behavior and design of double tees with web openings

8/15/2019 Behavior and Design of Double Tees With Web Openings

1/17

Behavior and Design of

Double Tees With

Web Openings

6

John M Savage

Structural Project Coordinator

Henningsen, Durham

Richardson, Inc.

Omaha, Nebraska

Maher

K

Tadros

Ph.D. P E

Cheryl Prewett Professor

of Civil Engineering

University of Nebraska-Lincoln

Omaha, Nebraska

Panchy Arumugasaamy

Ph.D. P E

Research Associate Professor

Center for Infrastructure Research

University of Nebraska-Lincoln

Omaha, Nebraska

Larry G. Fischer P E

Vice President

Concrete Industries, Inc.

Lincoln, Nebraska

This paper presents the results of a research

project aimed

at

providing

standard

sized

web openings to the popular precast

concrete double tee. The main advantage of

these openings is that mechanical equipment

can pass through the webs of double tees

instead of

under them. This reduces the

floor-to-floor height

and

overall cost of the

building. Another

advantage is a slight

reduction in double tee weight that would

improve the demand on the supporting frame

both

under gravity loading and seismic

excitation. The design

of

the web openings

was based on prior research and a finite

element

analysis. Opening size

and

placement and required material strengths

were investigated. Also, the effects of using a

two-point

depression rather than the

standard one-point depression of the

prestressing strands were investigated. Four

45ft

13.

m) long single tee specimens one

leg of

a double tee) were tested to failure.

The test results obtained from

this

investigation show that the performance of

the specimens with web openings

was

almost identical

to that

of

the

specimen

without web openings. Based on these tests,

design recommendations are made that will

allow the addition

of

web openings to double

tees with minimal additional calculation.

PCI JOURNAL


2/17

P

ecast concrete double tees are

one of the most popular precast

concrete floor framing systems.

However, compared to open web steel

joist

s,

they are heavy and

do

not allow

mechanical equipment to pass through

them. Placing web openings

in

double

tees allows mechanical equipment to

pass through them, reducing the floor

to-floor hei g

ht

and overall building

height. The reduced building height

can result

in

significant economy in

the cost of the building envelope and

in the mechanical and electrical sys

tems. A further benefit

of

weight re

duction is saving s in the supporting

beams, columns, and foundation due

to both vertical gravity loads and hori

zontal seismic forces.

This paper presents the

re

sults of a

research

project

that

investigated

adding web openings to the standard

PCI double tee. Existing floor and roof

framing systems were reviewed in ad

dition to prior research on precast, pre

stressed concrete double tees with web

openings. The analysis was performed

to investigate two-point depression of

the strand, opening size and place

ment, and required material strength .

This analysis was used to design four

full size specimens that were tested to

failure.

The results obtained from the testing

show that multiple, large web open

ings can be placed into a precast con

crete double tee without reducing the

strength or significantly increasing the

deflection

of

the double tee . Simple

de sign and

det

ailing

steps

are pro

posed for these double tees.

LITER TURE REVIEW

The first published work on precast,

prestressed concrete beams with web

openings was conducted by Ragan and

Warwaruk.' Since then , several other

researcher

s

have investigated pre

stre

sse

d concrete beam s with web

openings, including Suave,' LeBlanc,

3

Salam and Harrop , ' Dinakaran and

Sastry,

5

and Kennedy and El-Laithy.

6

Two of the more comprehensive stud

ies conducted on prestressed concrete

beams with web openings were done

by Barn

ey

, Han so n, Corley, and

Parmelee,

7

and Kennedy and Abdalla.•

Based on their research, both Barney

January February 1996

et al.

7

and Kennedy and Abdalla de

veloped de sig n

procedure

s for pre

stressed concrete beam s

with

web

openings.

Based on thi s prior research, several

conclusions can be made:

•

The

deflection

of

beams with web

openings is similar to

th

at

of

beams

without web openings.

• Web

openings

need to be

placed

outside

of

the strand development

length.

• Beams with web openings placed in

high shear regions do not perform as

well

as

beams with web openings

in

predominantly flexural areas.

• Vertical stirrups need to be placed

on each side of an opening to con

trol cracks extending from the edges

of

the openings.

• The chords below an opening may

crack at loads less than the service

load.

• The beams with openings

behave

similarly to a Vierendeel truss.

• The shear

in

a beam at an opening

should be di stributed between the

top and bottom chords

in

proportion

to their stiffness.

Kennedy a

nd

Abdalla

9

have recently

completed a comprehensive study

of

beams with one opening. They have

proposed a rather involved procedure

to design for the opening; however,

they have not considered simplifica

tion and possible standardization

of

beams with a large number of open

ings. Their paper gives a good di scus

sion of the types

of

cracking that can

occur around an opening in a

pre

stressed concrete beam and how these

cracks form.

THEORETIC L N LYSIS

The double tees with web openings

are envisioned primarily for use in of

fice

construction.

Based

on thi

s,

a

span of 45 ft (13.7 m) was c

ho

sen for

analys

is

, and an office live loading of

50

psf (245

kg/m ' ) plu s a 20

psf

I 00 kg/m' ) superimposed dead load

plus 25 psf (122 kg/m' ) to represent a

2 in. (50 mm) topping was use

d.

This

is a total superimposed uniform ser-

vice load of

95

psf (464 kg/m') and an

ultimate load

of

150 psf (730 kg/m'

.

The

PCI

De

sign

Handbook

'

0

show s

th

at a 24 in . (600 mm ) deep double tee

is required to carry the design load.

The design load included the weight

of a 2

in

. (50 mm) topping , although

the analysis and testing were per

formed

without

the topping

on the

tees. This is conservative because the

weight

of

the topping

is

added to the

load

of

the tees, but the additional

strength gained from the topping is

ignored.

A two-dimensional finite

element

analysis was conducted using ANSYS

4.4a. Two-dimen sional four-noded

isoparametri c elements were used to

model

the

concrete portion

s

of

the

tees. The thickness

of

the elements

was varied to account for the differ

ence in width between the flange a

nd

the web. Two-noded spars with an ini

tial strain were used to model the pre

stressing strand.

Three load stages were investigated:

tran

sfe

r, service load, and ultimate

load. The finite element models were

linear, so they were less exact for the

analysis with ultimate loads because

the model did not account for crack

ing.

