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 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 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.
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.
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.
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.
Fire Resistance of Materials & Structures - Analysing the Steel StructureArshia Mousavi
A library room, whose structural steel members are to be checked in fire conditions (in terms of bearing capacity, R criterion).
The aims of this project are as follows:
1. Design of the beam and the column at room temperature
a) design the beam capacity at the ULS and the check the deflection at the SLS (d ≤ L1/250 in the rare combination) b) design the column for its buckling resistance.
2. Design the beam fire protection (boards) for the required fire resistance under the quasi-permanent load
the combination and assuming a three-sided exposure (concrete deck on top)
suggested steps: design load under fire
ultimate load of the beam at time = 0
ductility class
global failure or just a critical section?
increased capacity of the critical sections by the adaptation factors degree of utilization of the structure (or the critical section)
critical temperature.
protection design & final check.
3. Design the column fire protection
for the required fire resistance under the quasi- permanent load combination (optional: accounting for the effect of the thermal elongation of the beam).
suggested steps: design load under fire
thermal elongation of the beam assessment of the equivalent. uniform moment critical temperature (spreadsheet file)
protection design & final check
If needed, the member cross-sections designed at room temperature may be adjusted in order to meet the required fire resistance (parts 2 and 3)
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.
Economic Concrete Frame Elements to Eurocode 2Yusuf Yıldız
Eurocode 2'ye göre betonarme çerçeve elemanlarının ekonomik tasarımlarını ele alan dokümanın içerisinde yerinde dökülen, prekast, kompozit, ardgerme kolonlar, kirişler, döşemeler, perdeler ve merdivenlerin tasarımlarına dair bilgiler yer almakta.
Every industry focus to build and improve the
chimney to create the eco-friend organization as well as to
satisfy the strict environmental board.
IS: 4998 criteria for design of reinforced concrete chimneys
is using working stress method for chimney designing.
There are some limitations of working stress method. Also
the designing is difficult involving lengthy, cumbersome
and iterative computational effort.
So we should recognize this problem and we should use
some time saving techniques like interaction envelopes to
optimize the structural design.
Chimneys with various heights from 65m to 280m are
analyzed and designed by working stress method and limit
state method for collapse and comparison of results are
discussed in this paper. Generation of interaction curves for
hollow circular section is also discussed in this paper.
Similar to Prestressed concrete course assignments 2018 (20)
We have compiled the most important slides from each speaker's presentation. This year’s compilation, available for free, captures the key insights and contributions shared during the DfMAy 2024 conference.
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Online aptitude test management system project report.pdfKamal Acharya
The purpose of on-line aptitude test system is to take online test in an efficient manner and no time wasting for checking the paper. The main objective of on-line aptitude test system is to efficiently evaluate the candidate thoroughly through a fully automated system that not only saves lot of time but also gives fast results. For students they give papers according to their convenience and time and there is no need of using extra thing like paper, pen etc. This can be used in educational institutions as well as in corporate world. Can be used anywhere any time as it is a web based application (user Location doesn’t matter). No restriction that examiner has to be present when the candidate takes the test.
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Examination System is very useful for Teachers/Professors. As in the teaching profession, you are responsible for writing question papers. In the conventional method, you write the question paper on paper, keep question papers separate from answers and all this information you have to keep in a locker to avoid unauthorized access. Using the Examination System you can create a question paper and everything will be written to a single exam file in encrypted format. You can set the General and Administrator password to avoid unauthorized access to your question paper. Every time you start the examination, the program shuffles all the questions and selects them randomly from the database, which reduces the chances of memorizing the questions.
Water billing management system project report.pdfKamal Acharya
Our project entitled “Water Billing Management System” aims is to generate Water bill with all the charges and penalty. Manual system that is employed is extremely laborious and quite inadequate. It only makes the process more difficult and hard.
The aim of our project is to develop a system that is meant to partially computerize the work performed in the Water Board like generating monthly Water bill, record of consuming unit of water, store record of the customer and previous unpaid record.
We used HTML/PHP as front end and MYSQL as back end for developing our project. HTML is primarily a visual design environment. We can create a android application by designing the form and that make up the user interface. Adding android application code to the form and the objects such as buttons and text boxes on them and adding any required support code in additional modular.
