Spring 2016 problems for the course Rak-43.3110 Prestressed and precast concrete. Problems include
-Working stress design
-Ultimate strength design
-Loadbalancing
-Prestress losses
-Composite structures
Spring 2014 problems for the course Rak-43.3110 Prestressed and precast concrete structures, Aalto University, Department of Civil and Structural Engineering. European standards EN 1990 and EN 1992-1-1 has been applied in the problems.
Spring 2014 problems for the course Rak-43.3110 Prestressed and precast concrete structures, Aalto University, Department of Civil and Structural Engineering. European standards EN 1990 and EN 1992-1-1 has been applied in the problems.
Spring 2015 problems for the course Rak-43.3110 Prestressed and precast concrete structures, Aalto University, Department of Civil and Structural Engineering. European standards EN 1990 and EN 1992-1-1 has been applied in the problems.
TALAT Lecture 2711: Design of a Helicopter DeckCORE-Materials
This lecture presents design of the main structural parts of an aluminium alloy helicopter deck. The design of a bolted connection on the supporting structure is also presented.
Sheryar Bismil
Student of Mirpur University of Science & Technology(MUST).
Student of Final Year Civil Engineering Department Main campus Mirpur.
Here we Gonna to learn about the basic to depth wise study of Plan Reinforced Concrete-i.
From basis terminology to wide information about the analysis and design of Concrete member like column,Beam,Slab,etc.
Abstract (Dutch)
Samengestelde betonnen liggers vervaardigd van prefab voorgespannen- en/of gewapende elementen zijn zeer populair in de huidige praktijk van de civiele techniek. Twee betonnen, samengestelde delen van de ligger worden gestort op verschillende tijdstippen. Verschillende elasticiteitsmoduli, opeenvolgende belastingaanbrenging, en verschillend krimp en kruip veroorzaken een herverdeling van de normaalspanning en ongelijke rekken en spanningen in twee aansluitende vezels in het aansluitvlak.
Dit seminar richt zich op de berekening volgens de EN 1992-1-1 en EN 1992-2. De aannames met betrekking tot de berekening en de controle van de gewapende en/of voorgespannen samengestelde liggers en doorsnedes zal worden toegelicht.
Ook wordt er ingegaan op:
• De spanning/rek respons van de doorsnede belast door normaalkracht en buigende momenten,
• De principes van het gebruik van de “initiële toestand” in berekeningen van de uiterste grenstoestand en de bruikbaarheidsgrenstoestand,
• De controle van dwarskracht en wringing,
• De interactie tussen alle snedekrachten,
• De principes van de controles van de spanningbeperking,
• De achtergrond van de scheurwijdtecontrole
Speciale aandacht zal er worden gegeven aan de berekening van de schuifspanning in het aansluitvlak, en de beschouwing van de invloed van de verschillende leeftijd van de betonnen delen met betrekking tot de schuifspanningen. Een alternatieve berekeningsmethode ten opzichte van de Eurocode 2 zal worden voorgesteld en worden getest.
De praktische voorbeelden volgens de Eurocode 2 zullen worden uitgevoerd met behulp van de IDEA StatiCa software.
Sheryar Bismil
Student of Mirpur University of Science & Technology(MUST).
Student of Final Year Civil Engineering Department Main campus Mirpur.
Here we Gonna to learn about the basic to depth wise study of Plan Reinforced Concrete-i.
From basis terminology to wide information about the analysis and design of Concrete member like column,Beam,Slab,etc.
Spring 2015 problems for the course Rak-43.3110 Prestressed and precast concrete structures, Aalto University, Department of Civil and Structural Engineering. European standards EN 1990 and EN 1992-1-1 has been applied in the problems.
TALAT Lecture 2711: Design of a Helicopter DeckCORE-Materials
This lecture presents design of the main structural parts of an aluminium alloy helicopter deck. The design of a bolted connection on the supporting structure is also presented.
Sheryar Bismil
Student of Mirpur University of Science & Technology(MUST).
Student of Final Year Civil Engineering Department Main campus Mirpur.
