analysis of slab by different methods

8/18/2019 Analysis of Slab by Different Methods

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ANALYSIS OF SLAB BY DIFFERENT METHODS

Ing. Paul Guerrero *

Ing. Pablo Sanchez Caiza, Msc. **

* Consorcio Santos CMI

[email protected]

** Center for Scientific Research, CEINCI-ESPE

[email protected]

Summary

Different methods for the design of two-way slabs are made;

Marcelo Romo method Eng.; Rigid beams method; Directmethod; Method Federal District and the results obtained withETABS moments are compared. It is intended that ETABSusers have more confidence in designing a slab in this programand in case you have doubts on the results obtained resortingto use a simple manual method and provides reliable results.

1. INTRODUCTION.

There are numerous methods for the analysis and design of reinforced concrete slabs,interested however find the easy and safe. For this purpose the results obtained with thesemethods are compared:- Ing method, Marcelo Romo.- rigid beams.- direct method.- method Federal District (Mexico).- ETABS results.

Moments for cores in the slab and not to the fringes of columns are calculated as the timefor these bands are much lower in all the methods listed above.

2. OBJECTIVES.

The main aim of this article is to present the design of slabs used to compare the resultsobtained with the modeling and design of a slab ETABS methods.

It is intended that ETABS users have more confidence in designing a slab in this programand in case you have doubts on the results obtained resorting to use a simple manual methodand provides reliable results.

3. ANALYSIS MODEL.(1,2,4,5)

mailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]


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For analysis the following structure is proposed:

2.8

3.0

3.0 4.0 3.5

Figure 1 Plan View and l i f t gantr y A

Figure 2 Dimens ional Vista

The characteristics of the materials, and structural elements used in sections of beams andcolumns are shown in table 1 and 2

Table 1 Characterist ics o f materials

MATERIAL FEATURES

CONCRETE fc = 210 Kg / cm ; 12000v210 = E = 173,897 Kg / cm

STEEL fy = 4200 Kg / cm

Table 2 Characterist ics o f struc tural elements

ELEMENT FEATURES

BEAM BASE HEIGHT = = 30cms 35cms

COLUMN BASE HEIGHT = = 35cms 35cms

LOSA Lightened, 20 cm thick, with tile compression of 5 cm


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Alivianadas use the slabs 20 cm to their right ful a sol id slab equivalent of 14.5 cm is

proposed.

4. CRITICAL ANALYSIS PANEL.(2)

To start the design will prevail h = thickness of the slab = 20 cm

The critical panel is larger corresponds to that between the axles 2-3 - C - D; To determine therelationship between the inertia of the beams and the slab is usedfollowingexpression:

to Iv

I slab (1)

on each axis of the panel are shown in the following table:Table 3 Calculation inert ia ratio at the cr i t ical panel

ITEM CALCULATI

RESULT

Iv (Inertia beams) (0,30x0,35 ^ 3) / 12 0.001072 m to

(0.001072) / (3.75 * 0.145 ^ 3/12) 1,125

to

(0.001072) / (3.5 * 0.145 ^ 3/12) 1,205

to

(0.001072) / (4.35 * 0.145 ^ 3/12) 0.969

to

(0.001072) / ((2.25 + 0.175) * 0.145 ^ 3/12) 1,739

tom 1+ 2+ C + D) / 4 1,259

The minimum height for a flat slab is calculated with:

Ln 0.8

fy

h min

14000

13cm.36 5am 0.12 (2)

Where Ln is the free length of side 4.5 to 0.3 = 4.2 m; fy is the yield stress of the steel (4200

kg / cm2); Factor is free lights relationship between major / minor vain m is the factor slab / beam stiffness average (1,259).

4.20 0.8

4200

h min 14000 13 cm.

36 5 * 1,135 * 1,259 0.12

h min = 0.1088 m> = 13cm; h = 13 cm min

A slab of 20 cm, has a height of 14.5 cm and the code requires a height of 13 cm so it canbe used without any problem.


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T

5. CALCULATION OF CHARGE.

5.1 Dead Lo ad (D):

Provides for the calculation of weight of the slab, floor, macillado, ceiling and walls, to the

design need not calculate the contribution of beams and columns because these are the weight orload of the slab and not vice versa.

The contribution of the slab is then analyzed

Figure 3 Plan view and cutt ing slab 1m2

As seen in Figure 3 the slab has different components:

Table 4 Dead weight o f the slab / m2

ELEMENT CALCULATI

LOAD T / m2

Compression slab 2.4 T / mree

* 1m * 1m * 0.05m 0.12

Jitters 2.4 T / mree

(2 * (0.1 * 1 * 0.15) + 2 * (0.1 * 0.8 * 0.1296

Alivianamientos 8 blocks * 0.010 T 0.08

Dead weigh t slab 0.12 + 0.1296 + 0.08 0.3296

It is time to analyze the finished slab

Table 5 finishes s lab / m 2

ELEMENT CALCULATI

LOAD T / m2

Ceiling 2.2 T / mree

* 1m * 1m * 0.01m 0,022

I putty 2.2 T / mree

* 1m * 1m * 0.04 m 0,088

Floor 2.2 T / mree

* 1m * 1m * 0.01m 0,022

Fin ish ing slab mezzanine

0.022 + 0.088 + 0.022 0,132

It is now necessary to calculate the contribution of the walls, suppose a case critical to bebuilt of brick:

and a specific 1.6 T /m

(+ Brick mortar)

and a specific *

Vol PREDES

area (slab)

(3)


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COEF. Lesser l ight / greater Light

1.00 0.90 0.80 0.70 0.60 0.5

265 347 443 545 635 691

597 736 899 1071 1222 1317

269 362 473 590 694 759

718 779 819 829 808 773

354 368 359 318 239 179

and wall area (slab) is the area of the slab.

In the case of this exercise is weigh ing w al ls on the slab assum es mezzanine = 0.15

T / m2

5.2Vivas loads or overloads (L):

Standards or local building codes for the case of this structure are:

Losa mezzanine: L (residences) = 0.2 T / m2

To summarize we have the following load values:

Table 6 Summ ary of loads T / m2

ELEMENT CALCULATI

LOAD T / m2

Dead weight slab See Table 4 0.3296

Finishing slabmezzanine

See Table 5 0,132

Weight of wallson the

mezzanine0.15

Dead load (qD) 0.3296 + 0.132 + 0.15 0.6116

Live load (qL) 0.2

Last load (qu) 1.2 qD + 1.6 qL 1,054

6. METHOD OF ING. MARCELO ROMO.(7)

In this method the moments per meter width according to the following equation iscalculated:

M 0.0001 * wor * L2 * m x

(4)

Where M is the time to design per meter width, wu is factored load per square meter, Lx is thesmallest axis at the sides of the panel, m is a coefficient for negative and positive momentsobtained from tables as those shown below, which depends on the boundary conditions of thepanel:

