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Starting from the ideas of Conventional Post Tensioning we present a heuristic argument of advantages of combined actions of post compression along with post tensioned technique for a PSC member through a Design Example. Our aim was to assess the characterization of a pre stressed member if it w as to be under the Load effects of post compressing a bar with post tensioned method through hydraulic jacks as the reinforcements in the tensioned zone of conventional PSC bridge were to be compressed in order to induce internal tensile stress similar to internal compressive stresses developed due to conventional post tensioned design. The results ultimately concluded that post compressing a Slender bar by a pre stressing force in the compression zone by a value equal to 0.1 - 0.7 times the pre stressing force in the tension zone would eventually lead to cancelling out of tensile and compressive stresses, thereby forming the desired section which is comparatively smaller in size but can account for sustainability. The anchorage at the top end w as provided by special slender steel rods to eliminate the compressive stresses. All the dead load s w ere counteracted by the action of prestress and the bridge section was able to carry only live load which is deduced through examples in the article.

Prestressing is the establishment of internal stresses in a structure or system to increase the durability of its performance. In pre stressed concrete the induced stresses are in such a magnitude that they can counteract on the applied external loads. The prestress developed by the means of hydraulic jacks introduces compressive stress below the neutral axis and thus gets back the structure into its original shape once it gets acted upon by the external loads [

1) Pre tensioning: In which the tendons are tensioned before the concrete is placed, tendons are temporarily anchored and tensioned and the pre stress is transferred to the concrete after it is hardened.

2) Post tensioning: In which the tendon is tensioned after the concrete has hardened.

Tendons are held up in holes provided with sheaths at different known locations along the section and are tensioned using hydraulic jacks once the member is hardened of concrete [

A different process of pre stressing which is known by the name of post compression was used in early 20th century by Kurt Billig [

Previous research on the use of advancement in pre stressed concrete in long span precast structures is limited. Further, to the best of the authors knowledge, only few research exists on the efforts of advancement of pre stressed concrete in terms of using tendons to stress at its compressed region. It can be noted from the research works of T. M. Yoo, J. H. Doh, H. Guan [

The mode of action of the beam subjected to post compressed reinforcement is shown in

The case study deals with the design and analysis of a PSC T-beam bridge, which provides access between two important villages using conventional

post-tensioning methods and a non-conventional post compressing methods. The proposed site for bridge construction is shown in

The process for anchorage for post compressed slender bar is as shown in

Span Arrangement | 14 × 35 m |
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Deck Width | 12 m |

Carriage Way Width | 7.5 m |

Type of Superstructure | PSC I-girder with cast in-situ slab |

Concrete Grade for Superstructure | M45 (Grade 45 N/mm^{2}) |

Concrete Grade for Substructure | M35 (Grade 35 N/mm^{2}) |

Grade of Reinforcement for Girder | Fe500 (500 N/mm^{2}) |

Grade of Reinforcement for Girder | Fe500 (500 N/mm^{2}) |

No of Lanes | 2 |

Single anchorage of each compressed bar was chosen for the reason of easy access. The compressed bar (diameter 36 mm S 1080/1320) transfers its force by means of a thread and nut assembly into the anchor plate. The plate is fixed in the beam’s concrete with the help of 8 button headed cold-drawn stressing steel wires (diameter 12.2 mm, S 1370/1570 with undulated ends). The anchorages of the post-compressed bars should be given care as they shouldn’t force the concrete in its vicinity to move out and this can be done easily, e.g. By setting the anchorages of the bars between anchorages of tendons.

Analysis of a PSC Structure forms the critical part in the getting to know their different characteristics under the action of critical loads. The most important analysis for a design can be made in Flexure as well as Shear, although Flexural Analysis forms the crucial stage to introspect the durability and overturning resistance of a PSC structure. In our analysis much of the consideration is given in determination in stress distribution in PSC beam under the serviceability condition to note down its moment carrying capacity. A rational pre stressing force for both approximation (post-tensioning and post compression) is deduced considering the independent and time dependent loses at transfer and service conditions. Limits are set on the deformation control as the span/depth ratios and level of pre stress are narrowed down. The concrete stresses that re developed during transfer and serviceability condition are also restricted in order to control

the longitudinal cracks and creep formation. In order to minimize the inelastic deformation of the beam there is also a limit on the value of effective prestress after the time independent loses have occurred.

