Two-Way Flat Plate Concrete Floor System Analysis and Design
The concrete floor slab system shown below is for an intermediate floor to be designed considering partition weight
= 20 psf, and unfactored live load = 40 psf. Flat plate concrete floor system does not use beams between columns or
drop panels and it is usually suited for lightly loaded floors with short spans typically for residential and hotel
buildings. The lateral loads are independently resisted by shear walls. The two design procedures shown in ACI 31814: Direct Design Method (DDM) and the Equivalent Frame Method (EFM) are illustrated in detail in this example.
The hand solution from EFM is also used for a detailed comparison with the analysis and design results of the
engineering software program spSlab.
Figure 1 - Two-Way Flat Concrete Floor System
Version: Jan-27-2017
Contents
1. Preliminary Member Sizing .....................................................................................................................................1
2. Two-Way Slab Analysis and Design ........................................................................................................................4
2.1. Direct Design Method (DDM) ..........................................................................................................................4
2.1.1. Direct design method limitations ............................................................................................................4
2.1.2. Design moments .....................................................................................................................................4
2.1.3. Flexural reinforcement requirements......................................................................................................5
2.1.4. Factored moments in columns ................................................................................................................8
2.2. Equivalent Frame Method (EFM) .....................................................................................................................8
2.2.1. Equivalent frame method limitations .....................................................................................................9
2.2.2. Frame members of equivalent frame ......................................................................................................9
2.2.3. Equivalent frame analysis .................................................................................................................... 11
2.2.4. Design moments ................................................................................................................................... 13
2.2.5. Distribution of design moments ........................................................................................................... 13
2.2.6. Flexural reinforcement requirements.................................................................................................... 14
2.2.7. Column design moments ...................................................................................................................... 17
3. Design of Interior, Edge, and Corner Columns ...................................................................................................... 19
3.1. Determination of factored loads ...................................................................................................................... 20
3.2. Column Capacity Diagram (Axial-Moment Interaction Diagram) ................................................................. 21
4. Two-Way Slab Shear Strength ............................................................................................................................... 25
4.1. One-Way (Beam action) Shear Strength ......................................................................................................... 25
4.2. Two-Way (Punching) Shear Strength ............................................................................................................. 26
5. Two-Way Slab Deflection Control (Serviceability Requirements) ........................................................................ 29
5.1. Immediate (Instantaneous) Deflections ........................................................................................................... 30
5.2. Time-Dependent (Long-Term) Deflections (Δlt) ............................................................................................. 39
6. Computer Program Solution ................................................................................................................................... 40
7. Summary and Comparison of Two-Way Slab Design Results ............................................................................... 60
8. Comparison of Two-Way Slab Analysis and Design Methods .............................................................................. 62
Version: Jan-27-2017
Code
Building Code Requirements for Structural Concrete (ACI 318-14) and Commentary (ACI 318R-14)
Minimum Design Loads for Buildings and Other Structures (ASCE/SEI 7-10)
International Code Council, 2012 International Building Code, Washington, D.C., 2012
Reference
Notes on ACI 318-11 Building Code Requirements for Structural Concrete, Twelfth Edition, 2013 Portland
Cement Association, Example 20.1
Concrete Floor Systems (Guide to Estimating and Economizing), Second Edition, 2002 David A. Fanella
Simplified Design of Reinforced Concrete Buildings, Fourth Edition, 2011 Mahmoud E. Kamara and Lawrence
C. Novak
Design Data
Floor-to-Floor Height = 9 ft (provided by architectural drawings)
Superimposed Dead Load, SDL =20 psf for framed partitions, wood studs plaster 2 sides
ASCE/SEI 7-10 (Table C3-1)
Live Load, LL = 40 psf for Residential floors
ASCE/SEI 7-10 (Table 4-1)
fc’ = 4000 psi (for slabs)
fc’ = 6000 psi (for columns)
fy = 60,000 psi
Required fire resistance rating = 2 hours
Solution
1.
Preliminary Member Sizing
a.
Slab minimum thickness - Deflection
ACI 318-14 (8.3.1.1)
In this example deflection will be calculated and checked to satisfy project deflection limits. Minimum
member thickness and depths from ACI 318-14 will be used for preliminary sizing.
Using ACI 318-14 minimum slab thickness for two-way construction without interior beams in Table 8.3.1.1.
Exterior Panels: h 
l n 200

 6.67 in.
30 30
But not less than 5 in.
Interior Panels: h 
l n 200

 6.06 in.
33 33
But not less than 5 in.
ACI 318-14 (Table 8.3.1.1)
ACI 318-14 (8.3.1.1(a))
ACI 318-14 (Table 8.3.1.1)
ACI 318-14 (8.3.1.1(a))
1
Where ln = length of clear span in the long direction = 216 – 16 = 200 in.
Try 7 in. slab for all panels (self-weight = 87.5 psf)
b.
Slab shear strength – one way shear
Evaluate the average effective depth (Figure 2):
db
0.5
 7  0.75  0.5 
 5.50 in.
2
2
d
0.5
d t  t slab  cclear  b  7  0.75 
 6.00 in.
2
2
d l  t slab  cclear  d b 
d
d d
t  5.50  6.00  5.75 in.
 l
avg
2
2
Where:
cclear = 3/4 in. for # 4 steel bar
ACI 318-14 (Table 20.6.1.3.1)
db = 0.5 in. for # 4 steel bar
Figure 2 - Two-Way Flat Concrete Floor System
Factored dead load,
q Du  1.2  (87.5  20)  129 psf
Factored live load,
q Lu  1.6  40  64 psf
Total factored load
q u  193 psf
Check the adequacy of slab thickness for beam action (one-way shear)
ACI 318-14 (5.3.1)
ACI 318-14 (22.5)
at an interior column:
Consider a 12-in. wide strip. The critical section for one-way shear is located at a distance d, from the face
of support (see Figure 3)
18
16
5.75
12
Tributary area for one-way shear is ATributary  [( )  (
)(
)]  ( )  7.854 ft2
2
2  12
12
12
Vu  q u  ATributary  0.193  7.854  1.5 kips
Vc  2 fc ' bwd
ACI 318-14 (Eq. 22.5.5.1)
where   1 for normal weight concrete
2
5.75
 6.6 kips  Vu
1000
Slab thickness of 7 in. is adequate for one-way shear.
Slab shear strength – two-way shear
Vc  0.75  2  1.0  4000  12 
c.
Check the adequacy of slab thickness for punching shear (two-way shear) at an interior column (Figure 4):
Tributary area for two-way shear is A
Tributary  (18  14)  (
16  5.75 2
)  248.7 ft2
12
Vu  q u  ATributary  0.193  248.7  48.0 kips
Vc  4 fc ' bo d (For square interior column)
Vc  4  4000  ( 4  21.75) 
5.75
ACI 318-14 (Table 22.6.5.2(a))
 126.6 kips
1000
Vc  0.75  126.6  95.0kips  Vu
Slab thickness of 7 in. is adequate for two-way shear.
d.
Figure 3 – Critical Section for One-Way
Figure 4 – Critical Section for Two-Way
Shear
Shear
Column dimensions - axial load
Check the adequacy of column dimensions for axial load:
Tributary area for interior column is ATributary  (18  14)  252 ft 2
Pu  qu  ATributary  0.193  252  48.6 kips
P  0.80 P  0.80  (0.85 f ' ( A  A )  f A ) (For square interior column)
n
o
c g
st
y st
ACI 318-14 (22.4.2)
P  0.80  (0.85(6000)(16  16  0)  0)  1,044,480 lb  1,044 kips
n
 P  0.65  1,044  679 kips  P  48.6 kips
n
u
Column dimensions of 16 in. x 16 in. are adequate for axial load.
3
2.
Two-Way Slab Analysis and Design
ACI 318 states that a slab system shall be designed by any procedure satisfying equilibrium and geometric
compatibility, provided that strength and serviceability criteria are satisfied. Distinction of two-systems from
one-way systems is given by ACI 318-14 (R8.10.2.3 & R8.3.1.2).
ACI 318 permits the use of Direct Design Method (DDM) and Equivalent Frame Method (EFM) for the gravity
load analysis of orthogonal frames and is applicable to flat plates, flat slabs, and slabs with beams. The following
sections outline the solution per DDM, EFM, and spSlab software respectively.
2.1. Direct Design Method (DDM)
Two-way slabs satisfying the limits in ACI 318-14 (8.10.2) are permitted to be designed in accordance with
the DDM.
2.1.1. Direct design method limitations
There is a minimum of three continuous spans in each direction
ACI 318-14 (8.10.2.1)
Successive span lengths are equal
ACI 318-14 (8.10.2.2)
Long-to-short span ratio is 1.29 < 2
ACI 318-14 (8.10.2.3)
Columns are not offset
ACI 318-14 (8.10.2.4)
Loads are uniformly distributed over the entire panel
ACI 318-14 (8.10.2.5)
Service live-to-dead load ratio of 0.37 < 2.0
ACI 318-14 (8.10.2.6)
Slab system is without beams and this requirement is not applicable
ACI 318-14 (8.10.2.7)
Since all the criteria are met, Direct Design Method can be utilized.
2.1.2. Design moments
a.
Calculate the total factored static moment:
Mo 
b.
qu  2  n 2 0.193  14  16.67 2

 93.6 ft-kips
8
8
ACI 318-14 (8.10.3.2)
Distribute the total factored moment, M o , in an interior and end span:
ACI 318-14 (8.10.4)
Table 1 - Distribution of Mo along the span
Location
Exterior Span
Interior Span
Exterior Negative
Positive
Interior Negative
Positive
Total Design Strip Moment,
MDS (ft-kips)
0.26 x Mo = 24.3
0.52 x Mo = 48.7
0.70 x Mo = 65.5
0.35 x Mo = 32.8
4
c.
Calculate the column strip moments.
ACI 318-14 (8.10.5)
That portion of negative and positive total design strip moments not resisted by column strips shall be
proportionally assigned to corresponding two half-middle strips.
ACI 318-14 (8.10.6.1)
Table 2 - Lateral Distribution of the Total Design Strip Moment, MDS
Location
Exterior Span
Interior Span
*
Total Design Strip
Moment, MDS (ft-kips)
Column Strip
Moment, (ft-kips)
Moment in Two
Half Middle Strips,
(ft-kips)
24.3
1.00 x MDS = 24.3
0.00 x MDS = 0.0
48.7
0.60 x MDS = 29.2
0.40 x MDS = 19.5
65.5
0.75 x MDS = 49.1
0.25 x MDS = 16.4
32.8
0.60 x MDS = 19.7
0.40 x MDS = 13.1
Exterior
Negative*
Positive
Interior
Negative*
Positive
All negative moments are at face of support.
2.1.3. Flexural reinforcement requirements
a.
Determine flexural reinforcement required for column and middle strips at all critical sections
The following calculation is for the exterior span exterior negative location of the column strip.
M u  24.3 ft-kips
Use average davg = 5.75 in.
To determine the area of steel, assumptions have to be made whether the section is tension or
compression controlled, and regarding the distance between the resultant compression and tension forces
along the slab section (jd). In this example, tension-controlled section will be assumed so the reduction
factor  is equal to 0.9, and jd will be taken equal to 0.95d. The assumptions will be verified once the
area of steel in finalized.
Assume jd  0.95  d  5.46 in.


Column strip width, b  14  12 / 2  84 in.
Middle strip width, b  14  12  84  84 in.
As 
Mu
f y jd

24.3  12000
0.9  60000  0.95  5.75
 0.99 in2
Recalculate ‘a’ for the actual As = 0.99 in.2:
5
a
c
Asf y
0.85f 'c b

0.99  60000
 0.208 in
0.85  4000  84
a 0.208

 0.244 in
1
0.85
t  (
0.003
0.003
)d t  0.003  (
)  5.75  0.003  0.0676  0.005
c
0.244
Therefore, the assumption that section is tension-controlled is valid.
As 
Mu
 f y (d  a / 2)

24.3  12000
0.9  60000  (5.75  0.208 / 2)
 0.96 in2
Min A s  0.018  84  7  1.06 in2  0.96 in2
ACI 318-14 (24.4.3.2)
Maximum spacing s max  2h  2  7  14 in  18 in
ACI 318-14 (8.7.2.2)
Provide 6 - #4 bars with A s  1.20 in2 and s  84 / 6  14 in  s max
Based on the procedure outlined above, values for all span locations are given in Table 3.
Span Location
84
5.75
0.96
1.06
6-#4
1.2
29
84
5.75
1.15
1.06
6-#4
1.2
Interior Negative
49.6
84
5.75
1.99
1.06
10-#4
2
Exterior Negative
0
84
5.75
0
1.06
6-#4
1.2
Positive
19.7
84
5.75
0.77
1.06
6-#4
1.2
Interior Negative
15.9
84
5.75
0.62
1.06
6-#4
1.2
Positive
Middle
Strip
As Prov. for
flexure (in2)
24.3
Exterior Negative
Column
Strip
Table 3 - Required Slab Reinforcement for Flexure (DDM)
Mu
b
d
As Req’d for
Min As
Reinforcement
(ft-kips)
(in.)
(in.)
flexure (in2)
(in2)
Provided
End Span
Interior Span
Column
Strip
Middle
Strip
b.
Positive
19.7
84
5.75
0.77
1.06
6-#4
1.2
Positive
13.1
84
5.75
0.51
1.06
6-#4
1.2
Calculate additional slab reinforcement at columns for moment transfer between slab and column
The factored slab moment resisted by the column (  f  M u ) shall be assumed to be transferred by
flexure. Concentration of reinforcement over the column by closer spacing or additional reinforcement
shall be used to resist this moment. The fraction of slab moment not calculated to be resisted by flexure
shall be assumed to be resisted by eccentricity of shear.
Portion of the unbalanced moment transferred by flexure is  f  M u
ACI 318-14 (8.4.2.3)
ACI 318-14 (8.4.2.3.1)
6
Where
f 
1
ACI 318-14 (8.4.2.3.2)
1  (2 / 3)  b1 / b 2
b1  Dimension of the critical section b o measured in the direction of the span for which moments are
determined in ACI 318, Chapter 8 (see Figure 5).
b 2  Dimension of the critical section b o measured in the direction perpendicular to b1 in ACI 318,
Chapter 8 (see Figure 5).
b b = Effective slab width = c 2  3  h
ACI 318-14 (8.4.2.3.3)
Figure 5 – Critical Shear Perimeters for Columns
Table 4 - Additional Slab Reinforcement required for moment transfer between slab and column (DDM)
Span Location
Mu*
(ft-kips)
γf
γf Mu
(ft-kips)
Effective slab
width, bb
(in.)
d
(in.)
As req’d
within bb
(in2)
As prov. For
flexure within bb
(in2)
Add’l
Reinf.
End Span
Exterior Negative
24.3
0.62
15.1
37
5.75
0.6
0.53
1-#4
Interior Negative
0.0
0.60
0.0
37
5.75
0.0
0.97
-
Column Strip
*Mu is taken at the centerline of the support in Equivalent Frame Method solution.
7
2.1.4. Factored moments in columns
a.
Interior columns:
 
