Evaluating performance of post-tensioned steel connections
with strands and reduced ange plates
Chung-Che Chou
1; ∗; †; ‡, Jun-Hen Chen
1; §, Yu-Chih Chen
1; §and Keh-Chyuan Tsai
2; ¶1Department of Civil Engineering; National Chiao Tung University; 1001 Ta-hsueh Rd.; Hsinchu 300; Taiwan
2National Center for Research on Earthquake Engineering; Taipei; Taiwan
SUMMARY
The seismic performance of post-tensioned steel connections for moment-resisting frames was examined experimentally and analytically. Cyclic tests were conducted on three full-scale subassemblies, which had two steel beams post-tensioned to a concrete-lled tube (CFT) column with high-strength strands to provide recentring response. Reduced ange plates (RFPs) welded to the column and bolted to the beam ange were used to increase the dissipation of energy. Test results indicated that (1) the proposed buckling-restrained RFP could dissipate energy in axial tension and compression, (2) the subassemblies could reach an interstorey drift of 4% without strength degradation, and (3) buckling of the beam occurred towards an interstorey drift of 5%, causing a loss of the strand force, the recentring response, and the moment capacity. A general-purpose non-linear nite element analysis program (ABAQUS) was used to perform a correlation study. The behaviour of the steel beam under both post-tensioning and exural loadings was compared to the test results and predictions. Copyright ? 2006 John Wiley & Sons, Ltd.
KEY WORDS: post-tensioned steel connections; strands; reduced ange plates; cyclic tests; nite element analysis
INTRODUCTION
Earlier studies [1–3] showed that the unbonded post-tensioned, precast concrete beam-to-column connection subassemblies can undergo large deformation with a small residual drift.
∗Correspondence to: Chung-Che Chou, Department of Civil Engineering, National Chiao Tung University,
1001 Ta-hsueh Rd., Hsinchu 300, Taiwan.
†E-mail: [email protected] ‡Assistant Professor.
§Graduate Student Researcher.
¶Director, National Center for Research on Earthquake Engineering and Professor, National Taiwan University.
Contract=grant sponsor: NCREE
Received 15 February 2005 Revised 14 February 2006
Unlike cast-in-place reinforced concrete monolithic connections, the exural behaviour of such subassemblies was characterized by the opening and closing of the gap at the beam–column interface under cyclic loading. This response could be maintained with the dissipation of only a little energy as long as the strands did not yield and the beam or column was not severely damaged.
Ricles et al. [4, 5], Garlock et al. [6], and Christopoulos et al. [7] applied the same technol-ogy to the steel beam-to-column connections. The systems in these studies used high-strength steel strands or bars to provide precompression between the beam and column, and provided seat angles or round bars to increase the dissipation of energy. Dierent limit states such as angle fracture, strand yielding, and beam local buckling were discussed.
This paper investigates further the cyclic responses of post-tensioned connections with a dierent energy-dissipating device, the limit state of beam local buckling, and the stress ow in the beam using the nite element computer program (ABAQUS). The beam-to-column sub-assembly incorporates high-strength bundled strands along with reduced ange plates (RFPs) for energy dissipation. The plate, shop welded to the tube and eld bolted outside the beam ange, is able to develop stable energy in both tension and compression when out-of-plane displacement of the RFP is limited. Experimental investigation shows that the proposed nection is able to achieve similar hysteretic behaviour comparable to the post-tensioned con-nection with either seat angles or round bars. Beam local buckling, however, occurs at a strain level less than reported by Garlock et al. [6]. The nite element analysis demonstrates that the longitudinal stresses in the beam subjected to both post-tensioning and bending ac-tions be predicted if the eect of stress concentration in the beam in initial post-tensioning is included.
OBJECTIVE
This work attempts to achieve the following: (1) investigate experimentally the behaviour of three post-tensioned connections with two steel beams and a concrete-lled tube (CFT) column; (2) examine how much the energy dissipation can be increased with the reduced ange plate (RFP) provided in the connection, and (3) perform a correlation study with a general-purpose non-linear nite element analysis program (ABAQUS) to compare local stresses to the test results and predictions.