Consider an simply supported isometric beam of length L width B and depth H which has been reinforced with post tensioned tendons and post compressed high strength steel bars at eccentricities e_{t} and e_{c} at bottom and top from the neutral axis respectively as shown in _{k}), superimposed dead load (DL), superimposed live load (LL). The cross sectional area of the beam is denoted by A_{c} and the sectional modulus at top and bottom of the surface is denoted as Z_{TOP} and Z_{BOT} respectively. The notation C_{g} refers to centroid of the concrete section and C_{T} and C_{B} denotes the centriods of reinforcement at post compression and post tensioned regions respectively.

The stresses at the extreme top and bottom fibres at transfer are

f T , t = − P C / A − P C × e C / Z T O P + P K / A + P K × Z B O T / Z T O P + M T / Z T O P ≥ f t , i (1)

f B , t = − P C / A + P C × e C / Z T O P + P K / A + P K × Z B O T / Z T O P − M T / Z T O P ≥ f t , i (2)

The stresses in the extreme top and bottom fibres of the concrete section at service are given by:

f T , S = μ ( − P C / A − P C × e C / Z T O P ) + α ( P K / A − P K × Z B O T / Z T O P ) + M S / Z T O P ≥ f C , S (3)

f B , S = μ ( − P C / A − P C × e C / Z B O T ) + α ( P K / A + P K × Z B O T / Z T O P ) − M S / Z T O P ≥ f T , S (4)

where µ and α are residual pre stress ratios after time dependent losses have taken place in relation to the pre stressing forces P_{T} and P_{B}.

M_{T} and M_{S} are the maximum bending moments at transfer and service respectively

M S = M D + M L + M P (5)

Combination of Equations (1) and (3) yields:

M 2 / Z T O P ≤ f C , S − f t , i − ( 1 − μ ) ( 1 / A + e C / Z T O P ) × P C + ( 1 − α ) ( 1 / A − e B / Z T O P ) × P K (6)

where M 2 = M T + M S .

A similar operation on Equations (2) and (4) yields

M 2 / Z B O T ≤ f t , i − f T , S + ( 1 − μ ) ( 1 / A − e C / Z B O T ) × P C − ( 1 − α ) ( 1 / A + e B / Z B O T ) × P K (7)

f T , t , f B , t = bottom and top fibre stress, respectively at transfer stage;

f T , s , f B , s = bottom and top fibre stress, respectively at service stage;

f c , i , f c , s = allowable compressive stress at transfer and service stage, respectively;

f t , i , f t , s = allowable flexural tensile stress at transfer and service stage respectively.

Also the top and bottom elastic section moduli can be obtained from Equations (6) and (7), respectively as follows

Z T O P ≥ M 2 / f c , s − f t , i (8a)

Z B O T ≥ M 2 / f c , i − f t , s (8b)

Also, the following general assumptions may be considered for a more reasonable approximation:

P K / A = 0.5 f c , s or f c , i (9a)

e B × A / Z B O T or e B × A / Z T O P = 2 (9b)

If P C / P K = λ and e C / e T = β , and Equations (9a) and (9b) are applied to Equations (6) and (7), the top andbottom elastic section moduli can be obtained as

Z T O P ≥ M 2 / 0.5 f c , s ( 1 + α − λ ( 1 − μ ) ( 1 + 2 β ) ) − f t , i (10a)

Z B O T ≥ M 2 / 0.5 f c , i ( 3 α − 1 + λ ( 1 − μ ) ( 1 − 2 β ) ) − f t , s (10b)

The analysis part of the design of PSC Bridge is made considering various assumptions as well as sign conventions, as the stress distribution along the length of the beam is considered to be linear in nature and both the concrete and steel tendons are assumed to act as elastic members in the vicinity of working stresses under the action of loading. The effects of creep and shrinkage are considered to develop after the member is subjected to constant sustained load. Sagging moments developed due to the action of compressive stresses are considered to be positive while on the other hand hogging moments due to tensile stresses are considered to be negative in nature. Eccentricity values which are above the centroid are deemed positive (post tensioned process) while those below the centroid are deemed negative (post compression technique).

The dead load carried by the girder and member shall consists of weight of the super structure which is supported wholly or in part by the girder or member including its own weight.