2
2
M u  0.07  [( qDu  0.5  qLu )   2   n  qDu '   2 '   n ' ]
ACI 318-14 (8.10.7.2)
2
2



16 
16  
M u  0.07   (129  0.5  64)  14  18    129  18  14     17.75 ft-kips
12 
12  





With the same column size and length above and below the slab,
M column 
b.
17.75
 8.87 ft-kips
2
Exterior Columns:
Total exterior negative moment from slab must be transferred directly to the column: Mu  24.3 ftkips. With the same column size and length above and below the slab,
M column 
24.3
 12.15 ft-kips
2
The moments determined above are combined with the factored axial loads (for each story) for design
of column sections as shown later in this example.
2.2. Equivalent Frame Method (EFM)
EFM is the most comprehensive and detailed procedure provided by the ACI 318 for the analysis and design
of two-way slab systems where the structure is modeled by a series of equivalent frames (interior and exterior)
on column lines taken longitudinally and transversely through the building.
The equivalent frame consists of three parts:
1) Horizontal slab-beam strip, including any beams spanning in the direction of the frame. Different values
of moment of inertia along the axis of slab-beams should be taken into account where the gross moment
of inertia at any cross section outside of joints or column capitals shall be taken, and the moment of
inertia of the slab-beam at the face of the column, bracket or capital divide by the quantity (1-c2/l2)2 shall
be assumed for the calculation of the moment of inertia of slab-beams from the center of the column to
the face of the column, bracket or capital.
ACI 318-14 (8.11.3)
2) Columns or other vertical supporting members, extending above and below the slab. Different values
of moment of inertia along the axis of columns should be taken into account where the moment of inertia
of columns from top and bottom of the slab-beam at a joint shall be assumed to be infinite, and the gross
cross section of the concrete is permitted to be used to determine the moment of inertia of columns at
any cross section outside of joints or column capitals.
ACI 318-14 (8.11.4)
3) Elements of the structure (Torsional members) that provide moment transfer between the horizontal and
vertical members. These elements shall be assumed to have a constant cross section throughout their
8
length consisting of the greatest of the following: (1) portion of slab having a width equal to that of the
column, bracket, or capital in the direction of the span for which moments are being determined, (2)
portion of slab specified in (1) plus that part of the transverse beam above and below the slab for
monolithic or fully composite construction, (3) the transverse beam includes that portion of slab on each
side of the beam extending a distance equal to the projection of the beam above or below the slab,
whichever is greater, but not greater than four times the slab thickness.
ACI 318-14 (8.11.5)
2.2.1. Equivalent frame method limitations
In EFM, live load shall be arranged in accordance with 6.4.3 which requires slab systems to be analyzed and
designed for the most demanding set of forces established by investigating the effects of live load placed in
various critical patterns.
ACI 318-14 (8.11.1.2 & 6.4.3)
Complete analysis must include representative interior and exterior equivalent frames in both the longitudinal
and transverse directions of the floor
ACI 318-14 (8.11.2.1)
Panels shall be rectangular, with a ratio of longer to shorter panel dimensions, measured center-to-center of
supports, not to exceed 2.
ACI 318-14 (8.10.2.3)
2.2.2. Frame members of equivalent frame
Determine moment distribution factors and fixed-end moments for the equivalent frame members. The
moment distribution procedure will be used to analyze the equivalent frame. Stiffness factors k , carry over
factors COF, and fixed-end moment factors FEM for the slab-beams and column members are determined
using the design aids tables at Appendix 20A of PCA Notes on ACI 318-11. These calculations are shown
below.
a. Flexural stiffness of slab-beams at both ends, K sb .
c N1
1

16
(18  12)
 0.07 ,
cN 2
2

16
(14  12)
 0.1
For cF1  cF2 , stiffness factors, k NF  k FN  4.13
Thus,
E I
E I
K sb  k NF cs s  4.13 cs s
1
1
PCA Notes on ACI 318-11 (Table A1)
PCA Notes on ACI 318-11 (Table A1)
3 4802
6
K sb  4.13  3834  10 
 352  10 in.-lb
216
where,
3
3
 h
168  (7)
Is  s

 4802 in4
12
12
1.5
1.5
3
Ecs  wc 33 fc  150  33  4000  3834  10 psi
ACI 318-14 (19.2.2.1.a)
9
Carry-over factor COF  0.509
PCA Notes on ACI 318-11 (Table A1)
Fixed-end moment FEM  0.0843w u  21
2
PCA Notes on ACI 318-11 (Table A1)
b. Flexural stiffness of column members at both ends, K c .
Referring to Table A7, Appendix 20A, t a  3.5 in., t b  3.5 in.,
H
t
H  9 ft  108 in., H c  101 in., a  1,
 1.07
tb
Hc
Thus, k AB  k BA  4.74 by interpolation.
Kc 
4.74E cc Ic
c
PCA Notes on ACI 318-11 (Table A7)
3 5461
6
K c  4.74  4696  10 
 1125.5  10 in.-lb
108
Where Ic 
c 4 (16) 4
4

 5461 in.
12
12
1.5
1.5
3
Ecc  wc 33 fc  150  33  6000  4696  10 psi
ACI 318-14 (19.2.2.1.a)
 c  9 ft  108 in.
c. Torsional stiffness of torsional members, K t .
Kt 
Kt 
9E cs C
c
[ 2 (1  2 ) 3 ]
2
ACI 318-14 (R.8.11.5)
3
9  3834  10  1325
6
 367  10 in.-lb
3
168(0.905)
x x3y
)
Where C  (1  0.63 )(
y 3
ACI 318-14 (Eq. 8.10.5.2b)
7
16
)(7 3  )  1325 in4.
16
3
c 2  16 in., and  2  14 ft  168 in.
C  (1  0.63 
10
d. Equivalent column stiffness K ec .
K ec 
K ec 
 K c   Kt
 K c   Kt
( 2  1125.5)( 2  367)
[( 2  1125.5)  ( 2  367)]
 10
6
Figure 6 - Torsional Member
6
K ec  553.7  10 in.-lb
Where  K t is for two torsional members one on each side of the
column, and  K c is for the upper and lower columns at the slabbeam joint of an intermediate floor.
e. Slab-beam joint distribution factors, DF.
At exterior joint,
DF 
352
(352  553.7)
 0.389
Figure 7 – Column and Edge of Slab
At interior joint,
DF 
352
(352  352  553.7)
 0.280
COF for slab-beam  0.509
Figure 8 – Slab and Column Stiffness
2.2.3. Equivalent frame analysis
Determine negative and positive moments for the slab-beams using the moment distribution method. Since
the unfactored live load does not exceed three-quarters of the unfactored dead load, design moments are
assumed to occur at all critical sections with full factored live on all spans.
ACI 318-14 (6.4.3.2)
L
40
3

 0.37 
D (87.5  20)
4
a. Factored load and Fixed-End Moments (FEM’s).
11
Factored dead load q Du  1.2(87.5  20)  129 psf
Factored live load q Lu  1.6(40)  64 psf
Factored load q u  q Du  q Lu  193 psf
FEM’s for slab-beams  m NFq u  21
2
PCA Notes on ACI 318-11 (Table A1)
2
 0.0841 (0.193  14) 18  73.8 ft-kips
b. Moment distribution. Computations are shown in Table 5. Counterclockwise rotational moments acting on
the member ends are taken as positive. Positive span moments are determined from the following equation:
(M uL  M uR )
M u (midspan)  M o 
2
Where M o is the moment at the midspan for a simple beam.
When the end moments are not equal, the maximum moment in the span does not occur at the midspan, but
its value is close to that midspan for this example.
Positive moment in span 1-2:
 M u  (0.193  14)
182 (46.6  84.0)

 44.1 ft-kips
8
2
Positive moment span 2-3:
 M u  (0.193  14)
182 (76.2  76.2)

 33.2 ft-kips
8
2
Table 5 – Moment Distribution for Equivalent Frame
Joint
Member
DF
COF
FEM
Dist
CO
Dist
CO
Dist
CO
Dist
CO
Dist
Neg. M
M at
midspan
1
1-2
0.389
0.509
+73.8
-28.7
0.0
0.0
2.1
-0.8
0.3
-0.1
0.1
0.0
46.6
2
2-1
0.280
0.509
-73.8
0.0
-14.6
4.1
0.0
0.6
-0.4
0.2
-0.1
0.0
-84.0
44.1
3
2-3
0.280
0.509
+73.8
0.0
0.0
4.1
-2.1
0.6
-0.3
0.2
-0.1
0.0
76.2
3-2
0.280
0.509
-73.8
0.0
0.0
-4.1
2.1
-0.6
0.3
-0.2
0.1
0.0
-76.2
33.2
3-4
0.280
0.509
+73.8
0.0
14.6
-4.1
0.0
-0.6
0.4
-.02
0.1
0.0
84.0
4
4-3
0.389
0.509
-73.8
28.7
0.0
0.0
-2.1
0.8
-0.3
0.1
-0.1
0.0
-46.6
44.1
12
2.2.4. Design moments
Positive and negative factored moments for the slab system in the direction of analysis are plotted in Figure
9. The negative moments used for design are taken at the faces of supports (rectangle section or equivalent
rectangle for circular or polygon sections) but not at distances greater than 0.175 1 from the centers of
supports.
16 in.
12  2
ACI 318-14 (8.11.6.1)
 0.67 ft  0.175 18  3.2 ft (use face of support location)
Figure 9 - Positive and Negative Design Moments for Slab-Beam (All Spans Loaded with Full Factored Live Load)
2.2.5. Distribution of design moments
a. Check whether the moments calculated above can take advantage of the reduction permitted by ACI 31814 (8.11.6.5):
13
If the slab system analyzed using EFM within the limitations of ACI 318-14 (8.10.2), it is permitted by the
ACI code to reduce the calculated moments obtained from EFM in such proportion that the absolute sum of
the positive and average negative design moments need not exceed the value obtained from the following
equation:
Mo 
q u  2 n 2
(16.67) 2
 0.193 14 
 93.9 ft-kips
8
8
End spans: 44.1 
ACI 318-14 (Eq. 8.10.3.2)
(32.3  67.0)
 93.8 ft-kips
2
Interior span: 33.2 
(60.8  60.8)
 94 ft-kips
2
The total design moments from the Equivalent Frame Method yield a static moment equal to that given by
the Direct Design Method and no appreciable reduction can be realized.
b. Distribute factored moments to column and middle strips:
After the negative and positive moments have been determined for the slab-beam strip, the ACI code permits
the distribution of the moments at critical sections to the column strips, beams (if any), and middle strips in
accordance with the DDM.
ACI 318-14 (8.11.6.6)
Distribution of factored moments at critical sections is summarized in Table 6.
Table 6 - Distribution of factored moments
Slab-beam Strip
Column Strip
Middle Strip
Moment
(ft-kips)
Percent
Moment
(ft-kips)
Percent
Moment
(ft-kips)
Exterior Negative
32.3
100
32.3
0
0
End Span
Positive
44.1
60
26.5
40
17.7
Interior Negative
67
75
50.3
25
16.7
Negative
60.8
75
45.6
25
15.2
Positive
33.2
60
19.9
40
13.2
Interior Span
2.2.6. Flexural reinforcement requirements
a. Determine flexural reinforcement required for strip moments
The flexural reinforcement calculation for the column strip of end span – exterior negative location is
provided below.
M u  32.3 ft-kips
Use average davg = 5.75 in.
14
To determine the area of steel, assumptions have to be made whether the section is tension or compression
controlled, and regarding the distance between the resultant compression and tension forces along the slab
section (jd). In this example, tension-controlled section will be assumed so the reduction factor  is equal to
0.9, and jd will be taken equal to 0.95d. The assumptions will be verified once the area of steel in finalized.
Assume jd  0.95  d  5.46 in.


Column strip width, b  14  12 / 2  84 in.
Middle strip width, b  14  12  84  84 in.
As 
Mu
32.3  12000

 1.31 in.2
f y jd 0.9  60000  0.95  5.75
Recalculate ‘a’ for the actual As = 1.31 in.2: a 
c
Asf y
0.85f 'c b

1.31 60000
 0.276 in.
0.85  4000  84
a
0.276

 0.325 in.
1
0.85
t  (
0.003
0.003
)d t  0.003  (
)  5.75  0.003  0.0501  0.005
c
0.325
Therefore, the assumption that section is tension-controlled is valid.
As 
Mu
32.3  12000

