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OCR for page 75
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Table 5-18. Force at stirrup yield · Stirrups. Regional transverse bending strength is directly
(0.2% strain). tied to stirrup area, but it controls the design only when
web/duct tie reinforcement is NOT used or when the web-
Total Force (K/ft)
Model # Web 1 Web 2
splitting/lateral shear-failure does not occur. In other words,
1S 25.83 28.18 if the failure mode is tending toward local duct breakout,
2S 16.05 17.88 stirrups are not a very effective deterrent against this failure
3S 26.21 28.6 mode. But if the duct layout and duct ties are properly de-
4S 20.1 26.17 tailed to eliminate the local pullout failure mode, the stirrup
5S 31.18 28.77 spacing does define the web "regional" beam strength.
6S 24.16 28.04 · Concrete Material Properties, Especially Assumed Ten-
7S 26.21 26.64 sile Strength. Web section strength can be significantly in-
8S 26.12 27.95
fluenced by concrete tensile strength only when the section
9S 29.87 23.78
is prone to web-splitting/local-lateral shear-failures, i.e.,
10S 16.09 18.38
when vulnerable duct placement is used or web/duct tie re-
inforcement is NOT used. When web/duct tie reinforce-
to the top slab, and the positive moment reinforcement ment is used, concrete tensile strength has little effect on the
is approximately 2 times that of the negative moment section strength. Thus designers should be directed toward
reinforcement. design rules that will ensure good performance, regardless
· Cover Thickness. Inside face duct cover influences lateral of variabilities in concrete tensile strength.
pullout resistance, but is not the only driver of pullout
resistance. The results of the parameter studies are influ-
enced by the fact that when the cover is reduced, for the Recommendations for Web Capacity Design
same overall web thickness, the moment arm for the stir- Web capacity design for lateral tendon force resistance
rups is increased, which is an offsetting influence on should be a three-step calculation: Regional flexure check, local-
pullout resistance. It appears appropriate to check cover lateral shear/breakout check, and cover concrete cracking check
concrete thickness for resistance to initial cracking, but not
to include cover concrete tensile strength in calculating
regional transverse bending strength. Regional Transverse Bending
· Number and Configuration of Tendon Ducts. When The regional mechanism is the web acting as a vertical
ducts are spread apart, the performance significantly beam loaded laterally near its center. Fundamentally, the cal-
improves. Roughly 20% resistance force improvement culation follows the equation:
was demonstrated by separating the 5-duct bundle into
two bundles, and an additional 4% improvement was Mu = (Load Factor)(Moment Fixity Factor)(1/4)(Pj/R) hc
demonstrated by spreading the bundles farther apart
(4.5 inches versus 1.5 inches of separation). It is believed This equation (a modified version of the Caltrans Equa-
prudent to require a maximum of 3 ducts per bundle. tion) and the corresponding stirrup spacing should be evalu-
When individual ducts were separated and moved toward ated for each web of a box-girder separately--not for the total
the curve's outside face of the web, performance further box divided by the number of webs. The radius is different for
improves. When measured by the delamination/local- each web, and it was found that the moment fixity factor is
lateral shear criteria, Duct Configuration 3A exceeded also different. AASHTO LRFD currently applies a load factor
200% Pc, so the improvement in delamination perform- of 1.2 to the Pjack tendon force, which is judged to be rea-
ance was very large. However, it is often impractical for sonable. Appropriate moment fixity factors are 0.6 for inte-
designers to spread individual ducts apart due to lack of rior webs and 0.7 for exterior webs.
space in the web and due to requirements on location of The stirrup sizing and spacing should then be calculated
the C.G. of the tendon group. using Ultimate Strength design such that
· Number and Configuration of Duct Ties contribute sig-
nificantly to resistance to lateral tendon breakout. Mn Mu
Table 5-19. Effect of cover thickness thick webs.
Model-Web Force at Stirrup Yield (kips) Difference
6S-1 vs. 1S-1 24.16 vs. 25.83 7% increase with 3" vs. 2"
6S-2 vs. 1S-2 28.04 vs. 28.18 0% increase with 3.5" vs. 2"
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Table 5-20. Effect of duct ties thick webs.
