A.1. Member capacities A.2. Limit analysis A.2.1. Tributary weight.. 7. A.2.2. Calculations. 7. A.3. Direct design 13

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Philomena Hicks
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1 APPENDIX A

2 APPENDIX A Due to its extension, the dissertation ould not inlude all the alulations and graphi explanantions whih, being not essential, are neessary to omplete the researh. This appendix inludes the explanations, figures and tables not inluded in hapter III of the previous dissertation. The ontent of this appendix is: A.. Member apaities.... A.. Limit analysis... 7 A... Tributary weight.. 7 A... Calulations. 7 A... Linear load onfiguration. 8 A... Uniform load onfiguration... 0 A.3. Diret design 3 A.4. Struture drawings... 5

3 A.. Member apaities For the study is neessary to alulate the moment apaity of multiple reinfored onrete setions. Instead of alulate the apaities by hand, omputer software was used. It is an exell sheet developed by Santiago Pujol at Purdue University in 000. This sheet alulates the moment urvature diagram when the parameters of the setion are introdued. There is no unit onvention; all the units must be onsistent in the data introdued. Next are shown the exel sheets used, there is two for the slab members (positive and negative) and two for olumn apaity, one with three reinforement layers and one with these layers distributed in two. The olumns have different axial load depending on its loation at the building, here is only the example for the first story entral olumn. All these examples are for the definitely onfiguration of the struture after the design. (next page)

4 Figure A.. Negative apity of the slab 3

5 Figure A.. Positive apity of the slab 4

6 Figure A.3. Column apity for three reinforement layers 5

7 Figure A.4. Column apity for two reinforement layers 6

8 A.. Limit analysis This setion explains, first the detailed alulation for the total tributary weight of the struture, and an explanation for the different axial load of eah olumn. Then summarize the alulations for the base shear for both if the loads onfigurations. All the alulations are for the definitely onfiguration of the struture. Finally presents a results table with all the onfigurations tried in the design in order to find the most appropriate one. A... Tributary weight Is based on the next onsiderations: Self weight of the onrete: 45 p ft in ft in Live load: 5 psf 73. g m Dead load: 0 psf 48.8 g m This makes a total of 0 psf 537 g m psf g m The tributary area for eah floor is 9.4 m (30 ft) by 5.4 m (50 ft) thus eah floor 734 N (65 ip). The whole building then is 0 N (495 ip). The weight of the olumns has been ignored. A... Calulations In table A. there are the apaities of all the members in the struture; all this apaities orresponds to the definitely struture onfiguration. Table A. Members apaity Slab Columns Negative moment Positive moment Position Exterior Interior 88 N-m 77 N-m 3rd Story 90 N-m 96 N-m nd Story 308 N-m 39 N-m st Story 35 N-m 34 N-m Slab Columns Negative moment Positive moment Position Exterior Interior 66 -in 680 -in 3rd Story 565 -in 60 -in nd Story 75 -in 87 -in st Story 880 -in in 7

9 It has been analyzed only one frame, so the total base shear will be twie as the obtained below. A... Linear load onfiguration The fores at eah story are: F V F V F 0. 5 V 3 Base shear for Mehanism I: Internal Work: Θ in 0 IW 880 in in Θ ( ) k 4 External Work: EW 0.67 V V V V Base Shear: IW 46.5 V EW Base Shear Strength Coeffiient: V TTW Base shear for Mehanism II: Internal Work: Θ in in in + 75 in + IW Θ in + 66 in in External Work: k 8

10 EW V V V V 40 Base Shear: IW 9. V EW Base Shear Strength Coeffiient: V TTW Base shear for Mehanism III: Internal Work: Θ3 in 880 in in in + IW3 Θ in in in External Work: k EW V V V V Base Shear: IW3 74. V EW Base Shear Strength Coeffiient: V TTW Base shear for Mehanism IV: Internal Work: Θ4 in IW 880 in in in in Θ ( ) k 4 4 9