However

,

the

analysis gave a

good indication of overall tee behav

ior, such as the deflection of the tees

under service loads, the location

of

stre ss concentrations, and an idea of

the magnitude of the stress concentra

tions. In this analysis, one leg

of

the

double tee was modeled for half of the

span with symmetry applied to the ele

ments at the centerline

of

the span .

Opening size and placement, strand

location , and material strengths were

refined using these analyses.

The opening depth was varied to

see what impact th at would have on

the tee stre sses . In order to better

transfer stress from the flange to the

web, 2 in. (50 mm)

of

concrete was

left between the top

of

the

opening

and the bottom

of

the flange .

Ba

sed

on required cover for the strands and

any mild steel reinforcement required,

the maximum opening depth could be

13 in. (33 0 mm). With 13 in. (33 0

mm) deep openings, there were hi gh

compressive stresses in the bottom

c

hord

s at tran sfe r and high ten sile

stresses at service. With a

12

in . (300

mm) deep opening, the tensile stresses

were between the 6

fJ

and 12

fJ

stress limits ,

which would

indicate

limited flexural cracking.

47


3/17

I

11'-6

End Section

)

-

c____)

c____)

11'-0

22'-6

Depression Points

5

1/2

DIA

270

ksi strands

stressed to

0.

75f pu

r

4'-0 1

[

=====rr====.·

===:;,=---------r-1

Y

2 ' ~ 0

\ ~

Spa.@

1/2

2 1/2

Section @ Midspan

2

2

fi3

L

'-8

11

1'-6

II 2'-4J_4

jf 4'J-

Typical Blockout Dimensions

Fig. 1. Typical dimensions

of

test specimens.

Although cracking

would signifi

cantly increase the deflection

of

the

tees, allowing the tees to crack was

preferable to reducing

the

opening

depth any further. The clear cover to

the prestressing strand was increased

by

50

percent in accordance with ACI

318-89

12

Section

7. 7 .3.2, and

the

12

j j

limit was used for the allow-

48

able tensile stress limit at service. The

final opening size used was 12 x 36 in.

(300

x

900

mm

).

Several different shapes were con

sidered for the web openings, includ

ing

ellipses

, rectangles, hexagons,

and

circles.

Rectan g

ular openings

were used because they provide more

flexibility

of

use than the other open-

1

=

25.4

mm

ing shapes considered. The corners of

the rectangular openings were cham

fered to reduce stress concentration s

at the corners

of

the openings under

service loads.

The width

of

the post between open

ings was

18

in. (450 mm), based on

strut-and-tie theory and because Bar

ney et aJ.7 recommended that the post

PCI JOURNAL


4/17

Fig 2. Locations of stress concentrations

be at least half the width of the open

ing.

This allowed

five

openings

be

tween depres sion points .

One

addi

tional opening was placed at each end

of the tee

outside

of the depression

points

.

These openings

had sloped

bottoms to accommodate the de

pressed strands. No

openings

were

placed in the length required for strand

development

or in

areas

of

high shear

(see Fig.

1)

.

One

of

the major variables investi

gated

in

this project was the effect

of

using

two-point depression

vs.

one

point depressed or straight prestress

ing strands used

in

previous research

projects. Two-point depression allows

placement

of

more larger openings

in

the webs than one-point depression or

straight strands

do.

The depression

points needed to be placed as far apart

as poss.ible in order to have the maxi

mum number

of

web openings in the

tee. However, if the depression points

were placed too

close to the ends of

the tees, the force required to depress

the strands during casting may be too

great. Accordingly the depression

point

should

be

approximately

be-

January-February

1996

T = tensile stress concentrationi UZ J

V = shear stress concentration J

a) Stresses at Release

T

T =tensile stress e n t r

V = shear stress concentration :.:

·:

b) Stresses at Service Load

tween the

one-quarter point

and

the

one-third point

of

the tee. The tees in

this project were analyzed with the de

pression points at

the one-quarter

points.

The PCI Design Handbook

'

shows

that four prestressing strands per leg

were required for the span and loading

chosen. In the finite element analyses,

both

three and four strands per leg

were investigated. The finite element

analyses showed that even with higher

concrete strength

and reduced self

weight, four strands were required.

Based on discussions with producers

and the finite element analysis, a fifth

prestressing strand per leg was added

in

the compression chord. This strand

was necessary bec ause as the tee is

loaded , the Vierendeel action

of

the

tees at the openings produces moments

on the ends of the tension and com

pre

ss

ion chords. These moments cause

tensile and compressive stress concen

trations at the ends

of

the chords. The

top strand provides additional com

pression in the compression chord to

counteract these tensile stress concen

trations. It also makes placement

of

the

auxiliary steel in the tee easier.

Both

h

and 0.6 in. (12 and 15 mm)

diameter,

270

and

300

ksi

(1860

and

2070

MPa) prestressing steel were in

vestigated. The results from the analy

sis showed that

h

in.

(12

mm) diame

ter 270 ksi (1860 MPa) low relaxation

strands were

adequate. Higher steel

strength and/or larger diameter strands

may be desirable

in

other applications

not considered in this study.

Concrete strengths between 6000

and 10 ,000 psi

(41

and 69 MPa) were

considered. The finite element analy

sis

showed that

a

higher concrete

strength

of

:

=

7000

psi (

48

MPa) and

J;; = 5500 psi (38 MPa) was required.

The higher concrete strength increased

the stiffness of the tee as well as the

code allowable stresses. The increased

stiffness

of

the tee reduced localized

stress

concentrations and

overall

deflection.

The

finite

element analyses

indi

cated several

other

stress concentra

tions (see Fig. 2). There was a com

pressive stress concentration near the

depres

sion

points

at tran

sfe

r of

the

prestressing force. There were tensile

49


5/17


6/17

For shear reinforcement, two types

of welded wire fabric

(WWF) com

monly used by Concrete Industries

were considered. The WWF comes in

flat sheets

LOft (3

m) long and approx

imately 20 in.

(510

mm) wide. The

WWF used at the ends

of

the beams

had D7 wires 4

in.

(100 mm) on center,

and the WWF used over the rest of the

span had W2.9 wires 7

1

2

in. (190 mm)

on center. The D7 wire

is

a deformed

wire with a cross-sectional area of 0.07

sq in . (45

mm

2

) ,

and a W2.9 wire is a

smooth wire with a cross-sectiona l

area of 0.029 sq in. (19 mm

2

.