Table 7 Coeff icients Ing method Romo

Ribbed rectangular slab TYPE 1 Ribbed rectangular slab TYPE 2

(Bordes wardrobes) (High side unrestricted) COEF. Lesser l ight / greater Light

1.00 0.90 0.80 0.70 0.60 0.5

200 241 281 315 336 339

564 659 752 830 878 887

258 319 378 428 459 464

564 577 574 559 538 520

258 242 208 157 126 123


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1.00 0.90 0.80 0.70 0.60 0.5

406 489 572 644 693 712839 980 1120 1240 1323 1353

428 525 621 704 761 782

839 857 852 827 793 764

428 409 369 310 271 238

Ribbed rectangular slab TYPE 3 Ribbed rectangular slab TYPE 6 (Lower side unrestricted) (Higher side and lower side without restriction)


1.00 0.90 0.80 0.70 0.60 0.5

265 297 322 339 345 339718 790 850 888 902 888

354 401 439 464 473 464

597 586 568 548 532 520

269 240 205 185 167 177

The explanation for the different coefficients of Table 7 is graphically in Figure 4, where the xmoments about the horizontal axis X and m moments around the vertical axis Y; secondly Ly is thesmaller dimension of the panel sides.

TYPE 1 TYPE 2 TYPE 3 TYPE 6

Figure 4 Models used by M. Romo

6.1 CALCULATION OF MOMENTS IN 9 PANELS.

Using tables, created at the Polytechnic School of the Army by Ing. Marcelo Romo. Designingthe slab includes the following panels, corresponding to the same one of the different types ofpanels offering these tables:

Table 8 Panels designed and match wi th m odels of Ing. Romo

Number Panel (Axis) Type (Tables)

O

1-2 - A - B 6

2 1 - 2 - B - C 2

T

1-2 - C - D 6

4 2 - 3 - A - B 2

5 2 - 3 - B - C O

6 2-3 - C - D T

7 3 - 4 - A - B 6

8 3 - 4 - B - C 2

9 3-4 - C - D 6

The result of the calculated moments in each panel can be appreciated in Table 9.


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PANEL TIME ING. ROMO

2-3-C-D

Mx -1.343

0.683

My -0.985

0,398

3-4-A-B

Mx -1.074

0.597

My -0.806

0,344

3-4-B-C

Mx -0.993

0.544

My -0.785

0.307

3-4-C-D

Mx -1.202

0.686

My -0.774

0.282

Table 9 Moments calculated on the slab

PANEL TIME ING. ROMO

1-2-A-B

Mx-1.227

0.651

My-1.102

0.533

1-2-B-C

Mx-1.091

0.563

My-1.04

0.467

1-2-C-D

Mx-1.48

0.826

My-1.093

0,459

2-3-A-B

Mx-1.139

0.549

My-1.014

0.48

2-3-B-C

Mx-1.027

0.484

My-0.961

0.422

7. METHOD OF RIGID BEAMS(1)

As the name suggests this method applies only if props are sufficiently rigid slab, is consideredto be so if the value of a is greater than 0.5 as indeed happens.

Moments design center strip (middle portion of the slab wheelbase) are calculated using thefollowing expressions:

X M C

x M and

C and

* w *

L2 x

* w *

L2 and

(5)

(6)

Where Mx is when the short direction of the panel, Cx is a coefficient obtained from tables, w isthe load per square meter, Lx is the length in the short direction of the panel, My is the moment inthe long direction panel, Cy is another factor obtained from tables and Ly is the length in the long

direction of the panel, the following values are obtained:

7.1 CALCULATION 9 MOMENTS IN PANELS

Using the tables, the method, the slab has the following design panels, corresponding to thesame one of the different types of panels offering these tables:


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Table 10 Panels designed and m atch ing mo dels wi th r ig id beams method

Number Panel (Axis) Type (Tables)

O

1-2 - A - B Case 4

2 1 - 2 - B - C Case 8

T

1-2 - C - D Case 4

4 2 - 3 - A - B Case 8

5 2 - 3 - B - C Case 2

6 2-3 - C - D Case 9

7 3 - 4 - A - B Case 4

8 3 - 4 - B - C Case 8

9 3-4 - C - D Case 4

Table 11 Design coefficients

PANEL LIGHTS (m) DESIGN FACTORS

lx ly m = lx / Cx neg. Cy neg. Cx + Cy + Cx + Cy +

1-2-A-B Case 4 3.50 3.80 0.92 0,058 0,042 0,032 0,023 0,037 0,027

1-2-B-C Case 8 3.50 4.20 0.83 0,051 0,044 0,030 0,016 0,042 0,0211-2-C-D Case 4 3.50 4.50 0.78 0.073 0,027 0,040 0,012 0,050 0,018

2-3-A-B Case 8 3.80 4.00 0.95 0,038 0.056 0,022 0,021 0,031 0,027

2-3-B-C Case 2 4.00 4.20 0.95 0,050 0.041 0,020 0,016 0,030 0,025

2-3-C-D Case 9 4.00 4.50 0.89 0,069 0,024 0,026 0,015 0,037 0,022

3-4-A-B Case 4 3.00 3.80 0.79 0,072 0,028 0,040 0,016 0,049 0,019

3-4-B-C Case 8 3.00 4.20 0.71 0,067 0,030 0,039 0,011 0,053 0,014

3-4-C-D Case 4 3.00 4.50 0.67 0,087 0,017 0,048 0,010 0,060 0,012

Table design 12Momentos

PANEL LIGHTS (m) MOMENTS OF DESIGN (T m)

lx

ly

Mx neg. My neg.

Mx + (1.2d + 1.6L)

My + (1.2d + 1.6L)

1-2-A-B Case 4 3.50 3.80 0.749 0.639 0,433 0.369

1-2-B-C Case 8 3.50 4.20 0.658 0.818 0.434 0.326

1-2-C-D Case 4 3.50 4.50 0.943 0.576 0.556 0,295

2-3-A-B Case 8 3.80 4.00 0.578 0.944 0.376 0.385

2-3-B-C Case 2 4.00 4.20 0.843 0,762 0.388 0.348

2-3-C-D Case 9 4.00 4.50 1,164 0.512 0,495 0.365

3-4-A-B Case 4 3.00 3.80 0.683 0,426 0,405 0.257

3-4-B-C Case 8 3.00 4.20 0,636 0.558 0.410 0.221

3-4-C-D Case 4 3.00 4.50 0,825 0,363 0.490 0.226

To compare the results of different methods in the following table design moments previously

calculated according to its coincidence with the X axis is displayed and the Y axis

The central strip is an intermediate strip between two strips of columns with a width equal to half of the

analyzed vain.