Here we Gonna to learn about the basic to depth wise study of Plan Reinforced Concrete-i.
From basis terminology to wide information about the analysis and design of Concrete member like column,Beam,Slab,etc.
Abstract (Dutch)
Samengestelde betonnen liggers vervaardigd van prefab voorgespannen- en/of gewapende elementen zijn zeer populair in de huidige praktijk van de civiele techniek. Twee betonnen, samengestelde delen van de ligger worden gestort op verschillende tijdstippen. Verschillende elasticiteitsmoduli, opeenvolgende belastingaanbrenging, en verschillend krimp en kruip veroorzaken een herverdeling van de normaalspanning en ongelijke rekken en spanningen in twee aansluitende vezels in het aansluitvlak.
Dit seminar richt zich op de berekening volgens de EN 1992-1-1 en EN 1992-2. De aannames met betrekking tot de berekening en de controle van de gewapende en/of voorgespannen samengestelde liggers en doorsnedes zal worden toegelicht.
Ook wordt er ingegaan op:
• De spanning/rek respons van de doorsnede belast door normaalkracht en buigende momenten,
• De principes van het gebruik van de “initiële toestand” in berekeningen van de uiterste grenstoestand en de bruikbaarheidsgrenstoestand,
• De controle van dwarskracht en wringing,
• De interactie tussen alle snedekrachten,
• De principes van de controles van de spanningbeperking,
• De achtergrond van de scheurwijdtecontrole
Speciale aandacht zal er worden gegeven aan de berekening van de schuifspanning in het aansluitvlak, en de beschouwing van de invloed van de verschillende leeftijd van de betonnen delen met betrekking tot de schuifspanningen. Een alternatieve berekeningsmethode ten opzichte van de Eurocode 2 zal worden voorgesteld en worden getest.
De praktische voorbeelden volgens de Eurocode 2 zullen worden uitgevoerd met behulp van de IDEA StatiCa software.
Sheryar Bismil
Student of Mirpur University of Science & Technology(MUST).
Student of Final Year Civil Engineering Department Main campus Mirpur.
Here we Gonna to learn about the basic to depth wise study of Plan Reinforced Concrete-i.
From basis terminology to wide information about the analysis and design of Concrete member like column,Beam,Slab,etc.
Reinforced concrete Course Assignments, 2023.
Educational material for the RCS course. Design examples for reinforced concrete structures regarding beams and mast columns.
Prestress loss due to friction & anchorage take upAyaz Malik
This document provides a detailed procedure for calculating prestress loss due to anchorage take-up. Prestress Loss due to friction is also discussed in detail.
Cost Optimization of a Tubular Steel Truss Using Limit State Method of DesignIJERA Editor
Limit state method helps to design structures based on both safety and serviceability. The structures are designed to withstand ultimate loads or the loads at which failure occurs unlike working stress method where only service loads are considered. This leads to enhanced safety. Also unlike the working stress method, the structures are economical. It is also better than ultimate load method as serviceability requirement is also taken care of by considering various safety factors for all the load types and structures do not undergo massive deflection and cracks. For tubular sections, higher strength to weight ratio could result in upto 30% savings in steel .Due to the high torsional rigidity and compressive strength, Tubular sections behave more efficiently than conventional steel section This study is regarding the economy, load carrying capacity of all structural members and their corresponding safety measures.
