. [8] Douty RT, McGuire W. High strength bolted moment connections. J Struct Div 1965;91(2):101–28. [9] Kulak GL, Fisher JP, Struick JHA. Guide to design criteria for bolted and riveted joints. 2nd ed. New York: Wiley; 1987. [10] Jaspart JP, Maquoi R. Plasticity capacity of end-plate and flange cleated connections predictions and design rules. In: Second international workshop on connections in steel structures: behavior, strength and design. Pittsburgh (PA); 1991. p. 343–52. [11] Swanson JA, Leon RT. Bolted steel connections: tests on T-stub components. J Struct Eng 2000;126(1):50–6. [12] Swanson JA, Leon RT. Stiffness modeling of bolted T-stub connection components. J Struct Eng 2001;127(5):498–505. [13] Swanson JA, Kokan DS, Leon RT. Advanced finite element modeling of bolted Tstub connection components. J Construct Steel Res 2002;58:1015–31. [14] Comité Europènne de Normalisation CEN. Eurocode3: Design of steel structures, Part 1–8: design of joints and building frames, ENV 1993-1-8. Brussels (Belgium), 2005. [15] Piluso V, Rizzano G. Experimental analysis and modeling of bolted T-stubs under cyclic loads. J Construct Steel Res 2008;64:655–69. [16] Garrett B, Wittich C. Evaluation of secondary prying action in bolted steel frame connections, NSF REU Summer Research for Undergraduate Summer Research Program. Cincinnati (OH): University of Cincinnati; 2009. [17] Hantouche EG, Rassati GA, Swanson JA. Built-up T-stub connection for special and intermediate moment frames. Numerical and experimental testing for prequalification. STESSA 2009 conference. Lehigh (PA), 2009. p. 275–80. [18] Takhirov SM, Popov EP. Bolted large seismic steel beam to column connections Part 2: numerical nonlinear analysis. J Eng Struct 2002;24:1535–45. [19] Hantouche EG. Behavioral characterization of built-up T-stub connections for use in moment resisting frames, Ph.D. dissertation. Cincinnati (OH): University of Cincinnati; 2011. [20] Sato A, Newell J, Uang CM. Cyclic testing of bolted flange plate steel moment connections for special moment frames. San Diego (CA): University of California San Diego; 2007. [21] Swanson JA, Rassati GA. Design provisions of full-strength built-up T-stub connections. A draft submitted for review to AISC/ANSI 358 prequalified connections for special and intermediate steel moment frames for seismic applications. Chicago (IL): AISC; 2010 [in review]. [22] Swanson JA, Rassati GA, Schrader CA. Design provisions of full-strength rolled T-stub connections. A draft submitted for ballot for incorporation into AISC/ ANSI 358 prequalified connections for special and intermediate steel moment frames for seismic applications. Chicago (IL): AISC; 2010 [in review]. [23] Schrader CA. Prequalification and design of rolled bolted T-stub connections in moment resisting frames, M.S. thesis. Cincinnati (OH): University of Cincinnati; 2010. [24] American Institute of Steel Construction AISC. Prequalified connections for special and intermediate steel moment frames for seismic applications. Chicago (IL): AISC; 2005. [25] ABAQUS. Dassault Systèmes, Pawtucket, RI; 2009. [26] Riharb J, Thesing E, Meiser E. Study of the ductility and deformation of high strength fasteners in tension, NSF research experience for undergraduate summer research program. Cincinnati (OH): University of Cincinnati; 2008. [27] Swanson JA. Ultimate strength prying models for bolted T-stub connections. Eng J 2002;third quarter:136–47.
