06.177~184(10-079).fm

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1 Journal of the Korea Concrete Institute Vol. 23, No. 2, pp. 177~184, April, 2011 GGGGG DOI /JKCI x w w MRS w p s y 1) Á z 2) Á x 3) * 1) wû w œw 2) w œw 3) w Nonlinear Analysis for Negative Moment Distribution of MRS Slab End Joints Jeong-Ho Moon, 1) Young-Hun Oh, 2) and Jae-Hyung Lim 3) * 1) Division of Architecture, Hannam University, Daejeon , Korea 2) Dept. of Architecture, Konyang University, Nonsan , Korea 3) Dept. of Remodeling Architecture, Woosong College, Daejeon , Korea ABSTRACT This paper describes an analytical study on the design approach of PC system with continuous connections at member ends. In multi-ribbed moment resisting slab (MRS) system, double tee members are connected continuously over inverted tee beams with the continuous reinforcements placed within topping concrete. Thus, negative moments are concentrated within the narrow connection area. In order to propose a design method, experimental results of the companion study were examined using detailed nonlinear analysis. Then nonlinear static analysis was used to evaluate the partial continuity effect and the moment redistribution mechanism. Material and cross sectional properties were obtained from experimental results of the companion study. Plastic hinge properties for nonlinear static analysis were modeled with cracking moment, nominal moment, corresponding member deformations, etc. The analysis results showed that a large amount of negative moment of MRS slab can be reduced by applying partial continuity and moment redistribution in MRS joint. Keywords : continuous connection, double tee, nonlinear analysis, plastic hinge, rotational end-spring 1. MRS(multi-ribbed moment resisting slab) œ w PC p wš, w w l. q w p w œ, w w ³ z wš w œ 1-4). p ƒ wš œ w wì q w t œ ƒ v œ rw. w l w w ew, œ w œ. MRS œ w 1 1,2) 2 3,4) x w ww, MRS w w wš w. MRS œ p w» w p e gj p *Corresponding author Received September 27, 2010, Revised November 19, 2010, Accepted December 7, X by Korea Concrete Institute w. w j p w w» w Fig. 1 d j w w. MRS ¼ -1, - 2, -3 x. MRS w p w š w, œ j { p ü v w. x PC w p s wì p w z w v ƒ. ù PC w p ù p w» w x w v w. MRS w» x 3,4) wì x x w ww MRS w w wš w. MRS w x x w mw MRS w. š x w x w ww w l w. x x w mw MRS p p s w. x w w w 5) 6) MIDAS-GEN MIDAS-FEA w. 177

2 Fig. 1 Specimen details 2.» x w w w ww ww x 3,4) x, 6 x w. x w w, j». ù x RC-PC s w t k w, { p w x w. x e š w MRS s 1/2 w, x 1 k(stem) š. x x Fig. 1, œ ƒƒ -1, -2, -3 w. -3 p x w, k w x. w -3 p, ƒ¾ d f x. x x Table 1. RC-PC s w t k PC 7,8) w w. MRS-BL Table 1 Design variables and strength comparison Specimen Design variables RC-PC interface condition Design shear force of PC Test/prediction Flexure Shear MRS-A1 Rough 1.4D+1.7L MRS-A2 Rough 1.4D MRS-B1 Rough 1.4D+1.7L MRS-B2 Rough 1.4D MRS-BL Smooth 1.4D MRS-BS Shear key 1.4D PC PC s w e w x, MRS-BS w j w x. Ax Bx PC x 3,4) w. ù x w x ü w e ùkû. Fig. 2 6 x w x w. x { w, œe { zw ü ¾ w ü w ùkü (Table 1 3,4)). t œe x 178 w gj pwz 23«2y (2011)