NO1 Uk best vashikaran specialist in delhi vashikaran baba near me online vas...Amil Baba Dawood bangali
Contact with Dawood Bhai Just call on +92322-6382012 and we'll help you. We'll solve all your problems within 12 to 24 hours and with 101% guarantee and with astrology systematic. If you want to take any personal or professional advice then also you can call us on +92322-6382012 , ONLINE LOVE PROBLEM & Other all types of Daily Life Problem's.Then CALL or WHATSAPP us on +92322-6382012 and Get all these problems solutions here by Amil Baba DAWOOD BANGALI
#vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore#blackmagicformarriage #aamilbaba #kalajadu #kalailam #taweez #wazifaexpert #jadumantar #vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore #blackmagicforlove #blackmagicformarriage #aamilbaba #kalajadu #kalailam #taweez #wazifaexpert #jadumantar #vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore #Amilbabainuk #amilbabainspain #amilbabaindubai #Amilbabainnorway #amilbabainkrachi #amilbabainlahore #amilbabaingujranwalan #amilbabainislamabad
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
NUMERICAL SIMULATIONS OF HEAT AND MASS TRANSFER IN CONDENSING HEAT EXCHANGERS...ssuser7dcef0
Power plants release a large amount of water vapor into the
atmosphere through the stack. The flue gas can be a potential
source for obtaining much needed cooling water for a power
plant. If a power plant could recover and reuse a portion of this
moisture, it could reduce its total cooling water intake
requirement. One of the most practical way to recover water
from flue gas is to use a condensing heat exchanger. The power
plant could also recover latent heat due to condensation as well
as sensible heat due to lowering the flue gas exit temperature.
Additionally, harmful acids released from the stack can be
reduced in a condensing heat exchanger by acid condensation. reduced in a condensing heat exchanger by acid condensation.
Condensation of vapors in flue gas is a complicated
phenomenon since heat and mass transfer of water vapor and
various acids simultaneously occur in the presence of noncondensable
gases such as nitrogen and oxygen. Design of a
condenser depends on the knowledge and understanding of the
heat and mass transfer processes. A computer program for
numerical simulations of water (H2O) and sulfuric acid (H2SO4)
condensation in a flue gas condensing heat exchanger was
developed using MATLAB. Governing equations based on
mass and energy balances for the system were derived to
predict variables such as flue gas exit temperature, cooling
water outlet temperature, mole fraction and condensation rates
of water and sulfuric acid vapors. The equations were solved
using an iterative solution technique with calculations of heat
and mass transfer coefficients and physical properties.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
6th International Conference on Machine Learning & Applications (CMLA 2024)ClaraZara1
6th International Conference on Machine Learning & Applications (CMLA 2024) will provide an excellent international forum for sharing knowledge and results in theory, methodology and applications of on Machine Learning & Applications.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
1. Aalto University Janne Hanka
Rak-43.3111 Prestressed and Precast Concrete Structures 16-Apr-16
Homework assignments and solutions, Spring 2015
All rights reserved by the author.
Foreword:
This educational material includes assignments of the course named
Rak-43.3111 Prestressed and Precast Concrete Structures from the spring term 2016. Course is part
of the Master’s degree programme of Structural Engineering and Building Technology in Aalto
University.
Each assignment has a description of the problem and the model solution by the author. Description
of the problems and the solutions are given in Finnish and English. European standards EN 1990
and EN 1992-1-1 are applied in the problems and references are made to course text book Naaman
A.E. "Prestressed concrete analysis and design, Fundamentals”.
Questions or comments about the assignments or the model solutions can be sent to the author.
Author: MSc. Janne Hanka
janne.hanka@aalto.fi / janne.hanka@alumni.aalto.fi
Place: Finland
Year: 2016
Table of contents:
Homework 1. Working stress design of a prestressed T-beam
Homework 2. Ultimate strength design of a prestressed T-beam
Homework 3. Design of 3-span continuous slab using loadbalancing
Homework 4. Prestress losses of continunous slab
Homework 5. Stress analysis of shored composite slab
2. Aalto University J. Hanka
Rak-43.3111 Prestressed and Precast Concrete Structures 2016 20.1.2016
Homework 1, Working stress design 1(1)
Return to MyCourses in PDF-format.
You are designing a post-tensioned single-span T-beam-slab that will be prestressed with unbonded monostrand
tendons. Slab is loaded with a permanent dead load gk=0,5 kN/m2
and liveload qk=5 kN/m2
. Concrete selfweight is
ρc=25kN/m3
. Slab is prestressed before imposed dead loads are installed. Slab (=T-beam flange) thickness is 200mm.
Beam supports can be assumed to be hinged.