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Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Investigation of secondary prying in thick built-up T-stub connections using nonlinear finite element modeling Elie G. Hantouche a,⇑, Anant R. Kukreti b, Gian A. Rassati c a
Structural Engineering, Civil and Environmental Engineering Department, American University of Beirut, P.O. Box 11-0236, Riad El-Solh/Beirut 1107 2020, Lebanon Engineering Mechanics, School of Energy, Environmental, Biological and Medical Engineering, University of Cincinnati (ML-0021), P.O. Box 210012, Cincinnati, OH 452210071, USA c Structural Engineering, School of Advanced Structures, University of Cincinnati (ML-0071), P.O. Box 210071, Cincinnati, OH 452210071, USA b
a r t i c l e
i n f o
Article history: Received 11 March 2011 Revised 23 November 2011 Accepted 24 November 2011 Available online 29 December 2011 Keywords: Finite element Connection Secondary prying Continuity plates T-stub Thick-flange
a b s t r a c t This study investigates the prying behavior in thick-flange built-up T-stub/column systems that should be addressed in designing full-strength double tee connections for use in moment resisting frames which satisfy prequalification requirements. In particular, this study focuses on the phenomenon herein indicated as secondary prying, which is related to the additional forces that are introduced into the tension bolts due to significant bending of the column flange. Three-dimensional finite element models that incorporate pretension of fasteners, full contact interactions, and nonlinear material characteristics are used to investigate secondary prying effect in thickflange T-stub/column system with and without continuity plates. This study provides insight as to whether continuity plates are necessary in columns when designing and detailing full-scale T-stub connections for prequalification. The effect of secondary prying is incorporated into an existing prying strength model for thick T-stubs to quantify the amount of total prying encountered in thick built-up T-stub connections with and without continuity plates. Parameters that impact the secondary prying in thick flange T-stub/column systems were identified based on the geometric configuration that results from the design of full-strength double tee connections with deep girders. The results show that decreasing the effect of secondary prying is achieved through either increasing the column size, or adding continuity plates to the column. This study provides information for detailing columns without continuity plates as well as quantifying the amount of prying so engineers can design for the additional load by increasing the bolt diameter. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Continuity plates are often used in connections to stiffen the column flange and web in order to resist large forces transmitted by the beam flange. Continuity plates requirements in bolted/ welded connections are another consideration which may be important as greater ductility is required of moment frame connections. The state-of the-art report on connection performance by FEMA 350-D [1] discusses requirements for continuity plates to provide higher ductile connection performance. Continuity plates are designed consistent with Section J10.8 of ANSI/AISC 360-05 [2], and Section 9.5 or 10.5 of the AISC Seismic Provisions [3] for Special Moment Frames (SMF) systems or Intermediate Moment Frames (IMF) systems. The 2005 AISC seismic provisions classify a connection as prequalified if it is capable of sustaining an interstory drift of 4% with at least 80% of the beam plastic moment ⇑ Corresponding author. Tel.: +961 1 350000x3400; fax: +961 1 744462. E-mail addresses: [email protected] (E.G. Hantouche), [email protected] (A.R. Kukreti), [email protected] (G.A. Rassati). 0141-0296/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.engstruct.2011.11.030
for SMF, and an interstory drift of 2% for IMF. Connections used in SMF and IMF shall be prequalified by evaluating all yielding mechanism and failure modes [3]. Several experimental and analytical studies [4–7] have been conducted to investigate the behavior of bolted T-stub/column systems such as that shown in Fig. 1. One of the main characteristics of the behavior of such connections is the prying phenomenon (primary and secondary). Some of these studies [4–7] include experimental and analytical investigations on full-scale T-stub connections with and without continuity plates. Continuity plates were included in six full-scale tests on bolted T-stub connections conducted by Smallidge [5], Swanson [6], Popov and Takhirov [7]. Two tests conducted by Swanson [6] and Smallidge [5] did not include continuity plates. In most of these cases, no significant column flange yielding was reported. Four full-scale tests were performed by Larson [4] without continuity plates. For these tests it was reported that column flange bending displacements were relatively small compared to T-stub flange bending displacements, but Larson [4] reported that large bending displacements due to thinner column flanges may cause additional prying forces in the bolts.
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Fig. 1. Typical built-up T-stub moment connection [21].
Most of the earlier studies on T-stub connections have focused on issues related to classical prying action by neglecting column flange deformation [2,8–15]. Such classical prying action is caused by flexural deformations of the flange of a T-stub, which results in additional forces transferred to the bolts. Classical prying will be herein referred to as primary prying to distinguish it from a similar phenomenon caused by the flexural deformation of the column flange, which will be indicated as secondary prying. No prior studies in the literature dealt with the investigation of the effects of secondary prying in T-stub/column systems except for a pilot parametric analytical study conducted at the University of Cincinnati as a part of a NSF research experience for undergraduates summer program [16]. The study highlights the main parameters that influence the amount of secondary prying. In moment resisting frames, thick-flange built-up T-stub connections are needed with deep girders to resist the large moment expected. This may lead to a connection in which the T-stub flange is thicker than the column flange. In such cases, the column flange is subjected to bending, and may undergo significant deformations. This significant behavioral characteristic of the column flange causes the secondary prying phenomenon, in addition to the primary one. Secondary prying refers to the additional forces introduced in the tension bolts due to a significant deformation of the column flange. The column flange behaves similarly to the flange of the T-stub. The column flange deforms outwards at the connection (i.e., away from the T-flange), showing smaller deformations at the flange centerline, and larger toward the tips of the flange. This differential deformation causes secondary prying. This may lead to either column flange failure due to yield line mechanism, and/or tension bolt fracture due to secondary prying. Fig. 2 shows the deformation of the column flange and T-stub flange of a typical T-stub connection attached to a column.
Primary prying in thick flange T-stub connections has also been studied by various researchers [7,17,18] using experimental and finite element modeling to predict strength, stiffness, and ductility. This study is a part of a wider study that deals with the behavior of full strength thick flange T-stub connections for use in moment resisting frames. This included an experimental investigation on built-up thick flange T-stub connections including 24 connection component tests conducted to investigate the effect of connection variables and different fabrication and detailing practices used for welding and bolt holes fabrication. These physical test results were also used to develop and validate a finite element model of the thick flange T-stub connection which duplicates the test results within acceptable limits for load–deformation behavior and failure mechanism. The finite element results reported show excellent agreement with the experimental component tests [17,19]. Therefore, finite element modeling can be used as a reliable tool to study the significant behavioral characteristics occurring in thick T-stub/ column connections caused by the secondary prying phenomenon. The intent of this investigation is to study secondary prying in thick-flange T-stub/column systems with and without continuity plates using finite element modeling. The finite element study shows that the need for continuity plates is not only governed by panel zone shear strength, web yielding, and web crippling but also by the need to minimize the amount of secondary prying. Finite element results are also used to quantify the total prying by using the primary prying model developed and reported in [19], and incorporating the effect of secondary prying with and without continuity plates. The scope of this study is to investigate the amount of secondary prying encountered in thick T-stubs that are designed for fullscale connections having W24x76, W30x108, and W36x150 beams with different column sizes, with and without continuity plates. The 3 beam sizes selected for this study cover the range of deep girders
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115
Fig. 2. Two-dimensional top view of T-stub/column.