3 Fig. 4 Cracks of MRS-B1 and MRS-B2 3. Fig. 2 Test results Crack pattern 구조에 대한 비선형 상세 해석의 목적은 비선형 골조 해석의 전 단계로서 상세 해석을 통하여 실험 결 과를 분석하고, 그 결과를 이용하여 비선형 골조 해석 방법의 타당성을 검토하고자 한 것이다. 그리고 비교적 간략한 요소를 사용하는 비선형 골조 해석의 정확성을 실험 결과와 함께 검토한 후, 비선형 골조 해석에 의해 서 변수별 연구를 수행하고자 하였다. MRS 실험체에 대한 비선형 상세 해석은 MIDAS-FEA 를 사용하였으며, 8절점 솔리드 요소를 사용하여 모델링 하였다. 콘크리트는 TSC(total strain crack model) 의 고 정균열각(fixed crack) 모델을 적용하였으며, 콘크리트의 균열 후 연화 거동(softening)은 무시하였다. 또한 전단에 대한 전단 지연 계수(shear retention) 는 0.5를 선택하였 으며, 철근의 변형 경화는 항복 응력의 5%(E = 500 MPa) 까지 발생할 수 있도록 가정하였다. MIDAS-FEA에 의한 모델링 형상은 Fig. 5와 같으며, PC와 덧침 콘크리트는 실제와 같이 각각 특성에 따른 콘크리트 를 사용하여 모델링하였다. 실험체는 MRS 단부가 실험체의 중앙에 위치하도록 단 순보를 제작하고, 부모멘트가 단부에 작용하도록 하기 위 하여 실험체를 뒤집어서 설치한 후, 집중 하중을 실험체 중앙부에 가하였다. 해석 모델은 실험체의 대칭성 및 시 공 단계를 고려하여 Fig. 6과 같은 방법으로 모델링하였 다. Fig. 6에서 해석모델의 단부에 스프링이 표시되어 있 지만, 이는 비선형 상세 해석에서는 사용하지 않고, 비 선형 골조 해석에서만 사용하였다. MRS 조립 단계의 순서에 따른 영향을 반영하기 위하 여 이를 시공 단계로 재현하였다. 첫 번째 단계는 PC 부 재가 조립 단계에서는 단순 지지 상태 놓여지고, 여기에 굳지 않은 덧침 콘크리트가 자중으로 작용하는 단계이다 MRS 율(test/prediction)은 휨 및 전단에 대한 각각의 공칭강도 로 실험 강도를 나눈 값이다. 전단에 대해서 이 비율 값 들이 1.0보다 작은 이유는 전단에 대해서는 충분한 강도 로 설계되었으므로 전단 파괴 이전에 휨 파괴가 발생하 였음을 의미한다. 또한 실험 결과 인장 철근은 항복 변 형률 보다 큰 변형률을 보여주었으며, 특히 연성적인 휨 거동을 보여준 MRS-A1, MRS-B1 및 MRS-BS 실험체의 인장철근은 0.03 이상의 큰 변형률을 나타내었다. 그러 나 MRS-A2, MRS-B2 및 MRS-BL 실험체는 MRS-A1, MRS-B1, 그리고 MRS-BS 실험체에 비하여 연성도가 조 금 낮게 나타났다. 실험체가 최종 파괴 되는 순간의 파괴 모드를 비교한 결과, 실험체의 최종 파괴 모드는 강도가 저하되는 시점 에 발생하는 대각선 균열의 크기와 관계가 있는 것으로 나타났다. 모든 실험체는 강도 감소가 발생하기 전까지 Fig. 3과 같이 잘 분산된 휨 균열을 보였지만, 최종 단계 에서 Fig. 4(b)와 같은 사인장 균열이 발생하는 경우에 연성도가 낮게 나타났다. 그러나 최종 단계의 사인장 균 열은 실험체의 최대 강도를 저감시키는 않았다. 실험 결 과와 Fig. 1에 나타난 배근 상세를 보았을 때, 단부 부위 에 전단 보강 철근을 좀 더 배근하였다면 연성도를 높 힐 수 있었을 것으로 판단되었다. 이상과 같은 파괴는 향후 설계에서 예방이 가능하므로 해석에서는 Fig. 4(b) 와 같은 파괴가 발생하지 않도록 충분히 보강되었음을 가 정하고, 해석을 위한 모델링 과정에서 전단력에 대한 소 성힌지는 사용하지 않았다. Fig. 3 실험체에 대한 비선형 상세 해석 9) 9) p 3,4) Fig. 5 Analytical model with MIDAS-FEA 비선형 해석에 의한 MRS 슬래브 단부 접합부의 모멘트 분포 연구 179

