PCI MANUAL FOR THE DESIGN OF HOLLOW CORE SLABS
SECOND EDITION
by Donald R. Buettner and Roger J. Becker
Computerized Structural Design, S.C. Prepared for the
PCI Hollow Core Slab Producers Committee
John E. Saccoman, Chairperson James Beerbower
Ernest Markle Kevin Boyle
James Markle Jeffrey Butler
Milo J. Nimmer Loris Collavino
William C. Richardson, Jr. Edward J. Gregory
Klaus Rosenstern Pat Hynes
Wes Schrooten Paul Kourajian
Larry Stigler
PRECAST / PRESTRESSED CONCRETE INSTITUTE
175 WEST JACKSON BOULEVARD CHICAGO, ILLINOIS 60604
312 786--0300 FAX 312 786--0353
Copyright 1998 By Precast/Prestressed Concrete Institute
First edition, 1985 Second edition, 1998
All rights reserved. This book or any part thereof may not be reproduced in any form without the written permission of the Precast/Prestressed Concrete Institute.
ISBN 0--937040--57--6
Printed in U.S.A.
INTRODUCTION
Purpose of Manual
The application and design of precast, prestressed hollow core slabs is similar to that of other pre- stressed members. However, there are situations which are unique to hollow core slabs either be- cause of the way the slabs are produced or because of the application of the slabs.
For special situations, hollow core producers have developed design criteria and conducted in- house testing to verify that their approaches are valid. In fact, there is consistency between the many types of hollow core slabs available. The purpose of this manual is to bring together those things that are common, that are verified by test and that can be universally applied to hollow core slabs. Be- cause there are differences, some topics covered will also point to the differences where closer coor- dination with the local producer is required.
This manual was prepared by Computerized Structural Design, S.C., Milwaukee, Wisconsin with input and direction from the PCI Hollow Core Slab Producers Committee. Additionally, the fire and acoustical sections were prepared by Armand Gustaferro of The Consulting Engineers Group, Inc., Mt. Prospect, Illinois and Allen H. Shiner of Shiner and Associates, Inc., Skokie, Illinois, respective- ly. All reasonable care has been used to verify the accuracy of material contained in this manual. However, the manual should be used only by those experienced in structural design and should not replace good structural engineering judgment.
Scope of Manual
This document is intended to cover the primary design requirements for hollow core floor and roof systems. In instances where the design is no different than for other prestressed members, the PCI Design Handbook and the ACI Building Code should be consulted for more in-depth discussion.
For the architect or consulting engineer, this manual is intended as a guideline for working with hollow core slabs, a guide for the use and application of hollow core slabs and an indication of some of the limitations of hollow core slabs. For the plant engineer, the manual will hopefully present some backup and reference material for dealing with everyday design problems.
NOTATION
A = Cross-sectional area f d = Stress at extreme tension fiber due to a = Depth of equivalent compression stress
unfactored member self weight block
= Portion of base shear applied at level i a θ
= Depth of equivalent compression stress f pc = Compressive stress in concrete at the block under fire conditions
centroid of the section due to effective A cr = Area of crack face
prestress for non-composite sections or A e = Net effective slab bearing area
due to effective prestress and moments A ps = Area of prestressed reinforcement
resisted by the precast section alone for A vf = Area of shear friction reinforcement
composite sections
b = Width of compression face f pe = Compressive stress in concrete at extreme b w = Net web width of hollow core slab
fiber where external loads cause tension C = Confinement factor
due to the effective prestress only C = Compressive force
f ps = Stress in prestressed reinforcement at C = Seismic factor dependent on site and
nominal strength
structure fundamental period f psθ = Stress in prestressed reinforcement at fire C = Factor for calculating steel relaxation
strength
losses as given in Table 2.2.3.2 f′ ps = Maximum steel stress in partially c = Distance from extreme compression
developed strand
fiber to neutral axis f pu = Specified tensile strength of CR = Prestress loss due to concrete creep
prestressing steel
C s = Seismic coefficient f puθ = Tensile strength of prestressing steel at D = Dead load
elevated temperatures d = Distance from extreme compression fiber
F px = Force applied to diaphragm at level under to centroid of non-prestressed
consideration
tension reinforcement f se = Effective stress in prestressing steel after d b = Nominal diameter of reinforcement
all losses
d p = Distance from extreme compression fiber
= Stress in prestressing steel at initial to centroid of prestressed
f si
prestress
= Additional portion of base shear applied at DW = Distribution width
reinforcement
top level
e = Distance from neutral axis to centroid of
= Usable grout strength in a horizontal joint prestressed reinforcement
= Steel yield strength E c = Modulus of elasticity of concrete
h = Overall member depth E ci = Modulus of elasticity of concrete at the
= Net height of grout in keyway between time of initial prestress
slab units
ES = Prestress loss due to elastic shortening of I = Occupancy importance factor concrete
I = Cross-sectional moment of inertia E s
= Modulus of elasticity of steel
= Factor for calculating steel relaxation reinforcement
losses as given in Table 2.2.3.1 f′ c = Specified design compressive strength of
= Fraction of total load in a horizontal joint concrete
in a grout column
f′ ci = Compressive strength of concrete at the K cir = Factor for calculating elastic shortening time of initial prestress
prestress losses
f cir = Net compressive stress in concrete at K cr = Factor for calculating prestress losses due centroid of prestressed reinforcement at
to concrete creep
time of initial prestress K es = Factor for calculating prestress losses due f cds = Stress in concrete at centroid of
to elastic shortening prestressed reinforcement due to
K re = Factor for calculating prestress losses due superimposed dead load
to steel relaxation as given in Table 2.2.3.1
K sh = Factor for calculating prestress losses due
= Factored shear force due to externally to concrete shrinkage
applied loads occurring simultaneously K′ u = Factor from PCI Handbook Fig. 4.12.2 for
with M max
calculating flexural design strength
=V u -- V d
L = Live load V n = Nominal shear strength of a member
