Analysis and Design of One Way Post Tensioned Slab Using Ansys

Abstract

Global increase of nations wealth imposes constant improvement of development throughout the years and well known architectural forms, both visually and functionally. This forces the necessity to search for slenderer horizontal shell elements with greater spans. However, apart from general stability and capacity, those have to provide both good thermal and acoustical features, as well as vibration resistance, which become problematic in case of slender slabs. Despite number of disadvantages, all of the above mentioned factors may be reconciled by concrete, more precisely - prestressed concrete.

Quite large span is achieved using pre-tensioned hollow core slabs. The use of hidden steel beams and concrete topping significantly increases the attractiveness of this type of slab. The flat slab with large span is achieved in this way. However, much more slander slabs can be constructed using post-tensioned concrete. For years, post-tensioned concrete long-span slabs have been used as structural floors in buildings in the USA, Australia, Hong Kong and Singapore. Hereafter, they have been introduced to Europe.

In Poland, its growth dates back to the last ten years. During several decades of effective application of prestressed slabs many design guidelines were prepared and implemented in order to enable the simple engineering approach to the design of selected slab type.

Introduction

Prestressed concrete is a revolutionary method of building technique in which high strength steel cables are stressed before or after placing concrete so that this force balances the external force. Prestressed concrete is used in a wide range of building and civil structures where its improved performance can allow for longer spans, reduced structural thicknesses, and material savings compared with simple reinforced concrete.

Typical applications include high-rise buildings, residential slabs, foundation systems, bridge and dam structures, silos and tanks, industrial pavements and nuclear containment structures. Post-tensioning systems provide many benefits.

Use of post-tensioning in slabs reduces the amount of concrete required for a structure which offsets increased cost of labour and equipment, decreases the amount of formwork required, decreases the overall height of floors which allows more floors for a specified building height, decreases the weight of the building which is a benefit in seismic design, and increases the allowable span length, creating more open space in a structure.

Literature Review

In this paper the authors have discussed on long span posttensioned slabs and deflection control. The following paper presents representative projects of realized and future designs of long span prestressed slabs. It has been proven, with regard to two-year monitoring behaviour of slabs constructed in Kozienice, that design of elements exceeding values recommended by dated guidelines, of span lengths and span to depth ratios is feasible. The conclusions that have been made, will allow for the construction of longer span and slenderer slabs than it was in the past. he authors will continue to successively observe effects of future long span prestressed slabs designs and report the findings in technical and scientific literature.

It can be noted that the research of possibility to use lightweight aggregate concrete in construction of long-span post-tensioned slabs has begun in Cracow University of Technology. It is commonly known that it is difficult to provide the desired concrete modulus of elasticity with this type of aggregate. On the other hand, preliminary computational analysis carried out by the authors indicate that important decrease of slab self-weight can lead to reduction of amount of prestressing or deflection in comparison with dense concrete of similar strength. The successful results from observation of full-scale post-tensioned slabs in laboratory tests may contribute to design and realisation of long-span post-tensioned slab with lightweight aggregate in buildings in the future.

The behaviour of unbonded post-tensioned one-way concrete slabs is investigated experimentally and numerically in this paper. Two tests were conducted by the authors to measure the strains in the tendon during the post-tensioning stage and during the ultimate load test. The slabs were one-way simply-supported and reinforced with 15.7 mm nominal diameter seven-wire mono-strand tendons. Prestress losses were measured and a comparison with current design codes showed that the calculated design losses were higher than those measured. The load-deflection behaviour and modes of failure are presented for the two tests. A nonlinear finite element model, incorporating the correct load transfer from the tendon to the concrete, was developed and reified against the tests.

The model also ensured that the profile of the tendon retained its correct shape during deformation. A parametric study was conducted to study the effects on the global structural behaviour due to the change in the slab's geometry, prestress load, concrete strength and boundary conditions. The experimental and numerical results were compared with values calculated using current design codes. It is shown that the ultimate loads calculated using current codes are conservative for the unbonded post-tensioned one-way concrete slabs investigated in this study.

Analysis and Design of Post Tensioned One Way Continuous Slab

Post tensioned one way continuous slab consists of two spans of 7.5m wide and 20 m long panels which are acted upon by dead load and 3Kn/m2 live load for an industrial building. The slab is supported by three beams of size 450mmX750mm at the longer edges.

Calculation of Dead Load

Thickness of the slab = span/40=7500/40=187.5 =200mm

Self-weight of the slab= 0.2x24 = 4.8Kn/m2

Live load on the slab= 3 Kn/m2

Floor finish = 1 Kn/m2

Total Dead load = 5.8 Kn/m2

Factored dead load = 5.8x1.5 = 8.7 Kn/m2

Factored live load = 3x1.5 = 4.5 Kn/m2

Calculation of Effective Span

Effective span is smaller of

1. clear span +d = 7.5+.2 =7.7m
2. Clear span+bearing=7.5+.45=7.95m

Effective span = 7.7m

Calculation of Bending Moment

Referring to Is 456-2000 table 12 Bending moment coefficients

Bending moment at mid span = (8.7x7.72x/12) + (4.5x7.72/10)

= 69.66 KN-m

Bending moment at mid support = (8.7x7.72x/10) + (4.5x7.72/9)

