A PARAMETRIC STUDY OF CONCRETE SLAB SYSTEM DESIGN

by

PHILLIP TERRELL NASH, B.S. in C.E.

A THESIS

IN

CIVIL ENGINEERING

Submitted to the Graduate Faculty of Texas Tech University in

Partial Fulfillment of the Requirements for

the Degree of

MASTER OF SCIENCE

IN

CIVIL ENGINEERING

Approved

décember, 1972

AC

- - p / / ,

/l5H-^7íí.

ACKNOWLEDGMENTS

I am very grateful to Dr. James R. McDonald for his

guidance in the preparation of this thesis and to the

other members of my committee, Drs. Kishor Mehta and J. H

Smith, for t:heir helpful advice.

11

CONTENTS

ACKNOWLEDGMENTS ii

LIST OF FIGURES iv

I. INTRODUCTION 1

II. METHODOLOGY FOR DEVELOPMENT OF DESIGN GUIDELINES 2

Objectives 2

Parameters Considered 4

Chart Description 7

Computer Analysis 9

III. PROCEDURE 12

Frame Dimensions 12

Chart Production 13

Nondimensional Parameter Values 16

IV. USE OF THE CHARTS 29

Introduction 29

Comparison of Various Frame Dimensions 29

Insight into Choosing Slab System

Types 30

Examples 32

V. COMMENTARY ON THE USE OF THE DESIGN GUIDELINES 37 BIBLIOGRAPHY 39

111

LIST OF FIGURES

Figure Page

1. Typical Interior Frame 5

2. Frame Used For Analysis 8

3. A Typical Design Chart h,/h = 0.25, <^ = 0.0 10

4. Drop Panel Cross Section 14

5. Moment Diagram for a Uniformly Loaded

Member with Nonvarying Cross Section 17

6. Design Chart h./h = 0.25, ° = 0.0 19

7. Design Chart h^/h = 0.25, ° = 0.25 20

8. Design Chart h,/h = 0.25, «: = 0.50 21

9. Design Chart h^/h = 0.25, <^ = 0.75 22

10. Design Chart h./h = 0.25, «: = 1.0 23

11. Design Chart h^/h = 0.50, o = 0.0 24

12. Design Chart h^/h = 0.50, °c = 0.25 25

13. Design Chart h^/h = 0.50, < = 0.50 26

14. Design Chart h^/h = 0.50, « = 0.75 27

15. Design Chart h^/h = 0.50, °: = 1.0 28

IV

CHAPTER I

INTRODUCTION

Current methods of analysis and reliable past perfor-

mances have helped to make concrete slab systems practical

elements of structural design. The structural designer is

free to choose from several types of slab systems. The

choice of a flat slab, one-way or two-way slab depends upon

the conditions of the design. Often the design conditions

are not set and the designer has to determine the most prac-

tical design from among numerous possibilities. The de-

signer must consider the economy of the design as well as

the ease of analysis. Slab system designs based on the

designer's capabilities rather than logical material use

are both impractical and uneconomical. Thus, the designer

finds himself faced with the problem of determining the most

efficient slab design from among several types with a count-

less niomber of possible dimension parameters. The purpose

of this paper is to present a set of design aids which will

allow the designer to make quick comparisons of slab systems

in order to achieve maximum efficiency in his design. The

material presented is not meant to be a substitute for

slab analysis, but simply an aid to choosing the type of

slab system and efficient dimensional parameters.

CHAPTER II

METHODOLOGY FOR DEVELOPMENT OF DESIGN GUIDELINES

Objectives

Any procedure for aiding slab system design must be

efficient, comprehensive, general, simple, and accurate.

Designers are interested in methods that will help optimize

design yet be practical enough for office work. Sophisti-

cated design procedures of a highly analytical hature might

be helpful in solving difficult problems, but are worthless

unless usable to the designer.

Slab system designs are usually governed by economy.

An efficient design uses the least amount oî material to

the best advantage. Therefore, a good design aid helps the

designer choose the most efficient slab system. The Ameri-

can Concrete Institute building code requirements limit

dimensions of slab systems according to panel span ratios,

slab thicknesses, drop panel dimensions deflections, and

various other parameters. The method presented for choos-

ing slab system dimensions will be within the boundaries

set by the 1971 ACI code, but is not intended to replace

the guidelines of the code. After the parameters of a slab

system have been chosen, the analysis and design must be

Building Code Requirements for Reinforced Concrete (ACI :i8-71), Detroit, Michigan, pp. 27-28, 46-47.

carried out within the specifications of the current ACI

code. The objective of the proposed design aids is merely

to help the designer choose system dimensions for a slab

system.