The additional shear reinforcement

required around the web openings was

provided by deformed steel bars with

a yield strength of

60 ksi (415 MPa).

Reinforcement for the flange was pro

vided by a 4x4-W4.0xW4.0 WWF .

All

of

the specimens used this WWF.

Also, all of the WWF

had

a 75 ksi

(520 MPa) yield strength.

Tee 7G1

This tee

required only

m1mmum

shear reinforcement. No WWF was re

quired over the middle 4 ft (1.2

m)

of

the span; however, the

WWF

was pro

vided continuously over the length of

the tee (see Fig. 4a).

Tee

7G

The shear reinforcement

of

this tee

in the area

of

the openii:JgS was de

signed using strut-and-tie theory. In

the posts between openings, #3 U stir

rups were placed next

to

the open ings

to control any cracks extending from

the sides

of

the openings, and two #5

diagonal bars were placed in an X

pattern to carry the shear. Although

for a uniformly loaded tee only half

of

these #5

bars were needed

to

carry

shear, two #5 bars were placed in each

post in the

X

-pattern in case of

nonuniform loading. Two additional

#3 U stirrups were placed on the sup

port side

of

the end openings. These

stirrups were designed for the high

stress concentrations that extend from

the side

of

the end openings towards

the ends of the tee.

AU-shaped 4x4-W4.0xW4.0 WWF

was placed in the

chords

below the

openings.

This

U-shaped

WWF

was

designed to control cracks extending

January-February

1996

Standard Continuous Leg Mesh

22'-6

a) Tee

7G1

Standard Leg Mesh has W2.9 wire vertica lly@ 7 1/2 O.C.

Standard End Mesh has D7 wire vertically@ 3 O.C.

#5 Diagonal bar {TYP.)

4X4 W4.0XW4.0 U Mesh

{b

Tee 7G2

#4 Single leg stirrup (TYP.)

c)

Tees

7G3

and 7G4

Fig. 4 Reinforcement details of specimens.

from the bottom corners

of

the open

ings and to control shear cracking in

the tension chords. Because the stiff

ness of the tees was already reduced

by the openings,

it

was desired

to

pre

vent

shear cracking

of the tension

chord, which would reduce the stiff

ness

of

the tees even more.

The #3 U stirrups on each side of

the

openings

did not allow the U

shaped WWF below the openings to

be run continuously. This meant that

there had to be several small pieces

of

WWF across the length of the tee. The

I

=25.4

WWF

used was chosen because it

is

the same WWF as used in the flange.

The reinforcement details for Tee 702

are shown

in

Fig. 4b.

Tees

7G3

and

7G4

Tees

703

and 704 were reinforced

identically. The stirrups used in the

area

of

the openings were single-leg

4 stirrups. Stirrups were placed on

both sides of all the openings to con

trol cracks extending from the open

ings. Also, as in Tee

702,

additional

51


7/17

Fig 5 Measuring deflection near failure

Fig 6 Failed Tee 7G4

stirrups were placed on the support

side of the end openings. In the posts

between openings, additional stirrups

were placed as needed.

The stirrups were designed using the

stresses given by the finite element

analysis. Single leg stirrups were used

instead

of

U-shaped stirrups because

it

was thought that they would be easier

to place. Also, single leg stirrups al

lowed the U-shaped WWF below the

openings to be run nearly continuously

beneath the openings. The only dis

continuity

of

this WWF was at the end

of

each 10 ft

(3

m) section of WWF.

52

Reinforcement details for these two

tees are given in Fig. 4c.

CONSTRUCTION

During the construction

of

the tees

several problems were encountered. In

Tee

70 2

, the

5

bars were placed after

the blackouts for the openings were

in

place, so the bottom

of

the 5 bar had

to be placed by hand moving in a con

stricted area. Also, tying the bottom of

the stirrups

in Tees 703

and 704

proved difficult. Because neither side

of a double tee form is removable,

there

was

not

much

room to reach

down into the form to tie the stirrups.

During production ,

the

workers

made several recommendations. In

stead

of

using a combination of the

U-

shaped WWF below the openings and

the stirrups between the openings, a U-

shaped leg WWF could be used. The

WWF would be cut for the openings

and stirrups could be tied to the WWF

in areas where additional reinforce

ment

is

required. All

of

the steel could

be tied before placing it into the form,

and there would be less steel to tie.

TESTING

Instrumentation

During testing, deflection and con

crete strain readings were measured.

Deflection was measured at the one

quarter point and the midpoint

of

the

tees using dial gauges with an accuracy

of

0.001 in . (0.025 mm) . As the ap

plied moment on the tees approached

the design ultimate moment

of

the tees,

the dial gauges were removed and the

deflections were measured using a tape

measure (see Fig. 5).

Concrete

strains in the tees were

measured using a 200 mm (8 in.

Demec gauge. The Demec gauge mea

sures the relative

displacement of

gauge

points with

an accuracy of

4.0xi0 ·

6

strains.

The

externally

mounted strain gauges give a good in

dication of concrete strain up to the

point of cracking.

For Tee

701,

the solid tee, strain

gauges were located at the centerline

of

the tee. For the tees with openings,

strain gauges were placed above and

below the opening at midspan to in

vestigate flexural strains. They were

also placed at the left side, center, and

right side above and below the second

opening (first full opening)

of

the tees

to

determine if the openings were be

having similarly to a Vierendeel truss.

Observations efore Loading

Before testing of the tees began ,

there were small cracks approximately

I to 2 in. (50 to I 00 mm) long extend

ing from the comers of the openings.

One crack extended from each side

of

the opening. Kennedy and El-Laithy,'

Barney et al.,

7

and Kennedy and Ab-

PCI JOURNAL


8/17

Superimposed Moment

vs.

Deflection

Deflection mm)

0 100

200

300

400

300

400

275

350

250

225

300

200

s

250

i:i

175

i:i

.

s

s

0

0

E

150

200

E

0

0

.,

.

'

'

8

0

125

Service Live Load

S

150

·.:

§

100

§

Vl


9/17

able 1. Comparison of theoretical and experimental deflections [units :

in

. mm)].