ℓ = Span length
V s = Nominal shear strength provided by shear
ℓ d = Reinforcement development length
reinforcement
= Design shear force V/S = Volume to surface ratio
ℓ e = Strand embedment length from member
end to point of maximum stress
= Uniformly distributed load
ℓ f = Flexural bond length
= Bearing area length
= Total dead load plus other applicable M
ℓ t = Strand transfer length
= Service load moment loads for seismic design M cr = Cracking moment
= Portion of W at level i M d = Unfactored dead load moment
w px = Portion of W at level under M g = Unfactored self-weight moment
consideration
M n = Nominal flexural strength y b = Distance from neutral axis to extreme M nθ = Flexural strength under fire conditions
bottom fiber
M max = Maximum factored moment due to
= Used as either distance to top fiber or externally applied loads
tension fiber from neutral axis
= Seismic zone factor M sd = Unfactored moment due to
=M u -- M d Z
β 1 = Factor defined in ACI 318-95, Section superimposed dead load
M u = Factored design moment
= Factor for type of prestressing strand M θ = Applied fire moment
δ all = Limiting free end slip P
= Effective force in prestressing steel after
= Actual free end slip all losses
ε ps = Strain in prestressed reinforcement at P o
= Effective prestress force at release prior to nominal flexural strength long term losses
= Strain in prestressed reinforcement P i
= Initial prestress force after seating losses ε se = Strain in prestressed reinforcement after Q
= First moment of area
losses
R = Fire endurance rating
= Shear friction coefficient RE = Prestress loss due to steel relaxation
µ e = Effective shear friction coefficient R e = Reduction factor for load eccentricity in
= Ratio of prestressed reinforcement horizontal joints
= Ratio of compression reinforcement RH = Ambient relative humidity
= ACI strength reduction factor R w = Seismic coefficient dependent on
= ρf y /f′ c
structural system type
= ρ′f y /f′ c
S = Section modulus
ω p =ρ p f ps /f′ c
SH = Prestress loss due to concrete shrinkage ω w = Reinforcement index for flanged sections T
= Tensile force ω′ w = Reinforcement index for flanged sections t g = Width of grout column in horizontal joint
ω pw = Reinforcement index for flanged sections V = Seismic base shear
ω pu =ρ p f pu /f′ c
= Subscript denoting fire conditions V ci = Nominal shear strength of concrete in a
V c = Nominal shear strength of concrete
shear-flexure failure mode V cw = Nominal shear strength of concrete in a web shear failure mode V d = Shear due to unfactored self weight V h = Horizontal beam shear
CHAPTER 1 HOLLOW CORE SLAB SYSTEMS
1.1 Methods of Manufacturing
long. Slabs are then sawcut to the appropriate
A hollow core slab is a precast, prestressed con- length for the intended project. crete member with continuous voids provided to
The economy of the generalized hollow core reduce weight and, therefore, cost and, as a side
system is in the quantity of slabs that can be pro- benefit, to use for concealed electrical or mechan-
duced at a given time with a minimum of labor re- ical runs. Primarily used as floor or roof deck sys-
quired. Each slab on a given casting line will have tems, hollow core slabs also have applications as
the same number of prestressing strands. There- wall panels, spandrel members and bridge deck
fore, the greatest production efficiency is obtained units.
by mixing slabs with the same reinforcing re- An understanding of the methods used to
quirements from several projects on a single pro- manufacture hollow core slabs will aid in the spe-
duction line. This implies that best efficiency for a cial considerations sometimes required in the use
single project is obtained if slab requirements are of hollow core slabs. Hollow core slabs are cast
repetitive.
using various methods in the seven major systems
1.2 Materials
available today. Because each production system As stated previously, hollow core slabs are pro- is patented, producers are usually set up on a fran-
duced with two basic concrete mixes; low slump chise or license basis using the background,
and normal slump concrete. For the low slump knowledge and expertise provided with the ma-
concretes, water content is limited to slightly chine development. Each producer then has the
more than that required for cement hydration. technical support of a large network of associated
Water-cement ratios are typically about 0.3. Mix- producers.
ing is critical because the limited water available Two basic manufacturing methods are current-
must be well dispersed in the mix. Water reducing ly in use for the production of hollow core slabs.
admixtures can be used to optimize a mix by re- One is a dry cast or extrusion system where a very
ducing cement and water requirements while still low slump concrete is forced through the ma-
retaining adequate workability for proper com- chine. The cores are formed with augers or tubes
paction of the concrete by the machine. Air en- with the concrete being compacted around the
trainment admixtures are not effective in the dry cores. The second system uses a higher slump
mix concrete. With the low water-cement ratios concrete. Sides are formed either with stationary,
and compaction placing method, air is difficult to fixed forms or with forms attached to the machine
disperse well and maintain.
with the sides being slip formed. The cores in the normal slump, or wet cast, systems are formed
Table 1.1 Hollow Core Systems
with either lightweight aggregate fed through
Manufac-
Machine
Concrete Core Form
tubes attached to the casting machine, pneumatic
turer
Type
Type/Slump
tubes anchored in a fixed form or long tubes at-
Dy-Core
Extruder
Dry/Low Tubes
tached to the casting machine which slip form the
Dynaspan
Slip Form
Wet/Normal Tubes
Dry/Low Auger/Tube
Table 1.1 lists the seven major hollow core sys-
Flexicore
Fixed Form Wet/Normal Pneumatic
tems available today along with the basic in-
Tubes
formation on the casting technique. Various
Spancrete
Slip Form
Dry/Low Tubes
names may be used by local licensees to describe
SpanDeck Slip Form
Wet/Normal Filler
the same products. In most cases, the slabs are
aggregate
cast on long line beds, normally 300 ft to 600 ft
Ultra-Span Extruder
Dry/Low Augers
The wet cast products (those cast with normal slump concrete), have water-cement ratios in the range of 0.4 to 0.45. Depending on the slip form- ing system used, slumps of 2 to 5 inches (50 - 130 mm) are used. The mix design and use of admix- tures is dependent on achieving a mix that will hold its shape consistent with the forming tech- nique used.
