APPENDIX A

Appendix A

1

APPENDIX A

Due to its extension, the dissertation could not include all the calculations and graphic explanantions which, being not essential, are necessary to complete the research. This appendix includes the explanations, figures and tables not included in chapter III of the previous dissertation. The content of this appendix is:

A.1. Member capacities…………………………..………………….. 2 A.2. Limit analysis…………………………………….…………….. 7

A.2.1. Tributary weight……………………………………….. 7 A.2.2. Calculations……………………………………………. 7

A.2.2.1. Linear load configuration………………. 8 A.2.2.2. Uniform load configuration…………...... 10

A.3. Direct design…………………………………………………… 13

A.4. Structure drawings……………………………………………... 15

Appendix A

2

A.1. Member capacities For the study is necessary to calculate the moment capacity of multiple

reinforced concrete sections. Instead of calculate the capacities by hand, computer software was used. It is an excell sheet developed by Santiago Pujol at Purdue University in 2000. This sheet calculates the moment curvature diagram when the parameters of the section are introduced. There is no unit convention; all the units must be consistent in the data introduced. Next are shown the excel sheets used, there is two for the slab members (positive and negative) and two for column capacity, one with three reinforcement layers and one with these layers distributed in two. The columns have different axial load depending on its location at the building, here is only the example for the first story central column. All these examples are for the definitely configuration of the structure after the design. (next page)

Appendix A

3

Figure A.1. Negative capcity of the slab

Appendix A

4

Figure A.2. Positive capcity of the slab

Appendix A

5

Figure A.3. Column capcity for three reinforcement layers

Appendix A

6

Figure A.4. Column capcity for two reinforcement layers

Appendix A

7

A.2. Limit analysis This section explains, first the detailed calculation for the total tributary weight

of the structure, and an explanation for the different axial load of each column. Then summarize the calculations for the base shear for both if the loads configurations. All the calculations are for the definitely configuration of the structure. Finally presents a results table with all the configurations tried in the design in order to find the most appropriate one.

A.2.1. Tributary weight

Is based on the next considerations:

− Self weight of the concrete:

23 0.415851217145

mKgpsf

inftin

ftp ==⋅⋅

− Live load: 22.7315m

Kgpsf =

− Dead load: 28.4810m

Kgpsf =

This makes a total of 2537110m

Kgpsf =

The tributary area for each floor is 9.14 m (30 ft) by 15.24 m (50 ft) thus each floor 734 KN (165 Kip). The whole building then is 2202 KN (495 Kip). The weight of the columns has been ignored.

A.2.2. Calculations

In table A.1 there are the capacities of all the members in the structure; all this

capacities corresponds to the definitely structure configuration. Table A.1 Members capacity

Negative moment Positive moment Position Exterior Interior188 KN-m 77 KN-m 3rd Story 290 KN-m 296 KN-m

2nd Story 308 KN-m 319 KN-m1st Story 325 KN-m 342 KN-m

Negative moment Positive moment Position Exterior Interior1662 K-in 680 K-in 3rd Story 2565 K-in 2620 K-in

2nd Story 2725 K-in 2827 K-in1st Story 2880 K-in 3030 K-in

Slab Columns

Slab Columns

Appendix A

8

It has been analyzed only one frame, so the total base shear will be twice as the obtained below.

A.2.2.1. Linear load configuration

The forces at each story are:

VF ⋅= 167.01 VF ⋅= 333.02

VF ⋅= 5.03 Base shear for Mechanism I: − Internal Work:

11 120

1 −=Θ in

( ) kinKinKIW 5.1463030228804 11 =Θ⋅−⋅+−⋅= − External Work:

VVVVEW ⋅=⋅⋅+⋅⋅+⋅⋅= 115.01333.01167.01 − Base Shear:

KK

EWIWV 5.146

15.146

1

1 ===

− Base Shear Strength Coefficient:

