Mechanical behavior of reinforced concrete beam-column assemblage with different floor levels on both sides of column

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1 Mehanial ehavior of reinfored onrete eam-olumn assemlage with different floor levels on oth sides of olumn omohiko Kamimura 1 and Kazuhiko Ishiashi 2 and Mikio Fujitsuka 3 1 Professor, Dept. of Arhiteture,Shiaura Institute of ehnology, okyo, Japan 2 Professor, Dept. of Arhiteture and Civil Engineering,Chia Institute of ehnology,chia, Japan 3 Graduate Shool, okyo Institute of ehnology, Kanagawa, Japan kamimura@si.shiaura-it.a.jp ABSRAC: he ojets of this study are to give onsideration to the mehanial ehavior of eam-olumn suassemlage with different floor levels on oth sides of olumn, and also to estimate the shear strength of joint in suh a suassemlage. he numer of test speimens with eam ar anhorage of the ontinuous hoop form within a joint is three and the variale of the test series is the distane etween one eam axis and the other eam axis on oth sides of olumn only. he failure mode of two speimens with zero distane and with the distane of a half eam depth etween one eam axis and the other eam axis was the joint shear failure. At the maximum strength, the shear fore of the joint zone etween one eam axis and the other eam axis in the speimen with the distane of a half eam depth is larger than that of the joint zone in the speimen with zero distane. herefore, the ultimate strength of joint with different floor levels should e estimated y means of the shear fore of the joint zone etween one axis and the other eam axis. As a result, the ultimate strength of joint relates with the ratio of the distane etween one eam axis and the other eam axis to the olumn depth. Namely, as the value of ratio is smaller, the ultimate strength of joint inreases. KEYWORDS: Beam-olumn joint, Different floor levels, Shear strength of joint, Strut mehanism 1. INRODUCION Reinfored onrete strutures frequently are onstituted of a eam-olumn suassemlage with different floor levels on oth sides of olumn. However, it s impossile to estimate the mehanial ehavior of suh a eam-olumn suassemlage. he equations of joint shear strength for the shape of exterior and interior joint are proposed. But these proposed equations do not reflet the influene of the distane etween one eam axis and the other eam axis on oth sides of olumn. he ojets of this study are to give onsideration to the mehanial ehavior of eam-olumn suassemlage with different floor levels, and also to estimate the ultimate strength of joint in suh a suassemlage. 2. EXPERIMENAL SUDY ON HE MECHANICAL BEHAVIOR OF REINFORECED CONCREE BEAM COLUMN ASSEMBLAGE WIH DIFFEREN FLOOR LEVELS 2.1. Outline of Experimental Work est speimens are three interior eam-olumn joints with different floor levels removed from a plane frame y utting the eams and olumns at aritrary assumed infletion points, as shown in Fig 1. In these test speimens, eam ars within the joint are arranged in the ontinuous hoop form. he parameter of the test is the

2 distane etween one eam axis and the other eam axis on oth sides of olumn only. he seleted distane level is zero for speimen, a half eam depths for speimen.5d, and two and a half eam depths for speimen, respetively. Based on the proposed equation with the same floor level[arhitetural Institute of Japan, 1999], speimens and are designed to e a joint shear failure type. he speimens were tested in upright position, as shown in Fig 1. he olumn ends were supported y a horizontal rollers and a mehanial hinge. he onstant vertial load was applied at the top of the olumn y a hydrauli jak, and reversed yli load was applied to the eam ends y two hydrauli jaks. Column axial load: N735[kN] +P H3000 eam 200 H L3375 Speimen.5D + olumn L3375 Speimen H3000 +P L Speimen Joints 300,.5D,, Beam setion Figure 1 Details of speimen (unit in mm) op: 4-D22 Bot: 4-D ,.5D,, Column setion Joint Reinforement: -D10@100 Mateiral Properties: Conrete ompressive strength : σ B σ B 26.5[MPa] Steel yield strength : sσy D22 : sσy 412[MPa] D25 : sσy 438[MPa] D10 : sσy 345[Mpa] 8-D Experimental Results and Disussions Oserved Behavior Fig 2 shows the rak patterns oserved at the final stage of loading for eah speimen and the envelope urves of the eam shear(p) story drift angle(r) relations. For speimens and.5d, eam flexural yielding was not oserved and the rushing of onrete ourred in the joint panel. And also the joint reinforement yielded at maximum strength. he deterioration of strength progressed under the susequent yli loading after maximum strength and the spalling of onrete ourred in the joint. For speimen, the strain in the eam ars at the eam ritial setion and the joint reinforement reahed the yield strain at the ultimate strength. he strength deay progressed under the susequent yli loading after the maximum load. After the maximum load, the diagonal shear raks in joint appeared and the width of raks inreased. As a result, the spalling of onrete ourred remarkaly in the joint panel. Aordingly, it was onluded that the failure mode of speimens and.5d was the joint shear failure, and that of speimen was the joint shear failure after eam flexural yielding.

