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Ðề: Bàn bạc chi tiết về dầm Super T
dưới đây là tổng hợp một dự án về dầm SUPER T ..mời các bác tham khảo ............
5.3 Super Tee Beam Design
5.3.1 Grillage Analysis
The girder self weight and the weight of the deck slab are carried by the girder acting as a simply supported beam spanning 36.1m between bearings. The bending moments were calculated using simple beam theory.
The distribution of tertiary dead and live load bending moments has been analysed by a grillage analysis using the bridge deck analysis program ACES. Loadings comprised the tertiary dead loads due to kerbs, medians and AC surfacing as well as AASHTO and Vietnamese standard live load.
Envelopes of maximum bending moment and shear force were determined for HL-93, H30 and XB80 loading considering each lane separately. The results were then combined with appropriate multiple presence factors to produce the worst effects for each girder. The maximum bending moments were produced by trucks in 3 lanes
except XB80) with the maximum moments occurring in the second girder from the edge. In all cases the AASHTO truck and lane load was the most critical loading.
A comparison of the maximum live load moment envelopes for AASHTO and Vietnamese loading for Girder No.2 is shown in the graph below:
5.3.2 Prestress Design
(a) Prestress Losses
Loss of prestress due to elastic shortening, shrinkage and creep has been calculated in accordance with AASHTO. Relaxation losses however have been determined in accordance with the AustRoads Bridge Design code as this takes into account the increased relaxation resulting from the high concrete temperatures (from heat of hydration) which occurs prior to transfer. The AASHTO formula for does not allow for the effects of temperature on relaxation.
The design has been based on 15.2mm diameter Grade 270 low-relaxation strand initially stressed to 75% UTS. The following table summarises the calculated values for prestress losses:
Debonding of Strands
In order to comply with the code requirements for tensile and compressive stresses at transfer, 25% of the strands have been debonded at the end of the girder. For the purposes of the calculations it has been assumed that the concrete strength at transfer will be 32 MPa for which AASHTO specifies an allowable maximum compressive stress of 19.2 MPa. The maximum permissible tensile stress at transfer is –3.3 MPa.
The following graph shows the distribution of tensile and compressive stresses in the end zone of the girder.
It can be seen from the graph that the strand debonding is effective in controlling the stresses at transfer. The maximum bottom fibre stress was 16.8 MPa and the minimum tensile stress in the top fibre was –2.6 MPa. Both of these values are within the code limits.
5.3.3 Moment Capacity
(a) Serviceability Moment Capacity
The girders have been designed as partially prestressed members under full live load. The serviceability moment capacity has been based on a stress increment of 150MPa from decompression of the bottom flange.
The capacity has been calculated using PPCOMP – a computer program specially developed for partial prestress design. Input to the program consists of a definition of the cross-section in terms of heights and widths, the location and areas of prestressed and non-prestressed reinforcement together with the working load prestress forces and an initial stress distribution compatible with the working load prestress.
The program first calculates the applied moment required to reduce the concrete stress at the level of bottom layer of prestressing tendons to zero using un*****ed section properties. The steel strain increments are calculated for the decompression state and the moment is then increased, *****ing the concrete, until the specified stress increment is reached in the prestress. The program locates the centroid of the concrete compression zone and sums the moments of all tendon (and reinforcement) tensile forces to determine the working load capacity. For sections in which the concrete stress controls, the working load capacity is determined by limiting the maximum concrete stress to 0.45.fc.
It can be seen in the graph below that, under the maximum working load, the stress increment in the strands is about 50 MPa. The 150 MPa stress increment limit is based on the recommendations of the AustRoads Bridge Design code. The capacity of the girders calculated in accordance with AASHTO be determined by the limiting concrete stress of 0.45. fc which occurs at about 200 MPa.
(b) Ultimate Moment Capacity
The ultimate moment capacity has been calculated from first principles based on a *****ed section analysis. For any applied bending moment, the strains in the concrete and prestress can be calculated and from these the curvature can be determined. The calculations are repeated for increments of moment until yielding occurs in the prestress at which point the section is on the point of failure.
The results are shown in the moment-curvature graph below:
It can be seen from the above graph that the girders have significant reserve strength at ultimate load with the ultimate moment capacity exceeding the applied moment by approximately 40%.