59.05.2475.146

===TTWVc

Base shear for Mechanism II: − Internal Work:

1

2401 −=Θ in

k

inKinKinKinKinKinK

IW 2.9268021662228271272523030128802

22 =Θ⋅

−⋅+−⋅+−⋅

+−⋅+−⋅+−⋅=

− External Work:

Appendix A

9

VVVVEW ⋅=⋅⋅+⋅⋅+⋅⋅= 9165.015.01333.0240120167.02

− Base Shear:

KK

EWIW

V 6.1009165.0

2.92

2

2 ===

− Base Shear Strength Coefficient:

41.05.2471.102

===TTWVc

Base shear for Mechanism III: − Internal Work:

13 360

1 −=Θ in

k

inKinKinKinKinKinK

IW 1.7468041662426201256523030128802

33 =Θ⋅

−⋅+−⋅+−⋅

+−⋅+−⋅+−⋅=

− External Work:

VVVVEW ⋅=⋅⋅+⋅⋅+⋅⋅= 778.015.0360240333.0

360120167.03

− Base Shear:

KK

EWIW

V 3.95778.01.74

3

3 ===

− Base Shear Strength Coefficient:

38.05.247

7.97===

TTWVc

Base shear for Mechanism IV: − Internal Work:

14 360

1 −=Θ in

( ) kinKinKinKinKIW 6.666806166263030128802 44 =Θ⋅−⋅+−⋅+−⋅+−⋅=

Appendix A

10

− External Work:

VVVVEW ⋅=⋅⋅+⋅⋅+⋅⋅= 778.015.0360240333.0

360120167.04

− Base Shear:

KK

EWIW

V 7.85778.06.66

4

4 ===

− Base Shear Strength Coefficient:

35.05.247

7.85===

TTWVc

A.2.2.2. Uniform load configuration

The forces at each story are:

VF ⋅= 333.01 VF ⋅= 333.02 VF ⋅= 333.03

Base shear for Mechanism I: − Internal Work:

11 120

1 −=Θ in

( ) kinKinKIW 5.1463030228804 11 =Θ⋅−⋅+−⋅= − External Work:

VVVVEW ⋅=⋅⋅+⋅⋅+⋅⋅= 11333.01333.01333.01 − Base Shear:

KK

EWIWV 5.146

15.146

1

1 ===

− Base Shear Strength Coefficient:

Appendix A

11

59.05.2475.146

===TTWVc

Base shear for Mechanism II: − Internal Work:

1

2401 −=Θ in

k

inKinKinKinKinKinK

IW 2.9268021662228271272523030128802

22 =Θ⋅

−⋅+−⋅+−⋅

+−⋅+−⋅+−⋅=

− External Work:

VVVVEW ⋅=⋅⋅+⋅⋅+⋅⋅= 8325.01333.01333.0240120333.02

− Base Shear:

KK

EWIW

V 8.1108325.0

2.92

2

2 ===

− Base Shear Strength Coefficient:

45.05.2478.110

===TTWVc

Base shear for Mechanism III: − Internal Work:

13 360

1 −=Θ in

k

inKinKinKinKinKinK

IW 1.7468041662426201256523030128802

33 =Θ⋅

−⋅+−⋅+−⋅

+−⋅+−⋅+−⋅=

− External Work:

VVVVEW ⋅=⋅⋅+⋅⋅+⋅⋅= 666.01333.0360240333.0

360120333.03

− Base Shear:

Appendix A

12

KK

EWIW

V 3.111666.01.74

3

3 ===

− Base Shear Strength Coefficient:

45.05.2473.111

===TTWVc

Base shear for Mechanism IV: − Internal Work:

14 360

1 −=Θ in

( ) kinKinKinKinKIW 6.666806166263030128802 44 =Θ⋅−⋅+−⋅+−⋅+−⋅=

− External Work:

VVVVEW ⋅=⋅⋅+⋅⋅+⋅⋅= 666.01333.0360240333.0

360120333.04

− Base Shear:

KK

EWIW

V 0.100666.06.66

4

4 ===

− Base Shear Strength Coefficient:

40.05.2470.100

===TTWVc

Appendix A

13

f 'c 4000 psi LLdesign 5 psffy 60000 psi LLdesign 50 psfh 7 in wu 188 psfd 6 in Mo 1925 k-in

Slab Region Size of bars Number of bars As (in2) ρ Mu (k-in) ΠMn (k-in)Column Strip Negative 0.65 0.75 #4 18 3.6 0.0050 939 < 0Column Strip Positive 0.35 0.60 #4 9 1.8 0.0025 404 < 0Middle Strip Negative 0.65 0.25 #4 9 1.8 0.0025 313 < 0Middle Strip Positive 0.35 0.40 #4 9 1.8 0.0025 270 < 0

Sec

tion

prop

ertie

s

Load

s

Coefficients

A.3. Direct design This section contains the calculations to check if the definitely configuration

of the structure accomplishes with main ACI requirements. It is divided in two parts. The first one is the most important, is to check if the slab has enough strength to support design loads. The second is to find out if the loads can cause a punching failure of the slabs.

The table A.2 summarizes the process to find the flexural capacity of the slab,

in that table the following formulas have been used:

8

22 nu

ollw

M =

ou MCoeffCoeffM ⋅⋅= 21

⋅⋅⋅−⋅⋅=

c

ysysn fb

fAdfAM

'85.05.09.0φ

Table A.2. Slab design

In the table A.3 are the calculations for the punching shear failure. For that

table the followings formulas were used:

c

ABuv

c

g

JcM

AV

V ⋅⋅+=

γmax

Appendix A

14

cfV '4max ⋅=

( )dcbo +⋅= 4

dbAc ⋅= 0

2

1

321

111

bb

fv

+

−=−= γγ

( ) ( ) ( ) ( )

266

2121

331 dcdcddcddcd

J c+⋅+⋅

++⋅

++⋅

=

2dccAB

+=

Table A.3. Punching shear design

DLdesign 5 psf DLtest 10 psf

LLdesign 50 psf Design Test

LLtest 15 psf Mo 1925 k-in Mo 1125

k-in

wtest 110 psf Mu- 1251 k-in Mu- 731

k-in

Load

s

wu 188 psf Mu+ 674 k-in Mu+ 394

k-in

Vu 56 k Vu 56 k f 'c 4000 psi vu 205 psi vu 160 psi fy 60000 psi φVn 109 k Vn 146 k h 7 in φvn 190 psi vn 253 psi d 6 in

c1 18 in φvn < vu φvn > vu c2 18 in bo 96 in Ac 576 in2 Jc 56160 in4

cAB 12 in γf 0.6

Sec

tion

prop

ertie

s

γv 0.4 In the results the ACI design for the punching shear calculation is not valid.

However the difference between the ultimate shear stress and the nominal shear stress is not exaggerated. The ultimate shear is still lower than the non-factored nominal shear stress. Also the same check for the testing loads gives a shear stress below the nominal capacity.

Appendix A

15

A.4. Structure drawings In this section are all the drawings plotted after the design of the structure.

They do include the drawings result of this dissertation and also the drawings concerning to the future test. There are the figures necessary to have a detailed idea of the structure and its reinforcement configuration.

Figure A.5. Foundation lined with the holes at the laboratory floor

Appendix A

16

Figure A.6. Longitudinal reinforcement details

Appendix A

17

Figure A.7. Transverse reinforcement details

Appendix A

18

Figure A.8. Slab loading at the top floor

Appendix A

19

Figure A.9. Structure section

Appendix A

20

Figure A.10. Details of the footings and columns reinforcement bars

Appendix A

21

Figure A.11. Loading connection details

Appendix A

22

Figure A.12. Slab detail for load connection