Aggregates vary in the various manufacturing processes depending on what type is locally avail- able. Maximum aggregate size larger than pea gravel is rarely used because of the confined areas
Latex feathering ready for direct carpet application
into which concrete must be placed. Light weight aggregates are occasionally used to reduce the weight of the sections and to achieve a significant reduction in required equivalent thickness in a fire rated application. Concrete unit weights ranging
from 110 to 150 pcf (1760 - 2400 kg/m 3 ) are used
in the industry.
Strand use in hollow core slabs includes about every size and type of strand produced depending on what is available to a particular producer. The
trend is toward primary use of the larger 1 / 2 in (13 mm) diameter, low relaxation strand. The philos- ophy of strand use varies from using many strand sizes to optimize cost for a given project to using only one or two strand sizes for simplicity of in- ventory and production.
Except for special situations, keyway grout is normally a sand and Portland cement mixture in proportions of about 3:1. The amount of water used is a function of the method used to place the grout but will generally result in a wet mix so key-
Acoustical spray on exposed slab ceiling
ways may be easily filled. Shrinkage cracks may occur in the keyways, but configuration of the key is such that vertical load transfer can still occur with the presence of a shrinkage crack. Rarely is grout strength required in excess of 2000 psi (13.8 MPa) for vertical load transfer.
Although it is discouraged, non-shrink, non- staining grout is occasionally specified for use in keyways. In evaluating the potential benefits of non-shrink grout, the volume of grout must be compared to the overall volume of concrete in the slabs and support materials. Because the size of the keyway is small in relation to a floor or roof as- sembly of slabs, total shrinkage will be affected
Electrical and HVAC application
only to a minor degree. Shrinkage cracks can still only to a minor degree. Shrinkage cracks can still
be gained in comparison with the additional cost. Transmission Class rating ranges from about 47 to
57 without topping and the Impact Insulation
Class rating starts at about 23 for a plain slab and Hollow core slabs are most widely known for
1.3 Advantages of Hollow Core Slabs
may be increased to over 70 with the addition of providing economical, efficient floor and roof
carpeting and padding. Detailed information on systems. The top surface can be prepared for the
the acoustical properties of hollow core slabs is installation of a floor covering by feathering the
presented in Chapter 7.
joints with a latex cement, installing non-structur-
al fill concretes ranging from 1 / 2 in to 2 in (13 - 51
1.4 Framing Concepts
mm) thick depending on the material used, or by The primary consideration in developing a casting a composite structural concrete topping.
framing scheme using hollow core slabs is the The underside can be used as a finished ceiling as
span length. For a given loading and fire endur- installed, by painting, or by applying an acoustical
ance rating, span length and slab thickness may be spray.
optimized by consulting a producer’s published When properly coordinated for alignment, the
load tables. Section 1.7 presents sample load voids in a hollow core slab may be used for electri-
tables and instructions for the use of the tables. cal or mechanical runs. For example, routing of a
The PCI Design Handbook 1 recommends limits lighting circuit through the cores can allow fix-
on span-depth ratios for the hollow core slabs. For tures in an exposed slab ceiling without unsightly
roof slabs, a span-depth ratio limit of 50 is sug- surface mounted conduit. Slabs used as the heated
gested and for floor slabs, a limit of 40 is sug- mass in a passive solar application can be detailed
gested. In practice, a span-depth ratio of 45 is to distribute the heated air through the cores.
common for floors and roofs when fire endurance, Structurally, a hollow core slab provides the ef-
openings, or heavy or sustained live loads do not ficiency of a prestressed member for load capac-
control a design.
ity, span range, and deflection control. In addi- Consideration must be given to factors which tion, a basic diaphragm is provided for resisting
affect slab thickness selection for a given span. lateral loads by the grouted slab assembly pro-
Heavy superimposed loads, as required by the vided proper connections and details exist. A de-
function of a system, would require a lower span- tailed discussion of diaphragm capabilities is
depth ratio. Similarly, heavy partitions or a large presented in Chapter 4.
number of openings will result in higher load ca- Excellent fire resistance is another attribute of
pacity requirements. The fire resistance rating re- the hollow core slab. Depending on thickness and
quired for the application will also affect the load strand cover, ratings up to a 4 hour endurance can
capacity of a slab. As the code required fire rating
be achieved. A fire rating is dependent on equiva- increases, prestressing strands can be raised for lent thickness for heat transmission, concrete cov-
more protection from the heat. The smaller effec- er over the prestressing strands for strength in a
tive strand depth will result in a lower load capac- high temperature condition, and end restraint.
ity. Alternatively, a rational design procedure can Underwriters Laboratories publishes fire ratings
be used to consider the elevated strand tempera- for various assemblies. However, many building
tures during a fire. This fire design condition may codes allow a rational design procedure for
control a slab design and, again, result in a lower strength in a fire. This procedure, described in de-
load capacity.
tail in Chapter 6, considers strand temperature in Once slab thicknesses and spans are selected, calculating strength. Required fire ratings should
the economics of layout become important.
be clearly specified in the contract documents. While ends cut at an angle can be designed and Also, the fire rating should be considered in deter-
supplied, it is most efficient to have the bearing mining the slab thickness to be used in prelimi-
perpendicular to the span so square cut ends can nary design.
be used.