Time

PCI me

th

od

7G I

-

Initial camber 0.68 t 0.75 t

at release

(17)

(19)

Camber at

1

.2

1 t

I

1.38 t

erection

3 1)

I

(35)

Service load

0.

51

t

I

0.66 t

(13) (17)

dead load. The live load deflection

equals L/1285, which is acceptable.

After creep and shrinkage, the total

superimposed deflection would natu

ally be greater; however, the deflec

tion should still be within acceptable

limits. Using the PCI Design Hand

book 1

method for calculating long

term deflection, the estimated long

term deflection after attachment

of

non-structural elements will be ap

proximately 0.44

in

.

11

mm), which

equals L/1227.

Cracking

of

the tees significantly re

duced their stiffness, and in turn in

creased their deflection . This shows

that

it

is important to ensure that the

tension chord

does not

crack under

service loads. All of the tees displayed

Fig. 8. C

ra

ck developme t T

ee

7G

2

54

Tee des ignation

7G2

7G3

7G4

0.75 t

1.00 t 0.88 t

(1

9)

(25)

(22)

·

1.25 t 1.69 t

1.

44 t

(32)

(43)

(37)

0.49 t

1.05 t 0.83 t

( 1

2)

(27) (2 1)

a high degree of ductility before fail

ure (see Fig. 5). The deflection of the

solid tee did not increase as rapidly

after cracking as the deflections of the

tees with openings did.

This shows the contribution of the

concrete in the tension region to the

stiffness of the solid tee. Fig. 7 shows

a graph of superimposed moment vs.

deflection up to the point of failure for

the tees. Note that the final deflection

shown in the graph

is

not the actual

deflection

at

failure because the

gauges had to be removed to avoid

damage.

The deflection of the tees during the

testing was compared with the theoret

ical

values

calculated

using

the

method presented

in

the PCI Design

Initial Cracking

70 ofMu

80 ofMu

90 ofMu

Handbook,

1

using the gross moment

of inertia (ignoring any loss in the mo

ment

of

inertia caused by the open

ings). An ci of 4.27 x 10

6

psi (29440

MPa) and c of 4.82 x 10

6

psi (33200

MPa) was used

in

the calculations. A

comparison of the theoretical and ex

perimental values for deflection is

given in Table 1.

The results are consistent between

all

four tees

, but not with

the pre

dicted values derived from

the

PCI

Design Handbook method. It appears

that the added stiffness of the longitu

dinal wires

of

the U-shaped

WWF

in

the tension chord helped compensate

for the reduced moment of inertia of

the tees caused by the web openings.

The largest difference between the

theoretical deflections and the experi

mental deflections is in the camber

measurements.

These differences are within expec

tations based on past experience. They

are attributable to the variability in

c

and creep and shrinkage properties

among the four specimens as well as

with PCI Design Handbook

1

predic

tion formulas. Ignoring

camber

, the

values

of

deflection are

all

very simi

lar.

The experimental deflections

PCI

JOURNAL


10/17

Fig 9 Crack development Tee 7G3.

caused by superimposed loads range

from

0.61

to

0.

76 in. (15 to 19 mm)

with the

PCI

Design Handbook'

0

value

equal to 0.70 in . 18 mm).

racking

Although the finite element analysis

conducted for these tees indicated that

they may crack under service loads,

none of the tees showed any cracks

under service load levels. This

is

prob

abl y because the finite element analy

s

is

did not account for the added stiff

ness

of

the longitudinal wires

of

the

WWF in the tension chord. The cracks

that had been observed at the corners

of

the openings before testing began

did

not

propagate as the

tees

were

loaded.

Tee 7G 1, the solid tee, did not dis

play any cracks until approximately

179 percent of the superimposed ser

vice load moment had been applied.

When this load level was reached, uni

formly spaced flexural cracks appeared

across th e middle half

of

the tee. Addi

tional loading caused additional uni

formly spaced flexural cracks across

the middle portion

of

the tee.

January-February

1996

Initial Cracking

70%ofMu

80%ofMu

90%ofMu

The crack

pattern for Tee 7G2 is

given in Fig. 8. The crack pattern for

Tee 7G3 is shown

in

Fig.

9.

Figures

of

crack development for Tee 7G3 are de

picted

in

Fig.

10 In

the tees with open

ings, the initial cracks were caused by

localized stresses at the openings. The

cracking also indicated Vierendeel

truss like

end forces on the

chords

below some

of

the openings. As the

load on the tees increased, the cracking

changed from a localized cracking to a

more uniform cracking caused by the

flexure

of

the overall tee.

At failure, there were flexural cracks

across the middle half

of

the tees. Tee

7G2

first showed cracks at approxi

mately

137

percent of the superim

posed service load moment. Tees 7G3

and 7G4 behaved very similarly. These

tees showed their first cracking at ap

proximately 158 percent

of

the super

imposed service load moment.

Although the cracks in

Tee

s 7G3

and 7G4 were primarily due to flex

ure,

several

of the openings had a

shear crack that extended from th e top

corner

of

the opening to the underside

of

the

flange.

It

then fo

ll

owed

the

flange horizontally toward the mid-

span. These cracks were caused by the

web trying

to

shear off the flange. Tee

7G2 had similar cracks, but they did

not extend horizontally along the bot

tom

of

the flange.

This phenomenon may occur be

cause

the

ends

of the 3 U stirrups

used on each side

of

the openings in

Tee 7G2 were bent into the flange, but

the 4 stirrups in Tees 7G3 and 7G4

were not. Also, the diagonal 5 bars

may have prevented cracks that started

at the

corners of

the

opening

s from

continuing up to the bottom of the

flange .

Strains

The strains that were meas ured dur

ing testing were used to calculate the

midspan curvature

of

the tees. A su

perimposed moment

vs. curvature

graph is given in Fig .

11 .

As can be

see

n

the curvature for all of the tees

is

very consistent up to the point of

cracking. Also, the plots

of

the strains

at the left, center, and right sections of

the second opening (first full openi ng)

clearly showed that the chords were

behaving like members

of

a Vieren-

55


11/17

a) 80 percent of ultimate load

b) 110 percent of ultimate load

Fig. 10. Tee 7G3 crack pattern.

deel truss. After the tees cracked, it

was hard to determine the curvature

because the strain was no longer linear

across the tee cross section.