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ACEP Magazine edition 4th launched on 05.06.2024Rahul
This document provides information about the third edition of the magazine "Sthapatya" published by the Association of Civil Engineers (Practicing) Aurangabad. It includes messages from current and past presidents of ACEP, memories and photos from past ACEP events, information on life time achievement awards given by ACEP, and a technical article on concrete maintenance, repairs and strengthening. The document highlights activities of ACEP and provides a technical educational article for members.
Literature Review Basics and Understanding Reference Management.pptxDr Ramhari Poudyal
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1. Aalto University Janne Hanka
CIV-E4050 Prestressed concrete structures 17-Oct-18
Homework assignments and solutions, 2018
All rights reserved by the author.
Foreword:
This educational material includes assignments of the course named CIV-E4050 Prestressed
concrete from the 2017. 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 in English. European standards EN 1990 and EN 1992-1-1 are
applied in the problems.
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: 2018
Table of contents:
Homework 1. Free-body-diagrams of PT-structures
Homework 2. ULS Design of anchor area in post-tensioned beam
Homework 3. Design of post-tensioned slab
Homework 4. Prestress losses and deformations of a post-tensioned beam
Homework 5. Design of precast pretensioned composite beam using inequality equations
ANNEX:
Homework formulas
2. Aalto University J. Hanka
CIV-E4050 Prestressed and Precast Concrete Structures 2018 11.9.2018
Homework 1, Free body diagrams of post-tensioned structures 1(7)
Return to MyCourses in PDF-format.
Beams in pictures (a…h) are stressed with post-tensioned tendons. Profile of the tendon is shown in the
pictures. Tendon is stressed at the stressing end with force “P”. Curved parts of the tendon profile are
parabolas, which can be assumed to produce an evenly distributed vertical load over the length of each
parabola. Any losses in tendon force can be neglected due to simplification.
Goal of the assignment is to draw and sketch the forces transmitted from the tendon to the concrete as a free
body diagram of the concrete structure (=free-body diagram of the concrete structure after removal of
tendon).
- Load balancing force due to tendon profile
- Point moments due to eccentricity of the anchor at the anchor areas and change of cross section
Tip see also:
https://adaptsolutions.files.wordpress.com/2010/01/load-balancing.pdf
3. Aalto University J. Hanka
CIV-E4050 Prestressed and Precast Concrete Structures 2018 11.9.2018
Homework 1, Free body diagrams of post-tensioned structures 2(7)
Return to MyCourses in PDF-format.
Example2:
4. Aalto University J. Hanka
CIV-E4050 Prestressed and Precast Concrete Structures 2018 11.9.2018
Homework 1, Free body diagrams of post-tensioned structures 3(7)
Return to MyCourses in PDF-format.
5. Aalto University J. Hanka
CIV-E4050 Prestressed and Precast Concrete Structures 2018 11.9.2018
Homework 1, Free body diagrams of post-tensioned structures 4(7)
Return to MyCourses in PDF-format.
6. Aalto University J. Hanka
CIV-E4050 Prestressed and Precast Concrete Structures 2018 11.9.2018
Homework 1, Free body diagrams of post-tensioned structures 5(7)
Return to MyCourses in PDF-format.
7. Aalto University J. Hanka
CIV-E4050 Prestressed and Precast Concrete Structures 2018 11.9.2018
Homework 1, Free body diagrams of post-tensioned structures 6(7)
Return to MyCourses in PDF-format.
Tip: example of coupler anchor (p. 23/42 and 35/42):
https://www.naulankanta.fi/files/BBR_ETA-06-0165_CMM_EN_Rev4_0916.pdf
8. Aalto University J. Hanka
CIV-E4050 Prestressed and Precast Concrete Structures 2018 11.9.2018
Homework 1, Free body diagrams of post-tensioned structures 7(7)
Return to MyCourses in PDF-format.
9. Aalto University J. Hanka
CIV-E4050 Prestressed and Precast Concrete Structures 2018 11.9.2018
Homework 1, Free body diagrams of post-tensioned structures 8(7)
Return to MyCourses in PDF-format.