4 wš w. 4 x w z v ƒw w. 4. x w x w Fig. 6 Test and analysis model (Fig. 6(a)). e gj pƒ y w, w w (Fig. 6(b)). ó w w ƒ. w. w w œ w» w ƒ w w w. MRS-A1, MRS-B1 MRS-BS x w Fig. 7. x w x dw. l x w w û ùkûš, x w w ùkû. w x w w x w w ùkû. x w û PC p w w. ù ³ x w w p s MRS w x w w MIDAS- GEN x p-š w w. š y š w» w 3 (tri-linear) tx š w. (1, 2, 3 ) É (³ p, œe p) tx. ³, ³ z ³ w, œe z x y w p ü ƒ w. w ƒ 3 w. ƒ x w ww.» x w w, x w ƒ w x w, w x w. w x w x w (1.0A s ), 0.8 (0.8A s ), š 0.5 (0.5A s ) w. ƒ p Table 2 Fig. 8, 0.8A s t ùkü. w l z v -3 2 wš x x w. x w w w Fig. 9 ùkü -1 6, -2 4, -3 1 w (Fig. 9). MRS -3 p œ, e gj p PC óù.» w mw dw». z v -3 2 w wš, x w w w. z v 120,000 kn m/rad, x 77% w w. š -3 ³ z 2 Table 2 Hinge properties Fig. 7 Comparison with tests and analyses (MIDAS-FEA) A s 0.5A s Section I cr / I g M cr M n I cr / I g M cr M n Positive moment Negative moment Positive moment Negative moment Positive moment Negative moment w gj pwz 23«2y (2011)

5 Fig. 8 Hinge properties Fig. 9 Modeling method with MIDAS-GEN p 0.15I g w. w x w Fig. 10 ùkü. Figs w MIDAS-FEA x y š w, MIDAS-GEN x y š w». w x w, v w x w, š v w x w Fig. 10 Effects of partial continuity, x w. Fig. 10 v x 2 sƒ, x w ew. 5.1 w 5. MRS p s MRS k œ w ww w. k, ƒ k MRS p w w w. ƒ w š w. w x w w MRS ƒ w». MRS ƒ w p w pƒ sƒ. w Fig. 10 MRS ƒ w wì w z w w. MRS w p ƒ š w. 5 MRS» w p ƒƒ w. š ƒƒ w z ww w w w. 5.2» w MRS x w» z mw» w 8m x w ww. ƒ w ww, ³ w (case-1), MRS z v (case-2), MRS z v (case-3) sww. w w p-š -1 p, -2-3 p w w w. w w» e w 1/2 Fig. 11 w. ƒ w x w Fig. 12 p s ùkü. x wš w, p j» yw ùkü. case-1 case- 2 x wš p s ƒ p x w w MRS w p s 181