Information:
- Concrete strength at final condition: C30/37 ; fck=30MPa ; fctm=2,89MPa ; Ecm=32,8GPa
- Concrete strength during stressing: C25/30 ; fck.i=25MPa ; fctm.i=2,56MPa ; Ecm.i=31GPa
- Exposure classes XC3, XD1. Design working life: 50 years.
- Unbonded tendons. Grade St1600/1860, fp0,1k=1600 MPa, fpu=1860MPa, Ep=195GPa
- Area of one tendon Ap1=150mm2
. Assumed jacking force of one tendon is Pmax=210kN.
- Assumed smallest distance of tendon centroid from the bottom/top of the section ep=90mm
- Initial prestress losses (friction, slipping and elastic) are assumed to be Δini=10% [Pm.0=Pmax(1-Δini)]
- Total prestress losses (initial & timedependant) are assumed to be Δf=15% [Pm.t=Pmax(1-Δf)]
- Beam span length: L=14,5m. Spacing of beams (slab span lengths) L2=8,3m.
- Liveload combination factors; ψ0=0,7; ψ1=0,5; ψ2=0,3 (EN 1990 Class G, garages)
- Quasi-permanent combination of actions: pqp=∑gj + ∑ψ2qi
- Frequent combination of actions: pf=∑gj + ψ1q1 + ∑ψ2,i+1qi+1
- Characteristic combination of actions: pc=∑gj + q1 + ∑ψ2,i+1qi+1
Goal of the assignment is to design a typical T-beam section (find the beam height, beam width, number of tendons
and tendon geometry at midspan) in such a way that design criteria’s given in table 1 are satisfied.
Figure 1. Post-tensioned T-beam section.
Table 1. Allowable stresses of concrete in serviceability limit state (SLS) for unbonded tendons.
Condition # Combination EN1990 Limitation EC2 Clause
Initial
I Max tension Initial σct.ini < fctm.i
II Max compression Initial σcc.ini < 0,6*fck.i 5.10.2.2(5)
Final
III Max tension Frequent σct.f < fctm
IV Max compression Characteristic σcc.c < 0,6*fck 7.2(2)
V Max compression Quasi-permanent σcc.qp < 0,45*fck 7.2(3)
Max deflection Quasi-permanent Δ < Span / 250 7.4.1(4)
a) Form the calculation model of the beam. Choose the beam height H and width Bw. Calculate the effect of actions
due to selfweight, dead load and live load at midspan.
b) Calculate the effective flange width (beff) according to EN 1992-1-1 chapter 5.3.2.1(2).
c) Calculate the cross section properties for the gross-cross section used in the prestress design:
- Moment of inertia and cross section area Igr, Agr
d) Choose the amount of tendons and tendon geometry at midspan (distance of tendon centroid from bottom of
beam). Calculate the axial force and bending moment due to prestress at midspan.
e) Check that the allowable stresses given in table 1 are not exceeded in critical section at midspan.
f) Draw a schematic drawing (cross section) of the tendon geometry.
Tip for (c), (d):
http://www.adaptsoft.com/resources/ADAPT_T901_Effective-Width-PT-beamsr.pdf
200
Bw
H
3. Aalto University J. Hanka
Rak-43.3111 Prestressed and Precast Concrete Structures 2016 20.1.2016
Homework 1, Working stress design 1(1)
Return to MyCourses in PDF-format.
Tip (b): Effective flange width according to EN 1992-1-1:
4. Aalto University J. Hanka
Rak-43.3111 Prestressed and Precast Concrete Structures 2016 5.2.2016
Homework 2, Ultimate strength design of T-beam 1(1)
Return to MyCourses in PDF-format.
You are designing a post-tensioned single-span T-beam-slab that will be prestressed with unbonded tendons. Slab is
loaded with a permanent dead load gk=0,5 kN/m2
(surface structures) and liveload qk=5 kN/m2
. Concrete selfweight is
ρc=25kN/m3
. Beam supports can be assumed to be hinged. Width of the supports at beam ends is a0=400mm.
Information:
- Concrete strength: C30/37; fck=30MPa; fctm=2,89MPa; Ecm=32,8GPa ; εcu=0,35% ; λ=0,8 ; η=1,0
- Exposure classes XC3, XD1. Design working life: 50 years.