Used as floor-ceiling assemblies, hollow core It is also desirable to have the plan dimensions slabs have the excellent sound transmission char-
fit the slab module. This is dependent upon the fit the slab module. This is dependent upon the
floor is required in a structure consisting of multi- dated using partial width slabs. Some producers
ple bays of varying length and change in slab intentionally cast narrow widths as filler pieces
direction, the highest point will determine the top while others use a section split from a full slab.
elevation of the topping. A greater amount of top- Such a split section might be created by a longitu-
ping will then be required in “low” areas. These dinal sawcut or a break if the edge will not be ex-
considerations must be dealt with in the planning posed to view.
stages to both control costs and minimize ques- Construction tolerances must be accounted for
tions and potential for “extras” during construc- in developing a plan layout. Tolerance on slab
tion.
length may be taken up by allowing a gap at the Camber, camber growth, and deflections must slab ends in the bearing detail. On the non-bearing
be considered when slabs run parallel to a stiff ver- sides, clearance may be provided by using a detail
tical element such as a wall (e.g. slabs running where the slabs lap over a wall or beam. If the slab
parallel to the front wall of an elevator). The door edge butts a wall or beam, a gap should be pro-
rough opening should allow for camber to pro- vided. Refer to local producers’ information for
duce proper door installation. Alternatively, the recommendations of proper tolerances.
slab span might be rearranged so the front wall is a When a hollow core slab deck is exposed to
bearing wall. Then door problems would be alle- weather for a long period of time during construc-
viated.
tion, water can accumulate in the cores. The pri- Camber, camber growth, and deflections must mary source of water infiltration is at the butt
be taken into account in roofing details. Where joints. In cold weather, this water can freeze and
changes in relative slab position can occur, coun- expand causing localized damage. One remedy
terflashings are suggested to accommodate such for this situation is to drill weep holes at the slab
changes.
ends under each core. The need for such weep holes is generally known only after a construction
1.5 Wall Panel Applications
schedule is established. The specifier and the slab Some hollow core slab systems can also pro- supplier are not usually in a position to know of
vide slabs to be used as walls. Long line manufac- such a need in advance.
turing can result in economical cladding or load Hollow core members will be cambered as with
bearing panels used in manufacturing or commer- any other prestressed flexural member. In the
cial applications. The hollow core wall panels are planning stages, consideration should be given to
prestressed with two layers of strands for accom- the causes of differential camber. For two slabs of
modating handling, structural loadings and bow- identical length and prestressing, the camber may
ing considerations. Some manufacturers can add
2 in to 4 in (51 - 102 mm) of insulation to the hol- tions. This factor is independent of a framing
be different because of concrete and curing varia-
low core section with a 1 1 / 2 in thick to 3 in (38 - 76 scheme. However, joints between slabs of un-
mm) thick concrete facing to create an insulated equal spans or joints at which a change in the span
sandwich panel.
direction occurs, will cause a potential differential
A variety of architectural finishes are available camber problem. This must be recognized and
with hollow core wall panels. While the finishes dealt with in the design layout. Wall locations
can be very good, the variety of finishes available may hide such a joint, but the door swing might be
is different from those typically available with directed to the least variable side.
true architectural precast concrete panels. In Camber must also be accommodated when a
judging the quality of finish on hollow core wall topping is to be provided. The quantity of topping
panels, consideration must be given to the required must consider the amount of camber and
manufacturing process.
the function of the floor. In occupancies where flat floors are not a requirement, a constant top- ping thickness may be used to follow the curva-
Producer load tables define the allowable live It is customary in the hollow core industry for
1.6 Design Responsibilities
load that a given slab can safely support in addi- the producer to perform the final engineering for
tion to the slab self weight. The load capacity will the product to be supplied to the job. This would
be a function of the slab thickness, the amount of include design for vertical loads and lateral loads
prestressing provided, and the location of the pre- specified by the Engineer of Record, embedded
stressing strands. Fire rated slabs may require items for specified connection forces, and han-
additional concrete cover below the strands which dling and shipping. However, the Engineer of Re-
will affect the load capacity. cord plays a very important role in the design pro-
The design criteria used to develop these load cess. Prior to selection of the hollow core produc-
tables is defined by the ACI Building Code 2 as er, enough preliminary planning should be done to
outlined in Chapter 2. Depending on the design insure that the specified floor and roof system is
criteria controlling a slab’s load capacity, some achievable. That is, the project should be one that
advantage may be gained by understanding that in can be engineered without requiring changes from
most applications, superimposed loads will con- the contract documents.
sist of both dead and live loads. Where ultimate The contract documents must clearly indicate
strength controls, an equivalent live load can be design criteria to which hollow core slabs will
used to enter a load table. It is calculated as: have to conform. This is especially important
superimposed Dead load when the hollow core slabs must interface with
equivalent =
other construction materials. When connections
+ Live load
are required, the forces to be transmitted through However, if bottom fiber tensile stresses con- the connections must be specified in the contract
trol, no adjustment in superimposed loads may be documents. The producer is best able to deter-
used.
mine the most efficient connection element to be Similarly, many loading conditions consist of embedded in the slab. However, the balance of a
loads other than uniform loads. For preliminary connection which interfaces with another materi-
design only, an equivalent uniform load may be al should be detailed in the contract documents.
calculated from the maximum moment caused by The Engineer of Record also has a responsibil-
the actual loads.
ity in the review and approval of erection draw-
8M
ings prepared by the precast producer. Review of w superimposed
equivalent =
these drawings is the last opportunity to assure 2 ℓ
that the producer’s understanding of the project Shear will not be properly addressed in this sit- coincides with the intent of design. Erection
uation. Thus, the final design must consider the drawings should be checked for proper design
actual load pattern.
loads, proper details and bearing conditions, con- Because of the uniqueness of each hollow core formance with specified fire ratings, and the loca-
slab system and the many possibilities of strand tion of openings.
patterns available from various producers, a ge- neric hollow core slab has been developed to dem- onstrate design procedures. Figure 1.7.1 depicts the slab section and properties and illustrates a
typical form for a producer’s load tables. Each of the major hollow core slab systems has
1.7 Cross-Sections and Load Tables
Throughout this manual, this section will be used
a standard set of cross-sections that can be pro- to demonstrate various calculation procedures duced by their equipment. Available in thick-
where any one of the proprietary cross-sections nesses ranging from 4 in to 15 in (102 - 380 mm),
could be substituted. It must be emphasized that core configurations make each system unique.
