Draft
12.1Introduction 199
If we considerthefollowing:
- Anunstressedsteelcableof lengthls
- A concretebeamof lengthlc
- Prestressthebeamwiththecable,resultingin a stressedlengthof concreteandsteel
equaltol
0
s=l
0
c.
- Dueto shrinkageandcreep,therewillbe a changein length
lc= ("sh+"cr)lc (12.1)
we want to make surethatthisamoutof deformationis substantiallysmallerthanthe
stretch of thesteel(forprestressingto be e ective).
- Assumingordinarysteel:fs= 30ksi,Es= 29; 000 ksi,"s=
30
29 ; 000
= 1: 03 10
3
in=in- Thetotalsteelelongationis"sls= 1: 03 10
3
ls- Thecreepandshrinkagestrainsareabout"cr+"sh': 9 10
3
- Theresidualstreswhich is leftin thesteelaftercreepandshrinkagetookplaceis thus
(1: 03 :90) 10
3
(29 103
) = 4ksi (12.2)Thus thetotallossis
30 4
30
= 87%which is unacceptablytoo high.
- Alternativelyif initialstresswas 150ksiafterlosseswe wouldbe leftwith 124 ksior a
17%loss.
10.Notethattheactuallossis (: 90 10
3
)(29 103
) = 26ksiin each case9 Havingshownthatlosseswouldbe too highforlow strengthsteel,we willuse
Strandsusuallycomposedof 7 wires.Grade 250 or 270ksi,Fig.12.3.
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Figure12.3: 7 WirePrestressingTendon
Tendonhave diametersrangingfrom1/2to 1 3/8of aninch. Grade 145 or 160ksi.
Wires comein bundlesof 8 to 52.
Notethatyieldstressis notwell de nedforsteelusedin prestressedconcrete,usuallywe take
1%strainas e ective yield.
10 Steelrelaxationis thereductionin stress atconstant strain(asopposedtocreepwhich
is reductionof strainat constant stress)occrs. Relaxationoccursinde nitelyandproduces