- Unbonded tendons. Grade St1600/1860, fp0,1k=1600 MPa, fpu=1860MPa, Ep=195GPa
- Reinforcement steel Es=200GPa, fyk=500 MPa
- Area of one tendon Ap1=150mm2
. Total number of tendons is 14. Assumed jacking force of one tendon is
Pmax=210kN. Distance between bottom of the beam and centroid of the tendons at midspan is
eP(x=L/2)=90mm and at beam ends is ep(x=0)=ep(x=L)=700mm
- Initial prestress losses (friction, slipping and elastic) are assumed to be Δini=10% [Pm.0=Pmax(1-Δini)]
- Total prestress losses (initial & timedependant) are assumed to be Δf=15% [Pm.t=Pmax(1-Δf)]
- Beam span length: L=14,5m. Spacing of beams (slab span lengths) L2=8,3m.
- Liveload combination factors; ψ0=0,7; ψ1=0,5; ψ2=0,3 (EN 1990 Class G, garages)
- Partial factors for loads in ULS: γG=1,35 ; ξγG=1,15 ; γQ=1,5 ; KFI=1
- Partial factors for tendon force in ULS: γP.fav= γP.unfav=1,0
- ULS combination of actions: pEd=∑ ξγG gj + γQ q1 + ∑ γQ ψ0,i+1qi+1
- Assumed stress increase of unbonded tendons in ultimate limit state Δσp.ULS=50MPa [EN1992-1-1 5.10.8(2)]
- Partial factors for materials γc=1,5; αcc=0,85 ja γs=γp=1,15 [EN 1992-1-1 2.4.2.4(1)]
- Concrete cover to the shear reinforcement is c=35mm.
Goal of the assignment is to calculate the required amount of bending and shear reinforcement.
Figure 1. Post-tensioned T-beam section and sideview with the tendon geometry.
a) Form the calculation model of the beam. Calculate the design value of line load pEd in ULS for the beam.
b) Calculate the design value of effect of actions due bending moment MEd.
c) Calculate the required amount of reinforcement As.req for the bending moment MEd obtained in (a). Effective width
of the flange may be assumed to be beff=5600mm.
d) Calculate the design value of effects of actions due to shear force VEd at critical section.
e) Calculate the required amount of shear reinforcement Asw.req for the shear force VEd obtained in (a).
f) Choose the actual amount of bending & shear reinforcement and place them to the cross section. Sketch a drawing
of the cross section with the reinforcement.
=200
=700
=900
5. Aalto University J. Hanka
Rak-43.3111 Prestressed and Precast Concrete Structures 2016 5.2.2016
Homework 2, Ultimate strength design of T-beam 1(1)
Return to MyCourses in PDF-format.
(a) (b) (c)
Figure 2. (a) Calculation model in ultimate limit state. (b) Stress-strain curve of prestressing steel [EC2 fig 3.10].
(c) Stress-strain curve of reinforcing steel [EC2 fig 3.8].
Tip (c): Calculation model bending moment resistance in ULS for unbonded tendons:
6. Aalto University J. Hanka
Rak-43.3111 Prestressed and Precast Concrete Structures 10.1.2016
Homework 3, Predesign of a prestressed 3-span slab using loadbalancing 1(1)
Return to Optima in PDF-format.
3-span continuous slab of parking garage in figure 1 will be prestressed with unbonded tendons. Slab is loaded with a
dead load gk=0,5kN/m2
and liveload qk=5kN/m2
. Concrete selfweight is ρc=25kN/m3
. Slab is prestressed before surface
structures are installed. Live load may vary span by span.
Information:
- Concrete strength at final condition: C30/37 ; fck=30MPa ; fctm=2,89MPa ; Ecm=32,8GPa
- Concrete strength during stressing: C25/30 ; fck.i=25MPa ; fctm.i=2,56MPa ; Ecm.i=31GPa
- Exposure classes XC3, XD1. Design working life: 50 years.
