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Prestress Concrete Stress Analysis

This document summarizes the calculation of stresses in a prestressed concrete double-tee beam at transfer and at service loads. Stresses are checked at the assumed transfer point and at midspan. At transfer, the extreme fiber stresses are found to be below the permissible limits of -355 psi in tension and +2450 psi in compression. At service loads under sustained and total loads, the stresses are also below the permissible limits of +2250 psi in sustained compression, +3000 psi in total compression, and -849 psi in tension.

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Mario Antonio Gomez Cruz
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223 views3 pages

Prestress Concrete Stress Analysis

This document summarizes the calculation of stresses in a prestressed concrete double-tee beam at transfer and at service loads. Stresses are checked at the assumed transfer point and at midspan. At transfer, the extreme fiber stresses are found to be below the permissible limits of -355 psi in tension and +2450 psi in compression. At service loads under sustained and total loads, the stresses are also below the permissible limits of +2250 psi in sustained compression, +3000 psi in total compression, and -849 psi in tension.

Uploaded by

Mario Antonio Gomez Cruz
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© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Example 24.

2—Investigation of Stresses at Prestress Transfer and at Service Load

For the simply supported double-tee considered in Example 24.1, check all permissible concrete stresses im-
mediately after prestress transfer and at service load assuming the unit is used for roof framing. Use losses
computed in Example 24.1.

live load = 40 psf


roof load = 20 psf 10' - 0"
dead load = 47 psf = 468 plf 2"
5 3/4"
span = 48 ft
fci′ = 3500 psi
fc′ = 5000 psi
8 - 0.5 in. diameter low-relaxation strands .. .. 24"
.. ..
Aps = 8 (0.153 in.2) = 1.224 in.2 ..
..
..
..
.. ..
e = 9.77 in. (all strands straight) . . 8"
fpu = 270,000 psi 5' - 0"
fpy = 0.90fpu
3 3/4"
jacking stress = 0.74fpu = 200 ksi
stress after transfer = 193 ksi
force after transfer = Pp = 1.224 3 193 = 236 kips

Section Properties
Ac = 449 in.2
Ic = 22,469 in.4
yb = 17.77 in.
yt = 6.23 in.
V/S = 1.35 in.

Code
Calculations and Discussion Reference

1. Calculate permissible stresses in concrete. 18.4

At prestress transfer (before time-dependent losses): 18.4.1

Compression: 0.60 fci′ = 0.60(3500) = 2100 psi

Compression at the ends = 0.70› = 0.70(3500) = 2450 psi

Tension: 6 fci′ = 355 psi (at ends of simply supported members; otherwise 3 fci′ )

At service load (after allowance for all prestress losses): 18.4.2

Compression: 0.45 fc′ = 2250 psi - Due to sustained loads


Compression: 0.60 fc′ = 3000 psi - Due to total loads

Tension: 12 fc′ = 849 psi 18.3.3(b)

2. Calculate service load moments at midspan:

24-22
Code
Example 24.2 (cont’d) Calculations and Discussion Reference

w d l2 0.468 × 48 2
Md = = = 134.8 ft-kips (beam dead load)
8 8

w ds l2 0.02 × 10 × 48 2
Mds = = = 57.6 ft-kips (roof dead load)
8 8
Msus = Md + Mds = 134.8 + 57.6 = 192.4 ft-kips (sustained load)

w l l2 0.04 × 10 × 48 2
M l = = = 115.2 ft-kips (live load)
8 8
Mtot = Md + Mds + Ml = 134.8 + 57.6 + 115.2 = 307.6 ft-kips (total load)

3. Calculate service load moments at transfer point

Assume transfer point located at 50db = 25 in. from end of beam. Assume distance from 11.4.3
end of beam to center of support is 4 in. Therefore, x = 25 - 4 = 21 in. = 1.75 ft.

wdx 0.468 × 1.75


Md = (l - x) = (48 - 1.75) = 18.9 ft-kips (beam dead load)
2 2
Additional moment calculations at this location are unnecessary because conditions im-
mediately after release govern at this location.

4. Calculate extreme fiber stresses by “linear elastic theory” which leads to the following
well known formulas:

P Pey t My t
ft = - +
A I I

P Pey b My b
fb = + -
A I I
where, from Example 24.1

P = Pp = 236 kips (immediately after transfer)

P = Pe = 219 kips (at service load)

24-23
Code
Example 24.2 (cont’d) Calculations and Discussion Reference

Table 24-6 Stresses in Concrete Immediately after Prestress Transfer (psi)


At Assumed Transfer Point At Mid Span
Top Bottom Top Bottom
Pp/A +526 +526 +526 +526
Ppey/I -639 +1824 -639 +1824
Mdy/I +63 -180 +448 -1279
Total -50 (O.K.) +2170 (O.K.) +335 (O.K.) +1071 (O.K.)
Permissible -355 +2450 +2100 +2100
Compression (+)
Tension (-)

Table 24-7 Stresses in Concrete at Service Loads (psi)


At Midspan – Sustained Loads At Midspan – Total Loads
Top Bottom Top Bottom
Pe/A +488 +488 +488 +488
Peey/I -594 +1695 -594 +1695
My/I +640 -1826 +1023 -2919
Total +534 (O.K.) +357 (O.K.) +917 (O.K.) -736 (O.K.)
Permissible +2250 +2250 +3000 -849
Compression (+)
Tension (-)

24-24

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