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75 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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76 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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77 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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78 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.