- Unbonded tendons. Grade St1600/1860, fp0,1k=1600 MPa, fpu=1860MPa, Ep=195GPa
- Area of one tendon Ap1=150mm2
. Assumed jacking force of one tendon is Pmax.1=210kN.
- Assumed smallest distance of tendon centroid from the bottom/top of the section ep=50mm
- Initial prestress losses (friction,slipping and elastic) are assumed to be in all spans Δini=10% [Pm.0=Pmax(1-Δini)]
- Total prestress losses (initial & timedependant) are assumed to be in all spans Δf=15% [Pm.t=Pmax(1-Δf)]
- Slab span lengths L=8,3m. 2nd
degree parabolic tendon geometry: u(x)=ax2
+bx+c
- Liveload combination factors; ψ0=0,7; ψ1=0,5; ψ2=0,3 (EN 1990 Class G, garages)
- Quasi-permanent combination of actions: pqp=∑gj + ∑ψiqi
- Frequent combination of actions: pf=∑gj + ψ1q1 + ∑ψ2,i+1qi+1
- Characteristic combination of actions: pc=∑gj + q1 + ∑ψ2,i+1qi+1
- Allowable deflection for quasi-permanent combination: L/250
Goal of the assignment is to find the thickness of the slab (h), spacing of tendons (ccp) / number of tendons per unit
width (np) and tendon geometry (eA, eB, eC).
Figure 1. Three-span post-tensioned slab with hinged supports.
Design in SLS using theory of elasticity:
a) Choose thickness of the slab (h) and load to be balanced (pbal), so that the maximum value of deflection Δqp due to
quasi-permanent combination of actions does not exceed the allowable value for deflection (L/250). Coefficient of
creep for concrete may be assumed to be φ=2.
b) Choose the tendon geometry (eA, eB, eC) and required spacing of tendons (ccp) in such a way that the balancing load
chosen in (a) is reached.
c) Check that the allowable stresses (σct.max<fctm.i ; σc.max<0,6fck.i) are not exceeded in critical section when slab is
loaded with initial tendon force Pm.0 (initial situation during prestressing).
d) Check that the allowable stresses (σct.max<fctm ; σc.max<0,45fck) are not exceeded in critical section when slab is
loaded with final tendon force Pm.t and frequent combination combination of actions pf.
e) Draw a schematic drawing (sideview and cross section) of the tendon geometry.
EXTRA) How would the design differentiate if bonded tendons were used instead of unbonded tendons.
Instructions: You can make justified assumptions and simplifications in the calculations. It is not required to round the
tendon geometry on top of the support. Use gross-cross section properties in the calculations.
7. Aalto University J. Hanka
Rak-43.3111 Prestressed and Precast Concrete Structures 10.1.2016
Homework 3, Predesign of a prestressed 3-span slab using loadbalancing 1(1)
Return to Optima in PDF-format.
Tip: Bending moment diagrams for 3-span continuos beam.
8. Aalto University J. Hanka
Rak-43.3111 Prestressed and Precast Concrete Structures 10.1.2016
Homework 4, Prestress losses of a continuous slab 1(1)
Return to Optima in PDF-format.
Slab and tendon
Geometry:
L=8.3m ; a0=0,5m
h=200mm
L1=0,4L ; L0=L/10
eA=eB=eC=h/2-ep
1=Active end
2=Anchorage end
3-span continuous slab of parking garage in figure 1 will be prestressed with unbonded tendons. Slab is loaded with a
dead load gk=0,5kN/m2
(surface structures) and liveload qk=5kN/m2
. Slab is prestressed before surface structures are
installed. Live load may vary span by span.
Information:
- Concrete strength at final condition: C30/37 ; fck=30MPa ; fctm=2,89MPa ; Ecm=32,8GPa
- Concrete strength during stressing: C25/30 ; fck.i=25MPa ; fctm.i=2,56MPa ; Ecm.i=31GPa
- Unbonded tendons. Grade St1600/1860, fp0,1k=1600 MPa, fpu=1860MPa, Ep=195GPa
- Initial stress (force of jack/area of tendons) σmax=1400 MPa. Pmax=210kN / Tendon
- Area of one tendon Ap1=150mm2
. Spacing of tendons ccp=400mm
- Smallest distance of tendon centroid from the bottom/top of the section ep=50mm
- 2nd
degree parabolic tendon geometry: u(x)=ax2
+bx+c
Goal of the assignment is to calculate the immediate losses due to friction, deformation and anchorage set.