this cross -section is not available for use and Each individual producer has additional produc-
should not be specified .
tion practices which may affect the capabilities of Figures 1.7.2 through 1.7.8 present the propri- their product. Therefore, most producers prepare
etary slab cross-sections currently available. The and distribute load tables in their market area.
section properties are as provided by the manufac- section properties are as provided by the manufac-
particularly to check shear.
slightly from those given. The availability of any particular section in a given area must be verified
1.8 Tolerances 3
with the local producers. Figures 1.7.9 present Figure 1.8.1 shows the dimensional tolerances charts of the general range of load capacities
for precast hollow core slabs. These tolerances available in a given slab thickness. As with any
are guidelines only and each project must be con- chart of this nature, the chart should be carefully
sidered individually to ensure that the tolerances approached and verified with local producer load
shown are applicable.
tables, especially for the longest and shortest and Figure 1.8.2 shows erection tolerances for hol- lightest and heaviest conditions. Special care is
low core slabs. When establishing tolerances, the also required when fire rated slabs must be used
function of the slabs should be considered. For on a project. (See Chapter 6)
example, slabs covered by finish materials may The following examples demonstrate the ways
not need the close tolerances required for exposed in which load tables may be used.
slabs.
Example 1.7.1 Equivalent Uniform Load
From the load table in Figure 1.7.1 select a strand pattern to carry a uniform superimposed dead load of 20 psf and a uniform live load of 60 psf on a 24 foot span.
w total = 20 + 60 = 80 psf 4-7/16 in dia. strands required: capacity = 118 psf
flexural strength controls w
equivalent = 20 1.7 + 60 = 77 psf
Use 4-3/8 in dia. strands: capacity = 79 psf flexural strength controls.
Example 1.7.2 Non-Uniform Loads
From the load table in Figure 1.7.1 select a strand pattern to carry a superimposed uniform load of 20 psf dead plus 40 psf live and a continu- ous wall load of 600 plf located perpendicular to the span and at midspan. The design span is 25 feet. For preliminary design
= 8438 ft-#/ft
8 8438 w equivalent =
= 108 psf Try 6-3/8 in dia. strands - capacity = 120 psf
Fig. 1.7.1 Generic hollow core slab
Section Properties A = 154 in 2 1 1/4"
I = 1224.5 in 4 b w = 10.5 in
y b = 3.89 in 5 1/4"
S b = 314.8 in 3
SAMPLE LOAD TABLE 3
Allowable Superimposed Live Loads, psf Spans, ft
Strands, 270LR φMn, ft-k 14 15 16 17 18 19 20 21 22 23
85.0 343 1 311 1 283 6-7/16″ 1 258 231 208 4-1/2″
1 1 1 6-1/2″ 1 105.3 317 290 267 247
Strands, 270LR φMn, ft-k 24 25 26 27 28 29 30
1 - Values are governed by shear strength. 2 - Values are governed by allowable tension
3 - Table based on 5000 psi concrete with 6 f′ c allowable tension. Unless noted, values are governed by strength design.
Note: This slab is for illustration purposes only. Do not specify this slab for a project.
Fig. 1.7.2
Trade name: Dy-Core Equipment Manufacturer: Mixer Systems, Inc., Pewaukee, Wisconsin
Section
Untopped
with 2″ topping
4′-0″ x 6″
4′-0″ x 8″
4′-0″ x 10″ 215
4′-0″ x 12″ 264
4′-0″ x 15″ 289
Note: All sections not available from all producers. Check availability with local manufacturers.
Fig. 1.7.3
Trade name: Dynaspan Equipment Manufacturer: Dynamold Corporation, Salina, Kansas
Section
Untopped
with 2″ topping
4′-0″ x 4″
4′-0″ x 6″
4′-0″ x 8″
4′-0″ x 10″ 260
8′-0″ x 6″
8′-0″ x 8″
8′-0″ x 10″ 532
8′-0″ x 12″ 615
Note: All sections not available from all producers. Check availability with local manufacturers.
Fig. 1.7.4
Trade name: Elematic Equipment Manufacturer: Mixer Systems, Inc., Pewaukee, Wisconsin
Section
Untopped
with 2″ topping
4′-0″ x 6″
4′-0″ x 8″
4′-0″ x 10″(5)
4′-0″ x 10″(6)
4′-0″ x 12″
Note: Elematic is also availble in 96″ width. All sections not available from all producers. Check availability with local manufacturers.
Fig. 1.7.5
Trade name: Flexicore Licensing Organization: The Flexicore Co. Inc., Dayton, Ohio
Section
Untopped
with 2″ topping
1′-4″ x 6″
2′-0″ x 6″
1′-4″ x 8″
2′-0″ x 8″
1′-8″ x 10″
2′-0″ x 10″ 138
2′-0″ x 12″ 141
Note: All sections not available from all producers. Check availability with local manufacturers.
Fig. 1.7.6
Trade name: Spancrete Licensing Organization: Spancrete Machinery Corp., Milwaukee, Wisconsin
Section
Untopped
with 2″ topping
width
A y b I wt y 2 4 b I 4 depth wt in in in psf in in psf 4′-0″ x 4″
4′-0″ x 6″
63 5.22 3443 88 Ultralight Spancrete
4′-0″ x 8″
4′-0″ x 10″ 312
4′-0″ x 12″ 355
4′-0″ x 15″ 370
4′-0″ x 8″
4′-0″ x 10″ 277
4′-0″ x 12″ 316
Note: Spancrete is also available in 40″ and 96″ widths. All sections are not available from all producers. Check availability with
local manufacturer.
Fig. 1.7.7
Trade name: SpanDeck Licensing Organization: Fabcon, Incorporated, Savage, Minnesota
Section
Untopped
with 2″ topping
4′-0″ x 8″
4′-0″ x 12″ 298
8′-0″ x 8″
8′-0″ x 12″ 578
Note: All sections not available from all producers. Check availability with local manufacturers.