Optimizing slab system design is greatly complicated

by the number of variable parameters of the system. To say

that a particular design is the ultimate of efficiency is

virtually impossible. The purpose of the proposed design

aids is to help the designer compare different combinations

of slab system geometry, types, and dimensions. Perhaps an

optimum design cannot be obtained. But if the designer can

increase the efficiency of his design by narrowing the possi-

bilities of slab systems through comparison, then the pur-

pose of the design aids has been accomplished.

The design aid must encompass slab systems in general

if it allows a comparison of the various systems. The 1971

ACI code has attempted to generalize the design of different

slab system types. The Equivalent Frame method introduced 2

is used for analysis of the generalized slab systems. The

Equivalent Frame method is applicable to flat slabs, slabs

with supporting beams, slabs with drop panels, and column

capitals. The design aids presented in this paper were

2 Building Code Requirements for Reinforced Concrete

(ACI 318-71), pp. 49-51.

developed using the Equivalent Frame method of analysis and

are intended to be of an equally general natiire.

Rigorous, complicated analysis can be used to match

designs with given situations, but the engineer is interested

in solving the problem as efficiently as possible without

laboring through complicated theory. The methods developed

in this paper are aimed at helping the designer to make

quick, simple comparisons without becoming bogged down in

highly analytical considerations. Use of the proposed de-

sign aids may be carried out in the design office and is

easily accomplished. However simple and complete the pro-

posed method is, above all it should be accurate. The effi-

ciency of the design is governed by the accuracy of the

results.

Parameters Considered

The proposed method for aiding the design of slab sys-

tems will follow the 1971 ACI code. The parameters to be 3

considered are shown in Figure 1 and are given below.

hj - projection of drop panel below slab

h - slab thickness

L^ - drop panel length

L - length of span in direction of moments, measured

center to center of supports

3 Building Code Requirements for Reinforced Concrete

(ACI 318-71), pp. 45-46.

ir

r.5

^

k-^ r

S 1 ÚL L

^d

r n U J

u

^

~1 1

J

I 1

1. J '

I I

^

Jtl

J^

t ± h

T h.

I

T

Figure 1. Typical Interior Frame

E

L^ - length of span transverse to L^, measured center

to center of panels

C^ - cross width of drop panels measured transversely

to L^

" - ratio of flexural stiffness of beam section to

the flexural stiffness of a width of slab bounded

laterally by the center line of the adjacent

panel, if any, on each side of the beam

. - modulus of elasticity for beam concrete

I, - moment of inertia about centroidal axis of gross

section of a beam as defined in Section 13.1.5

of ACI Building Code Requirements

E - modulus of elasticity for slab concrete cs -^

I - moment of inertia about centroidal axis of gross

section of slab

In order to make the design aid general, the parameters

considered were nondimensionalized according to relationships

with other parameters. The first major subdivision consid-

ered was the ratio of drop panel thickness to slab thickness,

h,/h, which directly relates the stiffness of the drop panel

to the stiffness of the slab. Values of °c are nondimen-

sional and were used as the next subdivision because they,

too, are indicative of relative stiffnesses. The drop panel

sizes were nondimensionalized according to cross sectional

properties affecting the stiffness of the drop panel. Vari-

ous length-width ratios, L./C^, for drop panels were

considered.

Finally, the drop panel length, L,, and the cross

span width, L^, were related to the span length, L, by

ratios of L./L, and L^/L,.

Chart Description

Optimum design charts were constructed for the given

nondimensionalized parameters. The optimum or most effi-

cient design for a slab system would be that which balances

the value of maximum positive moment with the negative

moment at the face of the drop panel. The balanced condi-

tion assures the most efficient use of the depth of the

slab. Each of the. given parameters affects the distribution

of the design moments. A typical interior frame with vari-

able dimensions of C^, L,, L^, as shown in Figure 2, was ana-

lyzed by the Equivalent Frame method until the parameters

were such that the maximum positive design moment was equal

to the maximum negative moment in the slab as distributed 4

along the middle strip of the frame. Graphical plots were

made for the different parameters to develop charts

^Building Code Requirements for Reinforced Concrete (ACI 318-71), pp. 46, 48.