DESIGN OF TEST SPECIMEN
Figure 1(a) shows a frame, which incorporates high-strength steel strands that are anchored outside the exterior CFT column and RFPs that are used to increase energy dissipation of the connection. The experimental program [8] involved tests of three full-scale subassem-blies, each of which was composed of a CFT column (350×350×9) and two steel beams (W450×200×9×14). ASTM Grade 345 (50ksi) steel was specied for the beam and col-umn tube; the specied 28 day concrete strength was 35MPa. The width-thickness ratio of the beam ange was 7.1 less than the limiting width-thickness ratio ps (= 0:30
Es=Fy= 7:2),
CFT Column RFP Post-tensioned Strands Section A-A Section B-B Flange Reinforcing Plate
Bearing Plate A A B B 350 350 CFT Column 25 mm φ Bolt Beam Flange 60¢X 675 Flange Reinforcing Plate
22 0 100 51 0 RFP 185 154 201 Cover Plate RFP Cover Plate 8 TYP Beaning Plate Flange Reinforcing Plate 675 Exterior CFT Column Interior CFT Column RFP Strands Steel Beams Cover Plate 400×220×10 350×70×20 H450×200×9×14 (a) (b)
Figure 1. Proposed post-tensioned beam-to-CFT column connection: (a) frame with post-tensioned strands and RFPs; and (b) specimen 3 connection details.
Table I. Test matrix.
Specimen T0 tR Cover Beam buckling
no. (kN) T0 TST; u (mm) PL. (mm) Md Mnp R; 0:02 M0:02 Mnp P0:04 bPy g (rad) 1 968 0.33 — No. 0.31 — 0.51 0.65 — 2 968 0.33 5 No. 0.38 0.08 0.72 0.65 0.039 3 968 0.33 8 10 0.42 0.08 0.80 0.65 0.035
Note: TST; u= ultimate strand force, Mnp= nominal plastic moment of the beam, Py= yield strength of the beam, b= 0:9.
indicating that the maximum axial load demand–capacity ratio (Pu=bPy) of the web in
com-bined exure and axial compression should not exceed 0.66, which was determined as Pu
bPy
62:33− h=tw
1:12Es=Fy
= 0:66 (1)
where h, tw, Es, and Fy are the depth of the beam web, the thickness of the beam web, the
modulus of elasticity of the steel and the yield strength of the steel, respectively. This ratio was used to limit the maximum compression force in the steel beam. Figure 1(b) shows details of an interior beam-to-CFT column connection. Four DYWIDAG multistrand tendons, two of which are placed on each side of the web and pass through the column, provide the post-tensioning force. A tendon contains four 13mm diameter seven wire, uncoated, low-relaxation ASTM A416 Grade 270 strands. The modulus of elasticity and tensile strength provided by the manufacturer are 195GPa and 1860MPa, respectively.
These specimens were designed to investigate the energy dissipation of the connection with the RFPs and the limit state of beam local buckling. Table I summarizes the test matrix. All specimens had 16 strands and total initial post-tensioning force, T0 (968kN). Specimen 1 was
designed when only high-strength strands were present; Specimens 2 and 3 also had the RFPs bolted outside the ange reinforcing plates. The thicknesses, tR, of the RFPs of Specimens 2
and 3 were selected to be 5 and 8mm, respectively, but a cover plate (10mmthick) was bolted outside the RFP of only Specimen 3 to prevent the RFP from buckling under compression. Therefore, the eect of out-of-plane restraining on energy dissipation of the RFPs could be examined. The RFP shape shown in Figure 1(b) and steel grade (A36) remained the same in both specimens; the narrowest section was designed based on expected moment contribution (Mnp) and a tensile strain, R; 0:02, of 0.08 at a target gap opening angle, g, of 0:02rad. The
notation of Mnp is dened as the nominal plastic moment of the beam. Slot holes were made
in the RFP near the column to allow horizontal movement of 16mm-diameter bolts.
The experimental investigation [4, 7] described clearly the need for ange reinforcing plates and bearing plates, so that all specimens had them in the study. The ange reinforcing plates, 5mm thick for Specimen 1 and 12mm thick for Specimens 2 and 3, were tapered and llet welded outside the beam ange (Figure 1(b)). The length (675mm) of the ange reinforcing plate was the same for all specimens so that yielding in Specimens 2 and 3 beam anges at the end of the ange reinforcing plates was expected to occur about the target gap opening angle. The bearing plates were 350×70×20mm, llet welded to the end of the ange reinforcing plate, beam ange, and beam web.