= 81.2273 KN-m

Bending moment diagram

Calculation of Prestressing Force

The absolute maximum bending moment occurs at the mid support section. Using a minimum cover of 30mm to the cable, if no tensile stresses are permitted in the section the distance between the cable and the bottom of the kern is obtained as 70+33.3=103.3mm

P= prestressing force

Px103.3 = 81.22x106

P=786KN

At support = M/P = 81.22x106 /786x103 = 103.3mm

Therefore eccentricity of the cable at support = 103.3-(h/6) =70mm

At mid span= M/P = 69.x106 /786x103 = 88.6mm

Therefore eccentricity of the cable at support = 88.6-(h/6) =55mm

Check for stresses

Considering 1m width of span

Area of cross section = 1000x200=200x103mm2

Z= section modulus = 1000x2002/6 =6.66x106 mm3

P=786KN

At centre of span section

e=55mm; M=69.66 KN-m

P/A=786x103/(1000x200)=3.93N/mm2

Pe/Z= (786x103x55)/( 6.66x106)=6.49 N/mm2

M/Z = 10.459 N/mm2

At mid support section

e=70mm; M=81.22 KN-m

P/A=786x103/(1000x200)=3.93N/mm2

Pe/Z= (786x103x70)/( 6.66x106)=8.26 N/mm2

M/Z = 12.19 N/mm2

Number of Cables

Using 12 wires of 5 mm diameter stressed to 1500N/mm2

Area of each cable= 235.6mm2

Force in each cable=235.6x1500=353.4KN

Total prestressing force required for 20m span =786x20=15720KN

Number of cables = 15720/353.4=45

Spacing of cable= 20x103/45 = 440mm

Provide 12 wires of 5mm diameter cables at 440mm centre to centre at an eccentricity of 55mm at centre and concentric at external support and at an eccentricity of 70mm at mid support.

Check for limit state of collapse

M= fpu Ap (d-0.42Xu)

Apfp/bdfck =534.8x1500/(1000x170x40)=0.117

fpu/0.87fp =1 fpu=1305N/mm2

xu/d=0.2823 xu=48mm

M=1305x534.8x(170-0.42x50)

M=104.576 KN-m > 81.22 KN-m hence safe.

Check for deflection

Deflection at centre of the span due to dead and live load = 5wl4/384EI

I=6.66x108 mm4, Ec=5000 =31622 Mpa

W=8.8Kn/m

=17.21mm downward

Deflection due to prestressing force =5Pel2/48EI

Prestressing force per metre width of span=803.18 KN

Deflection=12.29 mm Upward

Net deflection at centre of span = 17.21-12.29 = 4.92mm

Deflection limit = span /250 =7500/250=30mm>4.92 Hence safe

Minimum reinforcement requirement

According to IS 1343-1980 provide a minimum longitudinal reinforcement of 0.2% of cross section.

10mm@195mm c/c along shorter and longer direction.

Analysis of One Way Continuous Slab Using Ansys Software

ANSYS Workbench combines access to ANSYS applications with utilities that manage the product workflow.Applications that can be accessed from Workbench include: ANSYS DesignModeler (for geometry creation); ANSYS Meshing (for mesh generation); ANSYS Polyflow (for setting up and solving computational fluid dynamics (CFD) simulations, where viscous and viscoelastic flows play an important role); and ANSYS CFD-Post (for postprocessing the results). In Workbench, a project is composed of a group of systems.

Ansys slab analysis gives the following Bending stress in the centre span and support section.

Centre of span= 9.90Mpa

Support section=12.819 Mpa

Using relation M/I=f/y

Moment at centre span= (I/y)*f = (6.66*10^6)9.9=66 KN

Moment at support section= (I/y)*f = (6.66*10^6)12.819=85.37 KN

Conclusion

• RC slab requires more cross sectional dimension compared to PT slab
• Moment carrying capacity of post tensioned slab is more for less cross section compared to reinforced concrete slab
• Prestressed concrete offers great technical advantages in comparison with other forms of construction such as reinforced concrete and steel. They possess improved resistance to shearing forces, due to the effect of compressive prestress, which reduces the principles tensile stress
• Prestressing of concrete helps in improving the ability of the material for energy absorption under impact loads. The economy of prestressed concrete is well established for long span structures. Standardized precast bridge beams between 10m and 30 m long and precast prestressed piles have proved to be more economical than steel and reinforced concrete.
• Due to utilization of concrete in the tension zone, an extra saving of 15 to 30% in concrete is possible in comparison with reinforced concrete
• Analysis of one way slab using Ansys software gives accurate results as compared to hand computations.

Reference

1. “Post-Tensioned Concrete Long-Span Slabs in Projects of Modern Building Construction”, Rafal Szydlowski and Barbara Labuzek 2017 IOP Conf. Ser.: Mater. Sci. Eng. 245022065.
2. “Detailing of post-tensioning”, D M. Rogowsky et.al vsl international ltd Bern, Switzerland.
3. Ellobody, Ehab & Bailey, Colin. (2008). “Behaviour of Unbonded Post-Tensioned One-way Concrete Slabs”. Advances in Structural Engineering - ADV STRUCT ENG. 11. 107-120. 10.1260/136943308784069504.
4. Aalami, B. O., and Jurgens, J. D. (2003), “Guidelines for the Design of Post-Tensioned Floors”.
5. “Prestressed concrete” by N krishnaraju, Fourth edition, Tata McGraw-hill publishing company limited.