Fig. 1.7.8
Trade name: Ultra-Span Licensing Organization: Ultra-Span Technologies, Inc., Winnipeg, Manitoba, Canada
Section
Untopped
with 2″ topping
4′-0″ x 4″
4′-0″ x 6″
4′-0″ x 8″
4′-0″ x 10″ 259
4′-0″ x 12″ 289
Note: All sections are not available from all producers. Check availability with local manufacturers.
Fig. 1.7.9(a) Slab load ranges
300 6" Hollow Core Slab
250 3/4" Concrete Cover
100 Superimposed Live Load, psf
10 20 30 40 Span, ft
Fig. 1.7.9 (b) Slab load ranges
300 8" Hollow Core Slab
250 3/4" Concrete Cover ~ = 45
150 8" + 2" Topping 8"
100 Superimposed Live Load, psf
Span, ft
Fig. 1.7.9(c) Slab load ranges
300 10" Hollow Core Slab
250 3/4" Concrete Cover 10" + 2" Topping
100 Superimposed Live Load, psf
Span, ft
Fig. 1.7.9 (d) Slab load ranges
300 12" Hollow Core Slab 3/4" Concrete Cover
100 Superimposed Live Load, psf
10 20 30 40 Span, ft
Fig. 1.7.9(e) Slab load ranges
200 15" Hollow Core Slab 3/4" Concrete Cover
100 Superimposed Live Load, psf
Span, ft
Fig. 1.8.1 Product tolerances -- hollow core slabs
a = Length ..................................... ± 1 / 2 in
= Center of gravity of strand group
b = Width ...................................... ± 1 / 4 in
The CG of the strand group relative to the top of the plank
shall be within ± 1 / 4 in of the nominal strand group CG. The d t = Top flange thickness
c = Depth ...................................... ± 1 / 4 in
position of any individual strand shall be within ± 1 / 2 in of Top flange area defined by the actual measured values of
nominal vertical position and ± 3 / 4 in of nominal horizontal average d t x b shall not be less than 85% of the nominal area
position and shall have a minimum cover of 3 / 4 in. calculated by d t nominal x b nominal.
k = Position of plates .............................. ± 2 in d b = Bottom flange thickness
= Tipping and flushness of plates ................ ± Bottom flange area defined by the actual measured values 1 / in ± 1 4 of average d b x b shall not be less than 85% of the nominal
m = Local smoothness ..................... / 4 in in 10 ft
(does not apply to top deck surface left rough to receive a e = Web thickness
topping or to visually concealed surfaces) The total cumulative web thickness defined by the actual
area calculated by d b nominal x b nominal.
Plank weight
measured value Σe shall not be less than 85% of the nominal Excess concrete material in the plank internal features is cumulative width calculated by Σe nominal.
within tolerance as long as the measured weight of the f = Blockout location .............................. ±
individual plank does not exceed 110% of the nominal g = Flange angle .............. 1
2 in / 8 in per 12 in, 1 / 2 in max.
published unit weight used in the load capacity calculation. h = Variation from specified end squareness
n = Applications requiring close control of differential camber
between adjacent members of the same design should be i
or skew .................................... ± 1 / 2 in
= Sweep (variation from straight line parallel to centerline of discussed in detail with the producer to determine applicable
member) ................................... ± 3 / 8 in
tolerances.
c e j CGS
d b l CROSS SECTION
g 10 ft
ELEVATION
a PLAN
CHAPTER 2 DESIGN OF HOLLOW CORE SLABS
b) Extreme fiber stress in tension except The design of hollow core slabs is governed by
2.1 General
as permitted in (c) ......... 3 f′ ci
the ACI (318-95) Building Code Requirements for Structural Concrete. 2
c) Extreme fiber stress in tension at ends
As with prestressed con-
of simply supported members . . . . . . crete members in general, hollow core slabs are
........................ 6 f′ ci
checked for prestress transfer stresses, handling
stresses, service load stresses, deflections and de-
2.2.1.2 Permissible stresses at service sign (ultimate) strength in shear and bending. For
loads (Section 18.4)
uniform load cases, the manufacturer’s load tables
a) Extreme fiber stress in compression will take into account these various design consid-
erations and print a load capacity based on the due to prestress plus sustained loads ........................
0.45 f′ governing criteria. For loading conditions other
b) Extreme fiber stress in compression than uniform, or for the development of load
due to prestress plus total load tables, the design steps presented in this section
are used. ........................
0.60 f′ c
c) Extreme fiber stress in tension in pre- An excellent reference for prestressed member
design exists in the PCI Design Handbook. 1 compressed tensile zone ..... 6 f′ c Charts and tables provide design aids to shorten
d) Extreme fiber stress in tension in pre- the calculation procedures. Another excellent
compressed tensile zone where deflec- source for design information is the PCI Standard
tions are calculated considering bili- Design Practice 4 which reflects design practices
near moment-deflection relationships in the industry.
........................ 12 f′ c The generic slab presented in Section 1.7 will
2.2.1.3 Loss of prestress (Section 18.6) tion. The cross-section was selected to provide a
be used for the calculations presented in this sec-
Calculation of losses shall consider: means of demonstrating calculation procedures
a) Seating loss
and does not represent any slab currently in use.
b) Elastic shortening of concrete Therefore, this generic slab should never be speci-
c) Creep of concrete
fied for use on a project. See Section 1.7 for the
d) Shrinkage of concrete slabs currently available.
e) Steel relaxation
2.2.1.4 Design (ultimate) strength
2.2 Flexural Design
a) Load Factors (Section 9.2)
U = 1.4D + 1.7L
b) Strength Reduction Factors (Section
2.2.1 ACI Requirements
Chapter 18 of ACI (318-95) presents provi-
Flexure φ = 0.9
sions for the flexural design of prestressed con-
c) Flexural Strength (Section 18.7) crete members. The applicable limits from ACI
are paraphrased as follows:
M u ≤ φM = ÔA f n a ps ps d p −
ps f ps
2.2.1.1 Permissible stresses at transfer
a=
(Section 18.4).