 1.28 in.2
f y (d  a / 2) 0.9  60000  (5.75  0.276 / 2)
Min A s  0.018  84  7  1.06 in2  1.28 in.2
Maximum spacing s max  2h  2  7  14 in.  18 in.
ACI 318-14 (24.4.3.2)
ACI 318-14 (8.7.2.2)
Provide 7 - #4 bars with As = 1.40 in.2 and s = 84/7 = 12 in.  s max
Based on the procedure outlined above, values for all span locations are given in Table 7.
15
Table 7 - Required Slab Reinforcement for Flexure [Equivalent Frame Method (EFM)]
Mu
b*
d **
As Req’d for
Min As† Reinforcement
Span Location
(ft-kips)
(in.) (in.)
flexure (in2)
(in2)
Provided‡
End Span
Column
Strip
Middle
Strip
As Prov. for
flexure (in2)
Exterior Negative
32.3
84
5.75
1.28
1.06
7-#4
1.4
Positive
26.5
84
5.75
1.04
1.06
6-#4
1.2
Interior Negative
50.3
84
5.75
2.02
1.06
11-#4
2.2
Exterior Negative
0
84
5.75
0
1.06
6-#4
1.2
Positive
17.7
84
5.75
0.69
1.06
6-#4
1.2
Interior Negative
16.7
84
5.75
0.65
1.06
6-#4
1.2
Interior Span
Column
Strip
Middle
Strip
Positive
19.9
84
5.75
0.78
1.06
6-#4
1.2
Positive
13.2
84
5.75
0.51
1.06
6-#4
1.2
b. Calculate additional slab reinforcement at columns for moment transfer between slab and column by
flexure
The factored slab moment resisted by the column (  f  M u ) shall be assumed to be transferred by flexure.
Concentration of reinforcement over the column by closer spacing or additional reinforcement shall be used
to resist this moment. The fraction of slab moment not calculated to be resisted by flexure shall be assumed
to be resisted by eccentricity of shear.
Portion of the unbalanced moment transferred by flexure is  f  M u
ACI 318-14 (8.4.2.3)
ACI 318-14 (8.4.2.3.1)
Where
f 
1
1  (2 / 3)  b1 / b 2
ACI 318-14 (8.4.2.3.2)
b1  Dimension of the critical section b o measured in the direction of the span for which moments are
determined in ACI 318, Chapter 8 (see Figure 5).
b 2  Dimension of the critical section b o measured in the direction perpendicular to b1 in ACI 318,
Chapter 8 (see Figure 5).
b b = Effective slab width = c 2  3  h
ACI 318-14 (8.4.2.3.3)
16
Table 8 - Additional Slab Reinforcement required for moment transfer between slab and column (EFM)
Span Location
Mu*
(ft-kips)
γf
γf Mu
(ft-kips)
Effective slab
width, bb
(in.)
d
(in.)
As req’d
within bb
(in2)
As prov. For
flexure within bb
(in2)
Add’l
Reinf.
End Span
Exterior Negative
46.6
0.60
28.9
37
5.75
1.17
0.62
3-#4
Interior Negative
7.8
0.60
4.7
37
5.75
0.18
0.97
-
Column Strip
*Mu is taken at the centerline of the support in Equivalent Frame Method solution.
2.2.7. Column design moments
The unbalanced moment from the slab-beams at the supports of the equivalent frame are distributed to the
support columns above and below the slab-beam in proportion to the relative stiffness of the support
columns. Referring to Figure 9, the unbalanced moment at joints 1 and 2 are:
Joint 1= +46.6 ft-kips
Joint 2= -84.0 + 76.2 = -7.8 ft-kips
The stiffness and carry-over factors of the actual columns and the distribution of the unbalanced slab
moments (Msc) to the exterior and interior columns are shown in Figure 10a.
17
Figure 10a - Column Moments (Unbalanced Moments from Slab-Beam)
In summary:
Mcol,Exterior= 22.08 ft-kips
Mcol,Interior = 3.66 ft-kips
The moments determined above are combined with the factored axial loads (for each story) and factored
moments in the transverse direction for design of column sections. Figure 10b shows the moment diagrams
in the longitudinal and transverse direction for the interior and exterior equivalent frames. Following the
previous procedure, the moment values at the face of interior, exterior, and corner columns from the
unbalanced moment values can be obtained. These values are shown in the following table.
18
Figure 10b – Moment Diagrams (kips-ft)
3.
Column number (See Figure 10b)
Mu
kips-ft
1
2
3
4
Mux
3.66
22.08
2.04
12.39
Muy
2.23
1.28
12.49
6.79
Design of Interior, Edge, and Corner Columns
This section includes the design of interior, edge, and corner columns using spColumn software. The preliminary
dimensions for these columns were calculated previously in section one. The reduction of live load per ASCE
7-10 will be ignored in this example. However, the detailed procedure to calculate the reduced live loads is
explained in the “wide-Module Joist System” example.
19
3.1. Determination of factored loads
Interior Column (Column #1):
Assume 4 story building
Tributary area for interior column is ATributary  (18  14)  252 ft 2
Pu  4  qu  ATributary  4  0.193  252  194.5 kips
Mu,x = 3.66 ft-kips (see the previous Table)
Mu,y = 2.23 ft-kips (see the previous Table)
Edge (Exterior) Column (Column #2):
Tributary area for interior column is ATributary  (18 / 2  14)  126 ft 2
Pu  4  qu  ATributary  4  0.193  126  97.3 kips
Mu,x = 22.08 ft-kips (see the previous Table)
Mu,y = 1.28 ft-kips (see the previous Table)
Edge (Exterior) Column (Column #3):
Tributary area for interior column is ATributary  (18  14 / 2)  126 ft 2
Pu  4  qu  ATributary  4  0.193  126  97.3 kips
Mu,x = 2.04 ft-kips (see the previous Table)
Mu,y = 12.49 ft-kips (see the previous Table)
Corner Column (Column #4):
Tributary area for interior column is ATributary  (18 / 2  14 / 2)  63 ft 2
Pu  4  qu  ATributary  4  0.193  63  48.6 kips
Mu,x = 12.39 ft-kips (see the previous Table)
Mu,y = 6.79 ft-kips (see the previous Table)
The factored loads are then input into spColumn to construct the axial load – moment interaction diagram.
20
3.2. Column Capacity Diagram (Axial-Moment Interaction Diagram)
Interior Column (Column #1):
21
Edge Column (Column #2):
22
Edge Column (Column #3):
23
Corner Column (Column #4):
24
4.
Two-Way Slab Shear Strength
Shear strength of the slab in the vicinity of columns/supports includes an evaluation of one-way shear (beam
action) and two-way shear (punching) in accordance with ACI 318 Chapter 22.
4.1. One-Way (Beam action) Shear Strength
ACI 318-14 (22.5)
One-way shear is critical at a distance d from the face of the column as shown in Figure 3. Figure 11 shows the
factored shear forces (Vu) at the critical sections around each column. In members without shear reinforcement,
the design shear capacity of the section equals to the design shear capacity of the concrete:
Vn  Vc  Vs  Vc
,
(Vs  0)
ACI 318-14 (Eq. 22.5.1.1)
Where:
'
Vc   2 f c bw d
ACI 318-14 (Eq. 22.5.5.1)
  1 for normal weight concrete
Vc  0.75  2  1.0 
4000
 (14  12)  5.75  91.64 kips
1000
Because Vc  Vu at all the critical sections, the slab has adequate one-way shear strength.
Figure 11 – One-way shear at critical sections (at distance d from the face of the supporting column)
25
4.2. Two-Way (Punching) Shear Strength
ACI 318-14 (22.6)
Two-way shear is critical on a rectangular section located at d/2 away from the face of the column as shown
in Figure 5.
a. Exterior column:
The factored shear force (Vu) in the critical section is computed as the reaction at the centroid of the critical
section minus the self-weight and any superimposed surface dead and live load acting within the critical
section (d/2 away from column face).
 21.72  18.88   21.65 kips

144


Vu  22.2  0.193
The factored unbalanced moment used for shear transfer, M unb, is computed as the sum of the joint moments
to the left and right. Moment of the vertical reaction with respect to the centroid of the critical section is also
taken into account.
M unb  46.6  21.65(
18.88  5.99  16 / 2
)  37.8 kips-ft
12
For the exterior column in Figure 5, the location of the centroidal axis z-z is:
c AB 
moment of area of the sides about AB
2(18.8  5.75  18.8 / 2)

 5.99 in.
area of the sides
2  18.8  5.75  21.75  5.75
The polar moment Jc of the shear perimeter is:
2
 b d 3 db 3
 b1
 
 1
2
1


J  2

 bd
c
 b dc
1  2
AB   2 AB
c
12
12


 

 
2
 18.88  5.753 5.75  18.883
18.88


2

J 2

 18.88  5.75
 5.99    21.75  5.75  5.99  14109 in.4
c


12
12
2

 

γ  1  γ  1  0.617  0.383
v
f
ACI 318-14 (Eq. 8.4.4.2.2)
The length of the critical perimeter for the exterior column:
b o  2  (16  5.75/2)  (16  5.75)  59.5 in.
The two-way shear stress (vu) can then be calculated as:
26
vu 
V
γ M
c
u  v unb AB
b d
J
o
c
vu 
21.65  1000 0.383  (37.8  12  1000)  5.99

 137.0 psi
59.5  5.75
14109

v c  min 4

4
' 
f c ,  2  


ACI 318-14 (R.8.4.4.2.3)

'  d
f c ,  s  2 
 bo

'
fc 
ACI 318-14 (Table 22.6.5.2)



 4
 40  5.75 
v c  min4  1  4000 ,  2    1  4000 , 
 2   1  4000 
 1
 59.5





v c  min 253 , 279.5 , 371 psi  253 psi
 v c  0.75  253  189.7 psi
Since  v c  v at the critical section, the slab has adequate two-way shear strength at this joint.
u
b. Interior column:
 21.72  21.72   50.07 kips

144


Vu  24.3  26.4  0.193
M unb  84  76.2  50.07(0)  7.8 kips-ft
For the interior column in Figure 5, the location of the centroidal axis z-z is:
b
21.75
c AB  1 
 10.88 in.
2
2
The polar moment Jc of the shear perimeter is:
2
 b d 3 db 3
 b1
 
 1
2
1


J  2

 bd
c
 2b2 dc AB
1  2
AB  
c
12
12


 

 
 21.75  5.753 5.75  21.753
J  2

c

γ
v
12

12



2
2
 21.75  5.750    2  21.75  5.75  5.99  40131 in.4
 1  γ  1  0.600  0.400
f
ACI 318-14 (Eq. 8.4.4.2.2)
The length of the critical perimeter for the interior column:
27
b o  2  (16  5.75)  2  (16  5.75)  87 in.
vu 
V
γ M
c
u  v unb AB
b d
J
o
c
vu 
50.07  1000 0.400  7.8  12  1000  10.88

 110.2 psi
87  5.75
40131

v c  min 4

4
' 
f c ,  2  





v c  min4  1  4000 ,  2 


ACI 318-14 (R.8.4.4.2.3)

'  d
f c ,  s  2 
 bo

'
fc 

ACI 318-14 (Table 22.6.5.2)

 40  5.75 
 2   1  4000 
  1  4000 , 
1
 87


4

v c  min 253 , 279.5 , 293.7 psi  253 psi
 v c  0.75  253  189.7 psi
Since  v c  v at the critical section, the slab has adequate two-way shear strength at this joint.
u
c. Corner column:
In this example, interior equivalent frame strip was selected where it only have exterior and interior supports
(no corner supports are included in this strip). However, the two-way shear strength of corner supports usually
governs. Thus, the two-way shear strength for the corner column in this example will be checked for educational
purposes. Same procedure is used to find the reaction and factored unbalanced moment used for shear transfer
at the centroid of the critical section for the corner support for the exterior equivalent frame strip.
 18.88  18.88   12.70 kips

144


Vu  13.18  0.193
M unb  25.75  12.70(
18.88  4.72  16 / 2
)  19.23 kips-ft
12
For the corner column in Figure 5, the location of the centroidal axis z-z is:
c AB 
moment of area of the sides about AB (18.8  5.75  18.8 / 2)

 4.72 in.
area of the sides
2  18.8  5.75
The polar moment Jc of the shear perimeter is:
2
 b d 3 db 3
 b1
 
 1
2
1


J 

 bd
c
 b2dc AB
1  2
AB  
c
12
12


 

 
28
 18.88  5.753
J 
c 
12


2
5.75  18.883
 18.88  5.99    18.88  5.75  4.722  8354 in.4
 18.88  5.75 

12
 2
 

γ  1  γ  1  0.600  0.400
v
f
ACI 318-14 (Eq. 8.4.4.2.2)
Where:
f 
f 
1
ACI 318-14 (8.4.2.3.2)
1  ( 2 / 3)  b1 / b2
1
1  ( 2 / 3)  18.88 / 18.88
 0.600
The length of the critical perimeter for the exterior column:
bo  (16  5.75/2)  (16  5.75/2)  37.75 in.
The two-way shear stress (vu) can then be calculated as:
vu 
V
γ M
c
u  v unb AB
b d
J
o
c
vu 
12.70  1000 0.400  (19.23  12  1000)  4.72

 110.6 psi
37.75  5.75
8354

v c  min 4


4
' 
f c ,  2  




vc  min4  1  4000 ,  2 


ACI 318-14 (R.8.4.4.2.3)

'  d
f c ,  s  2 
 bo

'
fc 

ACI 318-14 (Table 22.6.5.2)

 20  5.75 
 2   1  4000 
  1  4000 , 
1
 37.75


4

vc  min 253 , 279.5 , 319.2 psi = 253 psi
 v c  0.75  253  189.7 psi
Since  v c  v at the critical section, the slab has adequate two-way shear strength at this joint.
u
5.
Two-Way Slab Deflection Control (Serviceability Requirements)
Since the slab thickness was selected based on the minimum slab thickness tables in ACI 318-14, the deflection
calculations are not required. However, the calculations of immediate and time-dependent deflections are covered
in this section for illustration and comparison with spSlab model results.
29
5.1. Immediate (Instantaneous) Deflections
The calculation of deflections for two-way slabs is challenging even if linear elastic behavior can be assumed.
Elastic analysis for three service load levels (D, D + Lsustained, D+LFull) is used to obtain immediate deflections
of the two-way slab in this example. However, other procedures may be used if they result in predictions of
deflection in reasonable agreement with the results of comprehensive tests.
ACI 318-14 (24.2.3)
The effective moment of inertia (Ie) is used to account for the cracking effect on the flexural stiffness of the
slab. Ie for uncracked section (Mcr > Ma) is equal to Ig. When the section is cracked (Mcr < Ma), then the
following equation should be used:
3
  M 3 
 M cr 
 I  1   cr   I  I
Ie  
 M  g   M   cr
g
 a
  a  
ACI 318-14 (Eq. 24.2.3.5a)
Where:
Ma = Maximum moment in member due to service loads at stage deflection is calculated.
The values of the maximum moments for the three service load levels are calculated from structural analysis as
shown previously in this document. These moments are shown in Figure 12.
Figure 12 – Maximum Moments for the Three Service Load Levels
M
M
cr
cr
= cracking moment.

f I
1
r g 474.34  4802


 54.23 kip-ft
y
3.5
12  1000
t
ACI 318-14 (Eq. 24.2.3.5b)
f = Modulus of rapture of concrete.
r
f  7.5 f '  7.5  1.0  4000  474.34 psi
c
r
ACI 318-14 (Eq. 19.2.3.1)
30
I = Moment of inertia of the gross uncracked concrete section
g
l h3 14  12 7 3
2
I  2 
 4802 in
g
12
12
h 7
y    3.5 in
t 2 2
I
cr
= moment of inertia of the cracked section transformed to concrete PCA Notes on ACI 318-11 (9.5.2.2)
The calculations shown below are for the design strip (frame strip). The values of these parameters for column
and middle strips are shown in Table 9.
As calculated previously, the exterior span frame strip near the interior support is reinforced with 17 #4 bars
located at 1.25 in. along the section from the top of the slab. Figure 13 shows all the parameters needed to
calculate the moment of inertia of the cracked section transformed to concrete.
Figure 13 – Cracked Transformed Section
Ecs = Modulus of elasticity of slab concrete.
1.5
1.5
3
Ecs  wc 33 fc  150  33  4000  3834  10 psi
n
B
E
s  29000000  7.56
E
3834000
cs
PCA Notes on ACI 318-11 (Table 10-2)
b
14  12

 6.54 in.-1
nA
7.56  17  0.2 
s
PCA Notes on ACI 318-11 (Table 10-2)
kd 
I
I
cr
cr
ACI 318-14 (19.2.2.1.a)
2dB  1  1