Force at Stirrup Yield (kips) (and
Model-Web Difference
delamination at 100%Pc)
26.21 vs. 25.83 2% incr. with Duct ties
7S-1 vs. 1S-1
(0.024" vs. 0.035") (31% less delamination)
26.64 vs. 28.18 -5% change with Duct ties
7S-2 vs. 1S-2
(0.048" vs. 0.063") (24% less delamination)
27.95 vs. 28.60 -2% change with Duct ties
8S-2 vs. 3S-2
(0.050" vs. 0.046") (little change in delamination)
29.87 vs. 31.18 -4% change with Duct ties
9S-1 vs. 5S-1
(0.019" vs. 0.025") (24% less delamination)
However, the Vs stress in the stirrups due to vertical shear or
in the web should be added to the stress due to flexure in the
sizing and spacing of the stirrups. At the midheight of the deff = tw (Duct Diam)/2
web, on the inside-curve side of the web, these stresses are di-
rectly additive. whichever is least.
where
Local Lateral Shear Check
s = space between ducts (assume 0 if s < 1.5" or for single
The local lateral shear mechanism involves the complex
ducts)
behavior that develops in the concrete and stirrup region
tw = thickness of web
immediately adjacent to the duct bank. This may be checked
by the following equations developed by the University of When the spacing between ducts is less than the duct
Texas (Van Landuyt, 1991): diameter or for single ducts
For a strip of web 1 foot long, the applied lateral shear de-
mand along a plane deff long is deff = dc + (Duct Diam)/4
Vd = Pj/R 2
where dc = cover over the ducts
Figure 5-24 shows what is intended by the above equations
Vc capacity of the cover-beam along this plane may be
for deff.
taken as
There has been discussion within the industry as to
selecting deff (some refer to this as the "lateral shearing
Vc = 24d eff fc
plane depth"). Some say this should be no greater than dc
Where = 0.75 (reduced due to uncertainties in concrete (the cover concrete depth) due to uncertainties in the con-
quality within the cover-beam) crete interaction with the ducts, but the local analyses
When the spacing between ducts is greater than or equal to conducted here allow for the extra width of 1/4 of a duct
the duct diameter diameter.
If this lateral shear is exceeded, the most effective design
deff = dc + (Duct Diam.)/4 + s/2 remedy is the addition of duct-tie reinforcement.
Table 5-21. Effect of stirrup spacing thick webs. Table 5-22. Effect of material strength thick webs.
Force at stirrup Force at stirrup
Model-Web Difference Model-Web Difference
yield (kips) yield (kips)
4S-1 vs. 1S-1 20.1 vs. 25.83 29% increase with 50% more stirrup 3S-2 vs. 1S-2 28.60 vs. 28.18 2% increase with 50% larger
steel concrete tensile strength
5S-1 vs. 1S-1 31.18 vs. 25.83 21% decrease with 33% less stirrup 4S-2 vs. 1S-2 26.17 vs. 28.18 7% decrease with 50% smaller
steel concrete. strength
9S-1 vs. 7S-1 29.87 vs. 26.21 14% decrease with 50% less stirrup 8S-1 vs. 7S-1 26.12 vs. 26.21 0% change with 50% smaller
steel concrete. strength
9S-2 vs. 7S-2 23.78 vs. 26.64 21% increase with 50% more stirrup 8S-2 vs. 7S-2 27.95 vs. 26.64 5% increase with 50% larger
steel concrete. strength
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dc
dc
R R
inside face inside face
tw
For "s" For Single Ducts or for "s" <
deff = lesser of: deff = dc +
4
deff = tw -
2
deff = dc +
4 2
Figure 5-24. Definition of deff (after Van Landuyt, 1991).
Cover Concrete Cracking Check Where Mn is defined by an allowable tensile stress for concrete
of 5 fc , and = 0.55. The allowable tensile stress should
Evaluating the cracking of the cover concrete is a check that
also be reduced by the tensile stress in the concrete at the crit-
is made to ensure serviceability because it is recommend that
ical point due to regional transverse bending. Although this
the lateral tendon forces be completely carried by the strength
may appear quite conservative in terms of choice of tensile
elements of the above two checks. But this serviceability
strength and choice of , once cracking begins within the in-
check remains critical to achieving a good design, because sig-
terior of the cover concrete near the top and bottom of the
nificant cover cracks running along the tendons should be
duct bank, the moment at the center of the duct banks
avoided for long-term structure durability.