that may be used in SMF similar to the one tested for bolted flange plate steel moment connections [20]. The variation of the column flange thickness was selected to cover the practical range where the column considered as stiff (the column flange thickness is larger the T-stub flange thickness) or flexible (the T-stub flange thickness is larger the column flange thickness). A draft of the procedure for the design of full-strength T-stub connections has been developed [21,22], and submitted for ballot for incorporation into AISC/ANSI358 [23]. The design of the connections reported in this paper is based on the draft design procedure [21,22]. The connections considered in that design procedure are composed, respectively of W24x76, W30x108, and W36x150 beams connected to W14x257 columns. The design for a full-strength double tee connection between a W30x108 beam and a W14x257 column is presented in [19]. 2. Nonlinear finite element modeling The finite element analyses presented herein are intended to provide insight into the mechanisms of thick-flange T-stub/column flange behavior. Considering the T-stubs as three dimensional systems, twenty seven finite element models have been developed for T-stub connections using twenty-node quadratic brick elements available within the software package ABAQUS [24]. The finite element analyses presented herein are aimed at investigating the prying phenomenon (primary and secondary) using nonlinear material behavior, pretension of fasteners, and contact interactions. The same finite element technique was successfully used to reproduce component T-stubs tested experimentally as reported in [17,19]. 2.1. Mesh design of three-dimensional solid T-stub/column models Twenty-node quadratic brick elements with reduced integration (C3D20-R) are used to mesh the T-stub flange/column system.
The T-stub flange and the column flange consist of three layers of elements, and the continuity plates consist of two layers of elements. A full three dimensional finite element model of the T-stub/column assemblage considered is shown in Fig. 3. A finer mesh was used in the T-flange, tension bolts and column region surrounding the T-stub. A length of the column equal to 120 in. (305 cm) is used in the analysis. The model is subdivided into T-stem, T-flange, eight tension bolts, continuity plates, and a column. The continuity plates are placed using tie constraints representing the welds connecting them to the faces of column flange and column web. In order to allow for a full transfer of loads, surface based tie constraints were used between the T-stem and the T-flange for the built-up T-stub with Complete Joint Penetration (CJP) welds. A tie constraint allows fusing together two surfaces even though the meshes on both surfaces are not similar. Nodes on both surfaces have the same deformation. The interaction between plates, bolt head and plate, and bolt nut and plate are modeled using finite sliding with a coefficient of friction value of 0.3. 2.2. Material properties The von Mises yield criterion is used in the analysis to model yielding; isotropic hardening is used to model plastic behavior. Bolt tests were performed at the University of Cincinnati as a part of research experience for undergraduate summer project [25]. They revealed an average ultimate load of 100 kips (445 kN) for 1 in. (25.4 mm) A-490 bolts with 8 threads. The bolts were modeled in ABAQUS using their gross area, rather than their effective area. An idealized bilinear model with isotropic hardening for the bolt material was used in the finite element analysis. The bolt material properties used in the analysis are yield stress = 117,530 psi (811 MPa), ultimate stress = 126,500 psi (872 MPa), having a yield strain (ey) of 0.00405 and ultimate plastic strain of 0.03084 (=8ey), respectively. The stresses and strains are obtained from the bolt tests using gross
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load the T-stub stem. The bolt pretensioning is simulated by applying a temperature change to the restrained bolt shanks. The applied temperature change corresponds to the pretension which is equal to the minimum bolt pretension defined in Table J3.1 of the AISC specification [2]. A temperature change of 350 °C is applied for the following bolt diameters of 1–1/8 in. (28.6 mm), 1–1/ 4 in. (31.8 mm), and 1–1/2 in. (38.1 mm). The temperature change, DTemp, is calculated using the following expression:
DTemp ¼ Bo =aAE
ð1Þ
where Bo is the minimum bolt pretension (kip), A is the nominal gross area of the bolts (kips), a is the coefficient of thermal expansion, and E is the Young’s modulus of elasticity = 29,000,000 psi (203,000 MPa). The temperature change causes the heads and the nuts of the bolts to come into contact with the T-stub and column base material surrounding the bolt holes. The temperature change was applied by increasing it by 10% incrementally and in each load step nonlinear material behavior was modeled using an isotropic hardening rule and the von Mises yield criterion. The second load step was used to incrementally apply monotonic load acting on the T-stem by increasing it by 10% in each load increment. For design purposes, and since the initial stiffness and ultimate load are needed, force control was used in this step. The solution method used in the analysis was the Newton–Raphson (Full-Newton as designated in ABAQUS). The convergence criterion for residual force for this nonlinear problem is assumed to be 5 103 lb. 2.4. Boundary conditions
Fig. 3. Three-dimensional T-stub/column model.
