Draft

12.1Introduction 199

If we considerthefollowing:

1. Anunstressedsteelcableof lengthls


2. A concretebeamof lengthlc


3. Prestressthebeamwiththecable,resultingin a stressedlengthof concreteandsteel

equaltol

0

s

=l

0

c

.

4. Dueto shrinkageandcreep,therewillbe a changein length

lc= ("sh+"cr)lc (12.1)

we want to make surethatthisamoutof deformationis substantiallysmallerthanthe

stretch of thesteel(forprestressingto be eective).

5. Assumingordinarysteel:fs= 30ksi,Es= 29; 000 ksi,"s=

30

29 ; 000

= 1: 03  10

 3

in=in

6. Thetotalsteelelongationis"sls= 1: 03  10

 3

ls

7. Thecreepandshrinkagestrainsareabout"cr+"sh': 9  10

3

8. Theresidualstreswhich is leftin thesteelaftercreepandshrinkagetookplaceis thus

(1: 03 :90) 10

 3

(29 10

3

) = 4ksi (12.2)

Thus thetotallossis

30 4

30

= 87%which is unacceptablytoo high.

9. Alternativelyif initialstresswas 150ksiafterlosseswe wouldbe leftwith 124 ksior a

17%loss.

10.Notethattheactuallossis (: 90  10

 3

)(29 10

3

) = 26ksiin each case

9 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 eective yield.

10 Steelrelaxationis thereductionin stress atconstant strain(asopposedtocreepwhich

is reductionof strainat constant stress)occrs. Relaxationoccursindenitelyandproduces