quickly becomes
The flexure on the cover beam involves a complex mecha-
nism because it is uncertain what the level of adhesion is of wl 2
the cover concrete to the duct bank and to the concrete M center =
8
surrounding the duct bank. Assuming there is no adhesion
between the metal duct and the web concrete in the radial So these factors and conservative tensile strengths are
direction of the duct, the flexure calculation proceeds as fol- judged appropriate to prevent this progressive cracking
lows. The cover-beam acts as a vertical beam "built-in" or mechanism from occurring.
fixed at top and bottom. Thus the following moments are
produced:
Other Local Detailing Guidelines
wL2
M ends = = (Pj/R/L)L2 /12 A further guideline, which has come out of the local
12
analysis work and from examination of some local breakout
wL2
M center = failures in various bridges and test structures, is to limit the
24 number of ducts of a sub-bundle to no more than three.
L is the height of the duct bank Sub-bundles should then be separated by either a duct-tie
rebar or by a minimum of 1/3 of one duct diameter (for ex-
bdc3 ample, 11/2 inches for the analyses performed here).
I= Duct ties should be well anchored with hooks around
12
stirrup reinforcement. A generic duct tie detail is shown in
and Mn Mu Figure 5-25.
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12" Web inside of substantial reduction in concrete cover between the stirrup
Curve cage and the interior face of the web. This may be mitigated
3" clr 2" clr to
to Duct Stirrup
somewhat by rebar spacer requirements at midheight of webs
to help control stirrup movement during the pour, but the
designer should be aware of possible variations in the actually
constructed dimensions.
Several conditions can aggravate the chances for lateral
tendon breakout, including
1. Reduction of cover over the duct or rebar, which can af-
fect resistance to breakout.
2. Excessive wobble of the ducts, which can result in either
#4 Duct Tie reduced resistance to breakout or locally elevated lateral
forces.
3. Out-of-plane forces in a vertically curved tendon due to
#4 Web Tie, Typ
#5 Stirrups wedging of the stand.
4. Pressure from grout leakage due to poor quality duct (ex-
cessive flexibility), damaged duct, or improperly sealed
duct.
Figure 5-25. Generic web and duct tie detail. 5. Distortion of empty ducts acted on by adjacent stressed
ducts.
6. Local curvature in ducts near anchorage zones or blisters
Construction Tolerances
Designers should consider the practical aspects of con- The specified load and resistance factors (1.2 and 0.75) re-
struction tolerances when checking and implementing their flect the assumption that construction tolerances are reason-
designs. Construction tolerances should be held to industry ably well controlled. If this may not be the case, the designer
standards--it is not the point of this design recommendation may wish to consider one of the following three options.
to modify these, but designers may wish to consider conser-
vatively allowing for field variations in web width and in rebar 1. Use higher load factors and/or lower resistance factors.
placement of up to ±0.5 inch when evaluating issues of web Some engineers familiar with the potential problems have
regional transverse bending strength, local breakout resist- recommended factors be reduced from 0.75 to 0.55 for
ance, and, particularly, cover-beam strength. Dimensional local lateral shear failure. Load factors could also be raised
changes of 0.5 inch can make considerable difference in the above 1.2 to say 1.5.
stresses in the web concrete and reinforcing steel. 2. Use dimensions that include an allowance for misplace-
The following is an example of how design and construc- ment of the duct, rebar, or forms. As suggested above, crit-
tion issues can affect conditions for lateral tendon breakout. ical dimensions could be reduced by 0.5 inch or even
As a box-girder gets deeper, the stirrup cage gets deeper. As 1.0 inch
the stirrup cage gets deeper, it becomes more flexible laterally, 3. When in doubt, provide web and duct tie reinforcement
especially in areas of low lateral shear demand where designers
often specify stirrup spacing as large as 24 inches. During the Tendon breakout failures can be expensive to repair. Al-
web and soffit pour, the stirrup cage has been shown to deflect though the recommended design specifications should pro-
laterally within the web form due to unbalanced concrete vide an adequate factor of safety in most cases, the designer is
placement, vibration process, and duct float. Duct float, in ultimately responsible for assessing the likely conditions in
combination with sloped exterior webs, can often lead to a the field.