area, so that the failure load of the bolts is the same as obtained in the experiment. This approach is used since no coupon test was performed for the bolt material. The material properties of the bolts used in finite element modeling are similar to the ones used by Takhirov and Popov [18], where 1–1/4 in. (31.75 mm) A490 bolts were used in the finite element model of bolted T-stub connections. Since there was no coupon test performed for the base material, and according to the AISC seismic provisions [3], the stress–strain behavior for A572 Gr. 50 steel can be increased by an amount of 10%; so, RyFyt, the expected yield stress, and RtFut, the expected tensile strength with Ry = 1.1 and Rt = 1.1 were used. Note that Ry and Rt are the ratios of expected yield stress to the specified minimum yield stress, and the expected tensile strength to the specified minimum yield strength, respectively. Here Fyt and Fut are the specified minimum yield stress of 50,000 psi (350 MPa) and tensile stress of 65,000 psi (455 MPa), respectively. The yield strain (ey) used for the base material is 0.00189, and the plastic strain is 0.09827 (=50ey). The yield and ultimate stress used for the base material are 55,000 psi (385 MPa) and 71,500 psi (500 MPa), respectively. For all members of the connection, Young’s modulus was assumed as E = 29,000,000 psi (203,000 MPa), and Poisson’s ratio as t = 0.30. In summary, a bilinear model with isotropic hardening for both base and bolt material was used in the analysis [19]. 2.3. Loadings The model is loaded in two steps. The first step is used to pretension the bolts, and the second step is used to monotonically
Boundary conditions are applied through bolt pretensioning and static monotonic load applied to the T-stem. In the pretension loading step, the degrees-of-freedom of the column edge are constrained against any translation and rotation. The degrees-offreedom on all sides of the T-stub flange are constrained against translation along all directions, except in the X-direction, as shown in Fig. 3. The nodes on the tension bolt heads are fixed against translation in all directions and the bolt nuts are kept free, so that pretension can be applied. In the static monotonic loading step, all bolt and T-flange nodes are free to deform along all directions. In order to compute the net secondary prying force, QS, three model types with different boundary conditions are used: (1) the column flange is assumed fully rigid to compute the net primary prying force, QP; (2) the column edges are assumed to be pinned to compute the total prying force, QT/NO–CP, without continuity plates; and (3) the column edges are also assumed to be pinned to compute the net total prying force, QT/CP, with continuity plates. 2.5. Data analysis After the completion of the finite element analysis, two output files are obtained consisting of the average stress and average strain for a cluster of nodes centered at the neutral axis where the bending effect is minimum. An interior bolt is selected as it is subjected to higher prying forces. The axial force in these interior bolts, Bi, is determined by multiplying the calculated stress by the gross section area of the bolt shank. The primary prying force (QP) or total prying force (QT) in the bolt is computed by subtracting the interior bolt force from the applied load. The deformation of the bolts, illustrated in [19], show that the interior bolts experience greater deformation and thus the higher bolt force. The first model used for calculating the net primary prying force, QP, assumes no deformation of the column flange, and the flange of the column is fixed against displacement, resulting in a T-stub connected to a column whose all nodes on its flange are restrained against rotation and translation. The second model is the
E.G. Hantouche et al. / Engineering Structures 36 (2012) 113–122
same as the first one but with continuity plates, but the column edges are assumed to be pinned (with no translation but free to rotate) to be able to compute the total net prying, QT, with continuity plates. The third model corresponds to the case without continuity plates and assuming the same boundary conditions as the one analyzed with continuity plates. The total net prying, QT, with no continuity plates is obtained from the model. Therefore, the secondary prying, QS, is obtained by subtracting the total prying with/without continuity plates from the primary prying. Fig. 4 shows the deformed shape and stress distribution of a three-dimensional (3D) finite element model of a T-stub/column system. It is seen that the column flange is fully yielded and its cross-section has reached the ultimate stress and ultimate plastic strain. Figs. 5 and 6 show the deformed shape and stress distribution due to secondary prying force that occurs due to column flange bending with and without continuity plates, respectively. 3. Selection of cases and methodology Full-strength T-stub connections composed of W24x76, W30x108, and W36x150 beams all connected to W14x257 columns have been designed as a part of this research. The design procedure outlined by Swanson [26], and Swanson and Rassati [21] is used. Connection details obtained for the specimens are presented in Table 1. Using ABAQUS, three-dimensional finite element models are developed for the T-stub connections similar to the ones described in [19]. T-stubs are
