PS 강연선의 정착
PCI Bridge Design Manual 3rd Edition, Second Release, August 2014
8.3.1 Strand Transfer Length
8.3.1.1 Impact on Design
Transfer length is the bonded length of strand required to transfer the prestress force in the strand to the surrounding concrete in a pretensioned member. At any section which falls within the transfer length, the prestress force should be reduced in proportion to its distance from the end of the member. Specifically, within the transfer length, the stress in the strand is assumed to vary linearly from zero at the end of member, or the point where the strand is bonded if debonding is used, to the full effective prestress force at the end of the transfer length.
Overestimation of transfer length is generally conservative for shear design but may be unconservative when evaluating flexural stress limits in the end regions. Shear strength is reduced within the transfer length due to the reduced precompression in the concrete. On the other hand, the reduced prestress force in the transfer length zone protects the end of the beam from excessive tensile stresses. Such excessive stresses may require that the end of the beam be reinforced with additional bonded steel reinforcement near the top fibers.
8.3.1.2 Specifications
LRFD Article 5.11.4.1 requires a transfer length of 60 times the diameter of the strand for the purposes of estimation of development length.
8.3.1.3 Factors Affecting Transfer Length
The transfer length for prestressing strand is affected by many parameters. Some of the most important are as follows:
• Type of prestressing strand
• Strand diameter
• Strand stress level
• Surface condition of strand (i.e., clean, oiled, rusted, epoxy-coated, etc.)
• Concrete strength
• Type of loading (i.e., static, repeated or impact)
• Method of strand detensioning (i.e., gradual or sudden)
• Confining reinforcement around strand
• Consolidation and consistency of concrete around strand
• Concrete cover around the strand
• Strand spacing
• Time-dependent effects
• Vertical location in concrete (top versus bottom locations)
• 프리스트레싱 스트랜드 유형
• 스트랜드 직경
• 스트랜드 응력 수준
• 스트랜드의 표면 상태(예: 깨끗한 상태, 기름칠 상태, 녹슨 상태, 에폭시 코팅 상태 등)
• 콘크리트 강도
• 하중 유형(예: 정적, 반복 또는 충격)
• 스트랜드 디텐션 방법(예: 점진적 또는 갑작스러운)
• 스트랜드 주변의 제한 철근
• 스트랜드 주변 콘크리트의 통합 및 일관성
• 스트랜드 주변의 콘크리트 커버
• 스트랜드 간격
• 시간에 따른 효과
• 콘크리트 내 수직 위치(상단과 하단 위치)
8.3.1.4 Research Results
The Federal Highway Administration (FHWA), in 1996, approved the use of ½-in. diameter strands at a center-tocenter spacing of 1.75 in. and 0.6-in.-diameter strands at a spacing of 2 in. These spacings are less than the four strand diameters previously required in the Standard Specifications. This decision was based on studies which demonstrate that the transfer length for the more closely spaced strands remains conservatively estimated using he relationship found in the Standard Specifications. With only a 20% increase in diameter from 0.5 to 0.6 in., the prestress force per strand is increased by 40%. Using 0.6-in.-diameter strands at a 2 in. spacing, it is possible now to increase the amount of pretensioning force by up to 40% and still preserve the same prestress eccentricity. This dramatically improves the load carrying capacity of a given cross-section. For more information on this research, see Section 8.3.2.4.
8.3.1.5 Recommendations
The current recommendations of the LRFD Specifications to use 60 strand diameters are adequate for design of typical structures. For unusually short span products or for strands with marginal surface conditions, this transfer length may not be adequate. For high-strength concrete, the provisions may overestimate the transfer length (Ramirez and Russell, 2008).
8.3.1.6 End Zone Reinforcement
LRFD Article 5.10.10.1 requires that an area of nonprestressed reinforcing steel be provided near the ends of pretensioned members to resist 4% of the prestressing force. The stress in the reinforcement resisting this force is limited to 20.0 ksi. This reinforcement is usually provided as stirrups and must be placed within a distance equal to h/4 from the beam end, where h is the overall depth of the pretensioned element.
The requirement is a simplification of the equation proposed by Marshall and Mattock (1962). It appears to be reasonable for modest levels of prestressing. However, in recent years, larger prestressing forces are being used with high-strength concrete. This is especially true for sections such as the NU Bulb-Tee beams*, where up to 58 strands can be placed in the bottom flange.
