Lecture 4. beam, column, slab design for RC

Beam, column slab

1. Beam 3 6#9 bar 20” 17.5” 2.5” fc’ = 4000 psi fy = 60000 psi As = 6 x 1 = 6 in 2 dt=20- 2.5 = 17.5 in dcg = y = ε Ay/ ε A = (( 4 x 1x 2.5 )+ ( 2 x1 x 4.628 ))/6 = 3.21 in Effective depth, dt = 20 – 3.21 = 16.79 in Use dt = 17.5 ‘’ 1” 2.5 + 1.128+1

2. 6 2.9

3. 6 8.8 8.8 10.3 10.3 10.3 0.00189 16.8

4. Doubly reinforced design

5. 12’’ 20’’ 6#9 3#9 fc’ = 4000 psi fy = 60000 psi 2.5’’ 2.5’’ 350.13 Kips 360 Kips

6. Select c= d/4 ( or ) d/3 = 17.5/4 ( 0r ) 17.5/3 = 4.375 ( or ) 5.833 Assume c = 5 ‘’ c= a / ϐ 1 a = c ϐ 1 = 5 x 0.85 = 4.25’’ εs ’ = (c-d’/c) ε cu = ( 5 – 2.5/5 ) 0.003 = 0.0015< εs = 0.00207 fs’ =Es εs ’ = 29000 x 0.0015 43.5 ksi < fy Cs = As’ ( fs’ -0.85fc’ ) = 3 ( 43.5 – 0.85 x 4 ) = 120.3 Kips Cc = 0.85fc’ba = 0.85 x 4 x 12 x 4.25 = 173.4 Kips C = Cs + Cc = 1230.3+173.4 = 293.7 Kips T = As fy = 6 x 60 = 360 Kips 360 – 293.7 293.7 X 100 % = 23 % < 5% ( not Ok ) 293.7

7. Reassume c = 5.5 ‘’ c= a / ϐ 1 a = c ϐ 1 = 5.5 x 0.85 = 4.675’’ εs ’ = (c-d’/c) ε cu = ( 5.5 – 2.5/5.5 ) 0.003 = 0.0016< εs = 0.00207 fs’ =Es εs ’ = 29000 x 0.0016 46.4 ksi < fy Cs = As’ ( fs’ -0.85fc’ ) = 3 ( 46.4 – 0.85 x 4 ) = 129 Kips Cc = 0.85fc’ba = 0.85 x 4 x 12 x 4.675 = 190.74 Kips C = Cs + Cc = 319.74 Kips T = As fy = 6 x 60 = 360 Kips 360 – 319.74 319.74 X 100 % = 13 % < 5% ( not Ok )

8. Reassume c = 6‘’ c= a / ϐ 1 a = c ϐ 1 = 6 x 0.85 = 5.1’’ εs ’ = (c-d’/c) ε cu = ( 6 – 2.5/6) 0.003 = 0.00175< εs = 0.00207 fs’ =Es εs ’ = 29000 x 0.00175 50.75 ksi < fy Cs = As’ ( fs’ -0.85fc’ ) = 3 (50.75– 0.85 x 4 ) = 142.05Kips Cc = 0.85fc’ba = 0.85 x 4 x 12 x 5.1 = 208.08 Kips C = Cs + Cc = 350.13 Kips T = As fy = 6 x 60 = 360 Kips 360 – 350.13 350.13 X 100 % = 2.8% < 5% (Ok ) εs = d-c/c εcu = 16.79 – 6 / 6 x 0.003 = 0.00540 > εy = 0.00207

9. Mn = C c ( d-a/2) + C s ( d-d’) = ( 208.08 ( 16.75 – 5.1/2 ) + 142.05 ( 16.75 – 2.5 ))x1/12 = 416.37 K -ft Mn = T ( d-a/2) =360 (16.8- 5.1/2)x 1/12 = 427.5 K –ft Mn = ( 416.37 + 427.5 ) /2 = 421.93 K –ft Mu = ØMn = 0.9 x 421.93 = 379.73 K -ft