Tl,in Tu,in dl du dt Tu,in Tl,in LR A x 2Tin 2Tin x Tu,in Tl,in Vbr CR TR xc Vbl Tl,in Tu,in Vcl Mcl Vcu Mcu c C θg Tu Tl x c Tu Tl Vbr Vcl Mcl Vbl Vcu Mcu (a) (c) (b)
Figure 2. Behaviour of post-tensioned beam-to-column connection: (a) initial post-tensioning stage; (b) forces contributing decompression moment; and (c) gap opening.
Decompression moment
Figure 2(a) shows the free-body of the connection under initial post-tensioning force. One of the beams is placed away from the face of the column to show the stress distribution in the bearing plate. The shortening of the beam ange section, which is a distance LR from the
face of the column, is estimated as in= LR 0 4Tin Es×A dx (2)
where A is the cross-sectional area of the beam plus ange reinforcing plates, the areas of which vary along the beam length (Figure 1(b)). The post-tensioning forces, Tu; in and Tl; in, in
the upper and lower strands are assumed to be Tin. Note that the RFPs are stress-free before
applying beam shear because they are bolted to the beam ange after the application of the post-tensioning force.
Figure 2(b) shows the deformation of the connection just before the gap between the beam– column interface opens; the compression force, C, and the decompression moment, Md, are
C = dt xc Es 2fx dt dA = 2Tu; in+ 2Tl; in= 4Tin (3) Md= MST+ MERFP = dt xc Es 2f x dt xdA−2Tu; indu−2Tl; indl + CR dt+t2R + TRt2R = dt xc Es 2fx 2 dt dA−2Tindt + [CR(dt+ tR)] (4)
where MST and MERFP are the moments provided by the strands and the RFPs, respectively; tR
is the thickness of the RFP; dt (= du+ dl) is the sum of the beam depth and the thickness of
the ange reinforcing plates; du is the distance between the upper strand and the top ange
reinforcing plate, and dlis the distance between the lower strand and the top ange reinforcing
plate. The strain, f, was estimated from the total initial post-tensioning force, bearing area
at the end of the beam, and the modulus of elasticity of the steel. Prior to decompression, the post-tensioning forces, Tu; in and Tl; in, in the strands do not change noticeably from the initial
value, Tin; the tension force, TR, and the compression force, CR, in the RFPs are assumed to
be the same and determined based on the axial deformation, in, in Equation (2). To obtain
the relationship between the axial force and deformation of the RFP, the axial stress–strain relationship of the steel is approximated by a bi-linear relationship, as shown in Figure 3(a). The yield force, PRy, and the ultimate force, PRu, are determined as the smallest sectional
area of the RFP (Figure 3(b)) times the yield strength, y, and times the ultimate strength u,
respectively. The corresponding axial yield deformation, y, and the ultimate deformation,
u, are calculated by integrating the strain over the length LR from the column face. For
simplicity, the axial force–deformation relationship of the RFP is also approximated by a bi-linear relationship, as shown in Figure 3(c).
Moment-gap opening angle relationship following decompression
Considering strand elongation and beam shortening following decompression (Figure 2(c)), the strand forces, Tu and Tl, in the upper and lower strands are assumed to be TST, and are
Strain, ε Stress, σ 1 Es 1 Ep (εy , σy) (εu , σu) b(x) x R 60˚ X ∆x LR Bolt Position Column F ace Lc bR Ld Deformation, ∆ F orce, P Kae Kap 1 1 (∆y , PRy) (∆u , PRu) Bi-linear Approximation Bi-linear Approximation (a) (b) (c)
Figure 3. RFP axial force–deformation relationship: (a) – relationship; (b) RFP cut-out; and (c) P– relationship.
given by TST= Tin+ T = Tin+ 2(dt=2−c)g LST 1− 4AST Ab+ 4AST ESTAST (5)
where Ab is the cross-sectional area of the beam; c is the position of the neutral axis at the
beam end; AST is the cross-sectional area of four 13mm diameter strands; EST is the modulus
of elasticity of the strand; g is the gap opening angle between the beam–column interface,
and LST is the length of the strands (or the length of one bay).
Assuming a rigid-body rotation of the beam about the neutral axis, the deformations, t and c, of the RFPs in tension and compression, respectively, are estimated as
t= in+ dt+t2R −c g (6) c= in+ tR 2 + c g (7)
where in and the second term in the equations are used to estimate the deformation of the
RFP before and after decompression, respectively. Figure 3(c) is then used to determine the axial forces of the RFPs based on the deformations in Equations (6) and (7).