B
2  5.75  6.54  1  1
 1.18 in.
6.54

b( kd )3
2
 nA ( d  kd )
s
3

14  12  (1.18)3
2
 7.56  17  0.2 5.75  1.18  629 in.4
3
PCA Notes on ACI 318-11 (Table 10-2)
PCA Notes on ACI 318-11 (Table 10-2)
The effective moment of inertia procedure described in the Code is considered sufficiently accurate to estimate
deflections. The effective moment of inertia, Ie, was developed to provide a transition between the upper and
31
lower bounds of Ig and Icr as a function of the ratio Mcr/Ma. For conventionally reinforced (nonprestressed)
members, the effective moment of inertia, Ie, shall be calculated by Eq. (24.2.3.5a) unless obtained by a more
comprehensive analysis.
Ie shall be permitted to be taken as the value obtained from Eq. (24.2.3.5a) at midspan for simple and
continuous spans, and at the support for cantilevers.
ACI 318-14 (24.2.3.7)
For continuous one-way slabs and beams. Ie shall be permitted to be taken as the average of values obtained
from Eq. (24.2.3.5a) for the critical positive and negative moment sections.
ACI 318-14 (24.2.3.6)
For the exterior span (span with one end continuous) with service load level (D+LLfull):
M
 
I   cr
e M
 a
3
 M

 I  1   cr
 g   M

  a




3
 I , since M  54.23 kip-ft < M  64.17 kip-ft
a
cr
 cr

ACI 318-14 (24.2.3.5a)

Where I is the effective moment of inertia for the critical negative moment section (near the support).
e
I
3
  54.23 3 
  54.23 
   629  3148 in.4
1  


4802

e  64.17 
  64.17  

I


 I  4802 in.4 , since M cr  54.23 kip-ft > M a  34.25 kip-ft
e
g

Where I is the effective moment of inertia for the critical positive moment section (midspan).
e
Since midspan stiffness (including the effect of cracking) has a dominant effect on deflections, midspan
section is heavily represented in calculation of Ie and this is considered satisfactory in approximate deflection
calculations. The averaged effective moment of inertia (Ie,avg) is given by:
I e,avg  0.85 I


 0.15 I
e
e
PCA Notes on ACI 318-11 (9.5.2.4(1))
I e,avg  0.85 4802  0.15 3148  4554 in.4
For the interior span (span with both ends continuous) with service load level (D+LLfull):
M


I
I
  cr
e, l
e, R  M
 a
3
 M

 I  1   cr
 g   M

  a




3
 I , since M  54.23 kip-ft < M  58.27 kip-ft
cr
a
 cr

ACI 318-14 (24.2.3.5a)
32
Where I


and I
are the effective moment of inertia for the critical negative moment sections near the
e, l
e, R
left and right supports, respectively.
3
  54.23 3 
  54.23 
   629  3993 in.4
I 
 4802  1  
e  58.27 
  58.27  

I


 I  4802 in.4 , since M cr  54.23 kip-ft > M a  25.34 kip-ft
e
g

Where I is the effective moment of inertia for the critical positive moment section (midspan).
e
The averaged effective moment of inertia (Ie,avg) is given by:
I e,avg  0.70 I


 0.15 I   I 
e, l
e, r
e

PCA Notes on ACI 318-11 (9.5.2.4(2))
I e,avg  0.70 4802  0.15 3993  3993  4559 in.4
Table 9 provides a summary of the required parameters and calculated values needed for deflections for exterior
and interior equivalent frame. It also provides a summary of the same values for column strip and middle strip
to facilitate calculation of panel deflection.
Table 9 – Averaged Effective Moment of Inertia Calculations
For Frame Strip
Ie, in.4
Ma, kips-ft
Span
Ext
Icr,
in.4
D
D+
LLSus
D+
Lfull
Left
499
-26.10
-26.10
Midspan
465
24.95
629
629
zone
Right
Left
Int
Ig,
in.4
4802
Mcr,
k-ft
Ie,avg, in.4
D
D+
LLSus
D+
Lfull
-35.78
4802
4802
4802
24.95
34.25
4802
4802
4802
-46.76
-46.76
-64.17
4802
4802
3148
-42.47
-42.47
-58.27
4802
4802
3993
54.23
Mid
465
18.47
18.47
25.34
4802
4802
4802
Right
629
-42.47
-42.47
-58.27
4802
4802
3993
D
D+
LLSus
D+
Lfull
4802
4802
4554
4802
4802
4559
Deflections in two-way slab systems shall be calculated taking into account size and shape of the panel,
conditions of support, and nature of restraints at the panel edges. For immediate deflections two-way slab
systems the midpanel deflection is computed as the sum of deflection at midspan of the column strip or column
line in one direction (Δcx or Δcy) and deflection at midspan of the middle strip in the orthogonal direction (Δmx
or Δmy). Figure 14 shows the deflection computation for a rectangular panel. The average Δ for panels that have
different properties in the two direction is calculated as follows:
33

 

        
my   cy
mx 
 cx

2
PCA Notes on ACI 318-11 (9.5.3.4 Eq. 8)
Figure 14 – Deflection Computation for a rectangular Panel
To calculate each term of the previous equation, the following procedure should be used. Figure 15 shows the
procedure of calculating the term Δcx. same procedure can be used to find the other terms.
Figure 15 –Δcx calculation procedure
For exterior span - service dead load case:
34
 frame, fixed 
wl 4
384 E I
c frame, averaged
PCA Notes on ACI 318-11 (9.5.3.4 Eq. 10)
Where:
 frame, fixed = Deflection of column strip assuming fixed end condition.
w  (20  150  7 / 12)(14)  1505 lb/ft
1.5
1.5
3
Ec  wc 33 fc  150  33  4000  3834  10 psi
I
ACI 318-14 (19.2.2.1.a)
= The averaged effective moment of inertia (Ie,avg) for the frame strip for service dead load
frame, averaged
case from Table 9 = 4802 in.4
 frame, fixed 
(1505)(18) 4 (12)3
 0.039 in.
384(3834  103 )( 4802)
I
 c, fixed  LDF   frame, fixed 
c
frame, averaged
I
c, g
PCA Notes on ACI 318-11 (9.5.3.4 Eq. 11)
Where LDFc is the load distribution factor for the column strip. The load distribution factor for the column
strip can be found from the following equation:
LDF 
c
LDF  
LDF   LDF 
l
R
2
2
And the load distribution factor for the middle strip can be found from the following equation:
LDF  1  LDF
m
c
For the end span, LDF for exterior negative region (LDFL¯), interior negative region (LDFR¯), and positive
＋
region (LDFL ) are 1.00, 0.75, and 0.60, respectively (From Table 6 of this document). Thus, the load
distribution factor for the column strip for the end span is given by:
LDF 
c
I
c, g
0.6 
1.0  0.75
2
 0.738
2
= The gross moment of inertia (Ig) for the column strip for service dead load = 2401 in.4
35
I
 c, fixed  LDF   frame, fixed 
c
(M
 c,L 
4802
frame, averaged
 0.738  0.039 
 0.057 in.
I
2401
c, g
)
net , L frame
K
ec
PCA Notes on ACI 318-11 (9.5.3.4 Eq. 12)
Where:
 c,L = rotation of the span left support.
(M
K
)
 26.3 kip  ft = Net frame strip negative moment of the left support.
net , L frame
ec
= effective column stiffness = 553.7  106 in.-lb (calculated previously).
 c, L 
26.3  12  1000
 0.0006 rad
553.7  106
I
 l  g

 8  I e

 c,L   c , L 



 frame
PCA Notes on ACI 318-11 (9.5.3.4 Eq. 14)
Where:
 c, L = midspan deflection due to rotation of left support.
 Ig

I
 e


= Gross moment of inertia-to-effective moment of inertia ratio for frame strip.

 frame
 c,L  0.0006 
(M
 c, R 
18  12 4802

 0.0161 in.
8
4802
)
net , R frame ( 46.76  42.47)  12  1000

 0.00010 rad
K
553.7  106
ec
Where
 c,R = rotation of the span right support.
(M
= Net frame strip negative moment of the right support.
)
net , R frame
36
I
 l  g

 8  I e

 c,R   c , R 

18  12 4802

 0.00010 

 0.0027 in.

8
4802
 frame
Where:
 c,R = midspan deflection due to rotation of right support.
 cx   cx , fixed   cx , R   cx , L
PCA Notes on ACI 318-11 (9.5.3.4 Eq. 9)
 cx  0.057  0.0027  0.0161  0.076 in.
Following the same procedure, Δmx can be calculated for the middle strip. This procedure is repeated for the
equivalent frame in the orthogonal direction to obtain Δcy, and Δmy for the end and middle spans for the other
load levels (D+LLsus and D+LLfull).
Assuming square panel, Δcx = Δcy= 0.076 in. and Δmx = Δmy= 0.039 in. Then the total
The average Δ for the corner panel is calculated as follows:

 

        
my   cy
mx 
 cx

  cx   my   cy   mx  0.076  0.039  0.115 in.
2

 

37
Table 10 – Immediate (Instantaneous) Deflections in the x-direction
Column Strip
Middle Strip
D
D
Span
LDF
Δcx,
in.
LDF
Δframe-fixed,
in.
Δc-fixed,
in.
θc1,
rad
θc2,
rad
Δθc1,
in.
Δθc2,
in.
Δframe-fixed,
in.
Δm-fixed,
in.
θm1,
rad
θm2,
rad
Δθm1,
in.
Δθm2,
in.
Δmx,
in.
Ext
0.738
0.0386
0.0570
0.00059
0.00010
0.0161
0.0027
0.076
0.262
0.0386
0.0202
0.00059
0.00010
0.0161
0.0027
0.039
Int
0.675
0.0386
0.0521
-0.00010
-0.00010
-0.0027
-0.0027
0.047
0.325
0.0386
0.0251
-0.00010
-0.00010
-0.0027
-0.0027
0.020
Span
LDF
Δθc2,
in.
Δcx,
in.
LDF
Δframe-fixed,
in.
Δc-fixed,
in.
θc1,
rad
θc2,
rad
Δθc1,
in.
Δframe-fixed,
in.
Δm-fixed,
in.
θm1,
rad
θm2,
rad
Δθm1,
in.
Δθm2,
in.
Δmx,
in.
Ext
0.738
0.0386
0.0570
0.00059
0.00010
0.0161
0.0027
0.076
0.262
0.0386
0.0202
0.00059
0.00010
0.0161
0.0027
0.039
Int
0.675
0.0386
0.0521
-0.00010
-0.00010
-0.0027
-0.0027
0.047
0.325
0.0386
0.0251
-0.00010
-0.00010
-0.0027
-0.0027
0.020
Span
LDF
Δθc2,
in.
Δcx,
in.
LDF
Δframe-fixed,
in.
Δc-fixed,
in.
θc1,
rad
θc2,
rad
Δθc1,
in.
Δframe-fixed,
in.
Δm-fixed,
in.
θm1,
rad
θm2,
rad
Δθm1,
in.
Δθm2,
in.
Δmx,
in.
Ext
0.738
0.0559
0.0825
0.00082
0.00014
0.02333
0.00388
0.110
0.262
0.0559
0.0293
0.00082
0.00014
0.02333
0.00388
0.017
Int
0.675
0.0558
0.0753
-0.00014
-0.00014
-0.00387
-0.00387
0.068
0.325
0.0558
0.0363
-0.00014
-0.00014
-0.00387
-0.00387
0.009
Span
LDF
Ext
Int
D+LLsus
D+LLsus
D+LLfull
D+LLfull
LL
LL
Δcx,
in.
LDF
Δmx,
in.
0.738
0.034
0.262
0.017
0.675
0.021
0.325
0.009
38
From the analysis in the transverse direction the deflection values below are obtained:
For DL loading case:


my
cy
For DL+LLsust loading case:


my
cy
For DL+LLfull loading case:


my
cy
These values for the x-direction are shown in Table 10. Then, the total midpanel deflection is calculated by
combining the contributions of the column and middle strip deflections from the X and Y directions:
          
 cx my   cy mx 

2
PCA Notes on ACI 318-11 (9.5.3.4 Eq. 8)
5.2. Time-Dependent (Long-Term) Deflections (Δlt)
The additional time-dependent (long-term) deflection resulting from creep and shrinkage (Δcs) may be estimated
as follows:
cs    ( sust ) Inst
PCA Notes on ACI 318-11 (9.5.2.5 Eq. 4)
The total time-dependent (long-term) deflection is calculated as:
(total )  ( sust ) Inst  (1   )  [(total ) Inst  ( sust ) Inst ]
lt
CSA A23.3-04 (N9.8.2.5)
Where:
( sust )
Inst
 Immediate (instantaneous) deflection due to sustained load, in.

 
 1  50  '
ACI 318-14 (24.2.4.1.1)
(total )  Time-dependent (long-term) total deflection, in.
lt
39
(
)
 Total immediate (instantaneous) deflection, in.
total Inst
For the exterior span
 = 2, consider the sustained load duration to be 60 months or more.
ACI 318-14 (Table 24.2.4.1.3)
 ' = 0, conservatively.
 