3 150 P[kN] 140.4[kN] 115.3[kN] 133.7[kN] [kN] D Maximum Load Ultimate Deformation R[ 10-3 rad] heoretial eam flexural yielding.5d (a) rak patterns at final stage () Beam shear(p) story drift angle(r) relation Figure 2 rak patterns and deformation harateristis Comparison etween oserved and alulated strength Experimental values are ompared with theoretial values alulated y flexural theory [Fujii, 1972] and the shear strength of joint alulated y the following proposed equations. he eam shear fore(tpju) at the ultimate shear strength of joint is alulated y the following equations whih are defined in Eqn.2.1 and Eqn.2.2 [Arhitetural Institute of Japan, 1999]: For speimens and.5d, For speimen, Vju 1.56σ B j D (in kgf/m 2 units) Vju 1.13σ B j D (in kgf/m 2 units) (2.1) (2.2) where, Vju : joint shear strength, j : joint effetive width, D : olumn depth ale 1 Comparison of oserved and alulated strength (unit : kn) Speimens Beam Joint tpy epy tpju epju Pmax D epy and tpy : eam shear fores at yield strain in eam ar for experimental and alulated values epju and tpju : eam shear fores at the joint shear strength for experimental and alulated values he omparison of oserved and alulated strength is shown in ale 1.For speimen without the distane etween one eam axis and the other eam axis on oth sides of olumn, the joint shear strength an e estimated approximately y the proposed equation for the joint shear strength. But the eam shear fore at the joint shear strength for speimen.5d with the distane is 115.3kN and is larger than that for speimen.as desried aove, for speimen, the failure mode was the joint shear failure after eam flexural yielding.

4 herefore, the maximum strength of this speimen was otained approximately from flexural theory. 3. INFLUENCE OF HE DISANCE BEWEEN ONE BEAM AXIS AND HE OHER BEAM AXIS ON BOH SIDES OF COLUMN ON HE ULIMAE SRENGH OF JOIN 3.1. Horizontal Shear Fore in a Joint he horizontal shear fore in a joint with different floor levels is not a onstant value. Fores ating on a joint and horizontal shear fores(vj) in a joint at maximum strength are as follows.. C s C M` Vj1 M C For speimen, the horizontal shear fore V j1 C s C M Vj3-1 Vj3-2 C s C (the upper panel) (the under panel) For speimen, the horizontal shear fores V j3-1 and V j3-2 Figure 4 Shear fores in a joint M C M Vj2-1 Vj2-2 Vj2-3 For speimen.5d, the horizontal shear fores V j2-1, V j2-2 and V j2-3 M C, : tensile fores in eam longitudinal reinforement C C,C C : onrete ompressive fores C S,C S : ompressive fores in eam longitudinal reinforement V C : olumn shear fores M : eam moment 3.2. Comparison of Maximum Joint Shear Strength with Ultimate Joint Shear Strength Calulated y he Proposed Equation he omparison of maximum joint shear fores (Vj) with ultimate joint shear strength alulated y the proposed equations Eqn.2.1 and Eqn.2.2 is shown in ale 2. For speimens and, the joint shear strength an e estimated y the proposed equations. However the joint shear strength V j2-2 for speimen.5d is larger than that for speimen. his phenomenon indiates that the joint shear strength is influened y the distane etween one eam axis and the other eam axis on oth sides of olumn. herefore, the ultimate shear strength of joint with different floor levels should e estimated y the joint shear fore V j2-2, whih is the largest Influene of Shear Span Ratio on Joint Shear Strength Fig 5 shows joint shear strength index (Vj/Vju) plotted against the shear span ratio (M/(Vj j)). he previous