The design live load consists of standard wheeled or tracked class AA vehicle loading (according to Indian Road Congress Specifications) with a provision for impact or dynamic action shall be made by an increment of the live load by an impact allowance expressed as a fraction or a percentage of the applied load. In our case it is assumed to be 10%.

The Design of the PSC Bridge was done through CSI Bridge 2017 versioned software. In order to account for variability, the shape of the bridge was considered to be parabolic in nature with sloping at mid section from both left and right ends [

Through Analysis it was noted that the area of the steel required was found to be

A = 2.3418 × 10 6 mm 2

The respective section moduli for the bridge was found to be

Z b = 0.9743 × 10 9 mm 3

Z t = 1.102 × 10 9 mm 3 ^{ }

Comparing these values theoretically with post compression design we get the values as follows

M U = 8.190 × 10 9 N ⋅ mm

Additional moment of 2 M∙nm is added as extra moment as a product of truck load during analysis, thus

M U = 10.190 × 10 9 N ⋅ mm

4 conditions to check for minimum section

Z t = M 2 / f c w = 0.452 × 10 9 mm 3

Z b = M 2 / f c i = 0.629 × 10 9 mm 3

And from other conditions considering the loss ratios (µ and α) and prestressing ratios (λ and β) we get,

Z t ≥ M 2 / 0.5 f c s ( 1 + α − λ ( 1 − μ ) ( 1 + 2 β ) ) − f t i ≥ ( 10.190 × 10 9 ) ÷ 0.5 ( 16.5 ( 1 + 0.9 − 0.5 ( 1 − 0.9 ) ( 1 + 2 ( 2 ) ) ) ) − ( − 1 ) ≥ 0.697 × 10 9 mm 3 ^{ }

where, µ and α = 0.9 and λ = 0.5, β = 2. Considering f_{ti} = −1 N/mm^{2} and f_{ts} = 0 N/mm^{2}.^{ }

Z b > M 2 / 0.5 f c i ( 3 α − 1 + λ ( 1 − μ ) ( 1 + 2 β ) ) − f t s ≥ ( 10.190 × 10 9 ) ÷ ( 3 ( 0.9 ) − 1 + 0.5 ( 1 − 0.9 ) ( 1 + 2 ( 2 ) ) ) − 0 ≥ 0.464 × 10 9 mm 3 ^{ }

Hence here Z b = 0.697 × 10 9 mm 3

Z t = 0.464 × 10 9 mm 3

It can be seen that relatively both the section moduli in case of combined action of post compressed design were less that to the traditional post tensioned design even though the moment induced were increased significantly. Also the stresses developed were far lesser and are shown as below.

Stress developed in section

f s u p = ( P T / A ) − ( P T e t / Z B ) + ( P B / A ) − ( P B e b / Z t ) + ( M i / Z t ) = − 14.35 N / mm 2

f i n f = μ ( − ( P T / A ) + ( P T e t / Z B ) ) + α ( ( P B / A ) + ( P B e b / Z t ) ) − M s / Z B = − 1.08 N / mm 2

Through analysis and verifying the results it can be noted that for practical applications the prestress ratio should lie in the range of 0.1 ≤ λ ≤ 0.8 as it was also found out that the prestressing ratio are independent of the eccentricity ratio (β) in case of post compression technique whereas in conventional post tensioned method the eccentricity ratio was found to be viable in the range 0 ≤ β ≤ 4.

The Bridge has been designed as a PSC Bridge using both Conventional post-tensioned and post-compressed methods. And comparing the results, the following conclusions can be drawn out.

The depth of the main girder can be reduced in case of combined action of post compression and post tensioned reinforcements since the section moduli in the former case is comparatively lower when compared with conventional post tensioned design, even though the Horizontal ultimate moment remains the same. There is overall reduction of loading on pile due to combined post tensioning and post compressed reinforcement, as a result.

There is a provision for elimination of one pier by increasing the span (i.e. from 35 m to 70 m) and in turn resulting in 5% - 6% cost reduction. Very suitable and cost effective in case of Long span structures.

It is clearly evident from both graphs (

The authors declare no conflicts of interest regarding the publication of this paper.

Sundar, S.S. and Rao, S.S. (2018) PSC Bridge Subjected to Combined Post Tension and Post Compression―A Case Study. World Journal of Engineering and Technology, 6, 767-779. https://doi.org/10.4236/wjet.2018.64050