Tip: example of movable coupling (p. 30/40 and 24/40):
https://www.dywidag-systems.com/fileadmin/downloads/global/construction/approvals/en/dsi-suspa-systems-eta-03-
0036-monostrandsystem-en.pdf
10. Aalto University J. Hanka
Rak-43.3111 Prestressed and Precast Concrete Structures 2016 12.9.2018
Homework 2, ULS Design of anchor area in post-tensioned beam 1(1)
Return to MyCourses in PDF-format.
Goal of this HW is to design the anchor area reinforcement for the given unbonded beam. Beam dimensions:
h=1000mm and b=1200mm.
- Beam concrete strength During stressing of tendons: C25/30
At final condition: C35/45
- Consequence class CC3
- Tendons: Grade St1640/1820. Area of one tendon: AP=165 mm2
.
Unbonded tendons, Multianchors (4-tendons for 1-anchor)
ETA: http://www.bbrnetwork.com/fileadmin/bbr_network/PDFs/Approvals/CMM/BBR_ETA-06-0165_CMM_EN_Rev4_0916.pdf
- Rebar: A500HW.
- Prestress force each anchor: Jacking force: Pmax = 4x234 = 936kN/ANCHOR
Total number of anchors = 8. Layout of anchors see fig.1.
Anchors are stressed one-by-one with one stressing jack.
- Initial losses for each anchor (after locking of tendons) is are assumed to be Δini=10% [Pm.0=Pmax(1-Δini)]
a) Choose and justify your choice for the sequence of jacking of anchors.
a) Form the strut & tie model of the beam end due to jacking forces
b) Calculate the required rebar to be used in the anchorage zone.
d) Draw the reinforcement at the beam end. Tip. You can use the autocad file given in MyCourses
Figure 1. Layout of anchors at beam end.
11. Aalto University J. Hanka
CIV-E4050 Prestressed and Precast Concrete Structures 2018 26.9.2018
Homework 3, Design of post-tensioned one-way-slab 1(2)
Return to MyCourses in PDF-format.
You are designing a cast-on-situ cantilevering one-way-slab (figures 1 and 2) that will be prestressed with
post-tensioned unbonded tendons and monoanchors. Slab thickness is hL. Slab is supported by walls.
Connection between slab and walls is hinged.
- Concrete strength at final condition: C35/45
- Concrete strength during stressing of tendons: C25/30
- Exposure classes XC1. Design working life: 100 years. Consequence class CC3
- Unbonded tendons and monoanchors. Grade St1640/1860. Diameter 15,7mm. Area of one tendon
Ap1=150mm2
.
- Jacking force for one tendon Pmax= 210 kN
- Assumed smallest distance of tendon centroid from the bottom/top of the section eP=85 mm
- Assumed height of centroid of anchors at beam end is eA=hL/2
- Total prestress losses are assumed to be Δf=15% [Pm.t=Pmax(1-Δf)= ~180kN]
- Span length: L1=18m. Width of slab L2=50m. Cantilever lenght L3=4m
- Superimposed dead load: g1= 1,3 kN/m2
. Concrete selfweight ρc=25kN/m3
.
- Liveload q1=7 kN/m2
. Combination factors: ψ0=0,8; ψ1=0,7; ψ2=0,6 (Warehouses)
a) Form the calculation model of the slab (for the tendons to be designed in Y-direction). Choose the slab
thickness. Calculate the effect of actions due to selfweight, dead load and live load at midspan.
b) Calculate the cross-section properties used in the prestress design:
- Moment of inertia and cross section area IC , AC *
c) Choose the amount of tendons and tendon geometry. Calculate the load balancing forces along the
span and bending moment due to tendon forces at midspan.
d) Check that the allowable stresses given in table 1 are not exceeded in critical section at midspan.
e) Calculate the beam deflection at (midspan & end of cantilever) for the quasi-permanent
combination. Check that the allowable deflection given in table 1 is not exceeded. Calculate the beam
shortening due to prestress also.
f) Draw a schematic drawing (cross section) of the beam and place the tendons inside the beam. Assume
cover to stirrups c=40mm. Stirrup diameter 12mm.