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PANEL TIME V. RIGHIDAS

2-3-C-D

Mx -1.164

0,495

My -0.512

0.365

3-4-A-B

Mx -0.683

0,405

My -0.426

0.257

3-4-B-C

Mx -0.636

0.41 My

-0.558

0.221

3-4-C-D

Mx -0.825

0.49

My -0.363

0.226

Table 13 Summary of the final moments in the slab strip

PANEL TIME V. RIGHIDAS

1-2-A-B

Mx-0.749

0,433

My-0.639

0.369

1-2-B-C

Mx-0.658

0.434

My-0.818

0.326

1-2-C-D

Mx-0.943

0.556

My-0.576

0,295

2-3-A-B

Mx -0.9440.385

My-0.578

0.376

2-3-B-C

Mx-0.843

0.388

My-0.762

0.348

8. DIRECT METHOD OF DESIGN.(1,2,3,5,6,9)

Before starting the design constraints are important models designed slabs, which are:

1. In each direction should be three or more continuous lengths.2. The panels are rectangular slab with a ratio greater light and not more than 2 lesser light

(measured between the centers of the supports).3. The lengths of the successive lights in each direction (measured between the centers of

support) should not differ by more than 1/3 of the greater light.4. Columns should not be misaligned with respect to any axis joining centers of successive

columns more than 10% of the light (in the direction of misalignment).5. The loads should be evenly distributed and not factored overload or

service must not be greater than twice the dead load or service not factored (L / D = 2).6. For slabs in two directions with all sides supported by beams, the relative stiffness of the

beams in two perpendicular directions must meet minimum and maximum requirements.7. Not Redistribution of negative moments.

A total time which is distributed in positive and negative first time and each core and then instripes column is calculated, equations are:

w * l * L2

M or 2 n 0 8


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(7)

Where Mo is a global moment, Wu is factored load per square meter, L2 is the transverse distanceanalysis, equal to the average lights adjacent spans, Ln is the clear span of the span considered.

The method of direct design over time by various authors simplifications suffered so it is importantto know something of its history. With the publication of ACI 318-83, the Direct Design Methodgreatly simplified the analysis of the moments of slab systems in two directions, because allcalculations rigidities were removed to determine the design moments in an end section .Expressions for calculating the distribution function of the stiffness ratio were replaced by acoefficient table to distribute the total time moments in the final stages. Another change was that theapproximate equation for unbalanced momentum transfer between the slab and an inner columnalso simplified. From these changes the Direct Design Method became a truly direct design method,one can determine all stages of design by applying moment coefficients.

For this article the more simplified form of the direct method is shown by the distribution coefficientsfor global moment, see Figure 5 and Table 14.

Figure 5 Distr ibut ion of mom ent coeff ic ients design Indoor and

outdoor sect ions

Table 14 Coeff icients desig n time two -way slab with beams

List of lights Time

Outer section Inner section

(1) (2) (3) (4) (5)

Negative positive First inner negative Positive Negative

L2 / L1 Total time 0.16 MB 0.57 MB 0.70 MB 0.35 MB 0.65 MB

0.5 Strip columns Beam 0.12 MB 0.43 MB 0.54 MB 0.27 MB 0.50 MB

Column 0.02 MB 0.08 MB 0.09 MB 0.05 MB 0.09 MB

Middle ground 0.02 MB 0.06 MB 0.07 MB 0.03 MB 0.06 MB

On

Strip columns Beam 0.1 MB 0.37 MB 0.45 MB 0.22 MB 0.42 MB



2

Strip columns Beam 0.06 MB 0.22 MB 0.27 MB 0.14 MB 0.25 MB



NOTES: (1) All negative moments correspond to the face of the supports.

(2) Torsional rigidity of the edge beam is such that it verifies One 2.5(3) L L

In the above methods slab only analyzed in the intermediate strips so in Table 15summarizes the coefficients used in this article shows.


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EJ One Axis2 ITEM CALCULA

RESULT ITEM CALCULA

RESULT

L2 3.5 / 2 1.75 m L2 (3.50 + 4) 3.75 m

L1 A-B 3.8 m

L1 A-B 3.8 m

B-C 4.2 m B-C 4.2 mC-D 4.5 m C-D 4.5 m

L2 /0.46

L2 /0.99

0.42 0.890.39 0.83

Mo A-B 2.74 T * m

Mo A-B 5.88 T * m

B-C 3.42 T * m B-C 7.32 T * mC-D 3.97 T * m C-D 8.51 T * m

AXI

hree ITEM CALCULA

RESULT

L2 (3 + 4) / 2 3.5 m

L1 A-B 3.8 mB-C 4.2 mC-D 4.5 m

L2 /L1

0.920.830.77

Mo A-B 5.49 T * mB-C 6.84 T * mC-D 7.94 T * m

EJE4

ITEM Calcul r stumps L2 3/2 1.5 m

L1 A-B 3.8 m

B-C 4.2 mC-D 4.5 m

L2 /L1

0.39

0.360.33

Mo A-B 2.35 T * m

B-C 2.93 T * m

C-D 3.40 T * m

Table 15 Summ ary coeff icients us ed

LIST OF

LIGHTS

L2 / L1

INTERMEDIATE BAND MOMENTS

(1)

Neg. Foreign

(2)

Positive

(3)

Neg. interior

(4)

Positive

(5)

Neg. interior

0.5 0.02 MB 0.06 MB 0.07 MB 0.03 MB 0.06 MB

1.0 0.04 MB 0.14 MB 0.17 MB 0.09 MB 0.16 MB

2.0 0.09 MB 0.31 MB 0.38 MB 0.19 MB 0.36 MB

Parallel to the axis X 6 strips are designed for this in Tables 16 calculations per strip asregards relations between light and calculating the overall time shown.

Figure 6 Cut paral lel to the X axis beams

Table 16 Relationships b etween l ight and calculation of global moments

E

O

For best results it is desirable to interpolate the values of the table 15 with the relationsbetween light calculated in Table 16.