6 Fig. 11 Analysis model for continuous beams Fig. 12 Influence of sectional shape w -3, -1 ù -2 40~45% w w, -3 ¼ ƒ» w ùkù. ù case- 3 z v w», case-1 case-2 w p j»ƒ 36% w ùkû. š w 1.6 ƒw. x w w, MRS» p j. ù w k w m w. 5.3 p p x w sƒ m w, w w x w ww. x w w MRS-A1 x w ƒ x w, ƒƒ 1.0A s, 0.8A s, š 0.5A s w. p w ƒ w p w y, x 1.0A s w z w x 5 ƒ š. w z x 5 ¾ ƒw ù ƒw x ³. ù û 3.0 p mw. x w ƒ p w w z ƒ p» w. z ƒw z ƒ ƒ p w w z, ü ƒ x w ƒ w. z p-š ƒ¾ w. pƒ ƒw k x ƒw p ƒw, ƒw pƒ p z ƒ. Fig. 13 w ùkü, j x ¾ x w ww ƒ w x š w. ³ p 1 wš, z œe 2 w. š p w k d pƒ ƒw. ü ƒw ƒ p w œe w ƒ. ù ƒ p w w ¾ x x w w», ƒ q. Fig. 14 ƒ œe w z ƒ Fig. 13 Load-midspan deflection relation Fig. 14 Midspan moment increase 182 w gj pwz 23«2y (2011)

7 Table 3 Comparison of analytical results Item Linear analysis Nonlinear analysis Negative M M +M M +M redistribution 1.0A s % A s % A s % ε t Fig. 15 Increments of total static moment y p y ùkü. w w txw» w 1.0A s 0.5A s w txw. X Y ƒ œe w z ƒw z ƒ p œe z ƒ p ƒƒ ù ùkü. Fig. 14 p ƒ ƒ ƒ w ùkû. w z ƒ ƒ 3.0 p ƒ 12% ü. Fig. 15» ( œe ) ƒ 3 ƒw k p s w z ƒƒ ù kü. mw p w MRS w, j» w p ü w. 5.4 MRS p sƒ x w mw MRS p s w. w w» w p w w w. MRS» 5.2 w ƒ w p w 36% p j ùk û. ù» w ƒw, w w m v w. Table 3 w mw p wì ƒ ƒ w p x ùküš. Table 3 x w p» š w. gj p» (2007) xw» p w» w x w, p j» 1,000ε t 20% w ³ 7,8)wš. t ƒ ƒ w» w 0.8A s w, p 15%. MRS» w w Ì ƒ p w š w, w j» pƒ. MRS œ w wì wz MRS y w w w. 6. MRS w x x w mw wš, w x w ww. x w x w w, w x w, š ƒ w x w. mw MRS p s e w wš,. 1) MRS xk, x j»ƒ ( 3) j», x p s j w. 2) MRS» w š w, w w p s. 3) w mw MRS w x w, w z w p ƒ w. 4) MRS z v wì p š w, p j» w j»¾ k. 5) w MRS z m w, w w w wz ƒ x ƒ v w š wû w w w. x w w MRS w p s 183

8 š x 1. z, y, x,,, v p gj p w w MRS w {, wz, 14«, 1y, 2010, pp. 148~ ( ), w PC w sƒ w, š, 2007, 156 pp. 3. z, y, x,,, MRS w w w f p, gj pwz, 22«, 2y, 2010, pp. 247~ ( ), MRS l w sƒ w, š, 2008, 337 pp. 5. Midasit MIDAS-GEN, kor.midasuser.com/building/index.asp. 6. Midasit MIDAS-FEA, kor.midasuser.com/civil/product/ midasfea.asp. 7. w gj pwz, gj p» w,», 2007, 524 pp. 8. PCI Industry Handbook Committee, PCI Design Handbook- Precast Prestressed Concrete, 6th Edition, Precast/Prestressed Concrete Institute, Chicago, IL, 2005, pp. 4-8~ DIANA-8.1 User's Manual, 432 pp. PC w MRS(multi-ribbed moment resisting slab) w w wš w. MRS p ƒ p p w, p ƒ w. x x w mw p s f w, w w. w ww w x x w mw w. š z p w w x w kw ww. w w p wì w x l, x w w ³ p, œe p,. x x w l z v p mw MRS p w j» k. w :, p, x w,, z v 184 w gj pwz 23«2y (2011)

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