2
2
1  50  0
 cs  2  0.076  0.152 in.
total lt  0.076  1  2  0.110  0.076  0.262 in.
Table 11 shows long-term deflections for the exterior and interior spans for the analysis in the x-direction, for
column and middle strips.
Table 11 - Long-Term Deflections
Column Strip
6.
Span
(Δsust)Inst, in
Exterior
Interior
0.076
0.047
Exterior
Interior
0.039
0.020
λΔ
Δcs, in
2.000
0.152
2.000
0.095
Middle Strip
2.000
0.078
2.000
0.041
(Δtotal)Inst, in
(Δtotal)lt, in
0.110
0.068
0.261
0.162
0.056
0.029
0.134
0.069
Computer Program Solution
spSlab program utilizes the Equivalent Frame Method described and illustrated in details here for modeling,
analysis and design of two-way concrete floor slab systems. spSlab uses the exact geometry and boundary
conditions provided as input to perform an elastic stiffness (matrix) analysis of the equivalent frame taking into
account the torsional stiffness of the slabs framing into the column. It also takes into account the complications
introduced by a large number of parameters such as vertical and torsional stiffness of transverse beams, the
stiffening effect of drop panels, column capitals, and effective contribution of columns above and below the floor
slab using the of equivalent column concept (ACI 318-14 (R8.11.4)).
spSlab Program models the equivalent frame as a design strip. The design strip is, then, separated by spSlab into
column and middle strips. The program calculates the internal forces (Shear Force & Bending Moment), moment
and shear capacity vs. demand diagrams for column and middle strips, instantaneous and long-term deflection
results, and required flexural reinforcement for column and middle strips. The graphical and text results are
provided below for both input and output of the spSlab model.
40
X
Z
Y
spSlab v5.00. Licensed to: StructurePoint. License ID: 66184-1055152-4-2C6B6-2C6B6
File: C:\TSDA\TSDA-spSlab-Two-Way Flat Plate Floor.slb
Project: Two-Way Flat Plate Floor
Frame: Interior Frame
Engineer: SP
Code: ACI 318-14
Date: 12/19/16
Time: 09:18:18
40 lb/ft2
40 lb/ft2
40 lb/ft2
40 lb/ft2
40 lb/ft2
CASE/PATTERN: Live/All
20 lb/ft2
20 lb/ft2
20 lb/ft2
20 lb/ft2
20 lb/ft2
CASE: Dead
87.5 lb/ft2
87.5 lb/ft2
87.5 lb/ft2
87.5 lb/ft2
87.5 lb/ft2
CASE: SELF
spSlab v5.00. Licensed to: StructurePoint. License ID: 66184-1055152-4-2C6B6-2C6B6
File: C:\TSDA\TSDA-spSlab-Two-Way Flat Plate Floor.slb
Project: Two-Way Flat Plate Floor
Frame: Interior Frame
Engineer: SP
Code: ACI 318-14
Date: 12/19/16
Time: 09:20:52
30.0
Shear Diagram - kip
26.38
24.32
22.26
1.80
-1.80
-22.26
-24.32
-26.38
-30.0
Moment Diagram - k-ft
-90.0
-83.94
-76.24
-76.24
-83.94
-46.90
-46.90
-0.60
-0.60
33.17
44.78
90.0
spSlab v5.00. Licensed to: StructurePoint. License ID: 66184-1055152-4-2C6B6-2C6B6
File: C:\TSDA\TSDA-spSlab-Two-Way Flat Plate Floor.slb
Project: Two-Way Flat Plate Floor
Frame: Interior Frame
Engineer: SP
Code: ACI 318-14
Date: 12/19/16
Time: 09:22:12
44.78
LEGEND:
Envelope
Middle Strip Moment Capacity - k-ft
90.0
-16.74
-15.16
-15.16
-16.74
-0.20
-0.20
13.27
17.91
17.91
90.0
Column Strip Moment Capacity - k-ft
90.0
-50.21
-45.47
-45.47
-50.22
-32.66
-32.66
26.87
19.90
90.0
spSlab v5.00. Licensed to: StructurePoint. License ID: 66184-1055152-4-2C6B6-2C6B6
File: C:\TSDA\TSDA-spSlab-Two-Way Flat Plate Floor.slb
Project: Two-Way Flat Plate Floor
Frame: Interior Frame
Engineer: SP
Code: ACI 318-14
Date: 12/19/16
Time: 09:23:11
26.87
LEGEND:
Envelope Curve
Capacity Curve
Support Centerline
Face of Support
Zone Limits
Slab Shear Capacity - kip
100.0
23.28
21.22
19.16
-23.28
-21.22
-100.0
spSlab v5.00. Licensed to: StructurePoint. License ID: 66184-1055152-4-2C6B6-2C6B6
File: C:\TSDA\TSDA-spSlab-Two-Way Flat Plate Floor.slb
Project: Two-Way Flat Plate Floor
Frame: Interior Frame
Engineer: SP
Code: ACI 318-14
Date: 12/19/16
Time: 09:24:00
-19.16
LEGEND:
Envelope Curve
Capacity Curve
Support Centerline
Face of Support
Critical Section
Instantaneous Deflection - in
-0.078
LEGEND:
Dead Load
Sustained Load
Live Load
Total Deflection
0.078
spSlab v5.00. Licensed to: StructurePoint. License ID: 66184-1055152-4-2C6B6-2C6B6
File: C:\TSDA\TSDA-spSlab-Two-Way Flat Plate Floor.slb
Project: Two-Way Flat Plate Floor
Frame: Interior Frame
Engineer: SP
Code: ACI 318-14
Date: 12/19/16
Time: 09:25:54
6-#4(62.3)
6-#4(62.3)
6-#4(52.0)
6-#4(8.0)c
6-#4(8.0)c
6-#4(52.0)
6-#4(62.3)
6-#4(216.0)c
6-#4(62.3)
6-#4(216.0)c
6-#4(216.0)c
Middle Strip Flexural Reinforcement
1-#4(8.0)
1-#4(48.0)
6-#4(8.0)c
6-#4(74.0)
5-#4(48.0)
5-#4(48.0)
6-#4(74.0)
6-#4(216.0)c
6-#4(74.0)
5-#4(48.0)
6-#4(74.0)
6-#4(216.0)c
5-#4(48.0)
6-#4(74.0)
1-#4(48.0)
1-#4(8.0)
6-#4(8.0)c
6-#4(74.0)
6-#4(216.0)c
Column Strip Flexural Reinforcement
spSlab v5.00. Licensed to: StructurePoint. License ID: 66184-1055152-4-2C6B6-2C6B6
File: C:\TSDA\TSDA-spSlab-Two-Way Flat Plate Floor.slb
Project: Two-Way Flat Plate Floor
Frame: Interior Frame
Engineer: SP
Code: ACI 318-14
Date: 12/19/16
Time: 09:32:26
spSlab v5.00 © StructurePoint
Licensed to: StructurePoint, License ID: 66184-1055152-4-2C6B6-2C6B6
C:\TSDA\TSDA-spSlab-Two-Way Flat Plate Floor.slb
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12-19-2016, 09:33:04 AM
Page 1
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(TM)
=================================================================================================
spSlab v5.00 (TM)
A Computer Program for Analysis, Design, and Investigation of
Reinforced Concrete Beams, One-way and Two-way Slab Systems
Copyright © 2003-2015, STRUCTUREPOINT, LLC
All rights reserved
=================================================================================================
Licensee
stated
above
acknowledges
that
STRUCTUREPOINT
(SP)
is
not
and
cannot
be responsible for either the accuracy
or adequacy of the material supplied
as input
for processing by the spSlab computer program. Furthermore, STRUCTUREPOINT neither makes
any warranty expressed nor implied with respect
to the correctness of the output
prepared
by the spSlab program. Although STRUCTUREPOINT has endeavored to produce spSlab error free the
program is not and cannot
be certified infallible. The final and
only responsibility for
analysis,
design
and
engineering
documents
is
the
licensee's.
Accordingly,
STRUCTUREPOINT disclaims all responsibility in contract, negligence or other tort for
any
analysis, design or engineering documents prepared in connection with the use of the spSlab
program.
==================================================================================================================
[1] INPUT ECHO
==================================================================================================================
General Information
===================
File name: C:\TSDA\TSDA-spSlab-Two-Way Flat Plate Floor.slb
Project: Two-Way Flat Plate Floor
Frame: Interior Frame
Engineer: SP
Code: ACI 318-14
Reinforcement Database: ASTM A615
Mode: Design
Number of supports = 4 + Left cantilever + Right cantilever
Floor System: Two-Way
Live load pattern ratio = 0%
Minimum free edge distance for punching shear = 4 times slab thickness.
Circular critical section around circular supports used (if possible).
Deflections are based on cracked section properties.
In negative moment regions, Ig and Mcr DO NOT include flange/slab contribution (if available)
Long-term deflections are calculated for load duration of 60 months.
0% of live load is sustained.
Compression reinforcement calculations NOT selected.
Default incremental rebar design selected.
User-defined slab strip widths NOT selected.
User-defined distribution factors NOT selected.
One-way shear in drop panel NOT selected.
Distribution of shear to strips NOT selected.
Beam T-section design NOT selected.
Longitudinal beam contribution in negative reinforcement design over support NOT selected.
Transverse beam contribution in negative reinforcement design over support NOT selected.
Material Properties
===================
Slabs|Beams
-----------wc
=
150
f'c
=
4
Ec
=
3834.3
fr
=
0.47434
fy
fyt
Es
=
=
=
Columns
-----------150
6
4696
0.58095
lb/ft3
ksi
ksi
ksi
60 ksi, Bars are not epoxy-coated
60 ksi
29000 ksi
Reinforcement Database
======================
Units: Db (in), Ab (in^2), Wb (lb/ft)
Size
Db
Ab
Wb
Size
Db
Ab
Wb
---- -------- -------- ----------- -------- -------- -------#3
0.38
0.11
0.38
#4
0.50
0.20
0.67
#5
0.63
0.31
1.04
#6
0.75
0.44
1.50
#7
0.88
0.60
2.04
#8
1.00
0.79
2.67
#9
1.13
1.00
3.40
#10
1.27
1.27
4.30
spSlab v5.00 © StructurePoint
Licensed to: StructurePoint, License ID: 66184-1055152-4-2C6B6-2C6B6
C:\TSDA\TSDA-spSlab-Two-Way Flat Plate Floor.slb
#11
#18
1.41
2.26
1.56
4.00
5.31
13.60
#14
1.69
2.25
12-19-2016, 09:33:04 AM
7.65
Span Data
=========
Slabs
----Units: L1, wL, wR, L2L, L2R (ft); t, Hmin (in)
Span Loc
L1
t
wL
wR
L2L
L2R
Hmin
---- ---- -------- -------- -------- -------- -------- -------- -------1 Int
0.667
7.00
7.000
7.000
14.000
14.000
--- LC *i
2 Int
18.000
7.00
7.000
7.000
14.000
14.000
6.67
3 Int
18.000
7.00
7.000
7.000
14.000
14.000
6.06
4 Int
18.000
7.00
7.000
7.000
14.000
14.000
6.67
5 Int
0.667
7.00
7.000
7.000
14.000
14.000
--- RC *i
NOTES:
Deflection check required for panels where code-specified Hmin for two-way construction doesn't apply due to:
*i - cantilever end span (LC, RC) support condition
Support Data
============
Columns
------Units: c1a, c2a, c1b, c2b (in); Ha, Hb (ft)
Supp
c1a
c2a
Ha
c1b
c2b
Hb
---- -------- -------- --------------- -------- -------1
16.00
16.00
9.000
16.00
16.00
9.000
2
16.00
16.00
9.000
16.00
16.00
9.000
3
16.00
16.00
9.000
16.00
16.00
9.000
4
16.00
16.00
9.000
16.00
16.00
9.000
Red%
---100
100
100
100
Boundary Conditions
------------------Units: Kz (kip/in); Kry (kip-in/rad)
Supp
Spring Kz
Spring Kry Far End A Far End B
---- ------------ ------------ --------- --------1
0
0
Fixed
Fixed
2
0
0
Fixed
Fixed
3
0
0
Fixed
Fixed
4
0
0
Fixed
Fixed
Load Data
=========
Load Cases and Combinations
--------------------------Case
SELF
Dead
Live
Type
DEAD
DEAD
LIVE
---- -------- -------- -------U1
1.200
1.200
1.600
Area Loads
---------Units: Wa (lb/ft2)
Case/Patt Span
Wa
--------- ---- -----------SELF
1
87.50
2
87.50
3
87.50
4
87.50
5
87.50
Dead
2
20.00
3
20.00
4
20.00
1
20.00
5
20.00
Live
2
40.00
3
40.00
4
40.00
1
40.00
5
40.00
Reinforcement Criteria
======================
Slabs and Ribs
-------------_____Top bars___ __Bottom bars___
Min
Max
Min
Max
------- ------- ------- ------Bar Size
#4
#4
#4
#4
Bar spacing
1.00
18.00
1.00
18.00
Reinf ratio
0.18
2.00
0.18
2.00
Cover
1.00
1.00
There is NOT more than 12 in of concrete below
in
%
in
top bars.
Beams
----_____Top bars___
__Bottom bars___
____Stirrups____
Page 2
spSlab v5.00 © StructurePoint
Licensed to: StructurePoint, License ID: 66184-1055152-4-2C6B6-2C6B6
C:\TSDA\TSDA-spSlab-Two-Way Flat Plate Floor.slb
Min
Max
Min
Max
------- ------- ------- ------Bar Size
#5
#8
#5
#8
Bar spacing
1.00
18.00
1.00
18.00
Reinf ratio
0.14
5.00
0.14
5.00
Cover
1.50
1.50
Layer dist.
1.00
1.00
No. of legs
Side cover
1st Stirrup
There is NOT more than 12 in of concrete below
Min
------#3
6.00
12-19-2016, 09:33:04 AM
Page 3
Max
------#5
18.00 in
%
in
in
2
1.50
3.00
top bars.
6
in
in
spSlab v5.00 © StructurePoint
Licensed to: StructurePoint, License ID: 66184-1055152-4-2C6B6-2C6B6
C:\TSDA\TSDA-spSlab-Two-Way Flat Plate Floor.slb
ooooo
oo
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ooo
12-19-2016, 09:33:39 AM
Page 1
ooooo
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oo
oo
oo
oo
oo
ooooo o
o
oo
oo
oo
oooooo
oo
oo
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oo
ooooo
(TM)
=================================================================================================
spSlab v5.00 (TM)
A Computer Program for Analysis, Design, and Investigation of
Reinforced Concrete Beams, One-way and Two-way Slab Systems
Copyright © 2003-2015, STRUCTUREPOINT, LLC
All rights reserved
=================================================================================================
Licensee
stated
above
acknowledges
that
STRUCTUREPOINT
(SP)
is
not
and
cannot
be responsible for either the accuracy
or adequacy of the material supplied
as input
for processing by the spSlab computer program. Furthermore, STRUCTUREPOINT neither makes
any warranty expressed nor implied with respect
to the correctness of the output
prepared
by the spSlab program. Although STRUCTUREPOINT has endeavored to produce spSlab error free the
program is not and cannot
be certified infallible. The final and
only responsibility for
analysis,
design
and
engineering
documents
is
the
licensee's.
Accordingly,
STRUCTUREPOINT disclaims all responsibility in contract, negligence or other tort for
any
analysis, design or engineering documents prepared in connection with the use of the spSlab
program.
==================================================================================================================
[2] DESIGN RESULTS*
==================================================================================================================
*Unless otherwise noted, all results are in the direction of analysis only. Another analysis
in the perpendicular direction has to be carried out for two-way slab systems.
Strip Widths and Distribution Factors
=====================================
Units: Width (ft).
__________Width___________
Span Strip
Left** Right** Bottom*
---- ------ -------- -------- -------1 Column
7.00
7.00
7.00
Middle
7.00
7.00
7.00
______ Moment Factor______
Left** Right** Bottom*
-------- -------- -------1.000
1.000
0.600
0.000
0.000
0.400
2 Column
Middle
7.00
7.00
7.00
7.00
7.00
7.00
1.000
0.000
0.750
0.250
0.600
0.400
3 Column
Middle
7.00
7.00
7.00
7.00
7.00
7.00
0.750
0.250
0.750
0.250
0.600
0.400
4 Column
Middle
7.00
7.00
7.00
7.00
7.00
7.00
0.750
0.250
1.000
0.000
0.600
0.400
5 Column
7.00
7.00
Middle
7.00
7.00
*Used for bottom reinforcement.
7.00
1.000
1.000
0.600
7.00
0.000
0.000
0.400
**Used for top reinforcement.
Top Reinforcement
=================
Units: Width (ft), Mmax (k-ft), Xmax (ft), As (in^2), Sp (in)
Span Strip Zone
Width
Mmax
Xmax
AsMin
AsMax
AsReq
SpProv
Bars
---- ------ ------- -------- ---------- -------- -------- -------- -------- -------- ------1 Column Left
7.00
0.06
0.193
1.058
8.724
0.002
14.000
6-#4 *3
Midspan
7.00
0.19
0.358
1.058
8.724
0.007
14.000
6-#4 *3
Right
7.00
0.43
0.550
1.058
8.724
0.016
12.000
7-#4 *3
Middle Left
Midspan
Right
7.00
7.00
7.00
0.00
0.00
0.00
0.000
0.275
0.550
1.058
1.058
1.058
8.724
8.724
8.724
0.000
0.000
0.000
14.000
14.000
14.000
2 Column Left
Midspan
Right
7.00
7.00
7.00
32.66
0.00
50.21
0.667
9.000
17.333
1.058
0.000
1.058
8.724
8.724
8.724
1.293
0.000
2.015
12.000
0.000
7.636
Middle Left
Midspan
Right
7.00
7.00
7.00
0.20
0.00
16.74
1.662
9.000
17.333
1.058
0.000
1.058
8.724
8.724
8.724
0.008
0.000
0.655
14.000
0.000
14.000
3 Column Left
Midspan
Right
7.00
7.00
7.00
45.47
0.00
45.47
0.667
9.000
17.333
1.058
0.000
1.058
8.724
8.724
8.724
1.818
0.000
1.818
7.636
0.000
7.636
Middle Left
7.00
15.16
0.667
1.058
8.724
0.592
14.000
6-#4 *3
6-#4 *3
6-#4 *3
7-#4
--11-#4
6-#4 *3
--6-#4 *3
11-#4
--11-#4
6-#4 *3
spSlab v5.00 © StructurePoint
Licensed to: StructurePoint, License ID: 66184-1055152-4-2C6B6-2C6B6
C:\TSDA\TSDA-spSlab-Two-Way Flat Plate Floor.slb
12-19-2016, 09:33:39 AM
Page 2
Midspan
Right
7.00
7.00
0.00
15.16
9.000
17.333
0.000
1.058
8.724
8.724
0.000
0.592
0.000
14.000
--6-#4 *3