8

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similar to the one shown in Figure 3. Groups of charts were

developed for drop panel-slab thickness ratios, h^/h. For

each drop panel-slab thickness ratio, charts were developed

for different support beam-slab stiffness ratios, «. Each

chart is a plot of the value of the drop panel-slab length

ratio, L^/L,, which results in an optimum design for a given

slab span width-length ratio, L^/L,. Various drop panel

length-width ratios, L^/C^, are plotted on each chart.

Computer Analysis

The Equivalent Frame Method of analysis for the devel-

opment of the charts was carried out by use of a digital

computer. A base program was written for the general anal-

ysis of concrete frames. A modified version of the program

was used for the specific purpose of generating the design

charts. The base program was a stiffness analysis for con-

crete f rames. The frames analyzed were equivalent frcimes 5

developed according to the 1971 ACI code. The program

developed the stiffness properties of the frame members ac-

cording to the gross concrete cross sectional areas of the

members. Nodal points were placed so that all members of

the frame were prismatic. Drop panels were considered as

independent members for the formulation of the stiffness

matrix. The torsional stiffnesses at the column-slab

5 Moshe F. Rubinstein, Matrix Computer Analysis of

Structures (Englewood Cliffs, N. J., 1966), pp. 224-238.

10

h^/h =0.25

— ' •• •'•• L ^ / L ^

Figure 3. A Typical Design Chart, <^ = 0,0

11

joints were added to the stiffness matrix. The frames were

analyzed by matrix methods. The modified program used the

same method of analysis but varied the drop panel-span

length ratio, L,/L,, and compared maximum positive and

negative moments for the middle strip section of the frame

shown in Figure 2. Optimum drop panel-span length ratios,

Lj/L,, were found by the moment comparisons. Various slab

width-length ratios, L^/L^, were considered by iterations

of the program. The design charts were plotted from the

oiitput of the modified program.

CHAPTER III

PROCEDURE

Frame Dimensions

The typical interior frame shown in Figure 2 was ana-

lyzed and considered representative of the majority of

design cases. Joints 1 and 21 of the frame in Figure 2

represent typical slab-column joints- which have been re-

placed by fixed ends because of the negligible effect of

remote end conditions on interior bay moments. Points of

maximum slab moments for the symmetrically loaded frame of

Figure 2 occur at midspan and at the slab-drop panel inter-

face. Maximum moment points at joints 10 and 11 will be

used for comparison.

Column cross sectional dimensions for each analysis

were set at thirty inches square as a standard. The purpose

of the frame analysis was to compare the slab moments.

Since the rotation of the slab-column joints was negligible,

the stiffnesses of the columns were not critical. The

column heights were set at ten feet. All columns were fixed

ended at the base. A single story frame was analyzed and

used for developing the design charts. Additional stiffness

at the slab-column joints would be found for multistoried

frames. The additional stiffnesses due to the added columns

would have negligible effects on the slab moments because

12

13

the interior slab-column joints of the symmetrical frame

londergo virtually no rotation.

The cross section of the drop panels used for the frame

analysis is shown in Figure 4. In order to keep the frame

analysis general in nature, the dimensions were read into

the computer program as nondimensionalized parameters.

Drop panel stiffnesses were computed from given drop panel-

slab thickness ratios, h./h, drop panel length-width ratios,

Lj/C^, and slab span width-length ratios, L^/L,.

The cross sectional area properties of the slab sec-

tions had to be computed and entered into the data of the

computer program. Slabs with and without supporting beams

were considered. The slab thickness was in all cases set

at ten inches. When the analysis was done for a slab with

a support beam, the beam dimensions were a width of ten

inches and the height necessary to obtain the stiffness

ratio, <=", desired. Slab span width-length ratios, L^/L, ,

of 0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 1.8 and 2.0,

were used to produce the charts. With the span length, L^,

set at twenty feet, the cross sectional properties of the

slab were computed for each case and entered into the data

of the computer program.