Table 17 Coeff icients obtained by interpolation and l inear extrapolation

LIST OF

LIGHTS

L2 /

GAZA MOMENTS MIDDLE PILLAR 1

(1)

Neg. Foreign

(2)

Positive

(3)

Neg. interior

(4)

Positive

(5)

Neg. interior

0.39 0,016Mo 0.047 MB 0.055 MB 0.023 MB 0.047 MB

0.42 0.017 MB 0.050 MB 0.059 MB 0.025 MB 0.050 MB

0.46 0.018 MB 0.055 MB 0.064 MB 0.028 MB 0.055 MB

0.5 0.02 MB 0.06 MB 0.07 MB 0.03 MB 0.06 MB

LIST OF

LIGHTS

L2 / L1


(1)

Neg. Foreign

(2)

Positive

(3)

Neg. interior

(4)

Positive

(5)

Neg. interior

0.5 0.02 MB 0.06 MB 0.07 MB 0.03 MB 0.06 MB0.83 0.033 MB 0.113 MB 0.136 MB 0.07 MB 0.126 MB

0.89 0.036 MB 0.122 MB 0.148 MB 0.077 MB 0.138 MB

0.99 0.04 MB 0.14 MB 0.17 MB 0.09 MB 0.16 MB

1.0 0.04 MB 0.14 MB 0.17 MB 0.09 MB 0.16 MB

LIST OF

LIGHTS

L2 /


(1)

Neg. Foreign

(2)

Positive

(3)

Neg. interior

(4)

Positive

(5)

Neg. interior

0.5 0.02 MB 0.06 MB 0.07 MB 0.03 MB 0.06 MB

0.77 0.031 MB 0.103 MB 0.124 MB 0.062 MB 0.114 MB

0.82 0.033 MB 0.111 MB 0.134 MB 0.07 MB 0.126 MB

0.92 0.037 MB 0.127 MB 0.154 MB 0.08 MB 0.144 MB

1.0 0.04 MB 0.14 MB 0.17 MB 0.09 MB 0.16 MB


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EJEB

ITEM CALCULA

RESULT

L2 (3.8 + 4.2) 4 m

L1

1-2 3.5 m

2-3 4 m

3-4 Three m

L2 /L1

1.14

1.001.33

Mo 1-2 5.22 T * m2-3 7.02 T * m

3-4 3.70 T * m

EXEC

ITEM CALCULA

RESULT

L2 (4.2 + 4.5) 4.35 m

L1

1-2 3.5 m

2-3 4 m

3-4 T

m

L2 /L1

1.24

1.09

1.45

Mo

1-2 5.69 T * m

2-3 7.64 T * m

3-4 4.02 T * m

EJED ITEM Calcul RESULTADO L2 4.5 / 2 2.25 m

L1 1-2 3.5 m2-3 4 m3-4 3m

L2 /L

0.64ne 0.56

0.75

Mo 1-2 2.94 T * m2-3 3.95 T * m3-4 2.08 T * m

LIST OF

LIGHTS

L2 /

MOMENTS INTERMEDIATE BAND HUB 4

(1)

Neg. Foreign

(2)

Positive

(3)

Neg. interior

(4)

Positive

(5)

Neg. interior

0.33 0.013 MB 0.040 MB 0.046 MB 0.020 MB 0.040 MB

0.36 0.014 MB 0.043 MB 0.050 MB 0.022 MB 0.043 MB

0.39 0.016 MB 0.047 MB 0.055 MB 0.023 MB 0.047 MB

0.5 0.02 MB 0.06 MB 0.07 MB 0.03 MB 0.06 MB

To summarize the coefficients and moments calculated for the different bands can be seenin Tables 18 and 19 respectively of this article:

Table 18 Summ ary of coeff ic ients for ca lcu la t ing m oments

COEFFICIENTS FOR INTERMEDIATE BAND

AXIS A-B B-C C-D

Neg. Foreign Positive Neg. interior Positive Neg. interior Positive Neg. Foreign

One 0,018 0,055 0.059 0,025 0,050 0,047 0,016

2 0,040 0,140 0.148 0.077 0,138 0,113 0,033

T

0,037 0,127 0.134 0,070 0.126 0,103 0,031

4 0,016 0,047 0,050 0,022 0,043 0,040 0,013

Table 19 Summary o f in termediate str ip m oments

MOMENTS INTERMEDIATE BAND T * m

AXIS A-B B-C C-D


One 0,049 0,151 0,202 0,086 0,171 0.187 0.064

2 0,235 0.823 1,083 0.564 1,010 0.962 0,281

T

0,203 0.697 0.917 0,479 0,862 0.818 0.246

4 0,038 0,110 0,147 0.064 0.126 0.136 0,044

For the Y axis parallel strips 7, in Tables 20 to calculations made by each strip as regardsrelations between light and calculating the overall time shown.

Figure 7 Cut paral lel to the Y axis beams

Table 20 Relations hips betw een light and calculation o f global mom ents EJEA

ITEM CALCULA

RESULT L2 3.8 / 2 1.9 m

L1

1-2 3.5 m2-3 4 m

3-4 T

m

L2 /L1

0.54

0.480.63

Mo

1-2 2.48 T * m2-3 3.33 T * m3-4 13.76 T * m

Coefficient calculations are performed by linear interpolation formula and global timemoments are determined in each of the intermediate strips such


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as was done in parallel to the axis X, in Tables 21 and 22 slots are displayed in summary and

moments calculated coefficients for each band respectively.

Table 21 Summary of coefficients for calculating moments

COEFFICIENTS FOR INTERMEDIATE BAND

AXIS 1-2 2-3 3-4

Neg. Foreign Positive Neg. interior Positive Neg. interior Positive Neg. Foreign A 0,020 0,060 0,062 0,026 0,053 0.073 0,023

B 0,047 0,095 0,170 0,090 0,160 0.143 0,057

C 0,050 0,110 0,181 0,095 0,170 0,160 0,060

D 0,026 0,078 0.082 0,037 0,072 0,100 0,030

Table 22 Summary o f in termediate str ip m oments

MOMENTS INTERMEDIATE BAND T * m

AXIS 1-2 2-3 3-4


A 0,050 0.149 0.206 0,087 0,176 0,128 0,040

B 0,245 0.496 1,193 0.632 1,123 0.529 0.211

C 0,285 0.626 1,383 0.726 1,299 0.643 0.241

D 0,076 0,229 0.687 0.687 0.687 0,208 0,062

9. METHOD OF FEDERAL DISTRICT(3)

This method is originally based on one by Siess and Newmark, is a method of coefficientslike the method Ing. Romo above, to calculate times medians and edge and to its use must beentered data of spacings between axes and distributed load per square meter and factored.

Error! Figure 8 Core and Edge Strips

It is based on the following equation:

Mri ai * wr * Lx2

(8)


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TIME OF Lesser l ight / greater Light (Lx / Ly)

NEGATIVE EDGE INTERIOR SHORT

1.00 0.90 0.80 0.70 0.60 0.5 0

315 357 403 451 506 568 998

LARGO 297 326 350 372 391 409 516

NEGATIVE EDGE BATCH LARGO 190 206 222 236 248 258 326

POSITIVE SHORT 133 167 202 240 292 329 630

LARGO 129 129 131 133 137 142 179

TIME OF Lesser l ight / greater Light (Lx / Ly )


1.00 0.90 0.80 0.70 0.60 0.5 0

324 371 419 471 530 598 1060

LARGO 324 360 394 429 455 475 6

NEGATIVE EDGE BATCH SHORT 190 219 250 277 321 362 651

LARGO 190 206 222 236 248 258 326

POSITIVE SHORT 137 176 216 259 306 358 751

LARGO 137 138 140 142 146 152 191

Where Lx is the shortest length of the panel analyzed, Ly is the long length, ai is thecoefficient found in the tables of the method and wr is the last distributed load per square meter.

n used in the method andobtain the results of moments, you enter this table with realación of minor / major lights in eachpanel?.