Figure 1. Three-span unbonded post-tensioned slab with hinged supports.
a) Calculate the immediate losses due to friction ΔPμ and instantaneous deformation of
concrete ΔPel span by span. How much of the initial jacking stress is lost at the anchorage
end?
b) Calculate the immediate losses due to anchorage set ΔPsl.
c) Draw a curve that describes the tendon force after initial losses from jacking end (x=0) to
the dead anchorage end (x=3L).
d) How much of the initial maximum prestress is lost span-by-span?
e) What methods could be used to compensate prestress losses?
f) Calculate the theoretical elongation of the tendons at the active end after stressing.
Tip (a): Immediate prestress losses due to friction can be calculated with the following information
* Losses due to friction in post-tensioned tendons: ΔPμ(x)=P0(1-e-μ(θ+kx)
) [EC2 Eq.(5.45)]
* θ is the sum of the angular displacements over a distance x
* coefficient of friction between the tendon and its duct μ=0,05
* unintentional angular displacement for internal tendons (per unit length) k = 0,020 m-1
* slip of tendon δ= 5 mm
Tip (b): Losses due to anchorage set and elastic shortening is treated in the course textbook [Naaman] chapters 8.17 and
8.7 respectively.
Tip (d): http://www.kontek.ee/public/files/Post-tensioning%20MeKano4,%20S.A..pdf page 25
Instructions: You can make justified assumptions and simplifications in the calculations. Use gross-cross section
properties in the calculations.
1
2
9. Aalto University J. Hanka
Rak-43.3111 Prestressed and Precast Concrete Structures 10.1.2016
Homework 4, Prestress losses of a continuous slab 1(1)
Return to Optima in PDF-format.
Tip (a):
10. Aalto University J. Hanka
Rak-43.3111 Prestressed and Precast Concrete Structures 10.1.2016
Homework 5, Prestressed composite slab 1(1)
Return to Optima in PDF-format.
Slab in figure 1 is prestressed with pre-tensioned bonded tendons. Strenght class of the prestressed slab is C40/50.
Topping of C20/25 shall be casted on top of the slab. Prestressed slab is propped during casting of topping, see figure 1.
Temporary supports shall be removed when topping has reached strength of C25/30. Finally structure is loaded with a
live load qk.
Information:
- Composite slab concrete strength: C40/50 ; fck_C40=40MPa ; fctm_C40=3,51MPa ; Ecm_C40=35GPa
- Surface slab concrete strength: C20/25 ; fck_C20=20MPa ; fctm_C20=2,21MPa ; Ecm_C20=30GPa
- Bonded tendons. Grade St1600/1860, fp0,1k=1600 MPa, fpu=1860MPa, Ep=195GPa
- Stress of tendons at release σmax=1200MPa
- Area of one tendon Ap1=52mm2
. Total number of tendons np=10
- Liveload qk=5 kN/m2
. Liveload combination factors; ψ0=1,0; ψ1=1,0; ψ2=1,0
Figure 1. Prestressed composite slab with temporary supports.
a) Calculate the cross section properties of the prestressed slab (without composite action) using method of
transformed section.
b) Calculate the cross section properties of the composite section using method of transformed section.
c) Calculate the bottom stress of the concrete section at midspan (x=L/2) immediately after casting of surface slab
d) Calculate the bottom stress of the concrete section immediately after removal of temporary supports
e) Calculate the bottom stress of the concrete section in final condition when live load is effecting the slab. Does the
maximum tensile stress exceed the allowable stress fctm?
f) Calculate the total deflection Δtot of the structure in final condition when live load is effecting the slab.
Extra: e) Calculate the stresses of the section immediately in final condition if temporary support are not used.
Geometry:
L=9000mm
bw=1200m
h1=150m
h2=200mm
ep=50mm