Table 1. Allowable stresses of concrete in serviceability limit state (SLS) for unbonded tendons in XC3.
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.c < fctm
IV Max compression Characteristic σcc.c < 0,6*fck 7.2(2)
V Max compression Quasi-permanent σcc.c < 0,45*fck 7.2(3)
Max deflection Quasi-permanent
Creep factor = 2
Δ < Span / 250 7.4.1(4)
Max Crack width Quasi-permanent wk.max < 0,3mm 7.3.1(5)
Note (b): You can use simplified gross-cross section properties
12. Aalto University J. Hanka
CIV-E4050 Prestressed and Precast Concrete Structures 2018 26.9.2018
Homework 3, Design of post-tensioned one-way-slab 2(2)
Return to MyCourses in PDF-format.
Figure 1. Plan view and main section of the floor
Figure 2. Typical section of middle beam under consideration in this homework.
13. Aalto University J. Hanka
CIV-E4050 Prestressed and Precast Concrete Structures 2018 11.9.2018
Homework 4, Calculation of prestress losses and elongations 1(1)
Return to MyCourses in PDF-format.
You are investigating a post-tensioned beam JPV-2 that has unbonded tendons and a construction joint.
Fixed couplers are used at the construction joint. Time between construction and stressing of stage 1 and 2 is
approximately 3 weeks.
- Beam concrete strength at final condition: C35/45
- Beam concrete strength during stressing of tendons: C25/30
- Unbonded tendons, BBR anchors ETA-06/0165. Grade: fp0,1=1640MPa ; fpk=1820 MPa. Area of one
tendon Ap1=165mm2
. Diameter of tendons (with the plastic pipe) dP=20mm.
Number of tendons np=32 + 32 (stage1 + 2). Anchor type: Multianchors, 4-tendons for one anchor
- Tendon geometry: See the attached JPV-2 Beam drawing.
- Jacking force for one anchor Stage 1 Anchors: Pmax= 940 kN / for one anchor / 4-tendons
Stage 2 Anchors: Pmax= 900 kN / for one anchor / 4-tendons
- Allowable stress in tendons during stressing σmax.all = min{0,80 fpk ; 0,90 fp0,1 }
- Allowable stress in tendons after stressing and locking of anchors σpm0.all = min{0,75 fpk ; 0,85 fp0,1 }
- Friction coefficient, wobble coefficient and slipping of anchors can be found from ETA-06-0165 [1, s.10-11]
- Allowable force in the construction joint [1, p.8/42, ch.1.2.3]:
Anchor force in Stage 1 anchor (after immediate losses) > Anchor force in Stage 2 coupler (during stressing)
a) Calculate the immediate losses due to friction ΔPμ, anchorage set ΔPsl and instantaneous deformation of concrete ΔPel.
for the tendons in STAGE 1.
b) Draw a curve that describes the tendon force after initial losses from jacking end to the dead anchorage end for the
STAGE 1 tendons. What is the average tendon force after initial losses Pm.0?
c) Calculate the immediate losses due to friction ΔPμ, anchorage set ΔPsl and instantaneous deformation of concrete ΔPel.
for the tendons in STAGE 2.
d) Draw a curve that describes the tendon force after initial losses from jacking end to the dead anchorage end for the
STAGE 2 tendons. What is the average tendon force after initial losses Pm.0?
e) Check is the allowable stress in the tendon immediately after tensioning exceeded in any sections along the span.
f) Calculate the elongation of the tendons at the stressing end after stressing (for both Stage 1 and Stage 2 tendons).
[1] http://www.bbrnetwork.com/fileadmin/bbr_network/PDFs/Approvals/CMM/BBR_ETA-06-0165_CMM_EN_Rev4_0916.pdf
Dimensions of the cross section that can be assumed in the calculation:
bw=1200mm bf=8100 (spacing of beams)
h=800mm hf=300mm
14. Aalto University J. Hanka
CIV-E4050 Prestressed and Precast Concrete Structures 2018 26.9.2018
Homework 5, Design composite beam using inequality equations 1(3)
Return to MyCourses in PDF-format.