(b) Ultimate Moment Capacity
The ultimate moment capacity has been calculated from first principles based on a *****ed section analysis. For any applied bending moment, the strains in the concrete and prestress can be calculated and from these the curvature can be determined. The calculations are repeated for increments of moment until yielding occurs in the prestress at which point the section is on the point of failure.
The results are shown in the moment-curvature graph below:
It can be seen from the above graph that the girders have significant reserve strength at ultimate load with the ultimate moment capacity exceeding the applied moment by approximately 40%.
5.3.4 Shear Capacity
The shear capacity of the girders was checked and it was found that the design ULS shear force could be resisted by the reinforcement (16’s at 150) alone without any contribution from the concrete. The girders therefore have considerable reserve strength for shear.
5.3.5 Halving Joint Design
The design of the halving joints has been based on the strut-tie method. Using the truss analogy, the shear forces are represented by a diagonal compressive strut, which intersects the prestress tendons near the tensile face of the girder. ‘Suspension’ reinforcement is required to carry the shear force to the top of the section so that it can be transferred to the bearings by a compression strut.
The following sketch indicates the assumed pattern of compression struts and tensile tie forces in the end zone of the girder.
For a 45o strut angle the force in compression strut C1 is equal to the tie force T1. From simple statics T1 = Ru (ultimate bearing reaction). The ultimate tie force T1 was 1623 kN which compares with a factored capacity of 2430 kN. Because of the limited anchorage length available in the halving joint the horizontal reinforcement has been provided with plate anchorages at each end (as indicated in the sketch above).
The tie force T2 = C1 = 1623 kNs. The vertical reinforcement in the end zone of the girder serves two functions. It provides the necessary ‘suspension’ reinforcement and also resists the spalling tensions arising from the dispersion of the prestress in the bottom flange. The total calculated force from spalling and shear was found to be 2100 kN. Vertical mats of reinforcement with a centroid located 150mm from the end face were provided to resist these forces.
The assumption of a 45o angle for strut C1 is conservative, as live load shear forces will be applied on the composite section and the strut angle will be greater than 45o.
dưới đây là tổng hợp một dự án về dầm SUPER T ..mời các bác tham khảo ............
5.3 Super Tee Beam Design
5.3.1 Grillage Analysis
The girder self weight and the weight of the deck slab are carried by the girder acting as a simply supported beam spanning 36.1m between bearings. The bending moments were calculated using simple beam theory.
The distribution of tertiary dead and live load bending moments has been analysed by a grillage analysis using the bridge deck analysis program ACES. Loadings comprised the tertiary dead loads due to kerbs, medians and AC surfacing as well as AASHTO and Vietnamese standard live load.
Envelopes of maximum bending moment and shear force were determined for HL-93, H30 and XB80 loading considering each lane separately. The results were then combined with appropriate multiple presence factors to produce the worst effects for each girder. The maximum bending moments were produced by trucks in 3 lanes
except XB80) with the maximum moments occurring in the second girder from the edge. In all cases the AASHTO truck and lane load was the most critical loading.
A comparison of the maximum live load moment envelopes for AASHTO and Vietnamese loading for Girder No.2 is shown in the graph below:
5.3.2 Prestress Design
(a) Prestress Losses
Loss of prestress due to elastic shortening, shrinkage and creep has been calculated in accordance with AASHTO. Relaxation losses however have been determined in accordance with the AustRoads Bridge Design code as this takes into account the increased relaxation resulting from the high concrete temperatures (from heat of hydration) which occurs prior to transfer. The AASHTO formula for does not allow for the effects of temperature on relaxation.
The design has been based on 15.2mm diameter Grade 270 low-relaxation strand initially stressed to 75% UTS. The following table summarises the calculated values for prestress losses:
Debonding of Strands
In order to comply with the code requirements for tensile and compressive stresses at transfer, 25% of the strands have been debonded at the end of the girder. For the purposes of the calculations it has been assumed that the concrete strength at transfer will be 32 MPa for which AASHTO specifies an allowable maximum compressive stress of 19.2 MPa. The maximum permissible tensile stress at transfer is –3.3 MPa.