The position of the neutral axis, c, and the moment corresponding to a given gap opening angle, g, are determined from an iterative beam sectional analysis:
1. Assume a position of the neutral axis, c, at the end of the beam.
2. Compute the strand force using Equation (5) and the axial forces in the RFPs using Equations (6), (7), and Figure 3(c).
3. Construct a linear normal strain prole with the maximum compression strain max at
the ange reinforcing plate of the beam and zero at the neutral axis. The relationship between max and the position of the neutral axis c can be found in Christopoulos et al.
[7]. Compute the resulting normal stresses using the individual stress–strain relationships and integrate the normal stresses over the respective areas to obtain the corresponding forces in the beam.
0 0.01 0.02 0.03 0.04 0.05 0.06 0 100 200 300 400 Position of Neutral Axis, c (mm) Beam Web Flange Reinforcing Plate Beam Flange
Gap Opening Angle, θg (rad)
Figure 4. Position of neutral axis versus gap opening angle relationship.
4. Sum the normal forces and check for horizontal force equilibrium.
5. Iterate over a new c by returning to step 1 until horizontal force equilibrium is satised. Compute the moment corresponding to the given gap opening angle.
Table I shows the moment, M0:02, and post-tensioning force, P0:04, calculated at a gap opening
angle of 0.02 and 0:04rad, respectively; the axial load demand–capacity ratios, P0:04=bPy,
are less than 0.66 from Equation (1). The position of the neutral axis, c, obtained from the analysis is a function of the gap opening angle and close to the junction between the beam web and the ange beyond g= 0:015rad (Figure 4).
Flexural stiness of the post-tensioned beam with RFPs
Because the position of the neutral axis approaches to the junction between the beam web and ange, this position is used to evaluate the stiness of the post-tensioned beam after decompression. Figure 5 shows the relationship between the beam moment and the inter-storey drift, , which is computed by dividing the beam tip deection by the length, L, to the centreline of the CFT column. The precompression provided by the strands ensures full contact between the beam and the column before decompression. The moment–interstorey drift relationship exhibits elastic behaviour, which has the initial exural stiness similar to that in a fully restrained moment connection [5]. Hence, the elastic exural stiness of the post-tensioned beam, Kb, is approximated using that of a fully restrained beam [10]
Kb=3EsIbL
L2 b
(8) where Ib is the moment of inertia of the beam and Lb is the beam length measured from the
column face. The elastic exural stiness provided by the RFPs, KERFP, is computed as
KERFP= KbMERFP MST = Kb CR(dt+ tR) dt xc Es 2fx 2 dt dA−2Tindt (9)
Interstory Drift, θ Beam Moment KERFP Kb KST+KERFP KST KPRFP KST+KPRFP MST MERFP Kb+KERFP Md My 1 2 3 θd θy Post-tensioned Beam + RFPs Post-tensioned Beam RFPs
Figure 5. Flexural stiness of post-tensioned beam with RFPs.
Prior to decompression, the exural stiness of the post-tensioned beam with elastic RFPs equals the sum of the stiness Kb and KERFP.
Decompression begins at Step 1 after which the exural stiness of the post-tensioned beam is contributed by the post-tensioning strands and the beam. If the beam is assumed to rotate about the junction between the beam ange and the web, the increment in moment provided by the strands is M = 4Tdc= 4 ESTAST 2dcg LST 1− 4AST Ab+ 4AST dc= KST; tg (10)
where dc is the distance between the beam centreline and the junction and KST; t is the
ex-ural stiness provided by the strands. The exex-ural stiness of the post-tensioned beam, KST,
following decompression can be estimated as KST= 1 1 Kb + 1 KST; t (11)
As loading is increased, the RFP yields at Step 2. The inelastic exural stiness provided by the RFPs is
KPRFP; t=M
g = (d 2
1+ d22)Kap (12)
where d1 is the distance from the top RFP to the junction; d2 is the distance from the bottom
RFP to the junction, and Kap is the inelastic axial stiness of the RFP shown in Figure 3(c).
Considering the elastic exural stiness of the RFP, KPRFP as shown in Figure 5 can be
determined. The exural stiness of the post-tensioned beam with inelastic RFPs equals the sum of KST and KPRFP.
0 1000 2000 3000 Distance from Column Face (mm)
0 200 400 600 800 1000 Moment (kN-m) 0 2 4 6 0 0.5 1 1.5 2 Normalized Moment, M /M ny Md1 Mc1 Md2 Mc2 Md3 Mc3 Length of Flange Reinforcing Plate Normalized Distance, Lb/db
Figure 6. Comparison of moment demands and capacities (g= 0:02rad).