Chart Production

The actual balancing of the maximum negative and posi-

tive slab moments was done in three steps:

k

^-"2 -^

i

Figure 4. Drop Panel Cross Section

14

-ii h

^ d

r*- r*-

;L5

1. Set nondimensional parameter values h,/h, L^/C^

«, and L^/L^ to be used in the frame analysis.

2. Adjust drop panel and slab stiffnesses while ana-

lyzing the frame by incrementing the drop panel lengths.

3. Determine the drop panel-slab span length ratio,

Lj/L^, corresponding to the optimum moment distribution.

By setting the nondimensional parameter values and

assuming a drop panel length, the entire frame geometry

and dimensions were generated and the analysis was made for

a unit load of one kip per lineal foot. The maximum nega-

tive and positive slab moments were multiplied by their

appropriate middle strip distribution factors. The two

distributed moments were then compared by a ratio of maxi-

mum positive to maximum negative values. A ratio of one

corresponded to the optimum distribution. The parameter

values producing the optimum distribution for a given slab

span width-length ratio, L^/L,, were plotted to form the

design charts as shown in Figure 3.

The middle strip distribution factors used in the com-

puter analysis were determined from a linear interpolation

of the tables in sections 13.3.4.1 and 13.3.4.3 of the 1971

ACI code. Distribution factors relating to various slab

span width-length ratios, L^/L^, and support beam-slab

stiffness ratios, <^, were found.

Building Code Requirements for Reinforced Concrete (ACI 318-71), pp. 47-48.

16

The computer program was set up to vary drop panel

lengths, L,, which would also vary drop panel widths, Cjt

for each analysis. By incrementing drop panel dimensions

over a range of values, it was possible to determine the

drop panel length producing an optimum design moment distri-

bution for a given combination of drop panel and slab param-

eters. For a uniformly loaded prismatic beam the moment

diagram is of the form shown in Figure 5. The location of

the point where the negative moment value is equal to the

positive moment value is at a distance x equal to 0.0942L.

A drop panel-slab span length ratio, L,/L^, of 0.1884 corre-

sponds to the location of the negative moment value equal

to the maximum positive moment. A smaller drop panel-slab

span length ratio was anticipated because of the additional

stiffness of the drop panel to the slab system. In order

to find optimum lengths, drop panels were incremented fror.

0.03L, to the length necessary for optimum design. Frame

analyses were made for each drop panel length increment of

O.OIL^.

Nondimensional Parameter Values

According to the 1971 ACI code, for slab systems with-

out support beams having drop panel-slab thickness ratios,

h,/h, of 0.25 and sufficiently long drop panels, the slab a

deflections are decreased sufficiently enough to reduce the

17

wL'

e H Figure 5. Moment Diagram for a

Uniformly Loaded Member with Nonvarying Cross Section

'18

thickness of the slab. Drop panels are usually designed

with a thickness of from 0.25 to 0.5 the thickness of the g

slab. Design charts were developed for drop panel-slab

thickness ratios of 0.25 and 0.5. In order to make inter-

polation easier, charts were developed for values of support

beam-slab stiffness ratios, <^, equal to 0.0, 0.25, 0.5, 0.75,

and 1.0. Drop panel length-width ratios, L^/C^, or 0.75,

1.0, and 1.25 were plotted, but followed the same pattern

as can be seen in Figures 6-15. The charts in Figures 6

- 15 are the results of the analyses of the various frames

with different combinations of parametric values and are

intended to aid the designer in his choice of slab systems.

•7

Building Code Requirements for Reinforced Concrete (ACI 317-71), p. 28.

o George Winter, L. C. Urquhart, C. E. O'Rourke, and

Arthur H. Nilson, Design of Concrete Structures (New York, 1968), p. 208.

19

^d/^l

. 20

0 . 1 5

0 .10 i^. ^,

0 . 0 5

h ^ / h = 0 . 2 5

V ^ 2 = °-^5

V ^ 2 = +-0

- L •^A

VC2 = 1.25

0 . 0 2 ( ••^•i'nJMTMrTi.-^ %rT v-^^*-i f — • ni •<in« iw y « * ^ T ^ < r « ^ i W w i ^ w ^ * ^ «

L^/L^

0 . 2 0 . 5 1.0 1.5 2 . 0

F i g u r e 6 . Des ign C h a r t , QC = 0 .0

h ^ / h = 0 . 2 5

20

L^/L^

0 .20

0 . 1 5

0 .10

L . /Co = 0.7ÎI

0.05

0.02 i 0.'2

jTn.mtnm

1.25

0.5 1.0 1.5 2.0 L^/L^

Figure 7. Design Chart, <=^ =0.25

21

h^/h =0.25

0.10

0.05

0.02 0.2 0.5 1.0 1.5 2.0

Figure 8. Design Chart, « 0.50

L^/L^

22

^d/h 0 . 2 0

0 . 1 5

h ^ / h = 0 .25

L^/C2 = 1.0

I .