4 Column Left
Midspan
Right
7.00
7.00
7.00
50.22
0.00
32.66
0.667
9.000
17.333
1.058
0.000
1.058
8.724
8.724
8.724
2.015
0.000
1.293
7.636
0.000
12.000
Middle Left
Midspan
Right
7.00
7.00
7.00
16.74
0.00
0.20
0.667
9.000
16.338
1.058
0.000
1.058
8.724
8.724
8.724
0.655
0.000
0.008
14.000
0.000
14.000
6-#4 *3
--6-#4 *3
5 Column Left
Midspan
Right
7.00
7.00
7.00
0.43
0.19
0.06
0.117
0.309
0.474
1.058
1.058
1.058
8.724
8.724
8.724
0.016
0.007
0.002
12.000
14.000
14.000
7-#4 *3
6-#4 *3
6-#4 *3
Middle Left
Midspan
Right
NOTES:
*3 - Design governed by
7.00
7.00
7.00
0.00
0.00
0.00
0.117
0.392
0.667
1.058
1.058
1.058
8.724
8.724
8.724
0.000
0.000
0.000
14.000
14.000
14.000
6-#4 *3
6-#4 *3
6-#4 *3
11-#4
--7-#4
minimum reinforcement.
Top Bar Details
===============
Units: Length (ft)
_____________Left______________
Span Strip
Bars Length
Bars Length
---- ------ ------- ------- ------- ------1 Column
----Middle
-----
___Continuous__
Bars Length
------- ------6-#4
0.67
6-#4
0.67
_____________Right_____________
Bars Length
Bars Length
------- ------- ------- ------1-#4
0.67
-------
2 Column
Middle
6-#4
6-#4
6.17
4.33
1-#4
---
4.00
-----
6-#4
6-#4
6.17
5.19
5-#4
---
4.00
3 Column
Middle
6-#4
6-#4
6.17
5.19
5-#4
---
4.00
-----
6-#4
6-#4
6.17
5.19
5-#4
---
4.00
4 Column
Middle
6-#4
6-#4
6.17
5.19
5-#4
---
4.00
-----
6-#4
6-#4
6.17
4.33
1-#4
---
4.00
5 Column
Middle
1-#4
---
0.67
-----
6-#4
6-#4
Top Bar Development Lengths
===========================
Units: Length (in)
_____________Left______________
Span Strip
Bars DevLen
Bars DevLen
---- ------ ------- ------- ------- ------1 Column
----Middle
-----
0.67
0.67
___Continuous__
Bars DevLen
------- ------6-#4
12.00
6-#4
12.00
-----
-----
_____________Right_____________
Bars DevLen
Bars DevLen
------- ------- ------- ------1-#4
12.00
-------
2 Column
Middle
6-#4
6-#4
12.00
12.00
1-#4
---
12.00
-----
6-#4
6-#4
12.00
12.00
5-#4
---
12.00
3 Column
Middle
6-#4
6-#4
12.00
12.00
5-#4
---
12.00
-----
6-#4
6-#4
12.00
12.00
5-#4
---
12.00
4 Column
Middle
6-#4
6-#4
12.00
12.00
5-#4
---
12.00
-----
6-#4
6-#4
12.00
12.00
1-#4
---
12.00
5 Column
Middle
1-#4
---
12.00
-----
6-#4
6-#4
12.00
12.00
-----
-----
Bottom Reinforcement
====================
Units: Width (ft), Mmax (k-ft), Xmax (ft), As (in^2), Sp (in)
Span Strip
Width
Mmax
Xmax
AsMin
AsMax
AsReq
SpProv
Bars
---- ------ -------- ---------- -------- -------- -------- -------- -------- ------1 Column
7.00
0.00
0.275
0.000
8.724
0.000
0.000
--Middle
7.00
0.00
0.275
0.000
8.724
0.000
0.000
--2 Column
Middle
7.00
7.00
26.87
17.91
8.129
8.129
1.058
1.058
8.724
8.724
1.059
0.701
14.000
14.000
6-#4
6-#4 *3
3 Column
Middle
7.00
7.00
19.90
13.27
9.124
9.124
1.058
1.058
8.724
8.724
0.780
0.518
14.000
14.000
6-#4 *3
6-#4 *3
4 Column
Middle
7.00
7.00
26.87
17.91
9.871
9.871
1.058
1.058
8.724
8.724
1.059
0.701
14.000
14.000
6-#4
6-#4 *3
5 Column
7.00
0.00
0.392
0.000
Middle
7.00
0.00
0.392
0.000
NOTES:
*3 - Design governed by minimum reinforcement.
8.724
8.724
0.000
0.000
0.000
0.000
Bottom Bar Details
==================
-----
spSlab v5.00 © StructurePoint
Licensed to: StructurePoint, License ID: 66184-1055152-4-2C6B6-2C6B6
C:\TSDA\TSDA-spSlab-Two-Way Flat Plate Floor.slb
12-19-2016, 09:33:39 AM
Page 3
Units: Start (ft), Length (ft)
_______Long Bars_______ ______Short Bars_______
Span Strip
Bars
Start Length
Bars
Start Length
---- ------- ------- ------- ------- ------- ------- ------1 Column
----Middle
----2 Column
Middle
6-#4
6-#4
0.00
0.00
18.00
18.00
-----
3 Column
Middle
6-#4
6-#4
0.00
0.00
18.00
18.00
-----
4 Column
Middle
6-#4
6-#4
0.00
0.00
18.00
18.00
-----
5 Column
Middle
-----
-----
Bottom Bar Development Lengths
==============================
Units: DevLen (in)
___Long Bars___ __Short Bars___
Span Strip
Bars DevLen
Bars DevLen
---- ------- ------- ------- ------- ------1 Column
----Middle
----2 Column
Middle
6-#4
6-#4
12.00
12.00
-----
3 Column
Middle
6-#4
6-#4
12.00
12.00
-----
4 Column
Middle
6-#4
6-#4
12.00
12.00
-----
5 Column
Middle
-----
-----
Flexural Capacity
=================
Units: x (ft), As (in^2), PhiMn, Mu (k-ft)
_______________________Top___________________ ____________________Bottom___________________
Span Strip
x AsTop
PhiMnMu- Comb Pat Status
AsBot
PhiMn+
Mu+ Comb Pat Status
---- ------ ------- ----- --------- --------- ---- ---- --------- ----- --------- --------- ---- ---- --------1 Column
0.000 1.40
-35.30
0.00
U1 All OK
0.00
0.00
0.00
U1 All OK
0.193 1.40
-35.30
-0.06
U1 All OK
0.00
0.00
0.00
U1 All OK
0.333 1.40
-35.30
-0.17
U1 All OK
0.00
0.00
0.00
U1 All OK
0.358 1.40
-35.30
-0.19
U1 All OK
0.00
0.00
0.00
U1 All OK
0.550 1.40
-35.30
-0.43
U1 All OK
0.00
0.00
0.00
U1 All OK
0.667 1.40
-35.30
-0.60
U1 All --0.00
0.00
0.00
U1 All --Middle
0.000 1.20
-30.37
0.00
U1 All OK
0.00
0.00
0.00
U1 All OK
0.193 1.20
-30.37
-0.00
U1 All OK
0.00
0.00
0.00
U1 All OK
0.333 1.20
-30.37
-0.00
U1 All OK
0.00
0.00
0.00
U1 All OK
0.358 1.20
-30.37
-0.00
U1 All OK
0.00
0.00
0.00
U1 All OK
0.550 1.20
-30.37
-0.00
U1 All OK
0.00
0.00
0.00
U1 All OK
0.667 1.20
-30.37
-0.00
U1 All --0.00
0.00
0.00
U1 All --2 Column
Middle
0.000
0.444
0.667
3.000
4.000
5.167
6.167
6.500
8.129
9.000
11.500
11.833
12.833
14.000
15.000
17.333
17.778
18.000
0.000
0.667
1.662
3.333
4.333
6.500
8.129
9.000
11.500
12.809
1.40
1.40
1.40
1.40
1.20
1.20
0.00
0.00
0.00
0.00
0.00
0.00
1.20
1.20
2.20
2.20
2.20
2.20
1.20
1.20
1.20
1.20
0.00
0.00
0.00
0.00
0.00
0.00
-35.30
-35.30
-35.30
-35.30
-30.37
-30.37
0.00
0.00
0.00
0.00
0.00
0.00
-30.37
-30.37
-54.64
-54.64
-54.64
-54.64
-30.37
-30.37
-30.37
-30.37
0.00
0.00
0.00
0.00
0.00
0.00
-47.36
-37.39
-32.66
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
-0.05
-13.33
-50.21
-58.08
-62.11
0.47
-0.00
-0.20
0.00
0.00
0.00
0.00
0.00
0.00
0.00
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
----OK
OK
OK
OK
OK
OK
OK
OK
OK
OK
OK
OK
OK
OK
------OK
OK
OK
OK
OK
OK
OK
OK
OK
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
0.00
0.00
0.00
4.62
12.31
19.23
23.40
24.42
26.87
26.40
18.24
16.40
9.76
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
4.91
9.67
16.28
17.91
17.60
12.16
6.63
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
----OK
OK
OK
OK
OK
OK
OK
OK
OK
OK
OK
OK
OK
OK
------OK
OK
OK
OK
OK
OK
OK
OK
OK
spSlab v5.00 © StructurePoint
Licensed to: StructurePoint, License ID: 66184-1055152-4-2C6B6-2C6B6
C:\TSDA\TSDA-spSlab-Two-Way Flat Plate Floor.slb
3 Column
Middle
4 Column
Middle
5 Column
Middle
12-19-2016, 09:33:39 AM
Page 4
13.809
17.333
18.000
1.20
1.20
1.20
-30.37
-30.37
-30.37
0.00
-16.74
-21.82
U1 All
U1 All
U1 All
OK
OK
---
1.20
1.20
1.20
30.37
30.37
30.37
1.15
0.00
0.00
0.000
0.667
3.000
4.000
5.167
6.167
6.500
9.000
9.124
11.500
11.833
12.833
14.000
15.000
17.333
18.000
0.000
0.667
4.191
5.191
6.500
9.000
9.124
11.500
12.809
13.809
17.333
18.000
2.20
2.20
2.20
1.20
1.20
0.00
0.00
0.00
0.00
0.00
0.00
1.20
1.20
2.20
2.20
2.20
1.20
1.20
1.20
0.00
0.00
0.00
0.00
0.00
0.00
1.20
1.20
1.20
-54.64
-54.64
-54.64
-30.37
-30.37
0.00
0.00
0.00
0.00
0.00
0.00
-30.37
-30.37
-54.64
-54.64
-54.64
-30.37
-30.37
-30.37
0.00
0.00
0.00
0.00
0.00
0.00
-30.37
-30.37
-30.37
-57.18
-45.47
-11.60
-0.45
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
-0.45
-11.60
-45.47
-57.18
-19.06
-15.16
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
-15.16
-19.06
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
--OK
OK
OK
OK
OK
OK
OK
OK
OK
OK
OK
OK
OK
OK
----OK
OK
OK
OK
OK
OK
OK
OK
OK
OK
---
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
0.000
0.222
0.667
3.000
4.000
5.167
6.167
6.500
9.000
9.871
11.500
11.833
12.833
14.000
15.000
17.333
17.556
18.000
0.000
0.667
4.191
5.191
6.500
9.000
9.871
11.500
13.667
14.667
16.338
17.333
18.000
2.20
2.20
2.20
2.20
1.20
1.20
0.00
0.00
0.00
0.00
0.00
0.00
1.20
1.20
1.40
1.40
1.40
1.40
1.20
1.20
1.20
0.00
0.00
0.00
0.00
0.00
0.00
1.20
1.20
1.20
1.20
-54.64
-54.64
-54.64
-54.64
-30.37
-30.37
0.00
0.00
0.00
0.00
0.00
0.00
-30.37
-30.37
-35.30
-35.30
-35.30
-35.30
-30.37
-30.37
-30.37
0.00
0.00
0.00
0.00
0.00
0.00
-30.37
-30.37
-30.37
-30.37
-62.11
-58.08
-50.22
-13.34
-0.06
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
-32.66
-37.39
-47.36
-21.82
-16.74
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
-0.20
-0.00
0.47
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
----OK
OK
OK
OK
OK
OK
OK
OK
OK
OK
OK
OK
OK
OK
------OK
OK
OK
OK
OK
OK
OK
OK
OK
OK
OK
---
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
0.000
0.117
0.309
0.333
0.474
0.667
0.000
0.117
0.309
0.333
0.474
0.667
1.40
1.40
1.40
1.40
1.40
1.40
1.20
1.20
1.20
1.20
1.20
1.20
-35.30
-35.30
-35.30
-35.30
-35.30
-35.30
-30.37
-30.37
-30.37
-30.37
-30.37
-30.37
-0.60
-0.43
-0.19
-0.17
-0.06
0.00
-0.00
-0.00
-0.00
-0.00
-0.00
0.00
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
All
All
All
All
All
All
All
All
All
All
All
All
--OK
OK
OK
OK
OK
--OK
OK
OK
OK
OK
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
Slab Shear Capacity
===================
Units: b, d (in), Xu (ft), PhiVc, Vu(kip)
Span
b
d
Vratio
PhiVc
Vu
Xu
---- -------- -------- -------- ------------ ------------ -----------1
168.00
5.75
1.000
91.64
0.00
0.00
2
168.00
5.75
1.000
91.64
23.28
16.85
3
168.00
5.75
1.000
91.64
21.22
1.15
4
168.00
5.75
1.000
91.64
23.28
1.15
U1 All
U1 All
U1 All
OK
OK
---
0.00
0.00
0.00
0.00
8.00
13.40
14.84
19.90
19.90
14.84
13.40
8.00
0.00
0.00
0.00
0.00
0.00
0.00
0.77
5.43
9.89
13.27
13.27
9.89
5.43
0.77
0.00
0.00
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
--OK
OK
OK
OK
OK
OK
OK
OK
OK
OK
OK
OK
OK
OK
----OK
OK
OK
OK
OK
OK
OK
OK
OK
OK
---
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
30.37
0.00
0.00
0.00
0.00
0.00
9.76
16.40
18.24
26.40
26.87
24.42
23.40
19.23
12.31
4.62
0.00
0.00
0.00
0.00
0.00
1.14
6.62
12.16
17.60
17.91
16.28
9.67
4.91
0.00
0.00
0.00
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
All
----OK
OK
OK
OK
OK
OK
OK
OK
OK
OK
OK
OK
OK
OK
------OK
OK
OK
OK
OK
OK
OK
OK
OK
OK
OK
---
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
U1
All
All
All
All
All
All
All
All
All
All
All
All
--OK
OK
OK
OK
OK
--OK
OK
OK
OK
OK
spSlab v5.00 © StructurePoint
Licensed to: StructurePoint, License ID: 66184-1055152-4-2C6B6-2C6B6
C:\TSDA\TSDA-spSlab-Two-Way Flat Plate Floor.slb
5
168.00
5.75
1.000
91.64
0.00
12-19-2016, 09:33:39 AM
Page 5
0.00
Flexural Transfer of Negative Unbalanced Moment at Supports
===========================================================
Units: Width (in), Munb (k-ft), As (in^2)
Supp
Width Width-c
d
Munb Comb Pat GammaF
AsReq
AsProv Add Bars
---- -------- -------- -------- ---------- ---- ---- ------ -------- -------- -------1
37.00
37.00
5.75
46.30 U1
All
0.617
1.159
0.617
3-#4
2
37.00
37.00
5.75
7.69 U1
All
0.600
0.180
0.969
--3
37.00
37.00
5.75
7.69 U1
All
0.600
0.180
0.969
--4
37.00
37.00
5.75
46.30 U1
All
0.617
1.159
0.617
3-#4
Punching Shear Around Columns
=============================
Critical Section Properties
--------------------------Units: b1, b2, b0, davg, CG, c(left), c(right) (in), Ac (in^2), Jc (in^4)
Supp Type
b1
b2
b0
davg
CG c(left) c(right)
Ac
Jc
---- ---- -------- -------- -------- -------- -------- -------- -------- ------------ -----------1 Rect
18.88
21.75
59.50
5.75
4.89
12.89
5.99
342.13
14110
2 Rect
21.75
21.75
87.00
5.75
0.00
10.88
10.88
500.25
40131
3 Rect
21.75
21.75
87.00
5.75
0.00
10.88
10.88
500.25
40131
4 Rect
18.88
21.75
59.50
5.75
-4.89
5.99
12.89
342.13
14110
Punching Shear Results
---------------------Units: Vu (kip), Munb (k-ft), vu (psi),
Supp
Vu
vu
Munb
---- ------------ -------- -----------1
23.51
68.7
36.72
2
50.06
100.1
-7.69
3
50.06
100.1
7.69
4
23.51
68.7
-36.72
Phi*vc (psi)
Comb Pat GammaV
vu
Phi*vc
---- ---- ------ -------- -------U1
All
0.383
140.4
189.7
U1
All
0.400
110.1
189.7
U1
All
0.400
110.1
189.7
U1
All
0.383
140.4
189.7
Material Takeoff
================
Reinforcement in the Direction of Analysis
-----------------------------------------Top Bars:
336.6 lb
<=>
6.08 lb/ft
Bottom Bars:
432.9 lb
<=>
7.82 lb/ft
Stirrups:
0.0 lb
<=>
0.00 lb/ft
Total Steel:
769.5 lb
<=> 13.91 lb/ft
Concrete:
451.9 ft^3 <=>
8.17 ft^3/ft
<=>
<=>
<=>
<=>
<=>
0.435
0.559
0.000
0.993
0.583
lb/ft^2
lb/ft^2
lb/ft^2
lb/ft^2
ft^3/ft^2
spSlab v5.00 © StructurePoint
Licensed to: StructurePoint, License ID: 66184-1055152-4-2C6B6-2C6B6
C:\TSDA\TSDA-spSlab-Two-Way Flat Plate Floor.slb
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12-19-2016, 09:34:21 AM
Page 1
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(TM)
=================================================================================================
spSlab v5.00 (TM)
A Computer Program for Analysis, Design, and Investigation of
Reinforced Concrete Beams, One-way and Two-way Slab Systems
Copyright © 2003-2015, STRUCTUREPOINT, LLC
All rights reserved
=================================================================================================
Licensee
stated
above
acknowledges
that
STRUCTUREPOINT
(SP)
is
not
and
cannot
be responsible for either the accuracy
or adequacy of the material supplied
as input
for processing by the spSlab computer program. Furthermore, STRUCTUREPOINT neither makes
any warranty expressed nor implied with respect
to the correctness of the output
prepared
by the spSlab program. Although STRUCTUREPOINT has endeavored to produce spSlab error free the
program is not and cannot
be certified infallible. The final and
only responsibility for
analysis,
design
and
engineering
documents
is
the
licensee's.
Accordingly,
STRUCTUREPOINT disclaims all responsibility in contract, negligence or other tort for
any
analysis, design or engineering documents prepared in connection with the use of the spSlab
program.
==================================================================================================================
[3] DEFLECTION RESULTS
==================================================================================================================
Section Properties
==================
Frame Section Properties
-----------------------Units: Ig, Icr (in^4), Mcr (k-ft)
_______________M+ve_____________ _______________M-ve_____________
Span Zone
Ig
Icr
Mcr
Ig
Icr
Mcr
---- ------- ----------- ----------- -------- ----------- ----------- -------1 Left
4802
0
54.23
4802
466
-54.23
Midspan
4802
0
54.23
4802
499
-54.23
Right
4802
0
54.23
4802
499
-54.23
2 Left
4802
466
54.23
4802
499
-54.23
Midspan
4802
466
54.23
4802
0
-54.23
Right
4802
466
54.23
4802
629
-54.23
3 Left
4802
466
54.23
4802
629
-54.23
Midspan
4802
466
54.23
4802
0
-54.23
Right
4802
466
54.23
4802
629
-54.23
4 Left
4802
466
54.23
4802
629
-54.23
Midspan
4802
466
54.23
4802
0
-54.23
Right
4802
466
54.23
4802
499
-54.23
5 Left
4802
0
54.23
4802
499
-54.23
Midspan
4802
0
54.23
4802
499
-54.23
Right
4802
0
54.23
4802
466
-54.23
NOTES: M+ve values are for positive moments (tension at bottom face).
M-ve values are for negative moments (tension at top face).
Frame Effective Section Properties
---------------------------------Units: Ie, Ie,avg (in^4), Mmax (k-ft)
__________________________Load Level__________________________
_________Dead_______ ______Sustained_____ ______Dead+Live_____
Span Zone
Weight
Mmax
Ie
Mmax
Ie
Mmax
Ie
---- -------- -------- -------- ----------- -------- ----------- -------- ----------1 Right
1.000
-0.33
4802
-0.33
4802
-0.46
4802
Span Avg
------4802
---4802
---4802
2 Middle
0.850
24.94
4802
24.94
4802
34.23
4802
Right
0.150
-46.75
4802
-46.75
