Design of a Prestressed Concrete Beam

This assignment focuses on designing a continuous simply supported prestressed concrete beam with two spans. The beam is designed to carry a 120mm thick concrete deck under specified loads. The design process involves analyzing the stresses in various sections of the beam, including bound and unbounded tendons. Additionally, the assignment examines shear capacity, torsion capacity, and requires the determination of necessary reinforcement for these aspects. Various references are cited throughout the document to support the design principles and calculations.

Table of Contents
Introduction:..........................................................................................................................................1
Project Description:...............................................................................................................................1
Literature review...............................................................................................................................1
Summery:..............................................................................................................................................6
References.............................................................................................................................................7
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Introduction:
Objective:
“To design continuous simply supported prestressed concreate beam “
Definition
To design simply supported prestressed concrete beam which supported by two spans. The
beam carries 120 mm thick with concrete slab which have nominal live load 25 kN/m.
length of each span 16 m, effective width 860 mm. to discuss the suitability of beam section
from standard I-Girder sections. Obtain the prestressed force and eccentricity.
Project Description:
Literature review
Prestressed concrete is the fundamental concrete in which internal stress through suitability
magnitude and distribution are obtain. The resulting of prestressed is to obtain desire degree
of beam. Materials are used for preparing prestressed concreate beam such as concreate,
cement and steel. Also, beam strength depends on the grade of concreate and steel, higher
grades means more durable and good strength. In case fully prestressed beam, the beam is
free from tensile stress at working condition. Dead weight may counter balance through
eccentric prestressed load. The prestressed is effective for shear force due to compression
and eccentric load.
The prestressed compressed applied at the axial or eccentric loading situation and stress
induce due to external load below the neutral axis of the entire beam. Resulting of the beam
could tension or compression position.
Following data are given for the design prestressed concrete beam with simply supported
beam.
Concrete strength f '
c=60 MPa
Rebar Strength fy=60 MPa
Tendon Tensile strength fpu=1862 MPa
Standard Girder cross section:
Cross section area A=317 x 103 mm2
Section Modulus Zt=82.9 x 106 mm3
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Zb=91.1 x 106 mm3
Ixx=49900 x 106 mm4
Y b =548 mm
Cross section of Beam section from I-Girder Section:
T = 450 mm
B = 500 mm
C = 150 mm
D = 1150 mm
E = 175 mm
F = 150 mm
G = 130 mm
W = 150 mm
The tendon force immediately induce after prestressed transfer to the concrete beam cross
section:
Pi=1070.8 MPa
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Tendon force at the service load after allowance losses:
Pe=856.6 MPa
Further tendon behaviour obtain in order to applied external force.
The moment induce due to self-weight of beam M G = 1413 kN m
Momentduedeadload M D=1356 kN −m
MomentdueLiveload M L=1836 kN −m
FactoredShearforce V u =1112kN −m
FactoredtorsionalMoment T u=71 kN −m
Obtain the transfer loading condition:
The eccentric obtained (Prestressed eccentricity) e=745.51 mm
Minimum Top Fibre Stress Fti=−4.005 MPa
