## 077

2. Support section stresses

Check is made at the support face (a slightly less conservative check can be made at 50db from end)

615 V 97

b 615 97

= -2,202 psi (C) (15.2 MPa) < 0.60fi = -2,250 psi, OK

B. After the slab is cast and at service load, the support section stresses both at top and bottom extreme fibers were found to be below the allowable; hence, OK.

Summary of midspan stresses (psi)

Transfer Pe only WD at transfer Net at transfer External load (WL) Net total at service

3. Camber and deflection ca1cu1ation At transfer Initial

Eci = 57,000p3,570 = 3.49 x 106 psi (2.2 x 104 MPa) From before, 28 days

Due to initial prestress only, from Figure 8.10

_ (—347,004)(18.73)(72 x 12)2 = 8(3.49 x 106)59,720

24(3.49 x 106)59,720 = -2.90 + 0.30 = -2.6 in. (66 mm) "

Self-weight intensity w = 641/12 = 53.42 lb/in.

5wl4

- for uncrac g

Self-weight dD =- for uncracked section g D 384£ciig

Thus, the net camber at transfer is

4. Immediate service load deflection A. Effective Ie method Modulus of rupture fr = 7 . 5^/f7 = 7. 5p5000 = 530 psi fb at service load = 817 psi (5.4 MPa) in tension (from before). Hence, the section is cracked and the effective Ie from Equation 8.92a or 8.92b should be used dp = 18. 73 + 10 .02 + 2(topping) = 30 . 75 in . (780 mm)

From Equation 8.93

np = 28 .5 x 106/4.03 x 106 = 7 to be used in Equation 8 . 93

Equation 8.93a gives Icr = 11,110 in.4 (4.63 x 105 cm4), use. From Equation 8.93a and the stress fpe and fd values already calculated for the bottom fibers at midspan with fr = 7 . 5yf = 530 psi. Moment Mcr due to that portion of live load that causes cracking is

Ma, unfactored maximum live load moment = 2,177,288 in.-lb

Mcr 1,275,652

Ma 2,177,288

where Mcr is the moment due to that portion of the live load that causes cracking and Ma is the maximum service unfactored live load.

Using the preferable PCI expression of (Mcr/Ma) from Equation 8.91b, and the stress values previously tabulated

Ma fL V 693

Hence, from Equation 8.92b

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