0.85f′ c b
a) Extreme fiber stress in compression
f ps = value calculated by strain . .......................
0.6 f′ ci
compatibility compatibility
p f pu
β 1 f′ c
M d = 30.5 2.08 2.08 0.0535
M d 4.74 12 =
2.2.2 Stresses at Transfer
When the prestressing strands are cut to apply the prestressing force to the concrete, only the slab
= +0.191 ksi top fiber self weight is present to counteract the effects of
= --0.181 ksi bottom fiber eccentric prestress. A check of stresses is required
Net concrete stress at transfer point at this point to determine the concrete strength re-
quired to preclude cracking on the tension side or = --0.162 ksi top fiber crushing on the compression side. The concrete
= +1.542 ksi bottom fiber strength at the time of transfer may be only 50% to
Self weight at midspan
60% of the 28 day design strength.
d = 30.5 (0.0535)(3′) = 18.66 ft-k
Example 2.2.2.1 - Transfer Stresses
Using the generic hollow core cross-section
d 18.66 12 =
defined in Section 1.7, check stresses at transfer of
prestress using the following criteria:
Prestressing steel: 4 - 1 / ″ dia. 270 ksi, low relax-
= +0.752 ksi top fiber
ation strands. = --0.711 ksi bottom fiber
A = 4(0.153) = 0.612 in ps 2 Net concrete stress at midspan assume 5% initial loss
= +0.399 ksi top fiber
d p = 7″ = +1.012 ksi bottom fiber
ℓ = 30′-6″
Allowable stresses:
initial stress = 70% f pu
tension at end = 6 f′ ci
Solution:
f′ ci = − 162 = 729 psi
Stresses will be checked at the transfer point
and at midspan
tension at midspan = 3 f′
ci
At release prestress force
does not control
P o = (0.70)(0.95)(0.612)(270) = 109.9k Prestress effect
compression = 0.6 f′ ci
=P o P o
f′ = 1542 = 2570 psi
Concrete strength required at release
314.8 Note that if tension or compression in the end region exceeds allowables based on a reasonable
= --0.353 ksi top fiber concrete release strength, strands may be de- = +1.723 ksi bottom fiber
bonded in some manufacturing systems or, for tension, top mild reinforcement may be used in
Self weight at transfer point some manufacturing systems to resist the total
ℓ t = 50d b = 50(1/2) = 25 in
tension force.
If tension in the midspan region controls, either
1) Elastic Shortening
a high release strength must be used or mild rein-
forcement must be added to resist the total tension
force. Mild reinforcement should only be used in the wet cast manufacturing system.
K es = 1.0 for pretensioned members
M g e The calculation of prestress losses affects the
2.2.3 Prestress Losses
service load behavior of a slab. The accuracy of any calculation method is dependent on the pre-
K cir = 0.9 for pretensioned members ciseness of concrete and prestressing steel materi-
al properties as well as external factors such as hu- midity used in the calculation procedure. The
2) Concrete Creep
accuracy of loss calculations has little effect on
CR = K the ultimate strength of a member. s cr (f
E cir -- f cds c )
Prestress loss calculations are required for pre- diction of camber and for service load stress cal-
K cr = 2.0 for normal weight pretensioned culations. Since the success of a project is judged
members
on service load performance rather than ultimate strength, it behooves any slab producer to use a
= 1.6 for sand lightweight pretensioned loss calculation procedure which best predicts the
members
behavior of the product as produced.
For low relaxation strand and for special cases
cds =
f sd
(e.g., long spans or special loadings) using stress
relieved strand, the 1995 ACI Code references
3) Shrinkage of Concrete
several sources for prestress loss calculations.
SH = 8.2 x 10 -6 K E
sh s 1 − 0.06 VS
The method presented here was developed by Zia,
et al. 5 and considers the following parameters:
x (100 -- RH)
Fig. 2.2.3.1 Ambient relative humidity
Table 2.2.3.1 Table 2.2.3.2 Values of C Type of tendon
270 Grade stress-re-
relieved
bar or
lieved strand or wire
20,000 0.15 f si /f pu
strand or
low-relaxation
250 strand or wire Grade stress-re- lieved strand or wire
wire
0.79 1.22 240 or 235 Grade stress-
relieved wire 17,600 0.13 0.78 1.16
0.77 1.11 270 Grade low-relax-
0.76 1.05 ation strand
0.75 1.45 1.00 250 Grade low-relax-
0.74 1.36 0.95 ation wire
0.73 1.27 0.90 240 or 235 Grade low-re-
0.72 1.18 0.85 laxation wire
0.71 1.09 0.80 145 or 160 Grade stress-
0.70 1.00 0.75 relieved bar
0.68 0.89 0.66 K sh = 1.0 for pretensioned members
0.66 0.78 0.57 RH = Ambient relative humidity from Fig-
0.65 0.73 0.53 ure 2.2.3.1
4) Steel Relaxation
0.62 0.58 0.41 RE = [K re -- J (SH + CR + ES)]C
0.60 0.49 0.33 K re , J, C = factors from Tables 2.2.3.1
and 2.2.3.2
Solution:
5) Total Loss = ES + CR + SH + RE
1) Elastic Shortening
P i = 0.7(4)(41.3k) = 115.6k Observations and experience in a plant may
provide modifications to loss calculations to bet- 2 M g = 30.5 (0.0535)(3 ′ )
ter predict slab performance.