5 ale 2 Comparison of joint shear strength with ultimate shear strength of joint alulated y the proposed equations.5d V j1 V j2-1 V j2-2 V j2-3 V j3-1,2 V j V ju (kn) V j /V ju Vj : joint shear fore of V j1, V j2-1, V j2-2, V j2-3 and V j3-1, 2, as shown in Fig 4 at the maximum strength Vju : joint shear fore alulated y Eqn.2.1 and Eqn.2.2 Eqn.2.1 for V j1 and V j2-2, Eqn.2.2 for V j2-1, V j2-3 and V j3-1, 2 experimental data of interior - type + - shaped joints and the joints with different floor levels are plotted. he definition of shear span ratio is shown in Fig Vj/Vju D Interior type + - shaped joints Joint with different levels M/ Vj j 1.5 Figure 5 Joint shear strength index (V j /V ju ) shear span ratio relations j M M d M M d j M V j j V j a V j j a j M : ending moment a : shear span( j /2) j : distane from top eam ar to ottom eam ar j : distane from the entroid of ompression to entroid of tension of olumn((7/8) d) Figure 6 Definition of shear span ratio Fig 5 indiates that the joint shear strength derease with the shear span ratio level. Comparing the relations of the joint shear strength otained y experiment and alulated y proposed equation Eqn.2.1, the joint shear strength has a tendeny to overestimate with the shear span ratio level. Aordingly, proposed equation Eqn.2.1 does not refleted the influene of shear span ratio.

6 4. SHEAR RESISANCE MECHANISMS OF BEAM COLUMN JOIN 4.1. Compressive Strut Resultant Fore and Angle of Strut in Strut Mehanism he shear transfer mehanisms in a joint an e regarded mainly as strut ations at ultimate shear strength, onsidering the fores ating on the joint. Here, ompressive strut resultant fore and angle of strut in strut mehanism are disussed. he proess for alulating the ompressive strut resultant fore and angle of strut in strut mehanism onsists of the following steps. Step1 : he depths(a,a) of the onrete ompression zone in the olumn and eam setions at the end of the joint in Fig.7(a) are given the following equations, respetively. { M ( D 2 d) + ( D 2 d) N / 2} 2{ ( D d ) j } j a j { M ( D 2d) } / C a 2{ ( D d) j} / C (4.1) where C and C are respetively onrete ompressive fores at the eam and olumn ritial setion; and are respetively steel ompressive fores given y the measured strains in eam and olumn longitudinal reinforement ; N is olumn axial fore; M and M are the ending moments at the end of the joint ; d and d are respetively the distanes from the extreme fier of olumn and eam setion to the entroid of olumn and eam ar ; D and D are olumn and eam depths. Step2 : In this model, the horizontal and vertial joint shear fores (C H,C V ) resisted y the ompressive strut mehanism are given y C C H V C C + + s s V p (4.2) where ond fores ( s, s) of eam and olumn longitudinal reinforement in the main onrete strut, as shown in Fig 7(a). And the ompressive strut resultant fore(), and the strut stress(σs) are given y σ s / 2 2 CH + CV 2 2 ( a + a t ) p (4.3) where tp is equal to (B + B) /2 ; and B and B are respetively eam and olumn widths. Step3 : he angles (, ) of strut resultant fore and strut alulated y the depths of the onrete ompression zone in the olumn and eam setions are given the following equation, respetively. tanθ sr tanθ s C V ( D a )/( D a ) / C H (4.4)