The following graph shows the distribution of tensile and compressive stresses in the end zone of the girder.
It can be seen from the graph that the strand debonding is effective in controlling the stresses at transfer. The maximum bottom fibre stress was 16.8 MPa and the minimum tensile stress in the top fibre was –2.6 MPa. Both of these values are within the code limits.
5.3.3 Moment Capacity
(a) Serviceability Moment Capacity
The girders have been designed as partially prestressed members under full live load. The serviceability moment capacity has been based on a stress increment of 150MPa from decompression of the bottom flange.
The capacity has been calculated using PPCOMP – a computer program specially developed for partial prestress design. Input to the program consists of a definition of the cross-section in terms of heights and widths, the location and areas of prestressed and non-prestressed reinforcement together with the working load prestress forces and an initial stress distribution compatible with the working load prestress.
The program first calculates the applied moment required to reduce the concrete stress at the level of bottom layer of prestressing tendons to zero using un*****ed section properties. The steel strain increments are calculated for the decompression state and the moment is then increased, *****ing the concrete, until the specified stress increment is reached in the prestress. The program locates the centroid of the concrete compression zone and sums the moments of all tendon (and reinforcement) tensile forces to determine the working load capacity. For sections in which the concrete stress controls, the working load capacity is determined by limiting the maximum concrete stress to 0.45.fc.
It can be seen in the graph below that, under the maximum working load, the stress increment in the strands is about 50 MPa. The 150 MPa stress increment limit is based on the recommendations of the AustRoads Bridge Design code. The capacity of the girders calculated in accordance with AASHTO be determined by the limiting concrete stress of 0.45. fc which occurs at about 200 MPa.
(b) Ultimate Moment Capacity
The ultimate moment capacity has been calculated from first principles based on a *****ed section analysis. For any applied bending moment, the strains in the concrete and prestress can be calculated and from these the curvature can be determined. The calculations are repeated for increments of moment until yielding occurs in the prestress at which point the section is on the point of failure.
The results are shown in the moment-curvature graph below:
It can be seen from the above graph that the girders have significant reserve strength at ultimate load with the ultimate moment capacity exceeding the applied moment by approximately 40%.
(b) Ultimate Moment Capacity
The ultimate moment capacity has been calculated from first principles based on a *****ed section analysis. For any applied bending moment, the strains in the concrete and prestress can be calculated and from these the curvature can be determined. The calculations are repeated for increments of moment until yielding occurs in the prestress at which point the section is on the point of failure.
The results are shown in the moment-curvature graph below:
It can be seen from the above graph that the girders have significant reserve strength at ultimate load with the ultimate moment capacity exceeding the applied moment by approximately 40%.
5.3.4 Shear Capacity
The shear capacity of the girders was checked and it was found that the design ULS shear force could be resisted by the reinforcement (16’s at 150) alone without any contribution from the concrete. The girders therefore have considerable reserve strength for shear.
5.3.5 Halving Joint Design
The design of the halving joints has been based on the strut-tie method. Using the truss analogy, the shear forces are represented by a diagonal compressive strut, which intersects the prestress tendons near the tensile face of the girder. ‘Suspension’ reinforcement is required to carry the shear force to the top of the section so that it can be transferred to the bearings by a compression strut.
The following sketch indicates the assumed pattern of compression struts and tensile tie forces in the end zone of the girder.
For a 45o strut angle the force in compression strut C1 is equal to the tie force T1. From simple statics T1 = Ru (ultimate bearing reaction). The ultimate tie force T1 was 1623 kN which compares with a factored capacity of 2430 kN. Because of the limited anchorage length available in the halving joint the horizontal reinforcement has been provided with plate anchorages at each end (as indicated in the sketch above).
The tie force T2 = C1 = 1623 kNs. The vertical reinforcement in the end zone of the girder serves two functions. It provides the necessary ‘suspension’ reinforcement and also resists the spalling tensions arising from the dispersion of the prestress in the bottom flange. The total calculated force from spalling and shear was found to be 2100 kN. Vertical mats of reinforcement with a centroid located 150mm from the end face were provided to resist these forces.
The assumption of a 45o angle for strut C1 is conservative, as live load shear forces will be applied on the composite section and the strut angle will be greater than 45o.
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