Table 23 Coeff icients for tw o-way slab dropp ed beams

BOARD TIME OF 0 0.5 0.6 0.7 0.8 0.9 One

INTERIOR ALL CONTINUOUS

EDGES NEG. INSIDE EDGE

SHORT 998 553 489 432 381 333 288

LARGO 516 409 391 371 347 320 288

POSITIVE SHORT 630 312 268 228 192 158 126

LARGO 175 139 134 130 128 127 126

SHORT SIDE EDGE BATCH NEG. INSIDE EDGE SHORT 998 568 506 451 403 357 315

LARGO 516 409 391 372 350 326 297

NEG. EDGES DISCONTINUED LARGO 326 258 248 236 222 206 190

POSITIVE SHORT 630 329 292 240 202 167 133

LARGO 179 142 137 133 131 129 129

LONG SIDE EDGE BATCH NEG. INSIDE EDGE SHORT 1060 583 514 453 397 346 297

LARGO 587 465 442 411 379 317 315

NEG. EDGES DISCONTINUED SHORT 651 362 321 283 250 219 190

POSITIVE SHORT 751 334 285 241 202 164 129

LARGO 185 147 142 138 135 134 133

CORNER TWO ADJACENT SIDES

DISCONTINUED

NEG. INSIDE EDGE SHORT 1060 598 530 471 419 371 324

LARGO 6 475 455 429 394 360 324

NEG. EDGES DISCONTINUED SHORT 651 362 321 277 250 219 190

LARGO 326 258 248 236 222 206 190 POSITIVE SHORT 751 358 306 259 216 176 137

LARGO 191 152 146 142 140 138 137

These moments are coefficients for rectangular panels in the central strips of the panels, to theextreme fringes multiply by a factor of 0.6.

For this article the method can be summarized in Table 24 and Figure 9 Slab downstandbeams.

Table 24 Coeff icients metho d Federal Distr ict

Panel type 1 Type 2 Panel

TIME OF Lesser light / greater Light (Lx / Ly)

NEGATIVE SHORT

1.00 0.90 0.80 0.70 0.60 0.5 0

288 333 381 432 489 553 998

LARGO 288 320 347 371 391 409 516

POSITIVE SHORT 126 158 192 228 268 312 630

LARGO 126 127 128 130 134 139 175

3 Panel type Type 4 Panel

TIME OF Lesser l ight / greater Light (Lx / Ly)


1.00 0.90 0.80 0.70 0.60 0.5 0

297 346 397 453 514 583 1060

LARGO 315 317 379 411 442 465 587

NEGATIVE EDGE BATCH LARGO 190 219 250 283 321 362 651

POSITIVE SHORT 129 164 202 241 285 334 751

LARGO 133 134 135 138 142 147 185


15/28

PANEL TIME FEDERAL DISTRICT

2-3-C-D

Mx -0.611

0,288

My -0.554

0.218

3-4-A-B Mx -0.403 0.209

My -0.377

0,133

3-4-B-C

Mx -0.422

0,223

My -0.386

0.13

3-4-C-D

Mx -0,465

0,228

My -0.415

0.136

Panel type 1 Type 2 Panel 3 Panel type Type 4 Panel

Figure 9 Models used by the meth od of th e Federal Distr ict

METHOD FOR APPLYING THIS MUST BE MET THESE LIMITATIONS:

The boards are approximately rectangular.

Load distribution acting on the slab is approximately uniform in each board.

The negative experiences in the common support of two adjacent boards do not differ from

each other in more than 50% of the least of them. The ratio of live load to dead load is not greater than 2.5 for monolithic slabs with their

support, nor greater than 1.5 in other cases.

Results obtained in times per meter panels 9 are proposed exercise in Table 25:

Table 25 Summ ary of mom ents / m calcul ated with the method of the Federal Distr ict

PANEL TIME FEDERAL D ISTRICT

1-2-A-B

Mx -0.466

0,217

My -0.455

0,178

1-2-B-C

Mx -0.491 0.244

My -0.463

0.174

1-2-C-D

Mx -0.556

0.291

My -0.519

0,181

2-3-A-B

Mx -0.433

0,202

My -0.409

0,173

2-3-B-C

Mx -0.522

0.238

My -0.511

0.213

10. MODELING WITH ETABS. (8)

The model used has the following main features:

Columns and beams: cracked stiffness values recommended by the CEC2000, beam-column Knots are used: they are rigid with a length of area equal to half the real,


16/28

Slab: tile compression of 5 cm thick is formed by membrane-like shell elements but with reducedrigidity f11y f22 5%; nerves are rectangular beams 10x15 cm every 50 cm, and bending stiffnessalong the local axis 3 reduced to 50%; geometrically tile is above the nerves.

For this article the following results were obtained by nerve center, to not test all the nervesof each panel has taken the central nerves (Figure 10) and in some cases an average between twonerves located in the center of the panel should remembered that if a nerve parallel to the Y axismoments you will see in the nerve around the axis X and vice versa discussed.

In Figure 11 it can be seen a sketch of the shape of the times nerves.

Central Nerves

Figure 10 Central Nerves

Figure 11 Sketch moment s acting on a slab

In Figure 10 and 11 it should be noted that the horizontal elements which absorb greatermoments are beams structure and therefore in a slab strips not receive both columns time asmedians and the high location of the beams nerves the central part of a slab need larger armed.


17/28

PANEL TIME ETABS

2-3-C-D

Mx-0.472

0,207

My-0.479

0,176

3-4-A-B

Mx-0.316

0.142

My-0.292

0.097

3-4-B-C

Mx-0.33

0.15

My0.303

0,093

3-4-C-D

Mx-0.342

0.163

My-0.326

0,092

Table 26 Summ ary of mom ents / nerve calculated ETABS

PANEL TIME ETABS

1-2-A-B

Mx -0.37

0.143

My -0.35

0.134

1-2-B-C Mx

-0.389

0.156

My -0.366

0,129

1-2-C-D

Mx -0.417

0.18

My -0.396

0,129

2-3-A-B

Mx -0.404

0.158

My -0.414

0,177

2-3-B-C

Mx -0.425

0,157

My -0.438

0,171

11. COMPARISON OF RESULTS

Shown in Table 27 calculated by different methods but in different formats, these formats arespecific methods are now.

