24.02.2017 Views

Structural Concrete - Hassoun

You also want an ePaper? Increase the reach of your titles

YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.

17.10 Transfer of Unbalanced Moments to Columns 671<br />

( )<br />

αs d √f<br />

′<br />

φV c = φ + 2<br />

b c b 0 d<br />

0<br />

α s = 40<br />

(Interior panel)<br />

( )<br />

40 × 8.75<br />

φV c = φ<br />

+ 2 ×<br />

115<br />

√<br />

4000<br />

× 115 × 8.75<br />

1000<br />

= 240.75 K<br />

φV c = φλ4 √ √<br />

4000<br />

f cb ′ 0 d =(0.75)(4)(1)<br />

1000 (115)(8.75) =190.9K(controls) > V u<br />

b. In the slab: d = 8 − 0.75 − 0.5 = 6.75 in. and b 0 is measured at 6.75/2 in. (in slab) beyond the<br />

drop panel.<br />

V u = 0.287[24 × 20 −(102.75)(90.75)∕144] =119.2K<br />

b 0 = 2(8 × 12 + 6.75)+2(7 × 12 + 6.75) =387 in.<br />

(<br />

φV c = φ 2 + 4 ) √f<br />

′<br />

β c b 0 d<br />

β = 1.2<br />

(<br />

φV c = 0.75 2 + 4 )<br />

×<br />

1.2<br />

= 660.74 K<br />

( )<br />

αs d √f<br />

′<br />

φV c = φ + 2<br />

b c b 0 d<br />

0<br />

α s = 40<br />

√<br />

4000<br />

× 387 × 6.75<br />

1000<br />

( ) √ 40 × 6.75 4000<br />

φV c = 0.75<br />

+ 2 × 387 × 6.75<br />

387 1000<br />

= 334 K (controls)<br />

√<br />

4000<br />

φV c = 0.75(4)(1) (387)(6.75) =495.6K<br />

1000<br />

Since 334 K > V u , check OK.<br />

c. One-way shear is not critical.<br />

4. Calculate the total static moments in the long and short directions:<br />

M 0l = 0.287(20)(22.33)2<br />

8<br />

M 0s = 0.287(24)(18.33)2<br />

8<br />

= 357.8K⋅ ft<br />

= 289.3K⋅ ft<br />

The width of column strip in each direction is 20 = 10 ft, whereas the width of the middle strip is<br />

2<br />

10 ft in the long direction and 14 ft in the short direction.<br />

5. Calculations of moments and steel reinforcement are shown in Table 17.11. Use an average<br />

d = 10 − 1.5 = 8.5 in. in the column strip and d = 8 − 1.5 = 6.5 in. in the middle strip.<br />

Bars are chosen for adequate distribution in both the column and middle strip. Reinforcement<br />

details are similar to those in flat-plate examples.

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!