Because of this, the curvature points

after the tees crack are not very accu

rate. If an accurate moment vs curva

ture relationship of a tee with open

ings were required, a nonlinear finite

element analysis would be the appro

priate method to follow: because the

tees are so nonlinear after cracking, it

is recommended that the tees with

openings

be

designed so that they do

not crack under service loads.

56

RE OMMENDED

DESIGN PRO EDURE

Based on this research project and

the research done by Barney et al., the

design of double tees with web open

ings should follow the following steps.

The tees should be designed with high

stre

ngth

concrete [>7000 psi

48

MPa)] in order to reduce deflections

and increase the shear strength of the

tees. Because the diagonal bars used in

Tee 7G2 did not significantly improve

the performance

of

the tee, and the di

agonal bars were difficult to place, it

is recommended that the design using

diagonal bars not be used.

Double tees are generally not practi

cal for shorter spans than those used in

this study where shear may be more

dominant in the overall tee behavior.

Flexure and deflection will generally

be

satisfied if

a

relatively

h

eavy

WWF, as presented in this paper , is

placed in the tension chord. Further re

search may result in a reduction in the

size of this WWF with satisfac tory

performance.

Restrictions on the design procedure

are

as

follows:

• The openings should be placed hori

zontally in the flexural region and

vertically below the concrete com

pression stress block.

• The beams are subjected to a uni

form loading

• The distance between openings is at

least half the opening width. Prelim

inary results of ongoing research at

the University of Nebraska indicate

that this requirement may be too re

strictive, and that a 10 in. (250 mm)

wide post with a 36 in. (910 mm)

wide opening has given satisfactory

results .

• The beams are not allowed to crack

under service load.

The design procedure is as follows:

1. Calculate the required strand de-

velopment length.

2. Calculate the

service and

ulti

mate loads acting on the tee, assuming

a uniform tee weight.

3. Determine a preliminary number

of prestressing strands from the load

tables in the PCI Design Handbook.

0

An additional prestres sing strand

should be placed in each web at the

same level as the bottom of the flange.

4. Determine the location of the de

pression points. The depression point

should not be closer to the end of the

tee than the one-fifth

point

for

the

span range considered in this paper.

For other spans, the depression point

should be placed such that the vertical

prestress force component does not

exceed approximately 4000 lbs (17.8

kN) per strand.

5. Place the openings so that the de

pression points are located centered

below a post between openings. The

openings should not be substantially

larger than the ones used in this pro-

PCI

JOURN L


12/17

Curvature 1/mm xl0-6

0

4

8

12

3000

300

2000

200

,.-...

.5

?

i:

g

i:

8

0

E

1000

El=59 .8 x 10

6

k-iif

7G1

100

=172

X 10

9

kN-Illlli

]

t

7G2

.&

7G3

7G4

0

0

100

200

300

Curvature 1/in. x10

6

Fig. 11. Superimposed moment vs. curvature at mi dspan.

ject, and the posts should not be nar

rower than half the width of the open

ings until further testing confirms oth

erwise. The openings should not be

placed in the area required for strand

development. The comers

of

the open

ings should be chamfered. The cham

fers used in this project were equal to

one-third the depth

of

the openings,

which worked well.

6. Place the strands so that the cen

troid of the strands coincides with the

centroid of the bottom chord. This is

the most favorable

arrangement

for

counteracting localized tensile stresses

due

to

chord bending. The force

in

the

tension chord under service loads can

be calc ulated

approximately

usi

ng

stand ard working stress calculations.

Mild steel reinforcing bars should be

added to the tension chord to prevent

January-February 1996

cracking

of

the chord if the tensile

stress exceeds 6 fjj .

7. Place the strands at the end

of

the

tee as close

to

the bottom of the tee as

possible in order to minimize the re

quired depre

ss

ion force.

8. Check stre sses at release and at

service load at critical sections includ

ing the

transfer

point , depression

point, and midspan of the tee. Include

the effects of the additional top strand,

and for sections at the location of a

web opening, use the section proper

ties for the tee accounting for the web

opening.

9. Check the flexural strength

of

the

tee using commonly known formulas.

Ignore the openings and the prestress

ing strand above the openings in the

moment calculations.

10 Check crushing of the concrete in

the chords below the opening at trans

fer

of

prestressing force using working

stress design procedures.

11

Desig n shear reinforcement for

the tee as if it had no openings.

12. Design additional stirrups to be

placed

adjacent to the

openings to

control cracks extending from the cor

ners

of

the openings. These stirrups

should be placed with

1

in. (25.4 mm)

cover next to each side

of

the open

ings. Calculate the total factored shear

force at the center of the opening with

the highest applied shear, and size the

stirrups to carry this shear force. Use

the same sized stirrup adjacent to all

of the openings. The required area of

the stirrup is given

by

:

where

Av=required area of stirrup

Vu

=ultimate shear at center of

opening

1 >

= strength reduction factor

y =yield strength of stirrup steel

(1)

13

Provide a minimum

of

three stir

rups per post between openings.

14 For the end openings, place two

additional stirrups, of the same size as

the stirrups adjacent to the opening, 4

in . (100 mm) on center on the side of

the opening toward the support.

15. Calculate the forces in the com

pression and tension chords at ultimate

load:

C = T = u

ds

(2)

where

u =factored moment at centerline of

double tee

d

=di

s

tance between centroid of

compression chord and tension

chord

16

Assume that at the ultimate load,

the tension chord is cracked, and all of

the shear is carried by the compression

chord. Check the shear capacity of the

compression chord using the formula:

U.S. Customary unit

s:

V = [

1

)R

wd

<

6 fj j wd

(3a)

7


13/17

[

2

4

a) End Section

4 prestressing strands

1 prestressing strand

1-#4

[

2

3 Spa.@ 112

2 1/2

b) Section at Midspan

1

=25.4mm

Fig. 12. Strand location for design example.

SI units:

v

= [ l + ~ I I

b d

c

14A

6

V

g

where

bw = width

of

compression chord

= width

of top flange (in., mm)

d

= depth of flange (in., mm)

_. = concrete strength (psi, MPa)

(3 b)

Ag=cross-sectional area

of

compres

sion chord (sq in. ,

mm

2

)

N

= axial compression = C (lbs, kN)

Vc

= nominal shear strength provided

by

concrete (lbs, kN)

The value of Vc should be compared

to the applied shear:

Vu ¢V

c

where

V

= factored applied shear

¢

= strength reduction factor = 0.85

In

the unlikely event this is not true,

special slab shear reinforcement may

be required.