Table 27 Moments Design

COMPARISON OF FINDINGS MOMENTS

PANEL TIME ING. ROMO V. RIGIDAS M. DIRECT FEDERAL DISTRICT ETABS

TYPE T * m / m T * m / str ip T * m / str ip T * m / T * m / nerve

1-2-A-B

Mx -1.227 -0.749 -1.433 -0.466 -0.37

0.651 0,433 0.613 0,217 0.143

My -1.102 -0.639 -1.29 -0.455 -0.35

0.533 0.369 0,998 0,178 0.134

1-2-B-C

Mx -1.091 -0.658 -1.433 -0.491 -0.389

0.563 0.434 0.62 0.244 0.156

My -1.04 -0.818 -1.29 -0.463 -0.366

0.467 0.326 0.671 0.174 0,129

1-2-C-D

Mx -1.48 -0.943 -1.336 -0.556 -0.417

0.826 0.556 0.62 0.291 0.18

My -1.093 -0.576 -1.2 -0.519 -0.396

0,459 0,295 1.13 0,181 0,129

2-3-A-B

Mx -1.139 -0.944 -1.433 -0.433 -0.404

0.549 0.385 0.759 0,202 0.158

My -1.014 -0.578 -1.29 -0.409 -0.414

0.48 0.376 0,998 0,173 0,177

2-3-B-C

Mx -1.027 -0.843 -1.433 -0.522 -0.425

0.484 0.388 0.759 0.238 0,157

My -0.961 -0.762 -1.29 -0.511 -0.438

0.422 0.348 0.671 0.213 0,171

2-3-C-D

Mx -1.343 -1.164 -1.336 -0.611 -0.472

0.683 0,495 0.701 0,288 0,207

My -0.985 -0.512 -1.2 -0.554 -0.479

0,398 0.365 1.13 0.218 0,176

3-4-A-B

Mx -1.074 -0.683 -1.349 -0.403 -0.316

0.597 0,405 0.64 0.209 0.142

My -0.806 -0.426 -1.106 -0.377 -0.292

0,344 0.257 0.773 0,133 0.097

3-4-B-C

Mx -0.993 -0.636 -1.349 -0.422 -0.33

0.544 0.41 0.664 0,223 0.15

My -0.785 -0.558 -1.106 -0.386 0.303

0.307 0.221 0.569 0.13 0,093

3-4-C-D

Mx -1.202 -0.825 -1.255 -0,465 -0.342

0.686 0.49 0.664 0,228 0.163

My

-0.774 -0.363 -1.033 -0.415 -0.326

0.282 0.226 0.29 0.136 0,092


18/28

In order to compare the responses is necessary to transform the values to a standard, inthis case this is just the moment nerve, therefore the method of Ing, Romo and the method ofFederal District values obtained are divided by two in rigid for the width of the central strip andagain for 2 (two ribs per meter) beams, in the direct method also to the width of the central strip, butin this case is formed by two central semifranjas ( estimates are about an axis) and then for twohere also, in the case of model values ETABS midribs are used, The results are shown in Table 28.

Table 28 Moments design / web

COMPARISON OF FINDINGS MOMENTS

PANEL TIME ING. ROMO V. RIGIDAS M. DIRECT FEDERAL DISTRICT ETABS

TYPE T * m / nerve T * m / nerve T * m / nerve T * m / nerve T * m / nerve

1-2-A-B

Mx-0.614 -0.197 -0.377 -0.233 -0.370

0.326 0.114 0.161 0.109 0.143

My-0.551 -0.183 -0.369 -0.228 -0.350

0.267 0,105 0,285 0.089 0.134

1-2-B-C

Mx-0.546 -0.157 -0.341 -0.246 -0.389

0.282 0,103 0.148 0,122 0.156

My-0.520 -0.234 -0.369 -0.232 -0.366

0.234 0,093 0,192 0,087 0,129

1-2-C-D

Mx-0.740 -0.210 -0.297 -0.278 -0.4170.413 0,124 0,138 0,146 0,180

My-0.547 -0.165 -0.343 -0.260 -0.396

0,230 0.084 0.323 0.091 0,129

2-3-A-B

Mx-0.570 -0.248 -0.377 -0.217 -0.404

0,275 0.101 0,200 0.101 0.158

My-0.507 -0.145 -0.323 -0.205 -0.414

0,240 0.094 0,250 0,087 0,177

2-3-B-C

Mx-0.514 -0.201 -0.341 -0.261 -0.425

0,242 0,092 0,181 0.119 0,157

My-0.481 -0.191 -0.323 -0.256 -0.438

0.211 0,087 0,168 0,107 0,171

2-3-C-D

Mx-0.672 -0.259 -0.297 -0.306 -0.472

0.342 0,110 0.156 0,144 0,207My

-0.493 -0.128 -0.300 -0.277 -0.479

0,199 0.091 0.283 0.109 0,176

3-4-A-B

Mx-0.537 -0.180 -0.355 -0.202 -0.316

0.299 0,107 0,168 0,105 0.142

My-0.403 -0.142 -0.369 -0.189 -0.292

0,172 0,086 0.258 0,067 0.097

3-4-B-C

Mx-0.497 -0.151 -0.321 -0.211 -0.330

0.272 0.098 0.158 0.112 0,150

My-0.393 -0.186 -0.369 -0.193 0.303

0.154 0,074 0,190 0,065 0,093

3-4-C-D

Mx-0.601 -0.183 -0.279 -0.233 -0.342

0,343 0.109 0.148 0.114 0.163

My

-0.387 -0.121 -0.344 -0.208 -0.326

0,141 0,075 0.097 0,068 0,092


19/28

12. ANALYSIS OF RESULTS

Analyzing a lightened slab type 20 cm thick M. Romo, beams Rigid, Direct Method, Methodof Mexico City and ETABS model to compare the results was performed Ing methods were used..

TOTAL RESULTS OF ARTICLE

- The method of Ing. M. Romo gives thehighest values are 58% higher than theresults obtained with ETABS.

- The method of rigid beams gives lower valuesin 42% of those obtained with ETABS.

- The Direct Method gives similar values 7%more than those obtained with ETABS.

- The method gives lower values DistritoFederal 34% of those obtained with ETABS.

160

140

120

100

80

60

40

20

% TOTAL WITH RESPECT TO ETABS

0

ING. ROMO M. V. HARD LIVE DISTRICTFEDERAL ETABS

NEGATIVE RESULTS OF ARTICLE TOTALTIME AROUND THE SHAFT AND

- The method of Ing. M. Romo gives thehighest values, 29% more than the resultsobtained with ETABS.

- The method of rigid beams gives lower valuesby 54% of those obtained with ETABS.

- The Direct Method gives values 20% lowerthan those obtained with ETABS.

- The method gives values of the Federal

District39% smaller than those produced by ETABS.

140

120

100

80

60

40

20

% TIME AND NEGATIVE WITH RESPECT TO ETABS

0

ING. ROMO V. RIGIDAS M.

DIRECT

FEDERAL

DISTRICT

ETABS

TOTAL TIME POSITIVE RESULTS OF ARTICLE AROUND THE SHAFT AND

- The method Ing.M. Romo gives values 58%higher than the moments obtained withETABS.