4802
-64.15
3151
Span Avg
------4802
---4802
---4554
3 Left
0.150
-42.47
4802
-42.47
4802
-58.27
3994
Middle
0.700
18.47
4802
18.47
4802
25.35
4802
Right
0.150
-42.47
4802
-42.47
4802
-58.27
3994
Span Avg
------4802
---4802
---4560
4 Left
0.150
-46.75
4802
-46.75
4802
-64.15
3151
Middle
0.850
24.94
4802
24.94
4802
34.23
4802
Span Avg
------4802
---4802
---4554
5 Left
1.000
-0.33
4802
-0.33
4802
-0.46
4802
Span Avg
------4802
---4802
---4802
Strip Section Properties at Midspan
-----------------------------------
spSlab v5.00 © StructurePoint
Licensed to: StructurePoint, License ID: 66184-1055152-4-2C6B6-2C6B6
C:\TSDA\TSDA-spSlab-Two-Way Flat Plate Floor.slb
12-19-2016, 09:34:21 AM
Units: Ig (in^4)
_______Column Strip_______ _______Middle Strip_______
Span
Ig
LDF Ratio
Ig
LDF Ratio
---- ------------ ------ ------ ------------ ------ -----1
2401 0.800 1.600
2401 0.200 0.400
2
2401 0.738 1.475
2401 0.262 0.525
3
2401 0.675 1.350
2401 0.325 0.650
4
2401 0.738 1.475
2401 0.262 0.525
5
2401 0.800 1.600
2401 0.200 0.400
NOTES: Load distirubtion factor, LDL, averages moment distribution factors listed in [2] Design Results.
Ratio refers to proportion of strip to frame deflections under fix-end condtions.
Instantaneous Deflections
=========================
Extreme Instantaneous Frame Deflections and Corresponding Locations
------------------------------------------------------------------Units: Def (in), Loc (ft)
________________Live_______________ _________Total_________
Span Direction Value
Dead
Sustained Unsustained
Total
Sustained
Dead+Live
---- --------- ----- ----------- ----------- ----------- ----------- ----------- ----------1
Down
Def
------------Loc
------------Up
Def
-0.004
---0.002
-0.002
-0.004
-0.006
Loc
0.000
--0.000
0.000
0.000
0.000
2
Down
Def
0.055
--0.023
0.023
0.055
0.078
Loc
8.378
--8.378
8.378
8.378
8.378
Up
Def
------------Loc
------------3
Down
Def
0.032
--0.014
0.014
0.032
0.046
Loc
8.876
--8.876
8.876
8.876
8.876
Up
Def
-0.000
---0.000
-0.000
-0.000
-0.000
Loc
0.444
--0.444
0.444
0.444
0.444
4
Down
Def
0.055
--0.023
0.023
0.055
0.078
Loc
9.622
--9.622
9.622
9.622
9.622
Up
Def
------------Loc
------------5
Down
Def
------------Loc
------------Up
Def
-0.004
---0.002
-0.002
-0.004
-0.006
Loc
0.667
--0.667
0.667
0.667
0.667
Extreme Instantaneous Column Strip Deflections and Corresponding Locations
-------------------------------------------------------------------------Units: Def (in), Loc (ft)
________________Live_______________ _________Total_________
Span Direction Value
Dead
Sustained Unsustained
Total
Sustained
Dead+Live
---- --------- ----- ----------- ----------- ----------- ----------- ----------- ----------1
Down
Def
------------Loc
------------Up
Def
-0.004
---0.002
-0.002
-0.004
-0.006
Loc
0.000
--0.000
0.000
0.000
0.000
2
Down
Def
0.072
--0.031
0.031
0.072
0.103
Loc
8.627
--8.627
8.627
8.627
8.627
Up
Def
------------Loc
------------3
Down
Def
0.045
--0.019
0.019
0.045
0.064
Loc
8.876
--8.876
8.876
8.876
8.876
Up
Def
-0.000
---0.000
-0.000
-0.000
-0.000
Loc
0.222
--0.222
0.222
0.222
0.222
4
Down
Def
0.072
--0.031
0.031
0.072
0.103
Loc
9.373
--9.373
9.373
9.373
9.373
Up
Def
------------Loc
------------5
Down
Def
------------Loc
------------Up
Def
-0.004
---0.002
-0.002
-0.004
-0.006
Loc
0.667
--0.667
0.667
0.667
0.667
Extreme Instantaneous Middle Strip Deflections and Corresponding Locations
-------------------------------------------------------------------------Units: Def (in), Loc (ft)
________________Live_______________ _________Total_________
Span Direction Value
Dead
Sustained Unsustained
Total
Sustained
Dead+Live
---- --------- ----- ----------- ----------- ----------- ----------- ----------- ----------1
Down
Def
------------Loc
------------Up
Def
-0.004
---0.002
-0.002
-0.004
-0.006
Loc
0.000
--0.000
0.000
0.000
0.000
2
Down
Def
0.038
--0.016
0.016
0.038
0.054
Loc
7.881
--8.129
8.129
7.881
8.129
Up
Def
------------Loc
------------3
Down
Def
0.019
--0.008
0.008
0.019
0.027
Loc
8.876
--8.876
8.876
8.876
8.876
Up
Def
-0.000
---0.000
-0.000
-0.000
-0.000
Loc
0.667
--0.667
0.667
0.667
0.667
Page 2
spSlab v5.00 © StructurePoint
Licensed to: StructurePoint, License ID: 66184-1055152-4-2C6B6-2C6B6
C:\TSDA\TSDA-spSlab-Two-Way Flat Plate Floor.slb
4
Down
Up
5
Down
Up
Def
Loc
Def
Loc
Def
Loc
Def
Loc
0.038
9.871
---------0.004
0.667
-----------------
0.016
9.871
---------0.002
0.667
0.016
9.871
---------0.002
0.667
12-19-2016, 09:34:21 AM
Page 3
0.038
9.871
---------0.004
0.667
0.054
9.871
---------0.006
0.667
Long-term Deflections
=====================
Long-term Column Strip Deflection Factors
----------------------------------------Time dependant factor for sustained loads = 2.000
Units: Astop, Asbot (in^2), b, d (in), Rho' (%), Lambda (-)
__________________M+ve__________________ __________________M-ve__________________
Span
Zone
Astop
b
d
Rho' Lambda
Asbot
b
d
Rho' Lambda
---- ------- -------- -------- -------- ------ ------ -------- -------- -------- ------ -----1 Right
---------- 0.000 2.000
---------- 0.000 2.000
2 Midspan
---------- 0.000 2.000
---------- 0.000 2.000
3 Midspan
---------- 0.000 2.000
---------- 0.000 2.000
4 Midspan
---------- 0.000 2.000
---------- 0.000 2.000
5 Left
---------- 0.000 2.000
---------- 0.000 2.000
NOTES: Deflection multiplier, Lambda, depends on moment sign at sustained load level and Rho' in given zone.
Rho' is assumed zero because Compression Reinforcement option is NOT selected in Solve Options.
Long-term Middle Strip Deflection Factors
----------------------------------------Time dependant factor for sustained loads = 2.000
Units: Astop, Asbot (in^2), b, d (in), Rho' (%), Lambda (-)
__________________M+ve__________________ __________________M-ve__________________
Span
Zone
Astop
b
d
Rho' Lambda
Asbot
b
d
Rho' Lambda
---- ------- -------- -------- -------- ------ ------ -------- -------- -------- ------ -----1 Right
---------- 0.000 2.000
---------- 0.000 2.000
2 Midspan
---------- 0.000 2.000
---------- 0.000 2.000
3 Midspan
---------- 0.000 2.000
---------- 0.000 2.000
4 Midspan
---------- 0.000 2.000
---------- 0.000 2.000
5 Left
---------- 0.000 2.000
---------- 0.000 2.000
NOTES: Deflection multiplier, Lambda, depends on moment sign at sustained load level and Rho' in given zone.
Rho' is assumed zero because Compression Reinforcement option is NOT selected in Solve Options.
Extreme Long-term Column Strip Deflections and Corresponding Locations
---------------------------------------------------------------------Units: D (in), x (ft)
Span Direction Value
cs
cs+lu
cs+l
Total
---- --------- ----- ----------- ----------- ----------- ----------1
Down
Def
--------Loc
--------Up
Def
-0.009
-0.011
-0.011
-0.015
Loc
0.000
0.000
0.000
0.000
2
Down
Def
0.145
0.176
0.176
0.248
Loc
8.627
8.627
8.627
8.627
Up
Def
--------Loc
--------3
Down
Def
0.089
0.109
0.109
0.153
Loc
8.876
8.876
8.876
8.876
Up
Def
-0.000
-0.000
-0.000
-0.000
Loc
0.222
0.222
0.222
0.222
4
Down
Def
0.145
0.176
0.176
0.248
Loc
9.373
9.373
9.373
9.373
Up
Def
--------Loc
--------5
Down
Def
--------Loc
--------Up
Def
-0.009
-0.011
-0.011
-0.015
Loc
0.667
0.667
0.667
0.667
NOTES: Incremental deflections due to creep and shrinkage (cs) based on sustained load level values.
Incremental deflections after partitions are installed can be estimated by deflections due to:
- creep and shrinkage plus unsustained live load (cs+lu), if live load applied before partitions,
- creep and shrinkage plus live load (cs+l), if live load applied after partitions.
Total deflections consist of dead, live, and creep and shrinkage deflections.
Extreme Long-term Middle Strip Deflections and Corresponding Locations
---------------------------------------------------------------------Units: D (in), x (ft)
Span Direction Value
cs
cs+lu
cs+l
Total
---- --------- ----- ----------- ----------- ----------- ----------1
Down
Def
--------Loc
--------Up
Def
-0.009
-0.011
-0.011
-0.015
Loc
0.000
0.000
0.000
0.000
2
Down
Def
0.076
0.091
0.091
0.129
Loc
8.129
8.129
8.129
8.129
Up
Def
---------
spSlab v5.00 © StructurePoint
Licensed to: StructurePoint, License ID: 66184-1055152-4-2C6B6-2C6B6
C:\TSDA\TSDA-spSlab-Two-Way Flat Plate Floor.slb
3
Down
Up
4
Down
Up
5
Down
Up
Loc
Def
Loc
Def
Loc
Def
Loc
Def
Loc
Def
Loc
Def
Loc
--0.038
8.876
-0.001
0.667
0.076
9.871
---------0.009
0.667
--0.046
8.876
-0.001
0.667
0.091
9.871
---------0.011
0.667
--0.046
8.876
-0.001
0.667
0.091
9.871
---------0.011
0.667
12-19-2016, 09:34:21 AM
--0.065
8.876
-0.001
0.667
0.129
9.871
---------0.015
0.667
NOTES: Incremental deflections due to creep and shrinkage (cs) based on sustained load level values.
Incremental deflections after partitions are installed can be estimated by deflections due to:
- creep and shrinkage plus unsustained live load (cs+lu), if live load applied before partitions,
- creep and shrinkage plus live load (cs+l), if live load applied after partitions.
Total deflections consist of dead, live, and creep and shrinkage deflections.
Page 4
7.
Summary and Comparison of Two-Way Slab Design Results
Table 12 - Comparison of Moments obtained from Hand (EFM) and spSlab Solution
Hand (EFM)
spSlab
32.20
32.66
26.50
26.87
50.30
50.21
0.00
0.20
17.70
17.91
16.70
16.74
45.60
45.47
19.90
19.90
15.20
15.16
13.20
13.27
Exterior Span
Exterior Negative
Column Strip
Positive
Interior Negative
*
Exterior Negative
Middle Strip
*
*
Positive
Interior Negative
*
Interior Negative
*
Interior Span
Column Strip
Middle Strip
*
Positive
Interior Negative
*
Positive
negative moments are taken at the faces of supports
Table 13 - Comparison of Reinforcement Results with Hand and spSlab Solution
Span Location
Reinforcement Provided
for Flexure
Hand
Additional Reinforcement
Provided for Unbalanced
Moment Transfer*
spSlab
Total
Reinforcement
Provided
Hand
spSlab
Hand
spSlab
Exterior Span
Column
Strip
Exterior
Negative
7-#4
7-#4
3-#4
3-#4
10-#4
10-#4
Positive
6-#4
6-#4
n/a
n/a
6-#4
6-#4
11-#4
11-#4
---
---
11-#4
11-#4
6-#4
6-#4
n/a
n/a
6-#4
6-#4
Positive
6-#4
6-#4
n/a
n/a
6-#4
6-#4
Interior
Negative
6-#4
6-#4
n/a
n/a
6-#4
6-#4
Interior
Negative
Exterior
Negative
Middle
Strip
Interior Span
Column
Strip
Middle
Strip
Positive
6-#4
6-#4
n/a
n/a
6-#4
6-#4
Positive
6-#4
6-#4
n/a
n/a
6-#4
6-#4
*In the EFM, the unbalanced moment (Msc, Munb) at the support centerline is used to determine the value of the
additional reinforcement as compared with DDM using the moments at the face of support.
60
Table 14 - Comparison of One-Way (Beam Action) Shear Check Results Using Hand and spSlab Solution
*
φVc, kips
xu* , in.
Vu , kips
Span
Hand
spSlab
Exterior
23.3
23.3
Interior
21.2
21.2
Hand
spSlab
Hand
spSlab
1.15
1.15
91.64
91.64
16.85
16.85
91.64
91.64
xu calculated from the centerline of the left column for each span
Table 15 - Comparison of Two-Way (Punching) Shear Check Results Using Hand and spSlab Solution
b1, in.
b2, in.
Ac, in.2
bo, in.
Vu, kips
vu, psi
Support
Hand
spSlab
Hand
spSlab
Hand
spSlab
Hand
spSlab
Hand
spSlab
Hand
spSlab
Exterior
18.88
18.88
21.75
21.75
59.5
59.5
342.00
342.13
21.65
22.79
63.3
66.6
Interior
21.75
21.75
21.75
21.75
87
87
500.00
500.25
50.07
50.07
100.1
100.1
γv
Jc, in.4
cAB, in.
Munb, kips-ft
φvc, psi
vu, psi
Support
Hand
spSlab
Hand
spSlab
Hand
spSlab
Hand
spSlab
Hand
spSlab
Hand
spSlab
Exterior
5.99
5.99
14109
14110
0.383
0.383
37.8
37.2
137.0
139.2
189.7
189.7
Interior
10.88
10.88
40131
40131
0.400
0.400
-7.8
-7.7
110.2
110.1
189.7
189.7
Table 16 - Comparison of Immediate Deflection Results Using Hand and spSlab Solution (in.)
Column Strip
Span
D
D+LLsus
D+LLfull
LL
Hand
spSlab
Hand
spSlab
Hand
spSlab
Hand
spSlab
Exterior
0.076
0.072
0.076
0.072
0.110
0.103
0.034
0.031
Interior
0.047
0.045
0.047
0.045
0.068
0.064
0.021
0.019
Middle Strip
Span
D
D+LLsus
D+LLfull
LL
Hand
spSlab
Hand
spSlab
Hand
spSlab
Hand
spSlab
Exterior
0.039
0.038
0.039
0.038
0.056
0.054
0.017
0.016
Interior
0.020
0.019
0.020
0.019
0.029
0.027
0.009
0.008
Table 17 - Comparison of Time-Dependent Deflection Results Using Hand and spSlab Solution
Column Strip
λΔ
Δcs, in.
Δtotal, in.
Span
Hand
spSlab
Hand
spSlab
Hand
spSlab
Exterior
2.0
2.0
0.152
0.145
0.261
0.248
Interior
2.0
2.0
0.095
0.089
0.162
0.153
Middle Strip
λΔ
Δcs, in.
Δtotal, in.
Span
Hand
spSlab
Hand
spSlab
Hand
spSlab
Exterior
2.0
2.0
0.078
0.076
0.134
0.129
61
Interior
2.0
2.0
0.041
0.038
0.069
0.065
In all of the hand calculations illustrated above, the results are in close or exact agreement with the automated
analysis and design results obtained from the spSlab model. Excerpts of spSlab graphical and text output are given
below for illustration.
8.
Comparison of Two-Way Slab Analysis and Design Methods
A slab system can be analyzed and designed by any procedure satisfying equilibrium and geometric compatibility.
Three established methods are widely used. The requirements for two of them are described in detail in ACI 31814 Chapter 8 (8.2.1).
Direct Design Method (DDM) is an approximate method and is applicable to flat plate concrete floor systems that
meet the stringent requirements of ACI 318-14 (8.10.2). In many projects, however, these requirements limit the
usability of the Direct Design Method significantly.
The Equivalent Frame Method (EFM) does not have the limitations of Direct Design Method. It requires more
accurate analysis methods that, depending on the size and geometry can prove to be long, tedious, and timeconsuming.
StucturePoint’s spSlab software program solution utilizes the Equivalent Frame Method to automate the process
providing considerable time-savings in the analysis and design of two-way slab systems as compared to hand
solutions using DDM or EFM.
Finite Element Method (FEM) is another method for analyzing reinforced concrete slabs, particularly useful for
irregular slab systems with variable thicknesses, openings, and other features not permissible in DDM or EFM.
Many reputable commercial FEM analysis software packages are available on the market today such as spMats.
Using FEM requires critical understanding of the relationship between the actual behavior of the structure and
the numerical simulation since this method is an approximate numerical method. The method is based on several
assumptions and the operator has a great deal of decisions to make while setting up the model and applying loads
and boundary conditions. The results obtained from FEM models should be verified to confirm their suitability
for design and detailing of concrete structures.
The following table shows a general comparison between the DDM, EFM and FEM. This table covers general
limitations, drawbacks, advantages, and cost-time efficiency of each method where it helps the engineer in
deciding which method to use based on the project complexity, schedule, and budget.
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Applicable
ACI
318-14
Provision
Concrete Slab Analysis Method
Limitations/Applicability
DDM
(Hand)
EFM
(Hand//spSlab)
FEM
(spMats)
Minimum of three continuous spans in each
direction
Successive span lengths measured center-tocenter of supports in each direction shall not
differ by more than one-third the longer span
Panels shall be rectangular, with ratio of
longer to shorter panel dimensions, measured
center-to-center supports, not exceed 2.
Column offset shall not exceed 10% of the
span in direction of offset from either axis
between centerlines of successive columns

