Introduction 17/05/2015. How prestressing force transmitted to concrete?

Transcription

1 End Block Design Introduction How prestressing force transmitted to concrete? - Pretensioned : transmitted by an internal force system through bond between steel and concrete - Post-tensioned : through external anchorage system The zone within which the applied prestressing force on steel is fully dissipated in to concrete and made to act as a distributed force is known as transmission zone in pretensioned element and anchor zone in post-tensioned elements. 1

2 Introduction In post-tensioned construction, the prestressing force is transferred to the concrete through relatively small anchorage plates behind the anchorage by bearing. This results in a very high concrete bearing stress behind the anchorage plate. Failure of anchorage zone is perhaps the most common cause of problems arising during construction Such failures are difficult and expensive to repair and might require replacement of the entire member. Introduction Anchorage zones failure due to uncontrolled cracking or splitting of the concrete from insufficient transverse reinforcement. Bearing failures immediately behind the anchorage plate are also common and may be caused by inadequate dimensions of bearing plates or poor quality of concrete. 2

3 End Block 3

4 End Block End Block 4

5 Stress Distribution The prestressing force in a tendon is applied through the anchorages as a concentrated force. By St Venant s principle, the stress distribution in a member is reasonably uniform away from the anchorage, but in the region of the anchorage itself the stress distribution within the concrete is complex. The most significant effect for design is that the tensile stresses are set up transverse to the axis of the member, tending to split this concrete apart. This tensile force also known as bursting force. Reinforcement must be provided to resist these tensile stresses. Stress Distribution 5

6 Stress distribution Design for Bursting Force It is sufficiently accurate to consider the resultant of these stresses, Fbst At SLS, Fbst is assumed to act in a region extending from 0.2y o to 2y o. The value of Fbst as a proportion of Pi may be found from Table 4.7 BS8110. The values in Table can be defined by the following equation : With y po /y o 0.3, Fbst/Pi = 0.23 y po /y o 0.7, Fbst/Pi =

7 Design for Bursting Force For post-tensioned members which are grouted after tensioning, the maximum force applied to the member is the initial jacking force, Pi and the design is based on SLS. The bursting force is resisted by reinforcement in the form of spirals or closed links, uniformly distributed throughout the end block (from 0.2y o to 2.0y o ) and with a stress of 200 N/mm 2. Design for Bursting Force For post-tensioned members with unbonded tendons, area of reinforcement is design at ULS given by Fbst/0.87fy, where Fbst is obtained bti from Table Tbl BS8110. Where an end block contains several anchorages, it should be divided into a series of symmetrically loaded prisms and then each prism treated as a separate end block. Additional reinforcement should be provided around the whole group of anchorages to maintain overall equilibrium. 7

8 Example 1 End block of a T-beam is made solid rectangular in cross-section and the tendons are grouped in three bundles with a parabolic profile. Three plates are provided for the three bundles of tendon. Design and detail stirrups placement in the end block according to BS8110. Each bundle of tendons has a jacking force 1000 kn.a plate of 150mm x 150mm can be used for each bundle In the vertical direction Use formula 8

9 In the horizontal direction < 0.3 From Table 4.7, Max Fbst = 0.23Pi use T10 2 leg, Asv = 157 mm2 No of links = 1150/157 = 7.3, use 8 bars Provide 8T10 through a distance of 500mm (2y o ) For checking: Force provided by bar = = kn >230 kn..ok 9

10 Example 2 Design the end block reinforcement for the following bonded post-tensioned beam. A prestressing force of 1055 kn is applied by a single tendon using a bearing plate of 200 x 300mm. Take e = 0 at supports. In the vertical direction, From Table 4.7 or equation In horizontal direction, 10

11 Fbst = 0.17 (1055) = kn Use T12 2leg, As = 113 mm2 No of links = /113 = 7.9, use 8 Provide 8T12 through a distance of 600mm (2y o ) Example 3 The beam end shown below has six anchorages with 75mm x 75mm bearing plates and a jacking force of 500 kn applied to each anchorages. Determine the reinforcement required to contain the bursting forces if f y = 460 N/mm 2. y 11

12 Individual Prism (150mm x 250mm) In the vertical direction, In the horizontal direction, Max Fbst = 115 kn Use T10 2 leg, As = 157 mm2 No of links = 575/157 = 3.7, use 4 Provide 4T10 through a distance of 250mm (2y o ) 12

13 Overall Prism (350mm x 750mm) Equivalent 2y po = (6 x 75 x 75) 0.5 = 184mm In the vertical direction In the horizontal direction Max Fbst = 690 kn Use T16 2 leg, As = 402 mm2 No of links = 3450/402 = 8.5, use 9 Provide 9T16 through a distance of 750mm (2y o ) 13

14 Detailing Reinforcement 14