^ < - ; ^

.^1>''-^ L , / C ^ != 0 . 7 5 ^

0 .10 d^ 2 I - > - ^ i

0 . 0 5

0 .02 \ • IW I 11« É<«<WIW * •

1.0 1.5 2 . 0 L^/L^

Figure 9. Design Chart, oc =0.75

23

^d/^l 0.20

0.15

0.10

h^h 0.25

L^/bo =1.0

V^2 r ^''^^->

0.05

0.02

—I

1.25

0.2 0.5 1.0 1.5 2.0

Figure 10. Design Chart, o = 1.0

L^/L^

24

0.10

0.05

h^/h =0.50

0.02 L^/L^

0.2 0.5 1.0 1.5 2.0

Figure 11. Design Chart, °c = 0.0

25

h^/h =0.50

0.10

0.05

0.02 0.2 0.5 1.0 1.5 2.0

Figure 12. Design Chart, <=^ = 0.25

L^/L, - 2 1

h^/h =0.50

26

0.10 :

0.05

0.02 L 0.2

L^/L^

0.5 1.0 1.5 2.0

Figure 13. Design Chart, '^ = 0.50

27

h^A = 0.50

L^/L^

0.20

0.15

L^/C2 ^

0.10

0.75

./C^ =1.0 c' 2

L./Co = 1.25

0.05

0.02 i L^/L^

0.2 0.5 1.0 1.5 2.0

Figure 14. Design Chart, ^ = 0.75

28

h^/h =0.50

0.10

0.05

0.02 L^/L^

0.2 0.5 1.0 1.5 2.0

Figure 15. Design Chart, ° = 1.0

CHAPTER IV

USE OF THE CHARTS

Introduction

The charts shown in Figures 6-15 are specifically

designed to be used when certain parameters such as frame

geometry or member dimensions are prescribed for a slab

system. By knowing the previously set parameters of a slab

system, the designer is able to use the charts to decide

what combinations of other parameters would result in the

most economical design. If the design is not governed by

previously set dimensions, the designer is able to use the

charts along with his judgement to decide upon such things

as column spacing, drop panel dimensions, and slab support

beam sizes. The charts offer a means of slab system choices

based on logic rather than convenience or guesswork.

Comparison of Various Frame Dimensions

The design charts are very well adapted for selecting

various slab dimensions based on given dimensions of the

concrete frame. The designer can make a quick comparison

of the amount of material to be used by following the given

steps:

1. Arbitrarily select drop panel-slab thickness ratio,

h,/h, support beam-slab stiffness ratio, <=^, and slab span

29

30

width-length ratio, L^/L^, based on loading conditions,

allowable deflections, and ACI code requirements.

2. Determine drop panel size necessary for optimum

design from the charts of Figures 6-15.

3. Calculate the amount of material required for the

chosen design.

4. Repeat steps 1 - 3 until the most economical design

is obtained by comparing various trial dimensions.

5. Check the chosen frame design by analysis or use

the Direct Design Method.

For many design cases, a number of the frame dimensions

are set according to the nature of the building. The charts

can be used directly for determining variable unknown dimen-

sions if there are a sufficient number of known parameters.

If the designer is free to decide certain dimensions of the

frame, the charts allow him to compare various combinatiors

of frame dimensions and make his choice based on logic and

economy.

Insight into Choosing Slab System Types

The charts produced in this paper are directly applica-

ble to the design of slab systems by helping choose slab

system parameter values. However, uses of the charts are

not restricted only to direct design procedures. A closer

look at the charts reveals an insight into choosing flat

31

slcib or supported slab system types by noting the patterns

of the curves found in Figures 6-11.

Design charts for slabs without support beams are

given in Figures 6 and 11. The curves of Figures 6 and 11

are smooth and approach a minimum drop panel-slab span

length ratio, L^/L^, value of approximately 0.07 and 0.0 8

respectively for large slab width-length ratios, L^/L^.