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designed with W24x76, W30x108, W36x150 beams and W14x257 columns having a constant length. This is accomplished in the following steps: Using ABAQUS, finite element models of thick-flange T-stub connections, designed for W24x76, W30x108, and W36x150 beams and assuming a fully rigid (all nodes on the column flange are restrained against rotation and translation) W14x257 column of constant length, are analyzed to determine the primary prying force encountered for each connection, for a total of 3 models. Using ABAQUS, finite element models of thick-flange T-stub connections, designed for W24x76, W30x108, and W36x150 beams with 4 different column flange thickness (one corresponding to a W14x257 column) having a constant length, are analyzed within a T-stub/column system without continuity plates to determine the net total prying, for a total of 12 models. Using ABAQUS, finite element models of thick-flange T-stub connections, designed for W24x76, W30x108, and W36x150 beams with 4 different column flange thickness (one corresponding to a W14x257 column) having a constant length, are analyzed within a T-stub/column system with continuity plates to determine the net total prying, for a total of 12 models. For each of the 24 cases considered above (12 each for with/ without continuity plates), secondary prying is computed by subtracting the total prying from the primary prying. The primary, secondary and total prying are quantified for each T-stub/column flange system considered with/without continuity plates. Table 1 shows the test matrix that identifies the main geometric parameters of the T-stub connections designed for W24x76, W30x108, and W36x150 beams. It also shows the 4 different column flange thicknesses considered in this study, ranging from thin to thick flange columns for the T-stub connections for W24x76, W30x108, and W36x150 beams. The bolt gage arrangement or column gage distance, gc, for the connections resulting from W24x76, W30x108, and W36x150 beams are 6 in. (15.24 cm), 6–1/4 in. (15.87 cm), and 6–3/4 in. (17.15 cm), respectively (see Fig. 2). This column gage distance, gc, is not considered as a parameter that influences the amount of secondary prying, and is calculated according to the clearance needed for bolt tightening.
4. Results 4.1. Effect of continuity plates on secondary prying
Fig. 4. Deformed shape of a three-dimensional finite element model of T-stub/ column system.
The total, primary, and secondary prying with and without continuity plates were obtained as a function of geometrical parameters and material properties. To study the effect of secondary prying with and without continuity plates, first the percentage of total prying force at failure is obtained for a T-stub/column system without continuity plates for each case analyzed. The failure load of the cases without continuity plates is used as a datum to find the corresponding primary prying, and total prying with continuity plates. The results obtained are presented in Table 2. In this table, column (1) shows the dimensionless ratio of the column flange to T-stub flange (tcf/tTf) without and with continuity plates; columns (2) and (5) show the percentage of total prying encountered in the column/T-stub system without and with continuity plates, respectively; column (3) represents the percentage of primary prying encountered in the T-stub assuming a fully rigid column; columns (4) and (6) show the percentage of secondary prying encountered in the T-stub/column system without and with continuity plates, respectively.
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Fig. 5. Deformed shape causing secondary prying in a column (column/T-stub top view), (a) with no continuity plates; (b) with continuity plates.
stiffness of the column flange to the T-stub flange described by the dimensionless ratio (tcf/tTf) has a major impact on the secondary prying. When the dimensionless ratio (tcf/tTf) is greater than 1.00, continuity plates can be omitted since the amount of secondary prying is negligible. The secondary prying with and without continuity plates is obtained by subtracting the total from the primary prying as follows:
Applied Load vs. Bolt Force
Bolt Force (kips)
89
178
267
160
356
445
534
623
712 712
140
623
120
534
100
445
80
356
60
267 Prying-No Continuity Plates
40
Bolt Force (kN)
Applied Load (kN) 0
178
Prying-With Continuity Plates Prying-Rigid Column
20
89
No Prying
0 0
20
40
60
80
100
120
140
0 160
Applied Load (kips) Fig. 6. Prying in T-stub resulting from a W30x108 beam with a W14x257 column.