You are designing a precast single-span rectangular beam (figure 1 and 2) that will be prestressed with
pretensioned bonded tendons. Beams are supporting a floor made of precast panel slabs (height of panel slabs
hKL=120mm) and cast in place slab (total slab thickness hKL+hCIP=hTOT=220mm). Beams are supported by
columns. Connection between beam and columns may be assumed to be hinged. Composite action between the
slab and beam is to be considered. Beams are propped during casting of topping, see figure 1 and 2.
- Beam and panel slab concrete strength at final condition: C50/60
- Beam concrete strength during stressing/release of tendons: C25/30
- Cast-in-place concrete strength at final condition C35/45
- Cover to rebar and stirrups c=40mm
- Exposure classes XC3, XF1. Design working life: 50 years. Consequence class CC2
- Bonded tendons. Grade St1640/1860. Diameter 12,5mm. Area of one tendon Ap1=93mm2
Tendon geometry is straight.
- Prestress force in tendons at release is σmax= 1100 MPa
- Assumed smallest distance of tendon centroid from the bottom/top of the section ep=90mm
- Total prestress losses (initial & timedependant) are assumed to be Δf=15% [Pm.t=Pmax(1-Δf)]
- Beam span length: L1=17m. Spacing of beams (slab span lengths) L2=8,1m.
- Beam height & width: H=980mm Bw=880mm
- Superimposed dead load: gDL= 0,5 kN/m2
. Concrete selfweight ρc=25kN/m3
.
- Liveload qLL=5 kN/m2
. Combination factors: ψ0=0,7; ψ1=0,5; ψ2=0,3 (EN 1990 Class G, garages)
a) Form the calculation model of the beam. Calculate the effect of actions due to selfweight, dead load and live
load at midspan. Calculate also the combination of actions required for the flexural analysis of the section.
b) Calculate the cross-section properties used using method of transformed section properties:
- Effective width of the flange beff
- Moment of inertia and cross section area of the prestressed beam IB , AB
- Moment of inertia and cross section area of the composite beam section IC , AC
c) Determine the inequality equations required for the flexural analysis of the section using the stress condition I,
II, III and IV given in table 1. Initial value of the tendon force Fi is used in conditions I-II and final value Fiη is
used in conditions III-VI.
d) Present the equations determined in (c) in the form required for the graphical presentation of stress inequality
equations in the coordinate system (1/Pmax, e0). Draw the graphical representation (Magnel’s diagram) of the
stress inequality conditions where vertical axis is e0 and horizontal axis is 1/Pmax (figure 1).
e) Choose the value of initial prestress Pmax (=amount of tendons) and eccentricity e0 that satisfies the conditions
I-IV in table 1.
f) Draw a schematic drawing (cross section) of the structure and place the tendons inside the beam and the rebar
over panel slab supports. Assume cover to stirrups c=40mm. Stirrup diameter 12mm.
Table 1. Allowable stresses of concrete in serviceability limit state (SLS) for bonded tendons in XC3.
Condition # Combination EN1990 Limitation EC2 Clause
Initia
l
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
IIIb Max tension Quasi-permanent σct.qp < 0 * 7.3.1(5)
IV Max compression Characteristic σcc.c < 0,6*fck 7.2(2)
IVb Max compression Quasi-permanent σcc.c < 0,45*fck 7.2(3)
Max deflection Quasi-permanent
Creep factor = 2
Δ < Span / 250 7.4.1(4)
Max crack width Frequent wk.max < 0,2mm 7.3.1(5)
*Note: Bonded tendons require decompression (vetojännityksettömyys) for quasi-permanent combination.
15. Aalto University J. Hanka
CIV-E4050 Prestressed and Precast Concrete Structures 2018 26.9.2018
Homework 5, Design composite beam using inequality equations 2(3)
Return to MyCourses in PDF-format.
Figure 1. Plan view and main section of the floor.
Figure 2. Section of middle beam under consideration.
16. Aalto University J. Hanka
CIV-E4050 Prestressed and Precast Concrete Structures 2018 26.9.2018
Homework 5, Design composite beam using inequality equations 3(3)
Return to MyCourses in PDF-format.
Figure 3. Graphical presentation of stress inequality equations, cross section and stresses.