Larger drop panel-slab span length ratios, L,/L, , are re-

quired for smaller slab width-length ratios, L^/L,. Slab

width-length ratios, L^/L,, greater than or equal to 0.8

should be used in order to use drop panels more efficiently.

The complexity of the parametric relationships in-

creases for slab systems with support beams. The curves of

Figures 7 - 1 0 and 12 - 15 for the various support beam-

slab stiffness ratios, <^, are irregular due to the number of

combinations of dimensions possible for the slab systems.

It can be seen that despite the complexity of the curves,

the drop panel-slab length ratio, L,/L , value' is always

less than 0.2 for slab span width-length ratios, L^/L^,

between 0.2 and 2.0. Therefore, drop panel-slab length

ratios, L,/Lw greater than 0.2 are impractical unless slab

moment reduction is necessary for the design. It is inter-

esting to note that for small support beam-slab stiffness

ratios, °c, and small span width-length ratios, L^/L^ , the

curves of the design charts follow the same general pattern

32

as for unsupported slabs. However, for span width-length

ratios, L^/L^, greater than 0.6, a greater additional stiff-

ness of the drop panels is required to maintain a balanced

slab moment condition. Smaller drop panel-span length

ratios, L^/L^, are required for larger support beam-slab

stiffness ratios, ", and small span width-length ratios,

L^/L^. Necessary drop panel-slab length ratios, L,/L ,

increase rapidly for larger span width-length ratios,

L^/L^, until maximum values are reached at between 0.15 and

0.17. Maximum drop panel-span length ratios, L,/L^, occur

at span width-length ratios, L /L.. , dependent upon the sup-

port beam-slab stiffness ratios, a, The span width-length

ratio, L^/L^, for maximum drop panel-span length ratios,

L,/L^, increases with the stiffness of the support beam.

Therefore, column spacings for space frame systems should

be selected such that span width-length ratios, L^/L^, do

not occur at maximum drop panel-span length ratios, L,/L .

Optimum use of the slab results from careful selection of

the column spacing. The designer is able to compare various

combinations of frame dimensions and determine the optimum

design by using the design charts in Figures 6-15.

Examples

The following examples are given to illustrate the use

of the design charts.

33

Example 1

Given: « = 0.5

L^/L^ =1.0

To Find:

Solution

Optimum Drop Panel Dimensions

It can be directly determined from Figure

8 that a drop panel-slab thickness ratio, h,/h, of

0.25 requires a drop panel-span length ratio, L,/L,,

of 0.09 8 for a drop panel length-cross dimension ratio,

L V C ^ , equal to 1.0. A larger drop panel-span length

ratio, Lj/L^, is required for a drop panel-slab thick-

ness ratio, h^/h, of 0.50. The smaller thickness ratio

allows fuller use of the slab. Therefore, drop panel

dimensions are chosen as the following parameters:

V^2 = ^'^ h^/h =0.25

Example 2

Given:

L^/L^ = 0.09 8

h^/h =0.5 d

oc = 0.0

LyC2 = 1.1

To Find: Optimum Column Spacing

Solution

Select a trial value of the span width-length

ratio, L^/L,, and find the necessary drop panel-span

34

length ratio, L^/L^, required for optimum design. Next,

check to see if the optimum design of the equivalent

frame in the transverse direction is compatible with

the first frame design by matching the drop panel sizes

for the two directions. The same chart can be used for

the transverse frame provided the support beam-slab

stiffness ratio, °, is the same. Although the width

and length parameters of the drop panel and slab are

inverted, the charts are still valid and values can be

read directly from them. The procedure of the first

trial was to select a span width-length ratio, L^/L,,

of 0.7 and find the corresponding drop panel-span length

ratio, L,/L,, equal to 0.091 from Figure 11. The span

width-length ratio of the transverse frame is 1.43.

By using the drop panel length-width ratio of 0.91,

the drop panel-span length ratio is found to be 0.0 82.

Comparing the two frames, the actual drop panel length-

width ratio, L,/C^, is found to be 1.11 which is larger

than the required 1.1. Therefore, trials are made

until the required compatibility is reached.