= 18.66 ft-k = 224 in-k
Example 2.2.3.1 Loss of Prestress
154 + stress based on the following information: 1224.5
Using the generic hollow core cross-section 115.6 2 115.6(2.89) defined in Section 1.7, calculate the loss of pre-
f cir = 0.9
Prestressing steel: 4- 1 / 2 ″ dia. 270 ksi, low re-
laxation strands
A ps f pu = 0.153(270) = 41.3k/strand
= 0.857 ksi
d p = 7″ using E s = 28,500 ksi and E ci = 3250 ksi initial stress = 70% f pu
E ES = K s es f
E ci cir
ℓ = 30′-6″ Superimposed dead load = 20 psf
= 7.52 ksi %= 25.6 (100) = 13.5%
2) Concrete Creep
I 2.2.4 Service Load Stresses Service load concrete stresses are calculated as
a measure of performance or serviceability. For
the in-service state when deflections must be cal- 1224.5
culated, a stress check must first be made to deter- = 0.198 ksi
mine whether gross section properties or cracked- using E c = 4300 ksi and normal weight concrete
transformed section properties are to be used. In-service stresses are checked assuming that
E CR = K s cr (f cir -- f cds ) all prestress losses have occurred. The calculated
E c stresses are compared to the permissible stresses
= (2.0)28500 (0.857 -- 0.198) noted in Section 2.2.1. Hollow core slabs are nor- 4300
mally designed to be uncracked under full service = 8.74 ksi
loads. Tensile stress limits of between 6 f′ c and
3) Shrinkage of Concrete 7.5 f′ c are commonly used. In special circum-
stances where deflections will not be a problem =
V Area
and where cracking will not be of concern, the up-
use RH = 70% per limit of 12 f′ c can be used.
SH = 8.2 x 10 -6 K sh E s Example 2.2.4.1 Service Load Stresses 1 − 0.06 VS
Using the generic hollow core cross-section x (100 -- RH)
defined in Section 1.7, calculate the service load stresses given the following criteria:
= 8.2 x 10 -6 (1.0)28500
Prestressing steel:
x (1 -- 0.06 x 1.75)(100 -- 70)
4- 1 / 2 ″ dia. 270 ksi, low relaxation strands = 6.27 ksi
A ps f pu = 0.153(270) = 41.3k/strand
4) Steel Relaxation
From Table 2.2.3.1
Initial stress = 70% f pu
K re = 5000, J = 0.04
f′ c = 5000 psi
From Table 2.2.3.2
ℓ = 30′-6″
C = 0.75 for f si /f pu = 0.7
Clear Span = 30′-0″
RE = [K re -- J(SH + CR + ES)]C Superimposed Dead Load = 20 psf Live Load = 50 psf
= 5000 0.04x [
Solution:
(6.27 + 8.74 + 7.52) 0.75 M sustained = 30 ] (0.0535 + 0.020) 8
= 8.27 ft-k/ft = 99.2 in-k/ft = 3.07 ksi
5) Total Loss at Midspan M service = 30 (0.0535 + 0.020 + 0.050)
= 7.52 + 8.74 + 6.27 + 3.07 = 13.89 ft-k/ft = 167 in-k/ft = 25.6 ksi
With losses = 13.5% from Example 2.2.3.1
A ps f se = (0.7)(4)(41.3)(1 -- 0.135)
+ 7.5 f′ c = 100.0k
cr =I P y
Pe
b A+ S b
Top fiber compression with sustained loads This ensures that when the concrete develops flexural cracks, the prestressing steel will not have
reached its full design stress. Violation of this cri-
f top = 100.0 154 − 297.9 + 297.9 teria might result in strand fractures at the point of = 0.649 -- 0.970 + 0.999
flexural cracking with a resulting brittle failure. However, ACI (318-95) Section 18.8.3 allows
= + 0.679 ksi violation of this requirement for flexural members Permissible compression
with shear and flexural strength at least twice that required.
= 0.45f′c The upper limit of reinforcing requires that, = 0.45(5000)
ω p or,
d p + ω − ω′ or Top fiber compression with total load
= 2.25 ksi > 0.679 ksi OK
be not greater than 0.36β 1
= 0.649 -- 0.970 + 1.679 The need for an upper limit on reinforcing is re-
= 1.358 ksi lated to the assumptions of ultimate concrete com- Permissible compression
pressive strain. Using a uniform compression stress block forces more concrete to reach ulti-
= 0.60f′c mate strain as reinforcing ratios increase. There- = 0.60(5000)
fore when the upper reinforcing limit is exceeded, the moment capacity must be based on the com-
= 3.00 ksi > 1.358 ksi OK pression block. For this condition,
Bottom fiber tension
φM n =φ
2 f′
c bd p 0.36β
f bottom = 0.649 + (0.970 -- 1.679)297.9
for rectangular sections or for flanged sections = --0.022 ksi (tension)
with the neutral axis within the flange. The stress in the prestressing steel at ultimate
Permissible tension may be calculated in several ways. The ACI equa-
= 7.5 f′ tion (18-3) may be used as an approximation,
c charts and tables from the PCI Design Handbook = 7.5 5000
may be used, or a strain compatibility analysis may be made.
= 0.530 ksi > 0.022 ksi OK
Example 2.2.5.1 Design Flexural Strength
Using the generic hollow core slab defined in The moment capacity of a prestressed member
2.2.5 Design Flexural Strength
Section 1.7, check the design flexural strength is a function of the ultimate stress developed in the given the following criteria: prestressing strands. As with non-prestressed Prestressing steel: 4- 1 / 2 ″ dia., 270 ksi, low re- concrete, upper and lower limits are placed on the
laxation strands
amount of reinforcing to ensure that the stress in
d p = 7″
the strands is compatible with concrete stresses for ductile behavior.
initial stress = 70% f pu
The lower limit of reinforcing requires that:
f′c = 5000 psi
φM n ≥ 1.2 M cr
ℓ = 30′-6″
Clear span = 30′-0″
φM n ≥ 1.2 M cr
Superimposed Dead Load = 20 psf
From Example 2.2.3.1
Live Load = 50 psf
Loss = 13.5%
Solution: