RESEA RC H PRO PRO J EC T NO. NO . 5
DESIGN OF SPANDREL BEAMS
Wis Wiss, J a nney, nney, El Elstner As Assoc iates iates,, Inc. Inc . Northbrook, Illinois
SUPPORTING FIRMS
SPECIALLY PEC IALLY FUNDED FUNDED R D PROG PROG RAM Pha Ph a se I-1982-19 I-1982-1985 85
PRODUCER
Arnold Concrete Products Baass Concrete Co. Preca Prec a st, A Divis Division of of Heavy Construction, Inc. Blakeslee Prestress, Inc. Buehner Concrete Co. J oseph oseph P. Car Ca rrara ara Sons, ons, Inc. Central Pre-Mix Concrete Co. Colorado Concrete Structures, Inc. Concrete Technology Corporation Dura-Stress, Inc. C orporati orporation on Exposaic Industries, Inc. Fabcon Incorporated Featherlite Corporation (Prestress Div.) Industries, Inc. Florence Concrete Products, Inc. Forest C ity Dillon llon Preca Prec ast Sys Systems, tems, Inc Inc.. C orpo orporration F-S Prestr Prestre ess, ss, Inc . Genstar Structures Limited Heldenfels Brothers, Inc. High Concrete Structures, Inc. F. Co mpany Lone Star Industries, Inc. Lone Star/San-Vel
MEMBERS
Macon Prestressed Concrete Company Material Service Corporation Meekins-Bamman Prestress, Inc. Metromont Materials Corporation Morse Bros., Inc., Prestress Concrete Group New Enterpri Enterprisse Stone Lime me C o., Inc. Nitterhouse Concrete Products, Inc. J . Pomeroy Pomeroy C o., Inc. Prestressed Concrete Operations Price Brothers Co. C orpo orporration Rocky Mountain Prestress. Inc. Bros., Inc. Southeast Schokbeton, Inc. Southern Prestressed Concrete, Inc. Spancrete of California Stanley Structures Stresscon Corporation Thomas Thomas C onc rete Prod Produc ucts ts C o. Tinda Tindallll C onc rete Prod Prod ucts uc ts,, Inc. TX TXI Structu tructurral Produc Products ts,, Inc. The The United United Prec Prec a sting ting C orpor orpo ration Universal Concrete Products Corporation Wells Concrete Products Co. Western American Concrete, Inc.
ASSOCIATE
American Spring Wire American C om omp a ny ny, Inc . A rmc o Inc . J . C ase C ompa ny Da yto n Sup e rio r C or orp o ra tio n Dur-0-Wa l. Inc . Dy-C o re Syste ms Inc . C he mic a ls, Inc . Fehr Brothe Brothe rs, rs, Inc. Inc . Florid a Wire&C a b le C o.
MEMBERS
PGFRC, Inc. Ha mi milto n Fo rm C om omp a ny ny, Inc . M a rtin M a rie tta C e me nt Mi-J Mi-J ac k Produc Produc ts Mixer Systems, Inc . Te d Ne lso n C o mp a ny Pla nt C ity Ste e l C o mp a ny Prestress Supply, Inc . Com Co mpany Sp ring fie ld Ind ustrie s C o rp .
PROFESSIONAL
ABAM Engineers, Inc . Burr Bennett Ltd. Ross Bryan Associates, Inc. C o nra d A sso c ia te s Ea st The The C onsulti onsulting ng Enginee rs G roup , Inc.
MEMBERS
La ng stra nd A sso c ia te s. Inc . LEAP Assoc iates Interna tiona l, Inc . Irwin Irwin J . H. &Associates, Inc. Wiss Wiss, J a nney, Inc Inc .
Sp ec ially Funded R
D Prog Progrra m
Research Project No. 5
DESIGN IG N OF O F SPANDR PANDREL BEAMS
G a ry J . Kl Klein Wiss Wiss, J a nney, Els Elstner Assoc Assoc iates iate s, Inc. Inc . 330 Pfingsten Road
IL 60062
STEERING EERING C O M M ITT ITTEE Ned M. Cleland, Chairman Alex Kamal Chaudhari Keith Gum J ohn Hanlon Floyd J ones
Stuart tua rt J osep osep h A Miller Miller Kim C . P. Sies Siess s (RCRC (RC RC)) Robert Smith Tom Tom A. Thoma Thomas s, J r. Garry Turner
EXECUTIVE
The
behavior
and
design
under PCISFRAD Project
This
SUMMARY
of
precast
research
spandrel
project
was
beams
was
studied
primarily
toward spandrel beams commonly used in parking structures.
directed
Both L-beams and
pocket spandrels were included in the study. The practices,
research
analytical
included
studies
background
using
finite
investigation
element
load tests of two L-beams and one pocket spandrel. were 72 in. high, 8 in. wide and 28 ft long. based
on
90
psf
dead
load
and
50
psf
live
models,
of
and
design
full-scale
All three test specimens
The
target
load,
which
design
loads
were
typical for a
double tee parking structure with 60 ft spans. The published
background
procedures
research
vary
with
revealed
respect
to
that
industry
several
practices
fundamental
aspects
and of
spandrel beam design.
Behavior near the end regions is not well understood,
nor
of
is
the
influence
connections
to
deck
elements.
design of beam ledges is not consistently handled; no
consensus
attachment.
on
the
Also,
design
the
of
hanger
Building
In
general,
in particular, there is
reinforcement
Code
for does
combined sheer and torsion in prestressed beams.
the
Designers
ledge-to-web not
address
rely on
several
research reports that give design recommendations. Ledge-to-web spandrels this
were
attachment
identified
research.
The
as
the
and key
analytical
behavior issues
studies
near
and
and
the
were
the
laboratory
end
region
primary
focus
testing
of of
program
yielded several significant findings: Contrary section
to for
several shear
published
and
torsion
design
examples,
at
the
face
do
not
of
critical the
support
should be considered. Connections
to
deck
torsion: however,
elements
they
effective
in
substantially
reduce
restraining
lateral
displacement induced by bending about the weak principal axis. Shear
and
which
consider
two tests.
torsion a
design concrete
procedures
for
contribution
prestressed have
been
spandrels
verified
by
An approach for considering the effect of the pocket on the While
shear strength of pocket spandrels has been proposed.
the accuracy of this approach has not been fully verified by tests,
it is believed to be conservative.
With regard to detailing practices. it was found that the torsional response of deep spandrels is dominated by plane
bending.
The
use
of
lapped-splice
stirrups
and
longitudinal reinforcing bars without hooks does not appear to have any detrimental effect. Two independent design checks in the end region of spandrels are
recommended.
First, reinforcement should be provided to
resist out-of-plane bending caused by the horizontal torsional equilibrium the
reactions.
reinforcement
for
This reinforcement is not additive to internal
torsion.
longitudinal reinforcement in the bearing
Second, should
the be
sufficiently developed to resist the external normal force, well as the tension induced by the vertical reaction. The eccentricity of the ledge load cannot be neglected in the design of hanger reinforcement for ledge-to-web attachment. Nonetheless,
not all of the load acting on the ledge is
suspended from the web and the effective eccentricity of ledge load is significantly reduced due to torsion within the ledge.
A design procedure which considers these effects has
been recommended. reinforcement
is
In addition. it wss determined that hanger not
additive
to
shear
and
torsion
reinforcement. The
design equations for punching shear strength of beam
ledges may be
Further research in this ares
is recommended. In conclusion, this research has clarified many of the questions relating to spandrel beam design and the design recommendations will be of immediate benefit to the precast industry.
TABLE OF CONTENTS
EXECUTIVE SUMMARY. . . . . . . . . . . . . . . . . . . . . . .
i
1.
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . .
1
2.
BACKGROUND
5
2.1
2.2 2.3 2.4 2.5 2.6 3.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5 6 7 9
10 12 21 21 22
22 29
Test Specimens. . . . . . . . . . . . . . . . . . . . . . Test Procedure. . . . . . . . . . . . . . . . . . . . . . Behavior and Strength of Test Specimens . . . . . . . . .
29 31 32
ANALYSIS AND DISCUSSION . . . . . . . . . . . . . . . . . . . .
51
4.2 4.3
General Design Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shear and Torsion . . . . . . . . . . . . . . . . . . . . Beam End Design . . . . . . . . . . . . . . . . . . . . . Beam Ledges . . . . . . . . . . . . . . . . . . . . . . . Beam Pockets. . . . . . . . . . . . . . . . . . . . . . .
51 51
. . . . . . . . . . . . . . . . .
69
ACKNOWLEDGEMENTS. . . . . . . . . . . . . . . . . . . . . . . . NOTATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . REFERENCES. . . . . . . . . . . . . . . . . . . . . . . . . . .
71 72 74
5.1
5.2 5.3 5.4 5.5 5.6 6.
Description
. . . . . . . . . . . . . . . . .
LOADTESTS . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1
5.
General Design Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shear and Torsion . . . . . . . . . . . . . . . . . . . . Beam End Design . . . . . . . . . . . . . . . . . . . . . Beam Ledges . . . . . . . . . . . . . . . . . . . . . . . Beam Pockets. . . . . . . . . . . . . . . . . . . . . . .
FINITE ELEMENT MODEL STUDIES 3.1 3.2 3.3
4.
RESEARCH . . . . . . . . . . . . . . . . . . . . . .
FINDINGS AND RECOMMENDATIONS.
APPENDIX A APPENDIX B APPENDIX C
51
53 54 59
. . . . . . . . . . . .
Al
DESIGN EXAMPLE 2 . . . . . . . . . . . . . . . . .
Cl
SPANDREL DESIGN CHECKLIST.
Spandrel
several
are
INTRODUCTION
one
of
fundamental
aspects
e le me nt s.
I"
in
particular,
reinforcement
for
most
complex
design.
the
influence
design
there
not
their
is
is
ledge-to-web
does beams,
the
general,
of
nor
region is not well understood,
handled;
the
elements
in
precast
Industry practices and published procedures vary with respect
construction. to
beams
1.
of
no
beam
Behavior of
ledges
consensus
on
address
combined
connections is
not
the
attachment. and
to
end deck
consistently
design
the
shear
the
of
hanger
Building Code
torsion
in
prestressed
although several research reports give design recommendations. Specially Funded Research and Development Project
addressed
these issues by studying the behavior and design of precast spandrel beams. The
research
spandrels
program
such
as
was
those
primarily
commonly
directed
used
in
parking
Both
load-carrying and railing functions.
toward
deep
structures
L-beams
and
and
slender
to
serve
both
spandrel
beams
with
pockets for T-stem bearings (pocket spandrels) were included in the program. Figure
1.1
findings
shows
of
prestressed radically while
does
of
not
frame,
"or
spandrels. These
is
spandrel
beam
the Also,
may
geometric
research
design beam
effects
of
can
be
to
be
are
these to
or
as
to
load
beams.
The
and
spandrel
beams
of
Furthermore,
level.
comprehensive,
not all
In particular, the research
part
change
of
prestressed
applicable
reasonably
vehicular
very
types
both
covered.
design
volume
and be
apply
not
believed
handling
of
configuration
spandrel
considerations
sections
generally
but
spandrels,
address
cross
research
different
this
aspects
this
typical
of
on
impact
a
lateral-load-resisting
design loads
and are
detailing not
of
discussed.
important, but are considered beyond the
scope of this research. The research included the following: Study
of
design
requirements
and
practices
to
determine
the
state-of-the-art of spandrel beam design. Analytical studies using finite element models of a" L-beam and pocket spandrel. Full-scale
tests
of
two
L-beams
and
designed using state-of-the-art methods.
1.
one
pocket
spandrel
The following sections of this report describe the research. analyze the findings, and provide design recommendations.
10”
6” TO 10”
POCKET SPANDREL
L-BEAM
Fig.
1.1
Typical spandrel
3.
2.
BACKGROUND
RESEARCH
The background research included a review of code requirements, published
guides
and
research
reports
on
spandrel
beam
design.
A
questionnaire covering several aspects of spandrel beam design was sent to Later, a
the members of the Steering Committee for PCISFRAD Project
questionnaire on pocket spandrels was sent to selected committee members who Finally,
showed interest in that type of construction.
the collective
experience of the author and his associates was considered.
The following
discussion on spandrel beam design is based on this research. 2.1
General
Design
Critical section.
Considerations
In most precast beams, the loads and reactions
are applied at the top and bottom of the beam, respectively. said to be "directly loaded".
Spandrel beams,
Such beams are
on the other hand,
indirectly loaded, and the additional shear capacity due to arch action near the support is not available. forces at a distance d be not appropriate.
Therefore,
design for shear and torsion
for prestressed spandrels) from the support may
Figure 2.1
shows potential
critical
inclined
sections
which carry all the concentrated loads acting on the ledge rather than just loads farther than d from the support. The
among designers is that all loads acting on the
the critical section, based on inclined cracking from the edge of the beam base plate. must be considered as part of the shear/torsion load.
This consensus is contrary to the published design examples in
Section 4.4 of the
Design Handbook
on
318-83 does not address indirectly loaded beams;
however,
and Example 14.2 in the PCA notes
Article 11.1.2 of the Commentary recommends special consideration
for concentrated loads near supports. Equivalent uniform load.
It is common practice to simplify the
analysis by replacing concentrated loads with equivalent uniform loads. Some designers increase the equivalent uniform floor load such that the shear and torsion is correct at the critical section at the inside edge of the base plate i.e., the basic equivalent uniform load is multiplied by the ratio of grid span to design span.
5.
Eccentricity positioned erection
at
contributing
the
tolerances)
centerline
or
at
the
to
of
torsion.
bearing
outer
Typically, the ledge loads
(allowing
point
of
for
the
fabrication
ledge.
and
The former
approach is generally preferred because an increase in ledge projection does necessarily
require
an
increase
in
torsional
load.
The eccentricity
contributing to torsion is the distance from the centerline of the web to the
applied
load,
as
shown
in
Fig.
2.2.
Theoretically, the eccentricity
should be measured relative to the shear center. which, for an beam
section,
is slightly inside the centerline of the web.
difference is neglible in deep spandrels. not
consistent
with
the
based on the
prediction
experimental results are
of
shear
center
location
cross section.
Influence tees
theoretical
Further,
However, this
of
deck
connections.
Prior to connection of the double
topping to the spandrels, torsion
can be
computed as
a
product
of
the dead load and the eccentricity between the applied load and centerline of the web. applied
After
connections
to
deck
elements
are
made,
however,
the
"live load" torsion may be partially counteracted by the horizontal
force due to friction at the bearing pads coupled with restraint at the deck connections
(Fig.
2.2).
most
practitioners
believe
inappropriate to rely on a soft bearing pad for this purpose. recent
that
In
it
is
addition.
indicates that the effective "friction" at the bearing
pad may be 5 percent or less of the gravity load. 2.2
Flexure
design
of
spandrels
generally
follows
and
procedures for bending about the horizontal and vertical axes. However, shaped spandrel beams do not have symmetry about either axis.
The principal
axes are rotated‘slightly from the vertical and horizontal axes, as shown in Fig.
2.3.
axis
can
The be
particularly
influence neglected those
of
this
for
deep
employing
rotation spandrel
bending beams.
prestressing,
this
about
For
the
horizontal
shallow
spandrels.
influence
should
be
considered. Perhaps rotation
more on
important,
horizontal
however,
is
displacement
the of
influence spandrels.
of As
principal shown
in
Fig. 2.3, a component of the vertical load acts along the weak axis inducing
6.
All loading prior to making diaphragm
a" outward horizontal displacement. connections can
horizontal displacement.
found that this
was the most dominant behavior of long slender spandrels and suggests a principal
analysis when the spa" length is 40 to 50 times web width,
depending on the intermediate support conditions. I" general,
detailing
practice
follows
the
code.
noteworthy exception pertains to Article 10.6.7 of the applicable to non-prestressed spandrels.
318-83 which is
This provision requires that
reinforcement be placed in the side faces of webs more than 3 ft deep. The reinforcement is to be distributed in the zone of spacing not more than the web width, nor 12 in.
tension with a Designers do not often
check this provision; instead reinforcement in the side faces of the web is designed to resist torsion or handling. 2.3 Shear and Torsion
Prestressed prestressed
spandrels.
concrete.
A
The
procedure
code does not address torsion in for
concrete, which is a" extension of the
torsion design
the
(7)
The second edition
handbook included a modified version of the Zia and McGee The
t orsi onal
prestressed
provisions of torsion for non-
prestressed concrete. was developed by Zia and McGee. of
of
procedure uses a simplified method for computation of
stress which is conservative for most spandrel beams.
A further
refinement of these methods was subsequently developed by Zia and Hsu. While the general design approach follows that of Zia-McGee and PCI, new expressions are proposed for torsion/shear interaction and minimum torsion reinforcement. moments
rather
current
The Zia-Hsu equations are expressed in terms of forces and than
nominal
stresses, which is more consistent with the
code. Most designers follow one of these three similar procedures.
Practices vary with respect to the design of longitudinal reinforcement for torsion.
Some designers consider the prestressing strand to be part of the
longitudinal reinforcement while others consider only the mild reinforcing. In
their
original
paper.
Zia
and
McGee
recommended
prestressing steel in excess of that required for
7.
that
only
the
and located
around
perimeter of closed stirrups. should be
part of the
longitudinal torsion steel. third edition of the
handbook
which is based on compression field
developed by Collins and Mitchell, theory.
describes a procedure
This approach assumes that, after cracking, the concrete can carry
no tension and that shear and torsion are carried by Compression.
Because'
the "concrete contribution" is neglected, require somewhat
selection of the crack angle. however,
field of diagonal this
stirrup reinforcement The biggest difference,
is in the positive and negative moment capacity requirements which
based on the axial tension caused by shear and torsion. shown,
For the example
handbook, the required positive and negative bending strength
at the face of the support exceeds the
moment.
These
requirements
present considerable detailing difficulties, and many designers do not feel they are valid for deep spandrels. Detailing practices for the torsional reinforcement do not always code requirements.
that
t ransver se
reinforcement consist of closed stirrups, closed ties or spirals.
However,
the'commentary to the
Article
11.6.7.3
requires
code indicates that this requirement is primarily
'at hollow box sections and solid sections subjected primarily to torsion. spliced
In these members, the side cover stirrups
ineffective.
off, rendering
This type of behavior is unlikely in deep
spandrel beams, and transverse reinforcement is often provided by pairs of lapped-spliced
spacing limit of 12 in. lim it
most designers feel that the stirrup
U-stirrups.
is not appropriate for deep spandrels, and this
exceeded.
is
Non-prestressed spandrels. concrete generally follows
Torsion
design
of
non-prestressed
code requirements, except for the detailing
considerations discussed above. Pocket
spandrels.
Typically, pocket spandrels need not be
designed for torsion. However, the pockets complicate the shear Design practices vary for considering the effect of designers neglect this effect.
design.
the pocket; some
Fortunately, shear strength does not control
the dimensions of deep pocket spandrels and often only minimum reinforcement is required.
Welded wire fabric is frequently used for web reinforcement.
2.4
Beam
End
Torsion
Design
equilibrium.
The
eccentric
load
applied
on
the
ledge
produces torsion in the spandrel which must be resisted by reactions at the supports.
Customarily.
rotation.
Figures
the and
web
is
connected
the
column
restrain
show the torsion equilibrium reactions for
a normal and dapped connection, respectively. The vertical
torsional
and
horizontal
equilibrium web
and
reactions
reinforcement
prescribe
reinforcement.
similar
at
may
require
the
ends
methods
Vertical and longitudinal steel, A
for
of
supplemental the
design
and A
on
girder. of
the
this inside
face of the spandrel is calculated by:
A
where T
=
=
T
factored torsional moment at the end of girder = depth of
and
steel from outside face of
spandrel (in.), yield strength of reinforcement (psi) (or effective
and
strength reduction factor = 0.85.
The use of
= 0.85 instead of 0.90
compensates for the ratio of
internal moment to total effective depth, which is not in Equation 1. Osborn recommends the bars be evenly distributed width equal to
(see Fig.
a height and
2.4) from the concentrated reaction point.
Because shear cracks may coincide with diagonal cracks due of-plane
bending,
should be added to the shear reinforcement.
However,
most designers feel this reinforcement is not additive to reinforcement for internal function
torsion. as
reinforcement
A is
and
If
the
A
required
reinforcement
r e i n f o r c e me n t , provided
all
torsion
l it tl e
loads
considered as part of the shear/torsion load.
9.
for
or
acting
is no
considered
to
s up pl em en ta l
the
ledge
are
Figure
2.5
shows
a"
I" this case,
equilibrium at the support. alignment
with
the
ledge
upside-down corbel. may
lead
to
alternative
loads.
Most
the
end
to
provide
reactions
torsional
are
in
close
The projecting beam ledge is treated as an
designers rolling
excessive
means
surveyed
of
the
indicated
spandrel
that
this
approach
the
support,
Design
Handbook
beam
at
particularly where a soft bearing pad is used. Dapped-end presents
design
beams.
criteria
Section
for
dapped-end
connections under PCISFRAD Project with this project, dapped
end
established
the
connections.
Research
on
is expected to recommend modified procedures.
L-beams
often
of
is
often
interferes
complicated
design
procedures
the
are
by
reinforcement
the
Also,
with
dapped
which is being conducted concurrently
equilibrium connections (Fig. spandrel
6.13
last
reinforcing
modified
as
Design for
in
for
the
dapped
appropriate
to
of
torsion a
pocket
end.
handle
The these
special conditions.
2.5
Beam
Hanger between
the
ledge
Ledges
reinforcing. and
Collins
web
Figure 2.6 illustrates a possible separation
of
and
a"
L-shaped
Mitchell
spandrel.
provide
Design
hanger
examples
by
reinforcement
concentrated near the ledge load given by A
sh
= v
The notation is defined below. uses but
computes
the
all
required
the
hanger
reinforcement
reinforcement
between
based
summation
about the outside face of the spandrel, thus
V jd
I O.
on
the
ledge of
loads, moments
where
A
= area of transverse hanger reinforcement on
sh
inside
face
of
spandrel
for
each
ledge
load
in.).
factored ledge load
distance from ledge load to center of inside
a
face reinforcement (in.),
jd =
and
internal moment arm
(taken as d
in.).
= strength reduction factor = 0.85. recommends
an
additional
load
factor
of
for
design
hanger reinforcement. An alternate procedure for using concrete tension
of a
means of ledge-to-web attachment is also given. Equation 3 is based on sound principles of statics, yet there many
existing
reinforcement have
spandrels
than
occurred
ins tan ces,
this
where
beams
that
have
equation
there
was
very
light
with
performed
would no
require.
hanger
hanger
well
with
much
less
The only known failures
reinforcement.
reinforcement
have
In
severa l
survived
load
tests. Further
refinements
of
hanger
reinforcement
design
reduce the load that must be suspended from the web based on internal shear stress
distributio n,
relative
depth
of
the
ledge,
and
deflection
compatibility. There
is
reinforcement.
no
Some
consensus designers
among do
not
designers check
on
requirements
ledge-to-web
others use some combination of the above methods.
for
hanger
attachment,
while
Furthermore, there is no
agreement as to whether or not hanger reinforcement should be added to shear and
torsion
generally region
of
reinforcement.
controls the
the
The method for designing hanger reinforcement
quantity
of
transverse
reinforcement
in
the
middle
spandrel, and can have a very significant effect on material
and fabrication costs. Ledge
punching
shear.
The
design
for
punching
ledges generally follows the procedures in Section 6.14 of the
11.
shear
in
beam
Handbook.
Some
designers
follow
modified
on unpublished test results, on
the
vertical
shear
procedure
this
plane
method
along
the
and Krauklis and
recommended
considers inside
a
face
by
Raths;
lower
of
based
ultimate
the
stress
web.
et
have also found that the
design
equations may be
2.6
Beam
Pockets
It is customary to provide closed stirrups or U-bars in the plane of the web for the entire T-stem load in pocket spandrels. are
typically
Therefor e,
located
Equation
re qui rem ent s. relatively low so
The
near 2
the
is
concrete
used
T-stem to
tensile
load,
as
determine stress
horizontal crack at that
at
The
shown
location
is
bars
Fig.
2.7.
in
hanger the
hanger
reinforcement
"ledge"
level
unlikely.
is
Also,
because hanger reinforcement is customarily used, punching shear below the pocket is generally not
concern.
12.
13.
CONNECTION TO DECK
SHEAR CENTER
FRICTION AT BEARING
Fig. 2.2
Eccentricity contributing to torsion
14.
X-
-
-
Fig. 2.3
Principal
15.
of an L-beam
16.
Fig. 2.5
Beam end corbel behavior
17.
(INSIDE
LEG
ONLY)
POSSIBLE SEPARATION BETWEEN LEDGE AND WEB
Fig. 2.6
Ledge-to-web attachment
18.
Fig. 2.7
Hanger reinforcement in pocket spandrels
19.
20.
FINITE ELEMENT MODEL STUDIES
3.
3.1
Description
Finite
element
The
analyzed. essentially
models
geometry
the
same.
of
of
a"
these
L-beam
models
and
and
pocket
the
spandrel
test
were
specimens
was
The beams were 72 in. deep, 8 in. wide and 28 ft
Figures 4.1 and 4.2 provide
detailed information on the geometry
of the beams. The model studies had several objectives: Investigate
the
deflections
and
rotations
caused
by
the
eccentrically applied load. Determine
the
theoretical
torsional
equilibrium
reactions
at
elements
on
the supports. Study
the
influence
of
connections
to
deck
deformations and torsional equilibrium reactions. Investigate
the
Three-dimensional freedom
at
each
node.
across the ledge/web interface. solid
elements
were
used
with
three
degrees
of
Cross sections showing the finite element mesh are
shown in Figs. 3.1 and 3.2.
The models were assembled and analyzed using a
proprietary version of the SAP IV Program. Service
loads
included
reaction at 4 ft centers. from
the
The
web
centerline
restraints
at
each
The
beam
dead
the
end
of
L-beam the
and
16.8
kip
t ee- stem
load was applied at 8 in. and 2 in.
t ee- stem
for
load
and
beam
pocket
modeled
support where the bearing pad is placed at
the
spandrel, a
typical
respectively. spandrel
beam
centerline of the web, and
lateral support is provided near the bearing and at the top corners of the beam. For
both
the
L-beam
and
pocket
spandrel,
analyzed in which additional lateral restraint was of
the
beam
possibility deck
of
to
simulate
relative
connections
lateral
movement
deck
between
second
condition
was
provided near mid-height elements.
the
column
There
was
restraints
no and
elements, simulating the case where there is an independent connection
between the deck and the column. studies noted
to
a
and that
load
tests
direct
modeled
This the
connection
case
same
modeled
condition,
between
21.
was
the
so
although
col um n
and
the
analytical
it deck
should
be
is
not
necessarily
required.
Alternately,
the column can be indirectly connected
to the deck through the spandrel beam.
3.2
Spandrel
Figure load
without
Beam
Behavior
shows the
any
deflection of the L-beam at service
connections
to
deck
Note the overall outward
elements.
deflection due to the rotation of the principal axes. elements
effectively
Fig.
Usually
load
is
in
Fig.
3.2.
restrain
these
place,
this
connections
Similar
plots
Connections
outward
displacement,
are
made
for
not
the
until
pocket
as
all
spandrel
to
deck
shown
of are
the
in dead
shown
in
Due to the different cross-sectional shape and load eccentricity,
the lateral deflection is relatively small. Figure without
shows
connections
the
between
horizontal
the
reactions
spandrel
and
at
deck.
the
L-beam
These forces simply
balance the external torsion due to the eccentrically-applied loads. shows connections deck
the in
horizontal
the
connections
would
be
region
at
restrain rotation.
the The
counteracted
column-to-deck
reactions
support net
by
connection,
restrain
work
outward
the
with
with force
deck
connections.
the
outward
the
top
between
column-to-deck
support
The
deck
displacement.
The
corner the
Figure
connections
deck
connection.
and
to
spandrel
If there were no
the deck connection forces would tend to balance.
depending on the stiffness of the column.
3.3 Transfer of Ledge Loads to Web
Stresses (The
studied. at
the
Fig.
top
3.4.
geometry
of As
a
the
of
plane 3 the
expected,
finite
The
ledge). the
in. above the ledge/web interface were element
results
inside
face
mesh
of
that
of
the
prevented study
web
is
investigation
are in
presented tension.
in The
maximum tensile stress of 295 psi, which occurs at the ledge load, is about 40 percent greater than the average stress.
The compression
in the
outside
face of the web is significantly more uniform. The stresses
in
resultant the
of
these
individual
indicated in the figure,
the
stresses
elements resultant
22.
can
near is
be
the
slightly
computed ledge/web less
by
integrating
junction.
than
the
As
applied
ledge
load
differences
and
is
shifted
significantly
towards
centerline.
These
equilibrated by shear and torsion in the ledge itself.
This
mechanism is discussed further in Section 5.4.
23.
the
web
F.E. MODEL ( I N . ) HORIZ. ROT.
(A)
WITHOUT
Fig. 3.2
-0.053 -0.00085
DECK
F.E. MODEL
L OA D TESTS
-0.173 -0.00443
CONNECTIONS
VERT. HORIZ. ROT.
-0.053 (IN.
LOAD TESTS
-0.146
0. 0
-0.00083
-0.00346
WITH DECK CONNECTIONS
deflection of pocket spandrel (superimposed dead load
live load)
LOAD TESTS
behavior
Two
L-beams
and
and
verify
their
structural
laboratory
one
of
pocket
spandrel
strength.
The
were
tests
tested were
to
study
conducted
their
in
the
Elstner Associates in Northbrook,
Wiss,
Illinois.
4.1
Test
General. 2.8 ft long.
Specimens
All
three
spandrels
were
72
in.
high,
8
in.
wide
and
The target design loads were based on 90 psf dead load and 50
psf live load. which are typical for a double tee parking structure with 60 The reactions at each stem of a" 8 ft wide double tee was 16.8
spans. kips.
Design.
The design of the test specimens was based on the
of-the-art methods described in the background section.
Shear
and
torsion
design for the prestressed spandrels followed the procedure recommended by and Hsu.
Equation 11-10 (rather than Eq 11-11 or
was use to
compute the basic shear strength provided by the concrete section. design followed meet equal
the to
318-83.
provisions at
least
of 1.2
Some reserve
Article times
18.8.3.
the
strength was required to which requires a bending capacity
cracking
moment.
torsional equilibrium was checked by Equation 1.
Reinforcement
for
This reinforcement was not
added to the reinforcement for internal torsion. In
view
of
the
controversy
regarding
ledge-to-web
attachment,
alternate procedures were used for design of hanger reinforcement: Hanger reinforcement for Specimen 1 was designed by Equation 2, with
one-sixth reduction in the load suspended from the web
based
on
relative
reinforcement effec tive,
ledge
between
ledge
depth. loads
All was
of
the
transverse
considered
to
be
and hanger reinforcement was not added to shear and
torsion reinforcement. Equation 3 was used for design of the hanger reinforcement in Specimen
2.
A 7.4 percent reduction in the suspended load was
taken based on a" assumed parabolic shear Again,
all
the
hanger
reinforcement
between
distribution. ledge
loads
considered
effective, and
it
was
not
added
to
shear/torsion
reinforcement. Hanger
reinforcement
for
the
pocket
spandrel
(Specimen
In addition to a U-bar
designed by Equation 2.
was
the pocket,
one wire on each side of the pocket from the mesh reinforcing was considered to contribute. Design basically
of
followed
the
dapped-end
the
Handbook
connection procedure
for
with
the
two
pocket
spandrel First,
exceptions.
there was no special reinforcement provided
due to relatively low stresses,
for diagonal tension in the extended end or direct shear at the junction of the
dap
and
the
reinforcement, reinforcement
main
body
however,
of
the
continued
for
and
member.
into
axial
the
tension
The
welded
extended
end.
in
the
wire
extended
shear
Second,
the
end
not
was
continued past the potential diagonal tension crack extending to the bottom corner of the beam. Details.
The
dimensions
and
reinforcement
specimens are provided in Figs. 4.1 and 4.2.
details
of
the
test
The following features of the
reinforcing details should be noted: Due
to
the
different
design
methods,
Specimen
2
has
twice
This
much hanger reinforcement across the ledge-web interface. reinforcement
was
provided
by
partial-height
L-bars
add
about
4
percent
to
the
weight
of
the
mild
on
These
inside face of the spandrel between the stirrups.
steel
as
the bars
in
the
degree
end
beam. Closed
ties
formed
in
one
piece
by
overlapping
90
Stirrups
hooks are used on the left half of the L-beams.
on
the right side of the L-beams consist of lapped-spliced U-bars. The
longitudinal
bars
in
the
L-beams
are
not
hooked
at
the
ends. At the right side of the L-beams, two bearing
A
plate.
bars are welded to
U-bar is used on the left side of the
beams. Wire
mesh
spandrel. at
the
is
used
for
shear
reinforcement
of
the
pocket
The mesh is not hooked around the main reinforcement
top
and
bottom
of
30.
the
beam,
although
the
code
requirements
for
development
of
web
reinforcement
(Article 12.13.2.5) are satisfied. Materials. concrete, strand, were
60
ksi
Design
of
reinforcing
Table 4.1.
test
bars
specimens
(ASTM
was
based
270
ksi
on
5,000
psi
stress-relieved
Concrete cylinders and reinforcing bar samples
and ASTM A497 mesh.
tested
the
determine
actual
strengths.
The results are presented in
The yield strength of the X3 bars was much higher than expected. 4. 2
Test
Setup.
Procedure
The test setup is shown in Fig. 4.3.
The
spandrels
were
supported on rigid L-shaped frames which provided lateral restraint
the
four corners of the beam.
Load was applied at seven points along the beam
using
double
specially
designed
tees
(and
one two
long-term creep of elastomeric bearing pads, of
in.
single
To simulate
in. pads on either side
steel plate were used under the tee stems. These
wide (measured along the beam) by 3 in. long.
tee).
The pads were 6 in.
dimensions
were
chosen
so the load could be applied at the desired eccentricity without exceeding reasonable bearing stresses. The spandrels
test
setup
featured
double tees.
a
removable
connection
between
the
Pedestals were used to support the dapped ends
of the pocket spandrel (Fig. Instrumentation. the
loading
points
Finally,
the
double
tees.
included as
deflection
transducers
to
monitor
horizontal
and
single
element
strain
gages
and
vertical were
load
well
Three
reaction points. at
on
Instrumentation
cells
all one
four
ti l tm eter
deflections
placed
and
at
two
of
horizontal were
set
up
rotations.
on
selected
reinforcing
was
incrementally
as per Table 4.3. Load sequence.
Initially,
each
spandrel
loaded
to service load (16.8 kips per tee stem) without the connection between the double tees and spandrel.
After unloading, this sequence was repeated with
the
place.
deck
connections
in
Finally, the beams were loaded to failure
without the deck connections in increments of 2.5 kips per tee stem. third
specimen
was
tested
the end region in Phase 1, and the specimen
to the
failure
in
supports
were
reloaded to failure.
31.
two
phases. moved
in
After 4
ft
The
failure near from
each
end.
4.3 Behavior and Strength of Test Specimens
Deflection and rotation. deflections finite
of
the
element
L-beam
models.
and
Figures 3.1 and 3.2 compare the measured
pocket
spandrel
to
those
Although the measured deflections
they are two to three times the predicted deflections. vertical
deflection
predicted
and
of
the
rotation
the
quite small,
About
may
by
be
half
of
the
attributable
to
deformation of the bearing pads. Figure
4.4
shows
a
plot
of
stem
reaction
torsional
The stiffness of the beam is significantly reduced
rotation of Specimen 2.
after cracking was observed. Service load behavior. in
the
L-beams.
connection Fig.
of
However.
the
At service load. no
minor
pocket
spandrel.
patterns
were
cracks were observed "ear the
were all less than 10 Failure
cracks
These
cracks.
which
are
Specimen
1.
The
cracking
the ledge/web junction occurred
in
27.5 kips.
that
Diagonal cracks The
crack
at
This crack immediately opened
and extended end to end where it connected to inclined cracks in
ledge.
The ledge continued to separate from the web until the test was
stopped at a ledge load of 34.6 kips per stem. crack at the ledge/web junction was Failure
patterns
face of Specimen 2.
Specimen
Typically, these
several 1 to 3 mil
At the end of the test, the
in. wide, as show" in Fig. 4.7. 2.
As
developed patter" of inclined and "rainbow"
Also,
shown
patterns
began to appear on Specimen 1 at a load of 25 kips per stem.
the
dapped-end
(0.010 in.) in width.
occurred during loading to failure are shown in Fig.
to 20
observed
shown
in
Fig.
a
well
cracking developed on the inside
cracks
were
less
than
10
mils
wide.
cracks were observed on the outside face.
The crack at the ledge/web junction was restrained by the additional hanger reinforcement, punching
shear Figure
shown in Fig. 4.8. failures 4.9
occurred
shows
the
the
ledge
the
top
and
inclined
reinforcement
below is
first
punching
initiates behind the bearing pad. "ear
At a load of 42.7 kips per tee-stem,
The the
not
shear failure
ledge
very
plane.
32.
and
sixth
failures. surface
reinforcing.
well
tee
developed
stem
from
The failure
is As
almost a
across
cone
vertical
result, the
the
the
failure
Failure Phase
1
of
the
patterns Specimen
Specimen 3. 3
test
are
The
shown
cracks
in
which
formed
during
Cracks near the
Fig.
dapped-end connection which developed at service load continued to lengthen and
widen,
Cracks below the pockets began
and new inclined cracks formed.
to form at tee stem loads of 18 to 25 kips. diagonal
tension
cracks
developed
further
As
from
the
load
was
increased,
These cracks
support.
At a load of 26.5 kips per
typically initiated near midheight of the beam. tee
the
diagonal tension crack near the right support extended down to
stem.
the bottom corner of the beam and failure occurred immediately, as shown in Fig.
4.10. In Phase 2 of the Specimen 3 test, a wide "rainbow" crack formed
load
of
about
43
kips
per
tee-stem.
Apparently this crack is due to a
combination of diagonal tension due to shear and vertical tension due to the tee-stem below
The ultimate failure, however, occurred when the concrete
loads.
the
"rainbow"
fifth
pocket
from
the
left
punched
out
at
47.6
crack and punching failure are shown in Figs. Strengt h.
Table
4.2
summarizes
the
kips.
The
and 4.11.
design
force.
calculated
strength and test force for several potential and actual failure mechanisms. The
calculated
Because
the
strengths
hanger
are
based
reinforcement
for
on
the
equations
Specimens
1
and
2
used was
for
design.
designed
using
different equations, the calculated strength is roughly the same even though Specimen 2 had twice as much hanger reinforcement. The and
"predicted"
material The
calculated
strength.
is
The
expressed design
as
both
strength
is
a
"design"
based
on
strength specified
and includes the appropriate strength reduction factor.
properties,
predicted
strength
strength
uses
actual
material
properties
and
no
strength
reduction factor. As
shown
in
Table
4.2,
the spandrel beams were tested to
near or beyond their predicted capacity for several mechanisms.
of the primary failure
however, several notable exceptions.
There
The shear failure of Specimen 3 (Phase cracking
load
occurred at the diagonal
load, and the expected contribution from the shear reinforcing was
not realized. The considerably showed
no
ledge-to-web
attachment
strength
less than predicted by Equation 3.
sign
of
a
ledge-to-web
attachment
33 .
In
failure.
of
Specimen
contrast, even
1
was
Specimen
though
the
2
test
force was slightly above the capacity predicted by Equation 2. of
the
hanger
reinforcement
below
the
well beyond the predicted capacity.
pocket
of
Specimen
Apparently, the
3
shear
The strength (Phase
was
strength
of
the
concrete below the pocket contributed.
Specimen
The
most
surprising
2.
Although
result
the ledge
was
the
punching
loads were quite
shear
failure
at
high, the punching shear
strength was only about 60 percent of the predicted capacity. Horizontal
reactions.
At service loads, the measured horizontal
reactions at the supports were comparable to the reactions predicted by the finite element model, as shown in Fig. 3.3. Figure 4.12 shows a plot of tee stem load forces at the left support of Specimen 2.
horizontal reaction
The horizontal reactions did not
continue to increase proportionally with load after cracking of the L-beams. At a ledge load of 39 kips per stem, the horizontal reactions actually began to drop off. inside
Apparently,
face
of
the
the
torsion
spandrel
was
equilibrium
yielding
and
reinforcement
eccentric
on
bearing
the
helped
equilibrate the eccentric ledge load due to rotation at the support. Reinforcement strain
at
gaged
strain.
locations.
Table
Data
are
4.3
summarizes
provided
at
or
the "ear
reinforcement service
load,
factored load and the maximum test load. At service load reinforcement strains are insignificant except at the
dapped-end
hanger
connection
reinforcement
bar
of
the
nearest
pocket the
spandrel,
load
is
where
almost
the
0.1
strain
in
This
percent.
strain level corresponds to half the yield
for a Grade 60 bar.
though
and
the
strain
levels
in
the
ledge
flexure
hanger
the
reinforcing
are
very low, they are noticeably higher at the ledge load. At factored load, was this
accompanied cracking
reflected
was
in
reinforcement
by
very
high
limited
the remains
cracking of the ledge/web junction of Specimen 1 hanger
to
the
recorded low
at
vicinity
strains. factored
cracks at the ledge/web junction. end connection.
reinforcement of
the
Strain
loads
strain.
in
ledge the
because there
In Specimen 2, load
which
ledge are
no
is
flexure vertical
I" spite of early cracking at the
strain levels at factored loads are well below yield strain.
At the maximum test load, the strain in the ledge hanger bars in Specimen 1 are well into the strain hardening range. The ledge hanger bars in
Specimen
2
are
approaching
the
yield
strain.
(Using the 0.2 percent
offset method, the yield strain of the
bars is about 0.5 percent.)
The
hanger reinforcing bars at the pocket in Specimen 3 are also near the yield strain. yield
It
strain
should of
a
be
noted
Grade
60
that bar.
these
strains
would
exceed
the
nominal
Strain in the ledge flexure reinforcement
remains low at maximum test load, indicating cracks.
35.
the
absence
of
ledge
flexure
TABLE 4.1
MATERIAL STRENGTHS
Concrete
Specimen
Reinforcing Compressive Strength
Yield Strength Size
f
Tensile Strength f
Y
1
5,330
78.9
98.7
2
5,640
70.4
103.7
3
6,060
64.2
98.1
Average of 3 field-cured cylinders tested concurrently with load test (psi)
36.
4.2
SPANDREL DESIGN AND TEST RESULTS
37.
TABLE 4.3
Gage
Location Ledge hanger reinforcement (near
No. (a)
l-l l-2 l-3 1-4 1-5
Distance from load 0
12 24 12 0
REINFORCEMENT STRAINS
Service- LoadStrain Load
Factored Load Load Strain
Max Test Load Load Strain -
16.9 16.9 16.9 16.9 16.9
-
0.004 0.001 0.0 0.0 0.003
27.3 27.4 27.4 27.4 27.4
0.239 0.120 0.223 0.245
34.6 35.6 34.6 34.6 34.6
16.9 -0.002 16.9 -0.001
27.4 27.4
0.016 0.026
34.6 34.6
0.042
0.210
3.211 2.235
Ledge flexure reinforcement
l- 6 l- 7
24
Ledge hanger reinforcement (near
2-l 2-2 2-3 2-4 2-5
24 18 12 6 0
16.7 16.7
0.0 0.001
28.1 28.1
0.005 0.007
4i.7 42.7
16.7 16.7
0.002 0.004
28.1 28.1
0.023 0.035
42.7 42.7
0.412
Ledge flexure reinforcement
2-6 2-7
24 0
16.7 -0.002 16.7 -0.001
28.1 28.1
-0.003 0.007
42.7 42.7
0.016 0.034
Dapped end flexure reinf.
3-l
8
16.7
0.056
24.9
0.130
----
-----
Dapped end hanger reinf.
3-2 3-3
8 11
16.7 16.7
0.091 0.017
24.9 24.9
0.097 0.067
-------
---------
Hanger reinf. at pocket (at
3-4 3-5
6 6
16.7 16.7
0.006 0.005
24.9 24.9
0.101 0.093
46.8 46.8
0.414 0.162
0
First number indicates specimen number Average ledge load Bad readings due to gage failure bending in bar at crack
SECTION
Fig. 4.1
Dimensions and details of Specimens 1 and 2
39.
ELEVATION
CHAMFER AT POCKET STRANDS STRESS RELIEVED
SECTION
Fig. 4.2
Dimensions and details of Specimen 3
40.
(a) L-Beams
Pocket spandrel
Fig.
Test setup 41.
(A)
FRONT ELEVATION OF SPECIMEN 3 AT SERVICE LOAD
(B)
FRONT ELEVATION OF SPECIMEN
1)
AT ULTIMATE LOAD
FRONT ELEVATION OF SPECIMEN 3-(PHASE AT ULTIMATE LOAD (END REGION CRACKS NOT SHOWN)
Fig. 4.5
Crack patterns 43.
Specimen 3
CA)
FRONT ELEVATION OF SPECIMEN 1 AT ULTIMATE LOAD
FRONT ELEVATION OF SPECIMEN 2 AT ULTIMATE LOAD
-----
C R A C K
ON BACK (OUTSIDE) FACE
Fig. 4.6
Crack patterns
44.
Specimens 1 and 2
Fig.4.7
Crack at ledge/web junction
Fig.4.g
Crack at ledge/web junction
45 .
Specimen 2
(a) T-stem at left support
6th T-stem from left
Punching shear failures
46.
Specimen
Fig. 4.11
"Rainbow" crack and punching failure Specimen 3 Phase 2
ANALYSIS AND DISCUSSION
5.
5.1
General
Design
Considerations
The
Location of critical section. shown
in Fig.
shear
failure
Specimen
3,
4.10. confirms the possibility of an inclined failure plane
which carries all of the loads acting on the spandrel. which
of
occurred
in
Specimens
1
and
2
suggest
a
The
crack
similar
patterns
possibility.
Therefore, the shear and torsion design of spandrel beams should consider a critical section at the face of the support. Alternately, transfer
the
ledge
if
loads
separate to
the
hanger
top
of
reinforcement
the
beam,
the
is
provided
spandrel
can
to be
designed as a directly loaded beam with a critical section at d or h/2 from the
support
for
non-prestressed
and
prestressed
spandrels,
respectively.
However, this approach may lead to excessive transverse reinforcement in the region
because
hanger
reinforcement
is
added
to
shear
and
torsion
reinforcement. Influence
of
deck
As illustrated i n Fig. 3.3, the
connections.
The
connections to deck elements do not substantially reduce torsion. significant
effect
of
the
deck
connections
is
the
restraint
of
only
lateral
displacement induced by bending about the weak principal axis.
5.2
With regard to related
behavior
of
both
the
test
specimens
mentioning, however, that the
back
face.
the
strength
was
and
satisfactory.
It
is
worth
cracking of the L-beams only showed up on
This observation is attributable
bending about the weak
principal axis.
5.3
Shear
and
Torsion
L-beams. roughly which
equal
was
the
negative bending
to
the
basis
Specimens 1 and 2 were tested at load levels
predicted for
capacity
their required
capacity
based
on
design.
There
was
by
compression
51.
the no
field
Zia-Hsu
equations.
evidence theory
that
was
the
needed.
As discussed later,
level of positive bending capacity at the face of
the support is required. Pocket spandrels.
The
premature
shear
failure
through
the
full
section of the pocket spandrel near the dapped connection is attributable to poor anchorage of the primary th e
be am .
It
may
reinforcement at the bottom
have
helped
to
extend
the
of
dapped-end
reinforcement beyond the inclined crack: this reinforcement, however, is not very efficient in a deep dap. Recent importance
of
connections. the
shear
research
anchoring
the
strength
the
designing
Project
primary
of
the
web
(the
reinforcement of
PCIFSRAD
emphasizes
reinforcement
at
the
dapped
This research concludes that the reaction should be limited to
primary corner
under
beam.
is
lesser
of
typically
and
not
V
anchored
at
The example in Appendix C illustrates
dapped connection in
because the
the
bottom
procedure for
pocket spandrel.
Predicting the strength of the concrete section is complicated by the
found
pockets.
strength
of
concrete
joists
that
with
a
prediction
conservative
square
openings,
but
of
without
the
stirrup
reinforcement, was obtained by calculating the load at which cracking at the corner
of
proportion
the to
opening
the
area
develops, of
the
assuming
section
the
above
shear
is
distributed
below
the
opening.
and
approach to calculating this load is to substitute Code
equations
(Equations 11-11
or
11-3
11-13
or
for 11-6
the
shear
for
strength
non-prestressed
for
spandrels),
for
of
the
spandrels, where
h
is
in
concrete
or
in
section
Equations
the
height
of
the
V
is
P
pocket.
Similarly, the strength provided by the shear reinforcement,
given by
(d-h)
Y
which
reflects
an
unfavorable
shown in Fig. 5.1.
The
above
pocket
but
is
spandrels.
openings.
Using
crack
pattern
approach
not
P
is
generally
through
believed applicable
the to
pocket
be
to
Code Equation 11-13 and substituting
region,
conservative
beams
with
for
square
for
the predicted shear strength provided by the concrete section of Specimen 3
52 .
is
110
kips or
considered
93
to
kips,
depending
contribute
to
on
whether
shear
or
not
the
These
strength.
prestress
predictions
is are
comparable to the failure load of 101 kips. It
is
common
nearest the support. these cases, the
practice
not
torsion.
a
deep
pocket
for
the
T-stem
hanger is used instead. In
term need not be included for design of the end region. The torsional response of deep spandrels is There was no evidence of
dominated by out-of-plane bending. cover
use
A welded bracket or
Detailing practices.
side
to
which
can
occur
in
compact
sections
of the
subjected
primarily
to
The use of lapped-splice stirrups in lieu of closed stirrups did
not appear to have any detrimental effect, and the absence of hooks on the longitudinal reinforcement did not lead to any apparent problems. It is unlikely that there would have been any improvement in shear strength of the pocket spandrel had the wire mesh been anchored by a bend at the
longitudinal
The
reinforcement.
anchorage of the primary
failure
is
attributable
to
poor
reinforcement, and there was no sign of an
anchorage failure of the wire fabric.
5.4
Beam
Torsion Specimens
1
and
End
Design
equilibrium 2
was
reinforcement.
beyond
the
The
predicted
applied capacity To
equilibrium reinforcement required by Equation 1. bearing
may
Nonetheless,
have
helped
equilibrate
the
torsional load on
applied
of
the
extent
torsion eccentric
torsional
load.
the test results support the contention that reinforcement for
the torsion equilibrium reaction need not be added to the reinforcement for internal torsion. Longitudinal reinforcement at end. dapped
connection
beam supports.
points
out
a
possible
The premature failure near the
deficiency
at
non-dapped
spandrel
Figure 5.2 shows the forces acting on a free body cut off by
diagonal tension cracks at the support.
Neglecting
the
distance
from
the
top of the beam to the compressive force. the developed force required at the face of the support is given by =
+
53 .
where
sd support. spandrel,
=
developed
The
stress
remaining
in
notation
the is
reinforcement defined
in
at
Fig.
the
face
5.2.
of
For
the
dapped
a similar check of the free body forces across an inclined crack
through the full section is recommended. design examples in Appendices B
5.5
Beam
Hanger
Typical cases are included in the
C.
Ledges
reinforcement. -
The
load
tests
and
analytical
studies
indicate that the eccentricity of the ledge load cannot be neglected in the design of hanger reinforcement.
Nonetheless,
not all of the load acting on
the ledge is suspended from the web, and the effective eccentricity of the ledge load is significantly reduced due to torsion within the ledge. by Equation 2 may be somewhat overly conservative.
A
while use of Equation 3 may be
design
procedure
for hanger
reinforcement has
developed based on the transverse forces acting on Fig.
5.3.
Design
been
the free body shown in
Summation of moments about the outside face of the spandrel gives A
sh =
where
shear in ledge torsion in ledge width of the ledge measured along the bottom of the beam, and = strength reduction factor
Most
of
the
notation
defined in Fig. 5.4. 0.9
compensates
for
used
for
hanger
reinforcement
0.85, design
Similar to Equation 1, the use of the
ratio
of
internal
model
study
moment
arm
is
graphically
0.85 instead of to
total
effective
depth. The ledge,
finite depends
element on
the
calculated by integrating the
beam.
the
parabolic
internal
verified
shear
stress
that
the
shear
distribution,
in
which
the is
from the top of the ledge to the bottom of
In lieu of an exact solution, the following expression, based on shear
stress
distribution
conservative approximation of
54.
in
a
rectangular
beam,
gives
a
AV, overall height of the beam. and
where h
height of the ledge. depends on the torsional stiffness of the ledge compared to the total torsional stiffness of the beam.
Accordingly
2 t
where
= distance between the applied load and the centerline of the web,
ledge
=
whichever is smaller,
or
shorter overall dimension of a rectangular part of a cross section, and
y = longer overall dimension of a rectangular part of
in Equation 8 is intended to avoid assigning too much torsion
The use of to
the
cross section.
If
ledge.
closed
stirrups
are
provided
in
the
ledge
=
1.0;
otherwise Y
where T
1
= torsional moment strength provided by concrete. and = factored torsional moment at critical section.
Finally,
if
equilibrate
the
end
and
of
the .
L-beam
is
dapped,
the
end
reaction
will
not
Therefore, for dapped-end beams, the total hanger
reinforcement is given by
55.
For the L-beams included in this study,
Equation
6
would
require
about 30 to 60 percent more hanger reinforcement than Equation 2, depending As
previously
noted,
the
use
of
Equation
reinforcements requirements compared to Equation 2.
3
doubles
the
hanger
Hanger reinforcement is
not additive to shear and torsion reinforcement. The background research revealed that at least four spandrel During web.
beams
two
of
Data
specimens
were
conducted
these
load
pertaining
to
by
precast
producers
load tests of
several
years
ago.
tests, the ledge of an L-beam separated from the hanger
are summarized in
reinforcement
Table
5.1.
design
in
these
two
test
Similar to the test of Specimen 1.
in these prior load tests a wide horizontal crack developed at the ledge/web junction. off. in
In each case,
the test was stopped before the ledge actually fell
All three tests indicated the ledge-to-web connection was very ductile spite
of
specimens
very
suggests
reinforcing
light
hanger
that
approaching
due the
reinforcement.
to
strain
ultimate
The behavior of these test
hardening,
tensile
forces
strength
can
in
be
the
hanger
developed.
It
should also be noted that as the ledge begins to rotate due to separation from the web, the ledge load shifts in towards the face of the web. As shown in Table 5.1, calculated
using
Equation
calculated ultimate
load.
6.
the
yield
and
much
heavier
than
During
average
ledge
loads
were
The maximum test loads are comparable to the the
1974
test,
between the ledge and web occurred in the were
ultimate
(See
Fig.
a
localized
separation
region where ledge loads 5.6).
Therefore,
the
strength
contribution due to shear and torsion in the ledge was significantly greater than predicted by Equation 6. The reinforcement ratio of
these
minimum
spandrels
was
requirement
where s is the ledge load spacing)
roughly
for
. Y
structural
56.
This
slabs.
amount In
is
view
similar
of
the
to
the
ductility
minimum
demonstrated in these tests, recommended
for
hanger
reinforcement
reinforcement.
ratio
of
Y
is
The effective distribution width for
hanger reinforcement is discussed later.
was
the
Ledge punching shear.
The most unexpected result of the load tests
early
failures
punching
shear
in
the
ledge
of
Specimen
2.
As
discussed in the background section, other researchers have found that the equations for ledge may
be
between
that
the
the
equations
applied
eccentricity
is
punching
load
shown
and
shear may do
the
in
not
fully
centroid
Fig.
be
5.5.
""conservative. account
of The
the
for
the
critical
analysis
One eccentricity
section.
approach
This
used
to
investigate transfer of unbalanced moment between slabs and columns can be adapted
to
punching
shear
of
beam
The shear
ledges.
at the inside
edge of the ledge is given by
=
where
v
perimeter of the critical section, = distance between the ledge load and the centroid of the critical distance
between
the
section,
centroid
of
the
critical
section
and the inside face of the ledge, and = property of critical section analogous to polar moment of inertia (See Ref. 17).
This formula assumes that the full height of the ledge is effective and
none
of
the
eccentricity
is
resisted
by
ledge
flexure.
The computed
punching shear capacity of Specimen 2 using Equation 11 is 40.5 kips. which is comparable to the failure load of 42.7 kips. be
improved
developed
by
ledge
increasing flexure
the
ledge
reinforcement
Punching shear capacity can
projection should
capacity.
57.
also
or
depth.
increase
The
use
punching
of
shear
Equation
11
not
be
accurately
applied
to
conditions
where
reinforcement developed across the critical section can help resist eccentricity.
shear and tensile stresses acting on the full section
may reduce the punching shear resistance of the ledge. provides
evidence
situations, P
r
i
that
the
design
equations
and further o
r
t
this
may
study
be
in
recommended.
o
c
r
a
c
k
i
n
g
,
t
h
e
L
-
b
e
a
m
specimens showed evidence of higher stresses in the ledge hanger and flexure reinforcement in the vicinity of the applied load.
The finite element model
showed a similar concentration of stress.
the hanger reinforcement
strain
was
much
more
evenly
distributed
after
the
horizontal
crack
at
the
ledge/web junction had fully developed.
As the ledge separated from the web
along
it was clear that all of the hanger
the entire length
of
Specimen 1,
reinforcement between ledge loads was effective.
Ledge
cracks
did
not develop, so nothing was learned about the post-cracking distribution of strain in ledge flexure reinforcement. Of geometry
and
course.
these
results
are
reinforcement
similar
to
only the
applicable
test
to
L-beams
with
Local
ledge
specimens.
failures are conceivable, particularly if the loads or load spacing are not uniform. hanger
Figure 5.6 shows reinforcement
local failures in which the ledge flexure or
assumed
effective.
the
to
shear
resist
and
each
torsional
ledge
load
strength
reinforcing and shear strength may of
the
type
shown
in
Fig.
5.6
not
the
failure planes abc and def contribute to the strength. related to the punching shear strength of the ledge.
is
fully
inclined
This contribution is Even though the
ledge
be fully additive, premature failures are
unlikely.
On
the
other
reinforcement at the ledge load is required to supplement the punching shear strength, the
ledge
reinforcement
and
hanger
reinforcement
should
also be concentrated at the ledge load. Figure related
to
5.7
the
shows
bending is
a
local
strength evenly
separation of
the
distributed
between ledge.
the
Assuming
reinforcement
stress
neglecting
the upward force between loads is equal to
58.
ledge
between
ledge
and
the loads
web
hanger (and
where Vu is
the stem reaction and s is the ledge load spacing.
The corresponding sum of
the negative and positive bending moments in the ledge is equal to The reinforcement required to resist this bending moment is given by A
=v
where A
ledge reinforcement in the top or bottom of the ledge
addition to reinforcing
required for the primary moment, = effective depth of
and
= strength reduction factor = 0.85. Once instead
of
again.
0.9
use
of
compensates
a
strength
for
the
reduction
ratio
of
factor
internal
equal
moment
arm
to
0.85
to
total
effective depth. In
summary, or
considered
research
ledge
effective
strength
this
of
suggests
reinforcement
providing the
the
ledge
punching
are
that between
shear
adequate.
all
of
ledge
and
the loads
longitudinal
Further
testing
hanger can
be
bending
should
be
carried out to verify this assertion.
5.6
Beam
Pockets
During Phase 2 of the Specimen 3 test, the concrete the beam pockets punched out at a load of 47.6 kips. load
based
difference
on is
yielding apparently
Based on Equation 11. stem. stem
of
the
due
hanger
to
The
reinforcement
punching
shear
contributions
of
25
from
predicted 30.8
strength
failure
kips.
The
contribution.
the predicted punching shear strength is 31.1 kips per
Fully developed inclined cracks below the pocket loads
is
below one of
kips. hanger
These
results
reinforcement
additive.
59.
and
indicate punching
observed at tee that shear
the
strength
not
fully
d
Fig. 5.1
Shear in pocket spandrels
61.
d
(0.5
Fig. 5.2
Forces acting on free body cut off by diagonal tension cracks at support
62.
Fig. 5.4
Notation for hanger reinforcement design
64.
FACE OF WEB
BRG. PAD
Fig. 5.5
i I
Plan view of ledge showing eccentricity of ledge load relative to critical section
65.
FINDINGS AND
6.
The background
following
paragraphs
research.
analytical
Critical
section.
describe
the
findings
based
on
the
and load tests described herein.
studies,
Because spandrel beams are loaded "ear the
bottom, a critical section for shear and torsion at the face of the support should be considered. Influence
of deck
connections.
Connections
to
el em ent s
deck
do
not substantially reduce torsion, however, they are effective in restraining
lateral
displacement
induced
by
bending
about
the
weak principal axis. Shear
and
torsion
of
prestressed
L-beams.
Methods
which
consider a concrete contribution for shear and torsion design of prestressed methods, on
spandrels,
such
as
the
Zis-McGee
have been verified by two tests.
compression
field
theory
are
or
the
Zia-Hsu
Design methods based
somewhat
conservative,
particularly with regard to the requirement for negative bending strength Shear the
the face of the support.
strength effect
of
of
spandrels
has
pocket
the
spandrels.
pocket
been
on
An approach for considering
the
proposed.
shear
While
strength
the
of
accuracy
pocket of
this
approach has not been fully verified by tests, it is believed to be conservative. Detailing is
practices.
dominated
stirrups
by
and
The
torsional
out-of-plane
longitudinal
response
bending.
of
deep
spandrels
The use of lapped-splice
reinforcing
bars
without
hooks
does
not appear to have any detrimental effect. Beam
end
region
design.
of
Two
spandrels
independent are
design
recommended.
checks
First,
in
the
end
reinforcement
should be provided to resist out-of-plane bending caused by the horizontal is
not
very
torsional
additive
little
to
equilibrium the
reactions.
reinforcement
supplemental
steel
69.
will
for be
This
internal required
reinforcement torsion. provided
and a
critical
section
support
is
primary
for
shear
considered.
longitudinal
and
torsion
Second,
the
reinforcement
at
at
the
developed
the
face
of
face
of
the
force
in
the
the
or bottom corner of a dapped-end connection. should the applied normal force,
support,
equilibrate
as well as the axial force induced by
the vertical reaction. Ledge
hanger
reinforcing.
The
eccentricity
of
the
ledge
load
cannot be neglected in design of hanger reinforcement for to-web attachment. the
ledge
is
eccentricity torsion
Nonetheless, not
suspended
of
the
within
the
from
ledge
load
all
the is
web
and
Load
by
others
have
verified
addition, it
was
determined
that
hanger
additive
shear
reinforcement
amounts
torsion
are
acting
the
effective
reduced
tests
and
and
load
due
on
to
A design procedure which considers
ledge.
program
to
the
significantly
these effects has been recommended. this
of
conducted
this
procedure.
reinforcement
and
In
is
Minimum hanger
reinforcement.
recommended
under
distribution
of
ledge
reinforcing is discussed. Ledge shear
punching strength
shear. of
beam
design ledges
equations
may
for
the
punching Further
be
research in this area is recommended. In
closing,
it should be reemphasized that this study has focused In this regard, the research
on spandrel beams as load-carrying components. has
gone
a
long
way
toward
the
understanding
fundamental aspects of spandrel beam design.
The
and
resolution
findings
of
several
generally
apply
to both prestressed and conventionally-reinforced spandrels commonly used in forces from frame action, volume
buildings and parking structures. change. does
handling
not
details .
fully
and
vehicular
address
impact
tolerances,
were
not
corrosion
discussed,
and
protection
or
the
report
connection
These factors must also be carefully considered during the design
ACKNOWLEDGEMENTS Throughout the study, the Steering Committee for PCISFRAD Project provided helpful guidance and perspective.
and Kamal Chaudhari contributed significantly through their
Alex constructive
comments.
The conducting to
In particular, Ned
support
this
research
specifically
thank
of is
Wiss,
Elstner
gratefully
John
acknowledged.
Hanson,
Associates,
Inc.
in
The author would like
John
Dirk Heidbrink. and Doris Nelson for the assistance. The test specimens were fabricated by J. W. Peters.
Their
performance in this difficult and precise task is a credit to their talent a precast producer. Also, the author wishes to express his appreciation to Susan Klein of Susan Klein Graphic Design for her help in preparation of the graphic figures. Finally, this research was funded by the Research
and
Development
Program.
Specially Funded
The author wishes to thank the
administrators and contributors to that program who made this research possible.
71.
NOTATION
shear
span,
distance
between
concentrated
load
or
reaction and hanger reinforcement area of A
sh
A
tension reinforcement
area of hanger reinforcing area of reinforcement in the top or bottom of the ledge in
addition
to
the
reinforcement
required
for
the
primary moment A
area of shear reinforcement
A
area
of
longitudinal
web-reinforcement
for
bending
due
to torsional equilibrium reactions A
area
of
vertical
torsional b b
web
equilibrium
reinforcement
for
bending
due
to
reactions
bearing width of concentrated ledge load a
width of ledge measured along the bottom of the beam perimeter of critical section
b
web width distance from extreme fiber to neutral axis distance
d
from
extreme
tension
compression
fiber
to
centroid
of
reinforcement
effective depth of ledge reinforcing
d
distance from centerline web to ledge load distance from centroid of critical section for shear to ledge load compressive strength of concrete, psi square root of compressive strength of concrete, psi f
sd
f Y
developed stress in primary
reinforcement
yield strength of reinforcement
f
ultimate tensile strength of reinforcement
h
overall height of section
h
height of ledge
72.
h
=
height of pocket in pocket spandrel
=
height
P
of
beam
effective
in
resisting
bending
due
to
torsional equilibrium reactions ratio of internal moment arm to total effective depth
j
=
property
of
critical
section
to
moment
of inertia N
=
axial force at bearing spacing of shear or torsion reinforcing spacing of ledge loads
=
torsional moment strength provided by concrete
=
torsional moment in ledge
T
=
factored torsional moment at critical section
v
=
shear strength provided by concrete
=
shear in ledge factored shear force factored reaction shorter overall dimension of a rectangular cross section
Y
=
longer overall dimension of a rectangular cross section
A
=
symbol for difference
=
reduction factor for torsion in ledge capacity reduction factor summation symbol
73 .
REFERENCES
1.
Building Code Requirements American Concrete Institute,
2.
MacGregor, James G.. Chmn., "The Shear Strength of Reinforced Concrete Members, by the Task Committee on Masonry and Reinforced Concrete of the Structural Division," Journal of the Structural Division, ASCE, Vol. 99, No. ST6, Paper 9791, June 1973, pp. 1091-1187.