7 zone L a C s C s a C s P s s s C S a s C S C V C H s P s C s C d j θ H /( H j) zone R (a) Strut mehanism for speimen () Calulation proedure for the earing fore Figure 7 Shear Resistane Mehanism of Beam Column Joint ldh d sinθ ale 3 Angle of strut resultant fore in strut mehanism and the earing fore in the loation of the ent eam ar Speimen Loation θ s [rad] θ sr [rad] σ s [Mpa] d[kn] [kn] d/.5d ZoneR ZoneL ZoneR ZoneL Upper panel Under panel D (Upper panel zone) Figure 8 Angles of strut resultant fore and strut alulated y the depths of the onrete ompression zone (under panel zone) he ompressive strut stress(σs), and the angles(, ) of strut resultant fore and strut at maximum strength in strut mehanism are shown in ale 3. And also, the angles of strut resultant fore and strut alulated y the depths of the onrete ompression zone in the olumn and eam setions are shown in Fig 8. For speimen, the angle() of strut doesn t agree with that() of strut resultant fore, eause strut resultant fore is formed etween the orner of joint panel zone and the loation of ent eam ars within the joint arranged in the ontinuous hoop form. Namely, the earing fore in the ent eam ar equilirates the resultant fore of onrete ompressive fores at the eam and olumn ritial setion.

8 4.2. Comparison of Compressive Strut Resultant Fore with he Bearing Fore in he Loation of he Bent Beam Bar A alulation proedure for the earing fore (d) in the loation of the ent eam ar [Arhitetural Institute of Japan, 1999] is indiated in Fig 7(). he omparison of ompressive strut resultant fore () with the earing fore (d) is shown in ale 3. he ratio of ompressive strut resultant fore () and the earing fore (d) is approximately etween 0.8 and 0.9. he ontriution to ompressive strut resultant fore in the ompressive onrete strut mehanism is mainly represented y the earing fore. For all speimens, the strut stress (σs) in the strut mehanism at maximum strength is larger than the onrete effetive ompressive strength (νσ B : 18.2 [MPa]) otained y the following equation [NAGANUMA,1989] as shown in ale 3. B (.8 σ / ) υσ σ (in kgf/m 2 units) herefore, it is onsidered that the rushing of onrete in the joint panel ourred. B B (4.4) 5. CONCLUSIONS he following onlusions may e drawn from the test results and the analysis of the shear fore of the joint zone etween one eam axis and the other eam axis; 1. he ultimate strength of joint with different floor levels should e estimated y means of the shear fore of the joint zone etween one eam axis and the other axis. 2. he ultimate strength of joint relates with the ratio of the distane etween one eam axis and the other eam axis to olumn depth. As the value of ratio is smaller, the ultimate strength of joint inrease. he ultimate shear strength of joint with same floor levels is to the ratio of eam depth to olumn depth what that with different floor levels is to the ratio of distane etween one eam axis and the other eam axis to olumn depth. 3. In the speimen with eam ar anhorage of the ontinuous hoop form within the joint, the ontriution to ompressive strut resultant fore in the ompressive onrete strut mehanism is mainly represented y the earing fore. REFERENCES Arhitetural Institute of Japan (1999), Design Guidelines For Earthquake Resistant Reinfored Conrete Buildings Based on Inelasti Displaement Conept, AIJ, okyo Naganuma, K. (1989), Compressive Charateristis of Craked Conrete, Japan Conrete Institute Colloquium Analytial Studies On Shear Design of Reinfored Conrete Strutures, pp Fujii, S.(1972), Moment Curvature Charateristis of Reinfored Conrete Memers Based on Material Properties, Proeeding of AIJ Annual Meeting, pp

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