11 External Work: EW V V V V Base Shear: IW V EW Base Shear Strength Coeffiient: V TTW A... Uniform load onfiguration The fores at eah story are: F V F V F V 3 Base shear for Mehanism I: Internal Work: Θ in 0 IW 880 in in Θ ( ) k 4 External Work: EW V V V V Base Shear: IW 46.5 V EW Base Shear Strength Coeffiient: 0

12 V TTW Base shear for Mehanism II: Internal Work: Θ in in in + 75 in + IW Θ in + 66 in in External Work: k EW V V V V 40 Base Shear: IW 9. V 0. 8 EW Base Shear Strength Coeffiient: V TTW Base shear for Mehanism III: Internal Work: Θ3 in 880 in in in + IW3 Θ in in in k External Work: EW V V V V Base Shear:

13 IW3 74. V. 3 EW Base Shear Strength Coeffiient: V TTW Base shear for Mehanism IV: Internal Work: Θ4 in IW 880 in in in in Θ ( ) k 4 4 External Work: EW V V V V Base Shear: IW V EW Base Shear Strength Coeffiient: V TTW

14 A.3. Diret design This setion ontains the alulations to hek if the definitely onfiguration of the struture aomplishes with main ACI requirements. It is divided in two parts. The first one is the most important, is to hek if the slab has enough strength to support design loads. The seond is to find out if the loads an ause a punhing failure of the slabs. The table A. summarizes the proess to find the flexural apaity of the slab, in that table the following formulas have been used: M o w l u n 8 l M u Coeff Coeff M o φm n 0.9 As f y A s f y d b f ' Table A.. Slab design Setion properties f ' 4000 psi LL design 5psf f y psi LL design 50 psf Loads h 7 in w u 88 psf d 6 in M o 95 k-in Slab Region Coeffiients Size of bars Number of bars As (in ) ρ Mu (k-in) ΠMn (k-in) Column Strip Negative # < 0 Column Strip Positive # < 0 Middle Strip Negative # < 0 Middle Strip Positive # < 0 In the table A.3 are the alulations for the punhing shear failure. For that table the followings formulas were used: V max Vg A γ v M + J u AB 3

15 V max 4 f ' ( d) b o 4 + A v b 0 d γ γ f + 3 b b 3 3 ( + d ) d ( + d ) d ( + d ) ( ) d + J d + d AB Table A.3. Punhing shear design Loads Setion properties DL design 5 psf DL test 0 psf LL design 50 psf Design Test LL test 5 psf M o 95 k- in M o 5 k- in w test 0 psf Mu - 5 k- in Mu - 73 k- in k- k- w u 88 psf Mu in Mu in Vu 56 k Vu 56 k f ' 4000 psi v u 05 psi v u 60 psi f y psi φv n 09 k V n 46 k h 7 in φv n 90 psi v n 53 psi d 6 in 8 in φv n < v u φv n > v u 8 in b o 96 in A 576 in J 5660 in 4 AB in γ f 0.6 γ v 0.4 In the results the ACI design for the punhing shear alulation is not valid. However the differene between the ultimate shear stress and the nominal shear stress is not exaggerated. The ultimate shear is still lower than the non-fatored nominal shear stress. Also the same hek for the testing loads gives a shear stress below the nominal apaity. 4

16 A.4. Struture drawings In this setion are all the drawings plotted after the design of the struture. They do inlude the drawings result of this dissertation and also the drawings onerning to the future test. There are the figures neessary to have a detailed idea of the struture and its reinforement onfiguration. Figure A.5. Foundation lined with the holes at the laboratory floor 5

17 Figure A.6. Longitudinal reinforement details 6

18 Figure A.7. Transverse reinforement details 7

19 Figure A.8. Slab loading at the top floor 8

20 Figure A.9. Struture setion 9

21 Figure A.0. Details of the footings and olumns reinforement bars 0

22 Figure A.. Loading onnetion details

23 Figure A.. Slab detail for load onnetion

Slenderness Effects for Concrete Columns in Sway Frame - Moment Magnification Method

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