8.10.2.5
All loads shall be due to gravity only

8.10.2.5
All loads shall be uniformly distributed over
an entire panel (qu)

Unfactored live load shall not exceed two
times the unfactored dead load
For a panel with beams between supports on
all sides, slab-to-beam stiffness ratio shall be
satisfied for beams in the two perpendicular
directions.

Structural integrity steel detailing



8.5.4
Openings in slab systems



8.2.2
Concentrated loads
8.10.2.1
8.10.2.2
8.10.2.3
8.10.2.4
8.10.2.6
8.10.2.7
8.7.4.2
8.11.1.2






Not permitted

Engineering judgment required
based on modeling technique
Engineering judgment required
based on modeling technique
Engineering judgment required
Live load arrangement (Load Patterning)
Not required
Required
Reinforcement for unbalanced slab moment
transfer to column (Msc)
Irregularities (i.e. variable thickness, nonprismatic, partial bands, mixed systems,
support arrangement, etc.)
Moments @
support face
Not permitted
Moments @
support centerline
Engineering
judgment required
Complexity
Low
Average
Complex to very complex
Design time/costs
Fast
Limited
Unpredictable/Costly
Conservative
(see detailed
comparison with
spSlab output)
Somewhat
conservative
R8.10.4.5*
Unknown - highly dependent on
modeling assumptions:
1. Linear vs. non-linear
Design Economy
2. Isotropic vs non-isotropic
3. Plate element choice
4. Mesh size and aspect ratio
5. Design & detailing features
Very limited
Limited geometry
Limited guidance non-standard
applications
application (user dependent).
General (Drawbacks)
Required significant engineering
judgment
Very limited
Detailed analysis is
Unlimited applicability to handle
analysis is required
required or via
complex situations permissible by
General (Advantages)
software
the features of the software used
(e.g. spSlab)
(e.g. spMats)
*
The unbalanced slab moment transferred to the column Msc (Munb) is the difference in slab moment on either side of a column at a specific joint.
In DDM only moments at the face of the support are calculated and are also used to obtain Msc (Munb). In EFM where a frame analysis is used,
moments at the column center line are used to obtain Msc (Munb).
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