As can be seen from column (7) in Table 2, the secondary prying decreases when continuity plates are provided in the columns with thin flanges. The percentage decrease of secondary prying is 100% for the T-stub associated with the W30x108 beam with a dimensionless ratio of tcf/tTf = 0.60. The analysis shows that the relative
ðQ =TÞS=NO—CP ¼ ðQ =TÞT=NO—CP ðQ =TÞP
ð2Þ
ðQ =TÞS=CP ¼ ðQ =TÞT=CP ðQ =TÞP
ð3Þ
where (Q/T)S/NO–CP is the percentage of secondary prying with no continuity plates; (Q/T)S/CP is percentage of secondary prying with continuity plates; (Q/T)T/NO–CP is percentage of total prying with no continuity plates; (Q/T)T/CP is percentage of total prying with continuity plates; (Q/T)P is percentage of primary prying. Fig. 7 shows the prediction of the bolt prying forces in the Tstub/column associated with W30x108 beam and W14x257 column, with and without continuity plates. The 45° line in this figure represents a bolt force with zero pretension and no prying. At the same load level, the total prying is large when no continuity plates exist in the column. The total prying at tension bolt failure is estimated to be around 17.49%, whereas when continuity plates are available, the total prying is estimated to be 11.98%, as presented in Table 2 (Row (6) - columns (2) and (5)). Figs. 8 and 9 show the amount of secondary prying with and without continuity plates in a thick T-stub associated with W24x76, W30x108, and W36x150 beams with different column thicknesses (1.50 in. (3.81 cm) 6 tcf 6 3.00 in. (7.62 cm)). It can be seen that the secondary prying decreases as the dimensionless ra-
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E.G. Hantouche et al. / Engineering Structures 36 (2012) 113–122 Table 1 Secondary prying test matrix. Column flange thickness, tcf
Continuity plates thickness, tcp
T-stub flange thickness, ttf
Tension bolt diameter, db
Connection details resulting from beam W24x76 1.500 in. (3.81 cm) 3/4 in. (1.91 cm) 2.250 in. (5.72 cm) 1.890 in. (4.80 cm) 3/4 in. (1.91 cm) 2.250 in. (W14x257) (5.72 cm) 2.250 in. (5.72 cm) 3/4 in. (1.91 cm) 2.250 in. (5.72 cm) 3.000 in. (7.62 cm) 3/4 in. (1.91 cm) 2.250 in. (5.72 cm) Connection resulting from beam W30x108 1.500 in. (3.81 cm) 7/8 in. (2.22 cm) 1.890 in. (4.80 cm) (W14x257) 2.250 in. (5.72 cm)
7/8 in. (2.22 cm) 7/8 in. (2.22 cm)
3.000 in. (7.62 cm)
7/8 in. (2.22 cm)
Connection resulting from beam W36x150 1.500 in. (3.81 cm) 1.000 in. (2.54 cm) 1.890 in. (4.80 cm) (W14x257) 2.250 in. (5.72 cm)
1.000 in. (2.54 cm) 1.000 in. (2.54 cm)
3.000 in. (7.62 cm)
1.000 in. (2.54 cm)
1–1/8 in. (28.6 mm) 1–1/8 in. (28.6 mm) 1–1/8 in. (28.6 mm) 1-1/8 in. (28.6 mm)
2.500 in. (6.35 cm) 6.35 cm (2.500 in.) 6.35 cm (2.500 in.) 6.35 cm (2.500 in.)
1–1/4 in. (31.8 mm) 1–1/4 in. (31.8 mm) 1–1/4 in. (31.8 mm) 1–1/4 in. (31.8 mm)
2.625 in. (6.67 cm) 2.625 in. (6.67 cm) 2.625 in. (6.67 cm) 2.625 in. (6.67 cm)
1–1/2 in. (38.1 mm) 1–1/2 in. (38.1 mm) 1–1/2 in. (38.1 mm) 1–1/2 in. (38.1 mm)
that impact the amount of primary prying which was found to be the slenderness ratio (gt/tf), the selected cases were analyzed using finite element modeling. The cases cover most of the actual practical cases and they vary within acceptable current steel fabrication and current design practices. Since sufficient number of cases are considered within the practical range of variation gt/tf, the empirical equation obtained from the best fit of the finite element results for these cases, is expected to represent other cases which fall within the range of variation. This model represents the results of the finite element analysis that was used to determine the prying action in the flange-bolt system for thick flange T-stub connections built-up with CJP welds with various flange thicknesses and gage distances (3.00 6 gt/tf 6 4.00). The primary pring (Q/T)P–M is found at the failure of the bolts. A linear relationship was fitted to the finite element results to obtain an analytical model for predicting the prying force when partial yielding occurs in the flange followed by bolt fracture. The von Mises stress contours for the selected cases show that no full plastification of the flange at the K-zone is formed. Thus, the problem is statically indeterminate and an additional relationship that relates the prying force to the applied load is needed to solve the problem. More details about the model and its validation is available in Hantouche [19]. The primary prying in the thick-flange T-stubs is computed using the proposed equation below:
ðQ =TÞPM ¼ ð23:1ðg t =tf Þ 66:2Þð3=pÞ
The width of the T-stub tributary to a pair of tension bolts is computed using the following equation:
p ¼ 2W Tstub =n tio, tcf/tTf, increases for both T-flange/column flanges with/without continuity plates. It can be seen that the continuity plates can be omitted when using a column flange thickness equal to the T-stub flange thickness. Also, providing continuity plates in the column does not entirely eliminate the secondary prying when the thickness of the column flange (tcf) is less than the thickness of the T-stub flange (tTf). 4.2. Analytical investigation of secondary, primary, and total prying An equation is developed as a part of this study and described in Hantouche’s dissertation [19] to predict the primary prying force for thick built-up T-stub connections with CJP welds corresponding to the failure mode due to partial yielding of the flange followed by bolt fracture. After identifying the major geometric parameters
ð5Þ
In Eqs. (4) and (5), gt is the gage between the rows of the tension bolts in the T-stub, tf is the flange thickness of the T-stub, WT-stub is the overall width of the T-stub, and n is the number of bolts. It is necessary to know the amount of total prying force encountered in the T-stub/column system in order to be able to account for it in the design. To be able to use the primary prying strength model developed by Hantouche [19], the level of prying force needs to be normalized. The normalized values were presented in Table 2 and are retabulated in Table 3 along with the dimensionless thickness factor, tcf/tTf, and a normalizing factor b that relates the primary prying strength model to the primary prying finite element model. The factor, b, is expressed as follows:
b ¼ ðQ=TÞP—FE =ðQ =TÞP—M
ð6Þ
Table 2 Secondary prying in thick T-stub connections with/without continuity plates. Beam
a b c d e f
tcf/tTfa (1)
Column without continuity plates
Column with continuity plates
(Q/T)T/NO–CPb (2)
(Q/T)S/NO–CPd (4)
(Q/T)T/CPe (5)
(Q/T)S/CPf (6)
(Q/T)P–FEc (3)
ð4Þ
% Decrease in secondary prying due to continuity plates (7)
W24x76
0.67 0.84 1.00 1.33
19.85 14.18 12.38 11.48
3.33 3.33 3.33 3.33
16.52 10.85 9.05 8.15
11.87 11.52 11.40 11.21
8.54 8.19 8.07 7.88
48.31 24.52 10.83 3.31
W30x108
0.60 0.76 1.00 1.20
41.68 17.49 6.32 1.59
31.32 10.74 6.24 10.74
10.36 6.75 0.08 0.00
31.68 11.98 6.24 1.84
0.00 1.24 0.00 0.00
100.00 81.63 0.00 0.00
W36x150
0.57 0.72 1.00 1.14
45.31 39.63 22.57 4.89
35.47 21.93 16.25 3.97
9.84 17.70 6.32 0.92
36.84 22.09 16.73 3.37
1.37 0.16 0.48 0.00
86.08 33.62 92.41 100.00
Dimensionless ratio of column flange thickness to T-stub flange thickness. Total prying without continuity plates. Primary prying from finite element models. Secondary prying without continuity plates. Total prying with continuity plates. Secondary prying with continuity plates.
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20
Percentage of Secondary Prying
18 16 14 Column with CP 12
Column without CP
10 8 6 4 2 0 0.40
0.50
0.60
0.70
0.80
0.90
1.00
1.10
1.20
1.30
1.40
Column Flange to T-flange Thickness Ratio Fig. 7. Secondary prying in thick T-stubs resulting from W24x76 beam with different column flange thicknesses.
20
Percentage of Secondary Prying
18 16 14 12 10
Column with CP Column without CP
8 6 4 2 0 0.40
0.50
0.60
0.70
0.80
0.90
1.00
1.10
1.20
1.30
Column Flange to T-flange Thickness Ratio Fig. 8. Secondary prying in thick T-stubs resulting from a W30x108 beam with different column flange thicknesses.
20
Percentage of Secondary Prying
18 16 14 12 Column with CP
10
Column without CP
8 6 4 2 0 0.40
0.50
0.60
0.70
0.80
0.90
1.00
1.10
1.20
1.30
Column Flange to T-flange Thickness Ratio Fig. 9. Secondary prying in thick T-stubs resulting from a W36x150 beam with different column flange thicknesses.
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a
(Q/T)P–FE
a
Beam
tcf/tTf
(Q/T)P–M
b = (Q/T)P–FE/(Q/T)P–M
W24x76
0.67 0.84 1.00 1.33
3.33 3.33 3.33 3.33
4.25 4.25 4.25 4.25
0.78 0.78 0.78 0.78
W30x108
0.60 0.76 1.00 1.20
31.32 10.74 6.24 10.74
2.33 2.33 2.33 2.33
13.44 4.61 2.68 4.61
W36x150
0.57 0.72 1.00 1.14
35.47 21.93 16.25 3.97
2.46 2.46 2.46 2.46
14.42 8.91 6.61 1.61
Ratio of primary prying from finite element to primary prying from model.
Table 4 Results of total, primary, and secondary prying without continuity plates in a thick T-stub/column system. Beam
a b
Column without continuity plates a 0
b
0.78 0.78 0.78 0.78
4.96 3.26 2.72 2.45
5.96 4.26 3.72 3.45
3.33 3.33 3.33 3.33
19.85 14.18 12.38 11.48
2.33 2.33 2.33 2.33
13.44 4.61 2.68 4.61
0.30 1.05 0.01 0.00
1.30 2.05 1.01 1.00
31.32 10.74 6.24 10.74
40.70 21.99 6.32 10.74
2.46 2.46 2.46 2.46
14.42 8.91 6.61 1.61
0.50 0.81 0.39 0.23
1.50 1.81 1.39 1.23
35.47 21.93 16.25 3.97
53.27 39.63 22.57 4.89
tcf/tTf
(Q/T)P–M
W24x76
0.67 0.84 1.00 1.33
4.25 4.25 4.25 4.25
W30x108
0.60 0.76 1.00 1.20
W36x150
0.57 0.72 1.00 1.14
K = 1 + k0
k = (Q/T)S/NO–CP/a(Q/T)P–M
b
b(Q/T)P–M
(Q/T)T = Kb(Q/T)P–M
Ratio of secondary prying to the primary prying from finite element. Ratio of total prying to primary prying from finite element.
Table 5 Results of total, primary, and secondary prying with continuity plates in a thick T-stub/column system. Beam
a b
Column with continuity plates a 0
b
0.78 0.78 0.78 0.78
2.56 2.46 2.42 2.37
3.56 3.46 3.42 3.37
3.33 3.33 3.33 3.33
11.87 11.52 11.40 11.21
2.33 2.33 2.33 2.33
13.44 4.61 2.68 4.61
0.00 0.12 0.00 0.00
1.00 1.12 1.00 1.00
31.32 10.74 6.24 10.74
31.32 11.98 6.24 10.74
2.46 2.46 2.46 2.46
14.42 8.91 6.61 1.61
0.04 0.01 0.03 0.00
1.04 1.01 1.03 1.00
35.47 21.93 16.25 3.97
36.84 22.09 16.73 3.97
tcf/tTf
(Q/T)P–M
W24x76
0.67 0.84 1.00 1.33
4.25 4.25 4.25 4.25
W30x108
0.60 0.76 1.00 1.20
W36x150
0.57 0.72 1.00 1.14
k = (Q/T)S/CP/a(Q/T)P–M
b
K = 1 + k0
b(Q/T)
P–M
(Q/T)T = Kb(Q/T)P–M
Ratio of secondary prying to the primary prying from finite element. Ratio of total prying to primary prying from finite element.
The total prying (Q/T)T, can be determined by multiplying a factor K to the normalized primary prying b(Q/T)P–M. This representation incorporates the effect of secondary prying (Q/T)S, and can be written as follows:
K ¼ ðQ=TÞT =bðQ=TÞP—M
ð7Þ
where
ðQ=TÞT ¼ bðQ =TÞP—M þ ðQ =TÞS
ð8Þ
Another form of the factor, K, can be written as follows:
K ¼ 1 þ ððQ =TÞS =bðQ =TÞP—M Þ ¼ 1 þ k
0
ð9Þ
where k0 is the ratio of secondary prying to the normalized primary prying, b(Q/T)P–M. The results of the total, primary, and secondary prying are compiled in Tables 4 and 5 using the above equations. The total prying is computed using Eq. (8) by adding the secondary prying to the normalized primary prying model, b(Q/T)P–M. For columns without continuity plates, the results in
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Table 4 show that total prying is significant in thick flange T-stub connections when the dimensionless ratio (tcf/tTf) is less than 1.00 (W14x157 column). Total prying is significant and should be accounted for in design when the dimensionless ratio (tcf/tTf) is less than 1.00. The total prying is considered significant when it is greater than 10% of the applied load. Taking into account this increase in the bolt force and by recalculating the bolt diameter, the design requires a larger bolt diameter. The bolt diameter is recalculated to carry the additional force introduced to the bolts due to primary and secondary prying effect. This is achieved by increasing the applied load by the amount of total prying (Q/T)T, as given by Eq. (8). Therefore, the minimum bolt diameter can be computed [2,21,27]:
db ¼
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4F=npF nt
ð10Þ
where F is the total applied load (kip or kN) incorporating the prying effect, and Fnt is the tensile stress of the bolt (ksi or MPa). It should be noted that F = T [1 + (1/100) (Q/T)T]. By supplying continuity plates, the results in Table 5 show that total prying decreases. However, it is still considered significant for a dimensionless ratio (tcf/tTf) less than 0.72, as shown in Table 5. For W14x257 columns used with W24x76, W30x108, and W36x150 beams where the dimensionless ratio (tcf/tTf) is 0.84, 0.76, and 0.72, respectively, continuity plates should be provided unless larger column with thicker flange are used instead of the W14x257 column. 5. Conclusions An investigation using finite element modeling has been performed on the secondary prying encountered in thick T-stub connections with W24x76, W30x108, and W36x150 beams having different column sizes. In designing full-strength connections, all yielding mechanism and failure modes are needed to be identified including the secondary prying phenomenon which can be a potential failure mode that might happen especially when the thickness of the T-flange is larger than the column flange. In the cases considered in this study, the percentage of prying was quantified and showed whether it is significant or not, and whether continuity plates are needed to be supplied or not. Also by quantifying the amount of prying, the designer can check whether the bolt diameter is needed to be increased to carry the additional load that comes from the primary and secondary prying. It is concluded that the secondary prying force decreases by either adding continuity plates to the column, or by using larger column flange thicknesses as compared to the T-stub flange thickness. This is found to be true for T-stub/column systems in which tcf/tTf is greater or equal 1.00. Adding continuity plates to columns with thin flanges is not enough to solve the secondary prying force encountered in thickflange T-stub/column systems. However, increasing the thickness of the column flange decreases the amount of secondary prying force, so full T-stub connections can be detailed without continuity plates if other requirements are satisfied (column flange yielding, web yielding, and web crippling). Secondary prying forces are incorporated in the thick flange T-stub primary prying model to predict the total prying force encountered in thick flange T-stub/ column flange system. Continuity plates in W14x257 columns used with W24x76, W30x108, and W36x150 beams should be provided, unless larger columns with thicker flanges are used instead. This study provides the fabricator information for detailing columns without continuity plates as well as quantifying the amount of prying so engineers can design for the additional load by increasing the bolt diameter.
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