17

A U-shaped welded wire fabric

(WWF) should

be

placed in the tension

58

chord below the openings to help pre

vent shear cracks under service loads.

The dimensions of the U-shape should

be made

as

large as possible while still

maintaining the required

concrete

cover. The WWF can be the same size

as the WWF used

in

the flange, but

it

should not be less than the

4x4-

W4.0xW4.0 WWF that was used in

this project until further testing shows

that a smaller WWF is acceptable. The

WWF should be run as continuously as

possible below the openings. The spac

ing of the vertical wires

of

the WWF

should be approximately one-half the

depth of the tension chord.

18

Deflections should be checked

using any recognized method of analy

sis for tees without openings.

DESIGN EXAMPLE

Design

web

openings for

a 54 ft

(16.5 m) span, 24 in. (610 mm) deep,

8 ft (2.4 m) wide double tee. Design

for a

50 psf (2.39 kPa) live load, 52 psf

(2.49 kPa) dead load, and a 10

psf

(0.48 kPa) superimposed dead load.

Material properties:

f/; = 5500 psi (38 MPa)

J:

= 7000 psi (48 MPa)

h in . (12 mm) diameter 270 ksi (1860

MPa) prestressing strand

Loads:

Perform design for single leg

of

tee:

w = 448

lb

s per linear ft (6.5 kN/m)

IV

= 687 lbs per linear ft (10.0 kN/m)

M = 163ft-kips (221 kN-m)

M

=250ft-kips (339 kN-m)

Strand Development Length:

Assuming a strand stress of 0.7jP

im

mediately after transfer of prestress

and 15 percent losses due to creep,

shrinkage, and relaxation, ld = 81.5 in.

(2070 mm). The web openings should

be

placed outside of this distance.

Preliminary Number

o

Strands:

Using the tables given in the PCI De

sign Handbook,

10

select eight strands

for the given span and loading. Place

four strands in the bottom

of

each leg

and a fifth strand at the top of each leg.

Check Ultimate Strength:

dps=20 in . (510 mm)

to

center

strands in the center of the ten

sion chord (see Fig. 12b)

Aps = 4(0.153) = 0.612 sq in.

(395 mm

2

)

/3

1

=0.70 for 7000 psi (48.3 MPa)

concrete

r,

= 0.28

Calculating:

= Aps =

0

·

612

= 0.000638

Pp bd 48(20)

fp

s p,+- ;: p

; ~ w w

]}

=

270[

I - ~ ~ ~ ( 0.000638 0)]

= 267 ksi (1840

MPa)

a=

Apsfps Asfy

A;J

y

0.85J:b

0.612(267)+0-0

0.85(7)( 48)

= 0.57 in . (14.5 mm)

PCI

JOURNAL


14/17

L

)

..

13'-6

27'-0

a) Depression Po-ints

Standard End Mesh

Standard Leg Mesh

)

13'-6

)

~

5 112 DIA 270 ksi strands

stressed to 0.75f pu

4X4 W2.1XW2.1 U Mesh

#4 Single leg stirrup

#4 Single leg stirrup (TYP.)

Fig. 13. Double tee of design example.

¢1M,.=¢[ p s f p s d - ~ ) + A

d - ~ )

+ A

; t y ( ~ - d ) ]

= 0.9[0.

612(267{

20-

+0+0

C ~ )

=

242

ft- kips

(328 kN-

m)

< 250 f t- kips (339 kN - m)

Add 4 mild

steel reinforcing bar

below prestressing strand d = 21.25

in.

(540

mm ].

p

= 0.000196 for one #4 bar


b) Reinforcement Details

w

=

Ph =

0.00168

t:

Calculating

fps with the value

for

w

fps = 267 ksi (1840 MPa) and a = 0.62

in. (15.8 mm .

l JMn

=

0.9[ 0.612(267{20-

+0.20(60{21.25-

~

) J C ~ )

= 260 ft- kips (353

kN -

m)

>

250 ft- kips (339 kN - m) o.k.

Check Working Stress at

Transfer

of

Prestress:

Using

a

traditional

linear

stress

ap-

1

=

25.4 mm

proach with the section properties

of

a

single leg of the tee and fse = 182 ksi

(1254 MPa):

= 0.162(182) = 112 kips (498 kN)

bottom strands

= 0.153(182) = 28 kips (125 kN)

top strand

See Fig. 12 for strand locations.

At

end

of

beam:

fj

=

112+28

+ 112(10.2) 28(4.9)

b 200 612 612

=2 .34 ksi (16.1 MPa) compression

r = 112 + 28 - 112(10.2) + 28( 4.9)

t

200 1531 1531

= 0.04

ksi

(0.28

MPa) compression

59


15/17

Table

2

Total deflection [units: in. mm)].

1)

Load

Release Multiplier

Prestress

1.

54 (39.1) i

1.80x l )

Self weight

0.85 (2 1.6)

J

1.85 X

(I)

0.69 (17 .5) i

Superimposed

dead load

Live load

At opening near midspan:

112+28

163(12)

fb

= 140 497

112(14.41) 28(22-18.41)

+ ~ ~

497 497

= 0.109 ksi (0.75 MPa)

compression

j = 112+28 + 163(12)

I 140 1636

112(14.41) 28(22 -18.41)

- - - - - - - - - - ~ - - - - ~

1636 1636

= 1.27 ksi (8.76 MPa)

compression

These all meet the allowable stress

limits . For the section with the open

ing, use the

moment of

inertia and

area accounting for the web opening.

Depression Point and Opening

Placement:

Place the depression point at the one

quarter point of the beam. In this case,

place the depression points 13.5 ft (4.1

m) from the ends of the beam. This al

lows for six openings 12 x 36 in. (300

x 900 mm) with 18 in . (450 mm) posts

between them. See Fig. 13a for de

pression point placement.