^2/ 1

0.7 0.75 0.72

L^/L^

0.091 0.089 0.09

Trials

L1/C2

1.43 1.33 1.39

C2/C2

0.082 0.0825 0.082

^d/S

1.11 1.08 1.1

35

The optimum column spacing for the given problem is a

span width-length ratio, L^/L , of 0.72.

Example 3

Given: Uniform live load of 100 psf.

Floor Plan Area 100 feet by 125 feet

To Find: Choose Slab System to be used for design

Solution:

Several design choices are made and material

amounts are compared.

1. Set: h^/h =0.25

oc = 0.0

L^/L, = 1.0 (columns at 25' on center, both directions)

LyC^ = 1.0

From Figure 6 L V L ^ = 0.074

Determine the slab thickness according to the current

ACI code and calculate the volume of concrete and

number of columns required for the design.

2. Set: h^/h =0.5

= 1.0

L^/L^ = 0.8 (columns 20' on center in ^ 100' direction, 25' on

center in 125' direction)

V S = 1-° From Figure 15: Lj/Li = 0.117, C./L, =0.14

36

Therefore: L, = 2.92', C^ = 2.8'

V ^ 2 " 1-043 ^ 1.0

Determine the slab thickness according to the current

ACI code and calculate the volume of concrete and

number of columns required for the design.

The designer is now able to compare the material costs of

trials 1, 2 and any other trials he might want to check.

An analysis is made for the chosen trial and if suitable,

the design is made for the chosen frame dimensions.

CHAPTER V

COMMENTARY ON THE USE OF THE DESIGN GUIDELINES

The design charts developed in this paper are intended

to be used for the design of concrete slab systems. Use of

the charts should result in better designs for economy by

comparing various combinations of system parameters. Al-

though the charts are expected to give quick accurate re-

sults, they are not a substitute for frame analyses. The

charts are developed to help the designer choose the most

economical slab system, but the system must be designed in

accordance with the current ACI Building Code Requirements.

The economical design of the charts is based on using the

slab to the greatest advantage. Other considerations such

as formwork costs may govern the design. If the dimensions

of the frame are limited by the formwork, the charts can be

used only for those parameters the designer is free to

choose. Although the charts might not be directly applicable

to a particular design problem, they allow the designer to

use his insight in comparing slab system types for advan-

tages and disadvantages.

The charts are limited to slab systems with support

beam-slab stiffness ratios, <^, of 0.0, 0.25, 0.5, 0.75 and

1.0. A larger support beam-slab stiffness ratio, °, does

not allow the parameters to be nondimensionalized because

37

'38

the deeper support beam causes the cross section of the slab

to act more as a T beam. The T beam action of the section

invalidates the linear relation of the slab cross dimension,

L^, with the slab stiffness. Other limitations of the

charts are governed by the current ACI code. The slab sys-

tems may be designed with limitations or deflections or

frame dimensions. It is emphasized again that the final

slab design must meet ACI code requirements. The charts

developed in this paper are merely aids for the designer to

be used for choosing slab system types and dimensions.

Final slab designs must be made through conventional methods

of analysis and design procedures.

BIBLIOGRAPHY

Building Code Requirements for Reinforced Concrete (ACI 318-71)~ Detroit: American Concrete Institute, 19 70.

Commentary on Building Code Requirements for Reinforced Concrete (ACI 318-71). Detroit: American Concrete Institute, 1971.

Proceedings of the American Concrete Institute, LXVII. Detroit: American Concrete Institute, 19 70.

Pryemieniecki, J. Theory of Matrix Structural Analysis. New York: McGraw-Hill, Inc., 1968. ""

Robinson, John. Structural Matrix Analysis for the Engineer. New York: Wiley, 1966.

Rubinstein, Moshe F. Matrix Computer Analysis of Struc-tures. Englewood Cliffs, New Jersey: Prentice-Hall, Inc, 1966.

Simmonds, Sidney H., and Janko Misic. "Design Factors for the Equivalent Frame Method." Journal of the American Concrete Institute, No. 11 (November, 1971), 825-831.

Wang, Chu-kia. Matrix Methods of Structural Analysis. 2r.d ed. Scranton, Pennsylvania: International Textbook Co., 1970.

Winter, George, Urquhart, L. C., O'Rourke, C. E., and Arthur H. Nilson. Design of Concrete Structures. New York: McGraw-Hill, Inc, 1968.

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