Minimum bottom fibre Stress Fbi=22.753 MPa
Maximum allowable Stress Fsi=1303.109 MPa
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Figure: eccentricity produce due to external loading
f si=1340.341 MPa> F si
Fti=Pi ( 1
A − e
St ) + M G
St
=0.630 MPa>−Fti ( Satisfactory )
Fbi=Pi ( 1
A − e
Sb )+ M G
Sb
=12.95 MPa<Fbi ( Satisfactory )
Check Serviceability load condition:
Fte=0.6 f ' c=24.821 MPafortotalload
Fte ,G+ D=0.4 f ' c=16.547 MPa .. forsustainedloadsonly
Maximum fibre stress
Fbe=− ( 0.3 ∨6 ) f ' c0.5=−3.204 MPa
Maximum allowable stress
Fse=0.8 fy=1340.341 MPa .. Satisfactory
Fte=Pe ( 1
A − e
St ) + M G + M D + M L
St
=2.602 MPa< Fte ( Satisfactory )
M
0.5 (|G+ M D ) + M L
Sct
=2.344 MPa< Fte ( Satisfactory )
Fte ,G+ D=0.5 Pe ( 1
A − e
Sb ) +¿
¿
Fbe=Pe ( 1
A + e
Sb ) − M G + M D + M L
Scb
=3.455 MPa >−Fbe ( Satisfactory )
Check ultimate load condition
Compression Zone Factor β 1=0.75
Tendon Type Factor γp=0.280
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Ratio of Tension Reinρ=0.002
Ratio of Compression Rein ρ' =0.003
Ratio of prestressed Rein ρp=0.002
Index of Tension Reinf ω=¿ 0.022
Index of Compression Reinf ω ' = 0.033
Index of Prestressed. Reinf ω p = 0.086
Factor ultimate moment
Mu=γ ( βD M D + βL M L )
1.3 ( 1. ( MG +MD ) +1.67 ML )
Stress in Bound Tendons:
5594.134 MPa
1743.436 MPa
Stress in Unbounded Tendons:
Apsfps ( dp−dc ) + Asfy ( d−dc ) + Asfy ( dc−d ) =0.01469 kN −m> Mu … Satisfactory
∅ Mn=∅
1.2 Mcr=1.2 Sb [ Pe ( 1
Ac + e
Sb )+7.5 √fc ]−MG ( Scb
Sb −1 )=7 kN −m<∅ Mn ( Satisfactory )
Check Shear Capacity:
d= Max ( 0.8 h , dp )=1625.60 mm
√fc=MN (100 , √f ' cproved )=0.53 MPa
Vc= {Max {Min (0.6 √fc+700 Min (1 , Vudp
Mu ) )bwd , 5 bwd √fc }], 2bwd √fc }=517.75 kN
2 bwd √fc , forfsc <0.4 fpu
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Similarly for Vs
Vs=Min (Avfy d
s , 8 bwd √ fc )=1252.62 kN
Av=4.173 mm2
Smax= { Min ( 0.75 d , 24 ) , forVs≤ 4 bwd √fc
Min ( 0.375 d , 12 ) , forVs>4 bwd √fc=304.8mm
Noshearreinforcedrequire , forcase1 : Vu<∅ Vc
2
Av ( min ) , forcase2 :∅ Vc
2 ≤Vu<∅ Vc
Av , cal , Av ( min ) , forcase3 :∅ Vc ≤Vu ≤∅ ( Vs+Vc )
¿ ¿ unsatifactory , case4 :∅ ( Vs+Vc ) ≤ Vu
MAX =13.277 mm 2
Av , required=¿
¿
Check the torsion capacity:
As
S = Tu
1.7 ∅ Aohfvvcos 37.5 =0.013
Tu>∅ √ fc ( ACP
2
Pcp ) √ 1+ fpc
4 √ fc =0.015 Kn−m
Thus, Torsional Reinforcement Required.
AL=Max [ ( At
s ) Ph ( fyv
fyL ) cot 2 ( 37.5 ) , 5 Acp √ fc
fyL −Ph ( fyy
fyL ) Max ( At
S , 25 bw
fyv ) ] =80.95 mm 2
Additional longitudinal Reinforcement require for torsion.
( At
S )Total , RequD
=Max ( Av+ 2 At
s , 50 bw
fyy )=0.069< ( At
S )ProvD
=0.073
Satisfactory
Summery:
Distance to Centroid of compression d=114 mm
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Distance to centroid of Prestressed dp=1626 mm
Distance to centroid of tension d=1727 mm
Girder Span Length L=24.38 m
Girder spacing S=2.44 m
Concrete Deck Thickness t=203 mm
Section properties:
A=28575 mm 2
Yt=880.0863 mm
Yb=948.71 mm
I=19357968 mm4
St =558685 mm3
Sb =518274 mm3
References
https://www.researchgate.net/profile/Michael_Kotsovos/publication/
248122582_Toward_a_Consistent_Design_of_Structural_Concrete/links/
59cc94c80f7e9bbfdc3f7515/Toward-a-Consistent-Design-of-Structural-
Concrete.pdf. Accessed January 22, 2018.
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. Technopress3000com. 2018. Available at:
http://technopress3000.com/yahoo_site_admin/assets/docs/Web-Content-
PC-3rd.2211508.pdf. Accessed January 22, 2018.
https://www.researchgate.net/profile/Charles_Dolan2/publication/
275622990_Flexural_Design_of_Prestressed_Concrete_Beams_Using_FRP_
Tendons/links/5539aac30cf226723aba31fd.pdf. Accessed January 22,
2018.
http://www.pci.org/Design_Resources/Guides_and_Manuals/References/
Bridge_Design_Manual/JL-69-
April_Design_of_Continuous_Highway_Bridges_with_Precast_Prestressed_
Concrete_Girders/. Accessed January 22, 2018.
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