Shear Design:

Constructing a shear

diagram

as

though the beam had no openings, this

beam requires only minimum shear

steel along its length. This steel is de

signed like any prestressed concrete

beam

without

web openings. Addi

tional reinforcing bars should

be

placed adjacent to the web openings to

prevent cracks from spreading from

the edges of the openings. These stir

rups will need to be designed to carry

the total shear force at the center

of

the opening. The highest shear will be

60

(2)

3)

Erection Multiplier Final

2.77 70.4) i 2.45 X

I)

3.77 (95.8) i

1.57 (39.9) J, 2.70 x l)

2.30 (58.4) J,

1.20 30.5) i 1.47 (37.3) i

0.19 (4.8) J, 3.00 X (2)

0 .57 ( 14.5) J,

1.

0 1 (25.7)

i

0.90 (22.9)

i

0.94 (23 .9)

J

0.04 (1.0)

J,

at the first opening. The shear at the

centerline

of

the first opening

is:

v;

= 0.687

5

2

4

-1 1

.

25)

= 10.8 kips (48 kN)

A

_

v;

_

10 .8

v ¢

0.85(60)

=0.21 sq

in . (135 mm

2

)

Use a single-leg 4 stirrup adjacent to

the sides

of

each opening. Use a mini

mum

of

three stirrups per

post

be

tween openings, and place two addi

tional stirrups next

to

the end openings

on the side towards the supports.

Check Shear Capacity of Compres

sion Chord

At ultimate loads , the tension chord

will be cracked, and all of the shear

force will be carried by the compres

sion chord. This is a conservative ap

proach because even after cracking ,

the

tension chord

will

carry some

shear.

C = T=

f; Ap

s= 270 (4

X

0.153)

= 165 kips (734 kN)

Vc

= {

1

+

.JJ:

bwd

Letting N =

C:

v

=2[1+

165

,

000

] .,)7000(48)(2)

c

2000(2)( 48)

=29 .7 kips (132 kN)

¢Vc=25.4 kips (113 kN)

>11

kips (49 kN) o.k.

Check upper limit of shear strength

using Fig. 11.3 in the ACI 318-89

Code.

9

Use the area

of

the compres

sion chord for A

8

.

Nu = 165,000

A

8

96

= 1720 psi (11.9 MPa)

Using Fig. 11.3 of ACI 318-89,

9

limit

the shear strength of the concrete to

6

.Jf7. This gives a shear capacity of

41.0 kips (182 kN). Therefore, 25.4

kips (113 kN) controls and is greater

than the applied shear.

Size Mesh for Flange:

w,

= 1.4(25 + 10) + 1.7(50)

= 134 psf (6.42 kPa)

M

= 134 2?

u 2

= 0.268 ft- kips per ft

(1.19 kN-m/m)

With

d

= 1 in. (25 mm):

A

req

= 0.053 sq in. per ft (112 mm

2

/m)

Use 4.4 W2.lxW2.1 WWF

Check Cracking

of

Bottom

Chord

at

Service Loads

M

5

= 163ft-kips (221 kN-m)

p = 155(4 X 0.153)

= 94.9 kips (422 kN) bottom strands

p

= 155(0.153)

= 23.7 kips (105 kN) top strand

Use section properties for one leg

of

the double tee:

sb= 497 in.

3

(8144 mm

3

)

A

= 140

sq in

. (2294 mm

2

)

Check opening near midspan:

j

-

(94.9+23.7) 163(12)

b - 140 497

94.9(14.41) 23.7(22 -18.41)

+ ------ -------- -

497 497

= 0.508 ksi (3.50 MPa)

Tension:

6.Jf7

=6 .,)7000=0.502

ksi (3.46 MPa)

This is acceptable. The additional 4

bar in the tension chord should be suf

ficient

to carry any

excess tensile

stress and prevent cracking

of

the ten

sion chord. Place a 4x4 W4.0xW4.0

WWF U-shaped mesh in the tension

chord to improve the shear capacity of

the bottom chord and to reduce crack

ing

of

the tension chord

under

ulti

mate loads.

PC l J O URNAL


16/17

Check Deflections:

Material properties:

Eci

=

4273 ksi 29.5 MPa)

Ec

=

4821 ksi 33.2 MPa)

Section properties:

I= 10,492 in < 4367300 mm

4

)

=

648 in. 16460 mm)

P

0

=

112 kips 498 kN) bottom strands

P

0

=

28 kips 125 kN) top strand

ee = 10.15 in. 256 mm)

ec

=

13.15 in. 334 mm)

e =

3 in. 75 mm)

a

=

13.5 12)

=

162 in. 4114 mm)

Initial camber:

Bottom strands:

L1 == P

0

eeL

2

P

0

e L

2

_ ~

8EcJ EcJ 8 6

= 1.70 in. 43.2 mm) i

Top strands:

~ e L

0

. 1

L1 = = .16m. 4.1 mm)

.v

8£ /

Sel f weight:

5wL

. 6 I

L1 = = 0.85 m. 21. mm)

.v

384EcJ

Service loads:

Because the working stress analysis

for a section at midspan showed that

cracking will not occur, the service

load deflections will be

calculated

using the uncracked section properties.

Superimposed dead load:

w

= 4 10 psf) =

40

lbs per linear ft

1.92 kPa)

L1=

5

wL

4

=0.188

in. 4.8 mm)

1.

384£/

Superimposed live load:

w = 4 50 psf) = 200

1bs

per linear ft

2.92 kN/m)


L1 =

5

wL

4

= 0.939 in. 23.9 mm) 1.

384£/

Table

2

summarizes the method

of

calculating the deflection.

Allowable deflection:

648 .

= ==1.8

m 45.7 mm)

360 360

Total deflection after attachment of

non-structural elements:

L1

1

= 0.57 0.94 = 1 51 in. 38.4 mm) 1.

<

1.8 in. 68.6 mm) o.k.

See

Fig. 13b

for tee reinforcement

details.

CONCLUSIONS

The performance

of the tees with

openings studied in this project was

within acceptable limits. This project

showed

that in

prestressed concrete

double tees, the prestressing strands

could be two-point depressed, allow

ing multiple large web openings with

out reducing the strength or increasing

the deflections of the tees.

The

pro

posed reinforcement details can be

readily implemented by precast con

crete manufacturers. Additional find

ings

of

this study include:

1

The results

of

the analysis and

testing were based on the assumption

that the member was subjected primar

ily to uniform loading. They must be

validated for cases involving signifi

cant concentrated forces.