- The method of rigid beams gives lowervalues in 31% of those obtained with

ETABS.- The Direct Method gives the values 73%

higher than those obtained with ETABS.- The method gives the Federal District

values lower by 35% than those obtainedwith ETABS.

180

160

140

120

100

80

60

40

20

% TIME AND POSITIVE RELATIONSHIP WITH A ETABS

0

ING. ROMO M. V. HARD LIVE DISTRICT

FEDERAL

ETABS


20/28

NEGATIVE RESULTS OF ARTICLE TOTALTIME AROUND THE SHAFT X

- The method of Ing. M. Romo gives thehighest values are higher by 54% to theresults obtained with ETABS.

- The method of rigid beams gives lowervalues in 48% of those obtained withETABS.

- The Direct Method gives values 18% lessthan those obtained with ETABS.


160

140

120

100

80

60

40

20

% X NEGATIVE MOMENT WITH RESPECT TO ETABS

0


FEDERAL

ETABS

TOTAL TIME POSITIVE RESULTS OF ARTICLE AROUND THE SHAFT X

- The method of Ing. M. Romo gives highervalues by 92% to the results obtained withETABS.

- The method of rigid beams gives lowervalues by 34% to those obtained withETABS.

- The Direct Method gives the values 6%lower than those obtained with ETABS.

- The method of the Federal District giveslower values by 26% to those obtained withETABS.

200

180

160

140

120

100

80

60

40

20

% TIME RELATIONSHIP WITH A POSITIVE X ETABS

0

ING. ROMO M. V. HARD LIVE DISTRICTFEDERAL

ETABS

CORNER PANELS NEGATIVE RESULTSTIME AROUND THE SHAFT AND

- The method of Ing. M. Romo gives highervalues 34% higher than the results obtainedwith ETABS.




140

120

100

80

60

40

20

% TIME AND NEGATIVE IN CORNER PANEL

0


FEDERAL

ETABS


21/28

CORNER PANELS POSITIVE RESULTSTIME AROUND THE SHAFT AND

- The method of Engineer, M, Romogives values 34% more thanthe moments obtained with ETABS.

- The method of rigid beams giveslower values in 59% of those obtainedwith ETABS.

- The Direct Method gives values 21%lower than those obtained withETABS.

- The method gives lower valuesDistrito Federal 39% of thoseobtained with ETABS.

250

200

150

100

50

0

% TIME AND POSITIVE IN CORNER PANEL


FEDERAL

ETABS

NEGATIVE RESULTS PANELS TIME AROUND CORNER AXIS X

- The method of Ing. M. Romo gives thehighest values, 65% more than themoments obtained with ETABS.

- The method of rigid beams gives lowervalues by 45% of those obtained withETABS.

- The Direct Method gives values 20%lower than those obtained with ETABS.

- The method gives lower values DistritoFederal 37% of those obtained withETABS.

180

160

140

120

100

80

60

40

20

0

% X NEGATIVE MOMENT CORNER PANEL


ETABS

POSITIVE RESULTS PANELS TIME AROUNDCORNER AXIS X


- The method gives lower values rigidbeams 30% of those obtained withETABS.



250

200

150

100

50

0

% TIME X POSITIVE IN CORNER PANEL


FEDERAL

ETABS


22/28

INTERIM RESULTS WHICH SIDE PANELS OUTSIDE GREATER IS PARALLEL TO THE AXIS X

NEGATIVE TIME AROUND THE SHAFT AND





140

120

100

80

60

40

20

0

% TIME AND NEGATIVE IN OUTER PANEL


FEDERAL

ETABS


POSITIVE TIME AROUND THE SHAFT AND



- The Direct Method gives higher values 44% higher than those obtainedwith ETABS.


160

140

120

100

80

60

40

20

% TIME AND POSITIVE IN OUTER PANEL

0


FEDERAL

ETABS


NEGATIVE TIME AROUND THE SHAFT X




- The method gives the FederalDistrict

values below 36% of those obtained withETABS.

160

140

120

100

80

60

40

20

% X NEGATIVE TIME IN OUTER PANEL

0


FEDERAL

ETABS


23/28


POSITIVE TIME AROUND THE SHAFT X





180

160

140

120

100

80

60

40

20

% X POSITIVE MOMENT IN OUTER PANEL

0


FEDERAL

ETABS

INTERIM RESULTS EXTERIOR PANELS UNDER WHOSE SIDE IS PARALLEL TO THE AXIS

XNEGATIVE TIME AROUND THE SHAFT AND




- The method gives lower values DistritoFederal 51% of those obtained with

ETABS.

140

120

100

80

60

40

% TIME AND NEGATIVE IN OUTER PANEL

20

0


ETABS

INTERIM RESULTS EXTERIOR PANELS UNDER WHOSE SIDE IS PARALLEL TO THE AXISX

POSITIVE TIME AROUND THE SHAFT AND



- The Direct Method gives higher values 16% more than those obtained withETABS.


140

120

100

80

60

40

20

% TIME AND POSITIVE IN OUTER PANEL

0


ETABS


24/28

- The method of Ing. M. Romo gives thehigher values, 10% more than the 120ETABS times obtained.

- The method of rigid beams gives values 100

under 57% of those obtained with

40

INTERIM RESULTS EXTERIOR PANELS UNDER WHOSE SIDE IS PARALLEL TO THE AXISX

NEGATIVE TIME AROUND THE SHAFT X





160

140

120

100

80

60

40

% X NEGATIVE TIME IN OUTER PANEL

20

0


FEDERAL

ETABS

INTERIM RESULTS EXTERIOR PANELS UNDER WHOSE SIDE IS PARALLEL TO THE AXIS

X

POSITIVE TIME AROUND THE SHAFT X



- The Direct Method gives higher values by5% more than those obtained with ETABS.

- The method gives lower values Distrito

Federal 36% of those obtained with ETABS.

180

160

140

120

100

80

60

40

20

% X POSITIVE MOMENT IN OUTER PANEL

0


FEDERAL

ETABS

RESULTS CENTRAL PANELS

NEGATIVE TIME AROUND THE SHAFT AND

% TIME AND NEGATIVE IN CENTRAL PANEL

ETABS. 80 - The Direct Method gives values 38% less than

those obtained with ETABS.60

- The method gives the Federal Districtvalues below 42% of those obtained withETABS.

20

0


ETABS


25/28

POSITIVE RESULTS PANELS CENTRALTIME AROUND THE SHAFT AND




- The method gives the Federal Districtvalues below 38% of those obtained withETABS.