When this large number of strands is used with relatively shallow beams, such as the 43.3 in.-deep NU-1100, the specifications require that as much as 3.6 in.2 of reinforcement be placed within a distance of 9.0 in. from the end of the beam. It is very difficult to satisfy this requirement and provide adequate clearance to place and consolidate the concrete. Alternative details have been proposed by Tadros et al. (2010)
Designers should be aware that the most critical time is at prestress transfer. Areas of end zone reinforcement that are less than the required areas and that have been consistently used in actual production without objectionable cracking at member end may be acceptable.
* a family of metric-dimensioned beams developed at the University of Nebraska
8.3.2 Strand Development Length
8.3.2.1 Impact on Design
Strand development length is the length required for bond to develop the strand tension at the nominal flexural resistance. As shown in Section 8.2.2, this tension is generally lower than the specified ultimate strength of the strand. For bridge beams, the development length is insignificant unless the bridge beams are less than about 24 ft in length, or unless the beams are subjected to large bending moments near their ends. The development length becomes significant in deck panels used as stay-in-place forms.
8.3.2.2 LRFD Specifications
The equation for development length in the LRFD Specifications is similar to that used previously in the Standard Specifications. However, based on work by Cousins et al. (1986), which indicated that the existing equation was unconservative, the Federal Highway Administration (FHWA) imposed a 1.6 multiplier on the earlier AASHTO equation. As a result, the LRFD Specifications include a K factor in the equation as follows:
where
K = 1.6 for bonded strands in precast, prestressed beams
When a portion of the strand is debonded or “shielded” and where tension exists in the precompressed tensile
zone under service loads, the development length must be determined using LRFD Eq. 5.11.4.2-1 with a value of K = 2.0.
AASHTO LRFD Bridge Design Specifications
여기서 κ값이 부재의 두께에 따라 다르게 반영되고 있으나 도로교설계기준 2010 에서는 κ=1.0일때로 기준으로 하여 제시하고 있다.
도로교설계기준 2010
위 식(4.6.35)에서 1.5는 오기이다. 0.15이어야 한다.
도로교설계기준 해설 2008
4.6.4.4 PS 강연선의 정착
| 해설 |
이 절의 규정은 최소철근 피복두께가 50mm인 보통 콘크리트 부재에서 실시한 시험을 기초로 하여 만든 것이다. 이러한 시험들은 낮은 물-시멘트비, 즉 슬럼프 값이 0인 콘크리트에서 스트랜드의 거동을 나타내지 못한다.
정착길이 ld(mm)는 다음과 같이 표현할 수 있다.
여기서, 첫 번재 항은 스트랜드의 도입길이, 즉 스트랜드가 유효 프리스트레스 fpe를 발휘할 수 있도록 콘크리트에 부착되어야 하는 거리를 나타내고, 두 번째 항은 부재의 공칭강도에서 스트랜드가 fps를 발휘할 수 있도록 부착되어야 하는 추가길이 를 나타낸다. 스트랜드의 정착길이에 따라 생기는 응력의 변화가 해서 ㄹ그림 4.6.22에 나타나 있다.
스트랜드의 도입길이는 강재의 표면적과 표면 상태, 강재 내에 발생되는 응력과 콘크리트에 응력을 전달하는 방법에 따라 정해진다. 스트랜드 표면에 약간 녹이 슨 경우는 녹이 슬지 않은 스트랜드에 비해 도입길이를 짧게 할 수 있다. 또한 스트랜드를 서서히 풀어 프리스트레스를 도입하는 경우에는 스트랜드를 급하게 풀어 프리스트레스를 도입하는 경우에 비해 도입길이를 더 짧게 할 수 있다.
이 절의 규정은 원형 강선과 단정착된 긴장재에는 적용되지 않는다. 원형 강선을 사용하는 경우 도입 길이는 기계적 맞불림이 생기지 않으므로 훨씬 길어져야 한다.
도로교설계기준(한계상태설계법) 2016
다음은 USCS에서 SI unit로 어떻게 변환되었는지 단위변환을 해본것이다.
참고자료
Transfer And Development Length Of Strands In Post-tensioned Members After Anchor Head Failure
https://stars.library.ucf.edu/etd/4413/
Experimental investigation of simply-supported post-tensioned beam after anchorage system failure
https://www.sciencedirect.com/science/article/abs/pii/S0141029619339082?via%3Dihub
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