2 The ultimate strength

of

the tees

was not affected by the presence of

properly reinforced web openings.

3. The tees with web openings be

haved like Vierendeel trusses.

4

None of the compression chords

above the openings exhibited buckling

behavior.

5 Adding

a

prestressed strand

above the openings was effective in

counteracting

the

localized tensile

stress concentrations

caused by

end

moments

acting

on

the compression

chords.

6 The behavior of tees with two

point depression was not sensitive to

variation in the depression point loca

tion relative to the openings. In some

instances

the

depression point

was

under the corner

of an

opening, yet it

did not appear to cause damaging

stress concentrations.

7 When properly reinforced

the

deflection

of

tees with web openings

is comparable to tees

without

web

openings.

8 Due to the nonlinear behavior of

the tees with openings after cracking,

it is advised that they be designed not

to crack under service loads.

In a follow-up project sponsored by

the U.S. Army Corps

of

Engineers, re

searchers at the University

of

Ne

braska are continuing to optimize the

opening size and spacing for the dou

ble tee and to simplify the reinforce

ment details. Results of this additional

work are expected to be finalized by

the end of 1996.

CKNOWLEDGMENT

The authors would like to thank the

University of Nebraska Center for In

frastructure Research and Concrete In

dustries for their financial support. They

would also like to thank the Prestressed

Concrete Association of Nebraska; Uni

versity

of

Nebraska graduate students

Tom

Taylor

Say-Gunn

Low

and

Mohsen Saleh; Deborah Derrick; Dr.

Amin Einea; and Merwyn Pearson.

6


17/17

1.

Ragan,

H.

S

.

and Warwaruk,

J.,

Tee

Members With Large Web Openings,

PCI JOURNAL, V. 12 No. 4 August

1967

pp. 52-65.

2.

Suave, J. G., Prestressed Concrete

Tee

Tees With Large

Web

Openings,

MS Thesis, University of Alberta, Fall

1970.

3.

LeBlanc,

E.

P. Parallelogram Shaped

Openings in Prestressed Concrete Tee

Tees, MS Thesis, University of Al

berta, Fall 1971.

4.

Salam, Sk. Abdus, and Harrop, Jack,

Prestressed Concrete Beams With

Transverse Circular Holes, Journal of

the Structural Division,

ASCE V.

105

No. ST3 March 1979 pp. 635-652.

5. Dinakaran, V. and Sastry, M.

K.

Be-

a

= depth

of

compression block

A

= cross-sectional area

Ag

= gross concrete area

of beam

Aps = area of prestressing steel

As(req) = required steel area

Av

= area

of

shear reinforcement

be = effective flange width

bw

=

width

of compression chord

equals width

of

top flange

C = force in compression chord

d = distance from extreme com-

pression fiber

to

centroid of

nonprestressed tension rein

forcement, or depth of com-

pression chord

d

= distance from

extreme com-

pression fiber to centroid of

nonprestressed compression

reinforcement

dps

= distance

from extreme

com

pression fiber to centroid of

prestressed reinforcement

ds = distance between the cen-

troids

of

the compression

chord and the tension chord

Ec = modulus of elasticity of con

crete

Eci

= modulus

of

elasticity

of

con

crete at transfer

REFERENCES

havior of Post-Tensioned Prestressed

Concrete T-Tees With Large Web

Openings, Indian Concrete Journal,

V.

58 No.2, February

1984 pp. 3 4 ~ 3 8

6. Kennedy, John B., and El-Laithy,

A.

M. Cracking at Openings in Pre

stressed Beams at Transfer, Journal

of the Structural Division, ASCE, V.

I 08,

No. 6

June

1982

pp. 1250-1265.

7. Barney, George B. Corley,

W.

Gene,

Hanson, John M., and Parmelee,

Richard A. Behavior and Design of

Prestressed Concrete Tees With Large

Web

Openings,

PCI JOURNAL,

V. 22,

No.6,

November-December

1977

pp. 32-60.

8.

Kennedy, John B. and Abdalla, Hany,

Static Response of Prestressed Gird-

PPENDIX

NOT TION

ec

= eccentricity of prestress force

from neutral axis of beam at

beam

centerline

ee

= eccentricity

of

prestress force

from neutral axis of

beam

at

end of beam

e'

=

difference between

prestress

force

eccentricity

at

end of

beam and at

centerline of

beam= ec- ee

fb = stress in bottom fiber of cross

section

J = compressive strength of con

crete at 28 days

J;; =

compressive strength of con

crete at transfer

fse

=

effective prestress

after

al

lowance for losses

fps = stress in prestressing strand

at

nominal strength

pu = ultimate

tensile

strength of

prestressing strand

t

= stress

in

top fiber of cross

section

y

=

yield strength of reinforce-

ment

I

= moment of inertia

L

=

span length

ld

= development length

ers With Openings, Journal of Struc-

tural Engineering,

ASCE,

V.

118,

No.2, February 1992, pp. 488-504.

9.

Kennedy, John B.,

and

Abdalla,

Hany

Design Against Cracking at Openings

in Prestressed Concrete Beams, PCI

JOURNAL, V. 40 No. 6 November

December 1995 pp. 60-75.

10.

PC Design Handbook, Fourth Edition,

Precast/Prestressed Concrete Institute,

Chicago, IL 1992.

11. ANSYS Revision 4.4a, Engineering

Analysis System, Swanson Analysis

Systems, Inc., Huston,

PA

May

1990.

12.

ACI Committee 318, Building Code

Requirements for Reinforced Concrete

(ACI 318-89), American Concrete In-

stitute, Detroit,

MI 1989.

M

= service load moment

Mn = nominal

moment

capacity of

a section

Mu

= factored moment

Nu = axial compression = C

P = prestress force after losses

P

0

= prestress force at transfer

sb = section modulus of bottom

of

beam

T

= force in tension chord

t

= flange thickness

Vc =

nominal

shear

strength

pro

vided by concrete

Vu = factored shear force

w = unfactored uniform load

per

length

of

beam

wu = factored uniform load

per

length of beam

1

= compression block coefficient

1 = deflection (with subscripts)

l J = strength reduction factor

Yp

= factor for type of prestressing

tendon

p

= nonprestressed reinforcement

ratio

pP

= prestressed reinforcement

ratio

behavior and design of double tees with web openings

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