140

120

100

80

60

40

% TIME AND POSITIVE IN CENTRAL PANEL

20

0


ETABS

POWER PANELS NEGATIVE RESULTS

TIME AROUND THE SHAFT X





140

120

100

80

60

40

% X NEGATIVE IN CENTRAL TIME PANEL

20

0


ETABS

POSITIVE RESULTS PANELS CENTRALTIME AROUND THE SHAFT X





160

140

120

100

80

60

40

20

% X POSITIVE IN CENTRAL TIME PANEL

0


ETABS


26/28

mi

2

13. CALCULATION OF ARMOR. (2)

Already obtained the design time by different methods and with them the next step is tocalculate the armor of the slab, some authors differ in the methods of conception of nerves, somesee them as beams, fifura 12 and consider the contribution the tile compression, others simply workwith nerves as rectangular beams, the aim of this article is not compare these forms of calculationbut interesting show armor for the proposed exercise, it then uses the values obtained with the

method of lng. Marcelo Romo. Which are the highest values obtained and designed considering theslab below the nerves as beams and calculation is based on the ACI 318 indicating beams analysisand the results are shown in Table 29.

As CALCULATION OF UPPER AND LOWER minimum Effective height of the slab (d)

=

Figure 12 Equiv alent B eam T

d = 20 - 2 to 1.2 / 2 = 17.4 cm

As MINIMUM TOP

210 2 AceOne 0.8 *

Ace2 1.6*

4200

210

4200

100 * 17.4 * 4,803cm

17.4 * 20 * 1,921cm2 2

AceTh

ree

14

420017.4 * 20 * 1.16 cm2

SUPERIOR Asmin = 1,921 cm Acemin SUP / NERVE = 1,921 / 2 = 0.9605 cm

As MINIMUM BOTTOM

210 2 AceOne 0.8 *

144200

17.4 * 20 * 0.961 cm

2

AceTh

ree4200

17.4 * 20 * 1.16 cm

Ace BOTTOM = 1.16 cm2 2

Asmin INF / NERVE = 1.16 / 2 = 0.58 cm

Table 29 Calculation Of A rmo r

Panel Moo B P Ace As min Def As (cm2) As / nerve

nerve

1-2-A-BMx

1227 20 0.00575 2,001 1,921 2,001 1,001 120.651 100 0.00057 0.996 1.16 1.16 0.58 10


27/28

My1102 20 0.00512 1,783 1,921 1,921 0.9605 120.533 100 0.00046 0.815 1.16 1.16 0.58 10

1-2-B-C

Mx1091 20 0.00507 1,764 1,921 1,921 0.9605 120.563 100 0.00049 0,861 1.16 1.16 0.58 10

My1040 20 0.00482 1,676 1,921 1,921 0.9605 120.467 100 0.00041 0.713 1.16 1.16 0.58 10

1-2-C-D

Mx-1.48 20 0.00705 2,454 1,921 2,454 1,227 140.826 100 0.00073 1,267 1.16 1,267 0.6335 10

My1093 20 0.00508 1,767 1,921 1,921 0.9605 120.459 100 0.00040 0.701 1.16 1.16 0.58 10

2-3-A-B

Mx1139 20 0.00531 1,847 1,921 1,921 0.9605 120.549 100 0.00048 0.839 1.16 1.16 0.58 10

My1014 20 0.00469 1,632 1,921 1,921 0.9605 120.48 100 0.00042 0.733 1.16 1.16 0.58 10

2-3-B-C

Mx1027 20 0.00475 1,654 1,921 1,921 0.9605 120.484 100 0.00043 0.74 1.16 1.16 0.58 10

My-0961 20 0.00443 1,541 1,921 1,921 0.9605 12

0.422 100 0.00037 0.644 1.16 1.16 0.58 10

2-3-C-D

Mx1343 20 0.00634 2,206 1,921 2,206 1,103 120.683 100 0.00060 1,046 1.16 1.16 0.58 10

My-0985 20 0.00455 1,582 1,921 1,921 0.9605 120.398 100 0.000 0.947 1.16 1.16 0.58 10

3-4-A-B

Mx1074 20 0.00498 1,735 1,921 1,921 0.9605 120.597 100 0.00052 0.913 1.16 1.16 0.58 10

My-0806 20 0.00368 1,281 1,921 1,921 0.9605 120.344 100 0.00030 0,525 1.16 1.16 0.58 10

3-4-B-C

Mx-0993 20 0.00459 1,596 1,921 1,921 0.9605 120.544 100 0.00048 0.832 1.16 1.16 0.58 10

My

-0785 20 0.00358 1,246 1,921 1,921 0.9605 120.307 100 0.00027 0.468 1.16 1.16 0.58 10

3-4-C-D

Mx1202 20 0.00562 1,957 1,921 1,957 0.9785 120.686 100 0.00060 1.05 1.16 1.16 0.58 10

My-0774 20 0.00353 1,228 1,921 1,921 0.9605 120.282 100 0.00025 0,430 1.16 1.16 0.58 10

13.CONCLUSIONES,

Analysis of a slab lightened bidirectional type 20 cms thick M. Romo, beams Rigid, Direct Method,the Method Federal district and ETABS model was performed Ing methods were used. To compareresults.

- The method of Ing. M. Romo gives the highest values in relation to negative moments.- The Direct Method gives lower values than in the negative moments in 18-20% of those

obtained with ETABS.- The rigid beams method gives results in minor negative moments in 54-48% of those

obtained with ETABS.- The method gives results in Distrito Federal minor negative moments in 26-35% of those

obtained with ETABS.


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- Variations in the positive moments are considerable between the methods discussed butremember that are much smaller than the negative moments.

- The results obtained with ETABS results show conservative but not so far from the othermethods such as the Ing. Romo.

- Other methods for the analysis and design of two-way slabs but the results ETABS usercan be sure that if you use the model proposed in this paper the results will be reliable.

- The direct method is a good alternative for manual calculation and whether to use amethod of coefficients Method Engineer Romo is a good choice.

- Importantly, the armed resulting from using any of these methods in this article almostentirely minimal assembly, expressed in rods ø12 to ø10 negative arming and for thepositive.

REFERENCES

1. Colombian Association of Earthquake Engineering, Colombian standards for EarthquakeResistant Design and Construction NSR-98, Volume 2, 1998.

2. ACI Committee 318, Building Code Requirements for Structural Concrete (ACI 318M-02) andCommentary (ACI 318RM-02), ACI International, 2002.

3. Cuevas González - Robles, Fundamentals of Reinforced Concrete, Limusa Noriega Editores,1996.

4. INEN, Ecuadorian Code of Practice, CPE INEN5: 2001 Part 1, Chapter 12, INEN, 2001.5. Arthur Nilson, Design of Concrete Structures, McGraw Hill, 1999.6. Parker - Ambrose, Simplified Reinforced Concrete Design, Limusa Wiley, 2003.7. Marcelo Romo, Stitching Concrete, ESPE, 1995.8. Manuals ETABS Nonlinear Version 8.26, CSI Computers and Structures.9. Http // www.Inti.gov.ar / CIRSOC / complementary / chapter 19.pdf
http://www.inti.gov.ar/http://www.inti.gov.ar/

analysis of slab by different methods

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