3.
Design Handbook, Chicago, IL, 1985.
4.
Notes on pp. 14-28.
5.
Ned M.. "Identification of Secondary Behavior in Combined Bending, Shear, and Torsion of Reinforced Concrete Ledger Beams," Ph.D Dissertation, University of Virginia School of Engineering and Applied Science, August, 1984.
6.
James K. and Pfeifer, Donald W., "Bearing Pads for Precast Concrete Buildings," Journal, V. 30, No. 5, September-October 1985, pp. 128-154.
7.
Paul and McGee. W. "Torsion Design of Prestressed Con cre te, " Journal of the Prestressed Concrete Institute, Vol. 19, No. 2, March-April 1974, pp. 46-65.
8.
Design Handbook, Chicago, IL, 1978.
9.
Zia ,
Third
for
Reinforced MI.
Edition,
Concrete
Prestressed
Concrete
Institute,
318-83, Portland Cement Association, Fourth Edition, 1984.
Second
Edition, Prestressed Concrete Institute,
Paul and Hsu. Thomas, "Design for Torsion and Shear in Prestressed Concrete," Preprint 3424, ASCE Chicago Exposition, October, 1978.
10.
Raths, Charles H.. "Spandrel Beam Behavior and Design," Vol. 29. No. 2. March-April 1984, pp. 62-131.
11.
Osborn. Andrew E. N., "Design of Ledger Girders," Connection Details Committee, April 1984.
12 .
Collins, Michael P.. and Mitchell, Prestressed and Non-Prestressed Concrete September-October 1980, pp. 85-86.
13.
Edward R., "Theory of Deflection correspondence to Andrew Osborn. May 1984.
74.
Draft
Journal.
report
for
"Shear and Torsion Design of Beams," Journal, Vol. 25.
Compatibility,"
Private
REFERENCES (continued)
14.
"Serviceability Behavior and Sher and Furlong, Richard Failure Mechanisms of Concrete Inverted T-Beam Bridge Bentcaps." Journal, Proceedings Vol. 80, No. 4. July-August 1983, pp. 294-304.
15.
Krauklis, A. T. and Guedelhofer, 0. C., Comments on "Spandrel Beam Journal, V. 30, No. 5, Behavior and Design." (Ref. October 1985. pp. 171-174.
16.
Hanson, John M., "Square Openings in Webs of Continuous Joists." PCA Research and Development Bulletin, Portland Cement Association, 1969, 14 PP.
17.
Building Code, Rice, Paul F., et al, Structural Design Guide to the Third Edition, Van Nostrand Reinhold Co., Inc., New York, NY, 1985. 477 pp.
75.
EXAMPLE 1
APPENDIX B L-BEAM FOR PARKING STRUCTURE
DESIGN LOADS STEM REACTIONS DEAD LOAD LIVE LOAD
= 10.8 kips = 6.0 kips 16.8 kips
TOTAL SERVICE LOAD = FACTORED LOAD
1.4x10.8 + 1.7x6.0 = 25.3 kips
EQUIVALENT UNIFORM LOAD = SERVICE: FACTORED:
+ 0.675 = 4.88 7.27
BASIC UNIFORM LOADS ARE INCREASED BY RATIO OF GRID SPAN TO DESIGN SPAN. GRID SPAN = 28.0 ft. SHEAR SPAN = 27.0 ft. SERVICE (ADJUSTED): FACTORED (ADJUSTED):
= 4.88 = 7.27
= 5.06 7.54
FLEXIJRE
THE FOLLOWING IS A SUMMARY OF THE FLEXURE DESIGN. REFER TO HANDBOOK SECTION 4.2 FOR DETAILS OF THE DESIGN PROCEDURE. SERVICE LOAD MOMENT NOTE:
5533 in-k
THE MOMENT COMPUTED USING THE ADJUSTED EQUIVALENT UNIFORM LOAD IS ABOUT 2% GREATER THAN THE VALUE COMPUTED USING CONCENTRATED LOADS.
PRESTRESS:
4
in. DIAMETER STRAND
At Release (7% Loss) 483 -215 2100 -355
In Service (17% Loss) -166 525 148 430 -424 2250
5.0 in.
WT )
24 (NORMAL WT)
6 SPACES AT
DESIGN DATA
= 5000 psi
A
648
= 3500 psi
I
= 307,296
60 ksi = = 270 ksi
Y
=
f
Y f
SECTION PROPERTIES
P"
dia.
relieved strand)
Clearance to stirrups = 1
Fig.
32.67 in
=
9406
=
7813
WT =
0.675
L-beam geometry and design data
SUPPORT
13.5’
6.75’
6.75’
a245 I
0
Fig.
Moment, shear and torsion diagrams
B3
ULT IMATE A
STRENGTH :
= 0.612
=
=
= 0.80 in.
+
= 8245 in-k
2
11,897 in-k
11,897 in-k =
= 10.840 in-k
11.897 in-k
SHEAR AND TORSION THE SHEAR AND TORSION DESIGN FOLLOW THE METHOD (REF. 9). SEE FIG. B2 FOR BENDING SHEAR AND TORSION DIAGRAMS. SHEAR
A ND
TOR SIO N
PROPERTI ES
LEDGE)
LEDGE
8
60 3840
12
14
2016
5856
= 8x66.6 = 533 =
=
-1
=
MINIMUM TORSION = T .
=
+
= 1.14
=
201 in-k 708 in-k THEREFORE, TORSION DESIGN IS REQURIED.
B4
TRANSVERSE REINFORCEMENT SUMMARY (INSIDE FACE
SHEAR/TORSION
+
NEAR SUPPORT 0.32
TORSION EQUIL.
+
0.38
HANGER REINF.
(per
0.26 x4 at 6 (0.40)
PROVIDED
0.11
0.20 at 6 (0.22)
LEDGE DISTRIBUTION REINFORCING PUNCHING SHEAR STRENGH IS ADEQUATE, THEREFORE, ALL HANGER REINFORCEMENT AND LEDGE FLEXURE REINFORCEMENT BETWEEN LEDGE LOADS ARE CONSIDERED EFFECTIVE, PROVIDED STRENGTH OF LEDGE IS ADEQUATE.
= 12 A
3 = 9 in. f
= 0.33
THE BARS AT THE END OF THE LEDGE ARE NOT REQUIRED FOR THE ARE NEEDED TO HELP RESIST 1.2 BASIC MOMENT. THEREFORE THEY MAY BE CONSIDERED AS REINFORCEMENT.
APPENDIX C EXAMPLE 2
POCKET SPANDREL FOR PARKING STRUCTURE
THIS EXAMPLE ILLIJSTRATES DESIGN OF SHEAR, END REGION, AND HANGER REINFORCEMENT FOR A DAPPED POCKET SPANDREL. NOTE THAT A POCKET IS OFTEN THIS POCKET IS OMMITTED DUE PROVIDED NEAR THE DAPPED END. TO DETAILING DIFFICULTIES (A WELDED BRACKET OR CAZALY HANGER IS USED, INSTEAD). SHEAR AND BENDING FORCES ARE IDENTICAL TO THOSE IN REFER TO FIG. Cl FOR FRAMING DETAILS AND EXAMPLE 1 (FIG. DESIGN DATA. IN ADDITION, THE FOLLOWING IS GIVEN: = 167 psi, f
f
= 904 psi (AT POCKET), d = 67.0
SHEAR AND TORSION TORSION AT SUPPORT STEM REACTION
25.3 kips;
=
2.0 in.
= 177 in-k
INSIDE OUTER REACTION:
=
= 127 in-k
MINIMUM TORSION =
+
=
+
1.15
= 4608
= 159 in-k THEREFORE, TORSION DESIGN NOT REQUIRED INSIDE OUTER REACTION. DESIGN END REGION FOR TORSION EQUILIBRIUM REACTIONS AT SUPPORTS. SHEAR STRENGTH OF CONCRETE AT SUPPORT: + +
= 85.1 kips
AT QUARTER POINT (SEE ART 11.4.2 OF M
318-83 COMMENTARY):
=
= 6672 in-k (AT POCKET)
Cl
24
6 SPACES AT
DESIGN DATA
=
5000 psi
=
3500 psi
f
P"
=
FULL SECTION
AREA I
AT POCKET
576
432
248,832
204.288
60 ksi (bars)
36.0 i n
40.7 in
70 ksi (WWF)
6912
5023
6912
6520
270 ksi
Fig. Cl
Pocket spandrel geometry and design data c2
AT CENTERLINE WELDED TO END ANGLE
- i - - r
END DETAIL
FORCE MODEL bc
FORCE MODEL de
FORCE MODEL fg
Fig.
end detail and force models
FIG. 4.10.4: f
= 170 ksi 93.3 kips
SAY OK
CHECK DEPTH OF COMPRESSION BLOCK =
= 2.3 in =
=
1.2
in
2
in
OK
HANGER REINFORCEMENT AT POCKET
A
sh
=
USE
A
sh
=
0 . 4 7
Y
EA POCKET (PLUS
=
dh =
WIRES)
+ 2x0.04 = 0.47 =
= 8.5 in OK
C6
Copyright Conc rete Institute
All rights reserved. This book or any part thereof may not be reproduced in any form without the written permission of the Prestressed Concrete Institute.
This report is based an a research project supported by the Specially Funded Research and Development Program. The conduct of the research and the preparation of under the guidance of selected industry Steering Committees. It should be recognized that the research conclusions and recommendations those of the researchers, and that the established for other W-published technical reports and documents. It is intended recommendations of this be considered by appropriate PCI technical committees and included. if viable. in future reports coming from these committees. In the meantime. this research report is made available to producers, engineers and others to with appropriate engineering judgment similar to that applied to any new technical information.
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