Flange reinforcing plate
The post-tensioning force is transferred to the column through part of the beam following decompression (Figure 2(c)), so all specimens have ange reinforcing plates to minimize the yielding and potential buckling of the beam anges. The length of the ange reinforcing plate is determined to limit the beam ange strain at the end of the ange reinforcing plate to the yield strain at the target gap opening angle of 0:02rad. Figure 6 shows the moment distributions Md1, Md2, and Md3 along the length of the beam for Specimens 1, 2, and 3,
respectively. The moment capacities Mci (i = 1; 2, and 3 for Specimens 1, 2, and 3) are
calculated when the beam ange yields under corresponding axial force, TST
Mci= y−TST A 2I db (13) where db is the depth of the beam and I is the moment of inertia of the beam plus those of
ange reinforcing plates, which vary along the beam length. The intersection of Mdi and Mci
indicates the required minimum length of the ange reinforcing plate. The length (675mm) of the ange reinforcing plate is used for three specimens. Yielding in Specimens 2 and 3 beam anges at the end of the ange reinforcing plates is expected to occur at the target gap opening angle. Considering equilibrium of the axial force and bending moment in the beam, Table I lists the gap opening angle when the beam ange near the end of the ange reinforcing plate reaches two times the yield strain, y. The strain value of 2y [6] indicates
the onset of beam local buckling.
RFP design criteria and expected connection performance
Since the RFPs increase not only the energy dissipation but also the moment resistance, the RFPs are sized based on the expected moment contribution (Mnp) and a tensile strain,
R; 0:02 (0:08), at the target gap opening angle. The value of R; 0:02 is computed from the
Table II. Behaviours of connections with dierent RFPs and post-tensioning forces. Case bR tR T0 no. (mm) (mm) (kN) MST Mnp MERFP Mnp Md Mnp MST Md M0:02 Mnp R; 0:02 P0:04 bPy 1 50 5 968 0.32 0.05 0.37 0.86 0.66 0.07 0.11 0.65 2 100 5 968 0.32 0.06 0.38 0.84 0.72 0.13 0.08 0.65 3 100 8 968 0.32 0.10 0.42 0.76 0.80 0.21 0.08 0.65 4 100 8 1100 0.36 0.11 0.47 0.77 0.85 0.21 0.08 0.69 5 150 8 1100 0.36 0.12 0.48 0.75 0.95 0.31 0.07 0.69
Note: LR= 355 mm, Radius of cut R = 120 mm.
(Figure 3(b)), and the stress–strain relationship of the steel (Figure 3(a)). The value of Mnp must always be smaller than MST, generated by the initial post-tensioning forces, to
ensure full re-centring of the connection. The steps required to determine the size of the RFP corresponding to the target gap opening angle are:
1. Assume the thickness, tR, and length, LR, of the RFP (Figure 3(b)).
2. Estimate the required width, bR, of the RFP based on the expected moment contribution,
Mnp, and stress, FR, in the RFP corresponding to the strain 0.08
bR¿ Mnp
(dt+ tR)tRFR
(14) 3. Estimate the radius of the cut R based on the length of the cut, Lc, and the depth of the
cut, Ld, using the geometry of a circular arc relationship
R =4L
2 d+ L2c
8Ld
(15) 4. Construct the axial force–deformation relationship of the RFP (Figure 3(c)) based on a
bi-linear approximation of the steel stress–strain curve.
5. Compute the deformations of the RFPs by Equations (6) and (7), the corresponding forces in the RFPs, the moment contribution of the RFPs, and R; 0:02 in the smallest
sectional area. Iterate over the thickness tR and the length LR by returning to step 1 until
the strain R; 0:02 equal to 0.08 and re-centring criteria are satised.
Table II lists the expected performance of the post-tensioned connections with dierent RFP dimensions and total initial post-tensioning forces, T0. More than 75% (= MST=Md) of the
decompression moment is contributed from the initial post-tensioning force. The beam mo-ment at the target gap opening angle of 0:02rad, M0:02, ranges from 0.66 to 0:95Mnp;
mean-while, the moment contribution (Mnp) from the RFPs is proportional to the smallest sectional
area. The initial post-tensioning force (1100kN) causes the axial load demand–capacity ratio (P0:04=bPy) larger than the limiting value (0:66) at a gap opening angle of 0:04rad.
EXPERIMENTAL PROGRAM
Each specimen was tested in the setup (Figure 7) by displacing actuators at the ends of the beams through a series of displacement cycles. The displacement history consisted of three
3000 4700 Beam 1 Beam 2 Strands CFT Column 25 0 1650 1600 250 1600 3000 2700 2700 H450×200×9×14 350×350×9
Figure 7. Setup (unit: mm).
-200 -100 100 200 Beam Deflection (mm) -600 -400 -200 0 200 400 600 Moment (kN-m) -600 -400 -200 0 200 400 600 Moment (kN-m) -600 -400 -200 0 200 400 600 Moment (kN-m) -6 -4 -2 0 2 4 6 Interstory Drift (%) -6 -4 -2 0 2 4 6 Interstory Drift (%) -6 -4 -2 0 2 4 6 Interstory Drift (%) -1 -0.5 0 0.5 1 0 -200 -100 100 200 Beam Deflection (mm) 0 -200 -100 100 200 Beam Deflection (mm) 0 M /M np -1 -0.5 0 0.5 1 M /M np -1 -0.5 0 0.5 1 M /M np (a) (b) (c)
Figure 8. Moment versus beam deection relationship: (a) Specimen 1; (b) Specimen 2; and (c) Specimen 3.
cycles of interstorey drift with amplitudes of 0:25; 0:375; 0:5; 0:75 and 1%, followed by two cycles of drift with amplitudes of 1:5; 2; 3; 4, and 5%.
Figure 8 shows the relationships between the beam tip deection and the moment for three specimens. The moment and energy dissipation, Eh, of Specimen 3 were higher than that of
Specimen 2 (Table III), because buckling of the RFP, which was observed at an interstorey drift of 1% in Specimen 2 test, was delayed to an interstorey drift of 4% in Specimen 3 test by using the cover plate (Figure 9(a)). The area within the hysteresis loops was integrated up to an interstorey drift of 3% to determine Eh, which is the accumulated energy dissipation.
The energy dissipation at 4% drift cycles was not included. The ratio of energy dissipation between Specimens 3 and 2 was 3:2 (= 45=14), larger than the thickness ratio 1:6 (= 8=5)
Table III. Experimental responses.
Specimen T0 Eh Beam buckling
no. (kN) T0 TST; u Md Mnp M0:02 Mnp Pu bPy R; 0:02 (kN-m) g (rad) 1 943 0.32 0.31 0.52 0.54 — 9 — 2 982 0.33 0.36 0.71 0.51 0.09 14 0.034 3 943 0.32 0.40 0.74 0.49 0.08 45 0.032
Figure 9. Buckling of RFP and beam (Specimen 3): (a) 4% drift; and (b) 5% drift.
-0.4 -0.2 0 0.2 0.4 Strain (%) -600 -400 -200 0 200 400 600 Moment (kN-m) -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 Normalized Strain -1 -0.5 0 0.5 1 M /M np 0.75 1 1.5 2 3 4 5 Interstory Drift (%) 0 0.5 1 F o rce Ratio Specimen 1 Specimen 2 Specimen 3 (a) (b)
Figure 10. Eect of beam local buckling on subassembly behaviour: (a) moment versus strain relationship (Specimen 3); and (b) strand force ratio versus drift relationship.
of the RFPs. It indicated that the buckling-restrained RFP develops larger energy dissipation than that without out-of-plane restraining. The decompression moment, Md, the moment at
the target gap opening angle, M0:02, and the strain, R; 0:02, in the RFP listed in Table III were
The gap opening angle, g, was measured with a set of displacement transducers at the
beam–column interface. g was 0.023 and 0:022rad for Specimens 2 and 3, respectively,
reaching an interstorey drift of 3%, where yielding was noticed. The beam ange and web in compression buckled locally (Figure 9(b)) at the third time reaching an interstorey drift of 4%, where g was 0.034 and 0:032rad for Specimens 2 and 3, respectively, smaller than
the predictions (Table I). Figure 10(a) shows the relationship between the moment and strain at the beam ange where local ange buckling occurred. It was found that the beam ange developed signicant increase in plastic strain after 0:0026 (= 1:4y) not 2y reported by
Garlock et al. [6].
Figure 10(b) shows the ratio of the strand force to the initial post-tensioning force after each drift cycle is completed; the initial post-tensioning force decreases slowly with the yielding of the beam and signicantly with the buckling of the beam. The maximum axial load demand– capacity ratios, Pu=bPy, of Specimens 2 and 3 were about 0.5 (Table III) less than 0.66,
based on the AISC Seismic Provisions.
FINITE ELEMENT ANALYSIS
Specimen 1 was modelled with the non-linear nite element analysis program ABAQUS [11] to study the behaviour of the steel beam under combined post-tensioning and exural loadings. The steel beams and ange reinforcing plates were modelled using four-node shell elements, S4R. Rigid links were incorporated to simulate welding between the beam ange and the ange reinforcing plate. Steel stress–strain relationships obtained from tensile coupon tests were used, and material non-linearity with the von Mises yielding criterion was considered. Since the CFT column remained elastic during the test, the steel tube and concrete inll were modelled as having only elastic properties; eight-node solid elements, C3D8R, were used with full composite action between the steel and concrete. The bearing plate and strands were also modelled using the same eight-node solid elements. Interaction between the bearing plate and the steel tube was modelled with hard and rough contact behaviour, allowing separation of
0 40 80 120 160 Beam Deflection (mm) 0 200 400 600 Moment (kN-m) 0 1 2 3 4 5 6 Interstory Drift (%) 0 0.4 0.8 M /M np Test ABAQUS Model
Figure 12. Finite element model (unit: MPa): (a) initial post-tensioning stage; and (b) 2% drift.
the interface in tension and no penetration of that in compression. One end of the strands was connected to the beam end in the step before the application of the beam shear to generate the initial post-tensioning force in the beams and strands.
The predicted beam moment–deection relationship agrees well with the experimental re-sults, as shown in Figure 11. Figure 12(a) shows the longitudinal stresses in the beam under initial post-tensioning force. The region in which the stress eld is disturbed by the bearing
-100 -80 -100 -80 -80 -20-40 -60 -70 CL db (Disturbed Region) unit : MPa -90 Bearing Plate 120 mm 200 mm
Flange Reinforcing Plate Flange
0 200 400 600 800 1000
Distance from Column Face (mm) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 ξini 0 0.5 1 1.5 2
Distance from Beam Centerline 0 mm 120 mm 200 mm Flange Normalized Distance Lb/db (a) (b)
Figure 13. Stress variation in beam under initial post-tensioning force: (a) contour of longitudinal stresses; and (b) stress ratio.
plates extends over a length that is approximately equal, in this case, to the depth of the beam (Figure 13(a)). The ow of stresses in the disturbed region shows that the stresses near the bearing plates are higher and those in the centre part of the beam web are lower. Figure 13(b) shows the ratio, ini, between the stresses determined by the nite element
anal-ysis and those computed by dividing the initial post-tensioning force by the cross-sectional area A. The computed stresses were clearly overestimated in the centre part of the beam web and underestimated near the bearing plate.
After the beam–column interface opens, the region on the tension side of the beam has almost zero stress because of the combination of post-tensioning and exural loadings
0 200 400 600 800 1000 Distance from Column Face (mm)
-400 -300 -200 -100 0 Stress, σ (MP a) 0 0.5 1 1.5 2 Normalized Distance, Lb/db -0.8 -0.4 0 Normalized Stress, σ/σ y σpre ABAQUS Model Test -10 -50 -100 -150 -200 db ABAQUS Model σpre Test (-205) (-104) Bearing Plate
Flange Reinforcing Plate Flange
unit : MPa
CL (-68)
(-220) (a)
(b)
Figure 14. Comparison of longitudinal stress in beam (2% drift): (a) longitudinal stress in beam ange; and (b) contour of longitudinal stress in beam web.
(Figure 12(b)). Figure 14 compares the longitudinal stresses obtained from the model with those determined from the test; the strains caused by the initial post-tensioning force are in-cluded in the strain gauge data based on Figure 13. These data are also compared with those predicted by
pre= iniTST
A +
My
I (16)
where y is the distance measured from the beam centerline and M is the moment. Figure 14(b) indicates that the longitudinal stresses ow into the junction between the web and the ange and that the stresses can be predicted except the region near the bearing plate.
CONCLUSIONS
Three post-tensioned steel beam-to-CFT column connection subassemblies were tested under cyclic loading to evaluate the seismic behaviour of the connection. Specimen 1 had post-tensioning strands to provide contact between the beams and column. Furthermore, Speci-mens 2 and 3 incorporated the RFPs (Figure 1) to increase the moment capacity and energy dissipation. The experimental and analytical results support the following conclusions:
(1) Specimens 2 and 3 were designed and veried to remain elastic before the gap opening angle of 0:02rad, beyond which the steel beam ange yielded at the end of the ange reinforcing plate (Figure 6). The steel beam buckled towards an interstorey drift of 5%, resulting in the loss of the initial post-tensioning force (Figure 10(b)) and the recentring response (Figure 8). The maximum axial load demand–capacity ratios, Pu=bPy, were
about 0.5 (Table III) less than 0.66, based on the AISC seismic provisions. The beam ange strain, near the end of the ange reinforcing plate, was measured to be 1.4 times the yield strain, y, when beam local buckling occurred. This strain value as indicated
in Figure 10(a) is slightly less than 2y based on the experiments of Garlock et al. [6].
(2) The RFP without out-of-plane restraining yielded in tension and buckled in compres-sion. The buckling-restrained RFP of Specimen 3 was able to yield in tension and compression, dissipating more hysteretic energy than dissipated by Specimen 2 (Table III) before it underwent higher-mode buckling (Figure 9(a)).
(3) Non-linear nite element analysis reasonably predicted the response of Specimen 1 (Figure 11). Before the gap between the beam–column interface opened, the length of the disturbed region associated with the redistribution of stresses was approximately equal to the depth of the beam. The stress ratio, ini, indicated that the centre part
of the web was less eective in resisting the compression load (Figure 13). After the gap opened, the longitudinal stresses in the beam except near the bearing plate were predicted by considering ini in the calculation of the axial stresses (Figure 14).
The ag-shaped hysteretic model proposed by Christopoulos et al. [12] is representative of the behaviour of the frames incorporating post-tensioned connections both at all beam-to-column connections and at the base of each beam-to-column. The model with two independent response parameters, and , to describe the system response can be used to describe the hysteretic behaviour of the connection if all connections are described with the same parameters and open simultaneously. Parameters, and , are 0.13 and 0.61 for Specimen 3. The parameters are the intermediate values of the system in their study, indicating that the system can achieve equal or smaller displacement ductility compared to that of the bilinear elasto-plastic system. Studies of the seismic behaviour of frames with the proposed post-tensioned connections are currently in progress.
ACKNOWLEDGEMENTS
The nancial supports provided by the NCREE, Taiwan are greatly appreciated.
REFERENCES
1. Cheok G, Lew H. Model precast concrete beam-to-column connections subject to cyclic loading. PCI Journal 1993;38(4):80–92.
2. Priestley MJN, MacRae G. Seismic tests of precast beam-to-column joint subassemblages with unbonded tendons. PCI Journal 1994;41(1):64–81.
3. Pampanin S, Priestley MJN, Sritharan S. Press phase 3: the ve-story precast test building-frame direction response. Report No. SSRP 2000=08, University of California, San Diego, La Jolla, CA, 2000.
4. Ricles JM, Sause R, Garlock MM, Zhao C. Posttensioned seismic-resistant connections for steel frames. Journal of Structural Engineering 2001;127(2):113–121.
5. Ricles JM, Sause R, Peng SW, Lu LW. Experimental evaluation of earthquake resistant posttensioned steel connections. Journal of Structural Engineering 2002;128(7):850–859.
6. Garlock MM, Ricles JM, Sause R. Experimental studies of full-scale posttensioned steel connections. Journal of Structural Engineering 2005;131(3):438–448.
7. Christopoulos C, Filiatrault A, Uang C-M, Folz B. Posttensioned energy dissipating connections for moment-resisting steel frames. Journal of Structural Engineering 2002; 128(9):1111–1120.
8. Chou C-C, Chen J-H, Chen C-Y. Performance evaluation of post-tensioned steel connections for moment-resisting frames. 6th Korea–Japan–Taiwan Joint Seminar on Earthquake Engineering for Building Structures, Taiwan, 2004.
9. AISC. Seismic Provisions for Structural Steel Buildings. AISC: Chicago, IL, 2002. 10. Englekirk R. Steel Structures. Wiley: New York, 1994.
11. HKS. ABAQUS User’s Manual Version 6.3. Hibbitt, Karlsson & Sorensen, Inc.: Pawtucket, RI, 2003. 12. Christopoulos C, Filiatrault A, Folz B. Seismic response of self-centering hysteretic SDOF systems. Earthquake
