Design of FlatSlab - University of Asia Pacific

1 Design of Flat Slab (with edge beams) by Direct Design Method 16 14 14 3 C1 C2 C3 C4 13 C5 C6 C7 C8 C9 14 C10 C12

2 C13 C14 C15 C16 13 C17 C18 C19 C20 Building Plan Assume S = (16 + x/4), Building spans = (S, S2, S2, 3) by (S3, S2, S3, 6) Building Height = 4@10 = 40 Loads: LL = 40 psf, FF = 20 psf, RW = 20 psf [ , (40 + x/2), (20 + x/4), (20 + x/4) psf] Material Properties: fc = 3 ksi, fs = 20 ksi [ , fc = (3 + x/20) ksi, fs = (20 + x/4) ksi 6 7 7 7 7 (S1) (S3) (S6) (S8) (S4) (S5) 8 7 B1 B3 B4 B5 B6 B7 B8 B9 B10 B12 (S10) (S9) (S11) C11 (S2) (S7) B11 B2 7 7 7 7 Design of Slabs Maximum Clear Span = 15 Slab with edge beam, fy = 40 ksi Slab thickness = Ln( + fy/200)/36 = 15 ( + 40/200) 12/36 = 5.]

3 , assume 6 thick slab Self weight = 6150/12 = 75 psf Total load on slab = 75 + 20 + 20 + 40 = 155 psf = ksf For Design , n = 9, k = , j = , R = ksi d = 5 (or for Mmin) As = M/fsjd = M12/( ) = (or for Mmin) Mc(max) = Rbd2 = = k/ And, allowable punching shear stress, punch = 2fc = 2(3/1000) = ksi Also, As(Temp) = bt = = in2/ Edge Beam Section and Properties The edge beam is made of two rectangular sections 1216 and 106 y = (12168 +1063)/(1216 +106) = (1536 + 180)/(192 + 60) = Moment of Inertia of external beam-slab, Ib = 1063/3 + 12163/3 (192 + 60) = 5419 in4 Torsional rigidity of edge beam, C = ( ) 12316/3 + ( ) 6310/3 = 5309 in4 10 6 10 12 Panels in the Long Direction Panel 1 Width = 7; Moment of Inertia of edge slab, Is 71263/12 = 1512 in4 For the edge beam along panel length.

4 1 = EcbIb/EcsIs = 5419/1512 = , for all slabs t for Slab (S1) and (S3) = EcbC/2 EcsIs = 5309/(21512) = , and for Slab S2 = Column strip = Short span (c/c)/4 = 13/4 = , Middle strip = = Slab (S1) Slab size (= 1613 c/c) = 1512 M0 = wL2Ln2/8 = = k Support (d) MExt = M0 = k, M+ = M0 = k, MInt = M0 = k [Note: The Equivalent Frame Method does a more rational analysis in the above steps only] L2/L1 = 13/16 = , 1L2/L1 = Total column strip moments are MCExt = MExt = k; , = k in beam, = k/ in slab MC+ = M+ = k; , = k in beam, = k/ in slab MCInt = MInt = k; , = k in beam, = k/ in slab Total middle strip moments are MMExt = = k; , = k/ in slab MM+ = = k; , = k/ in slab MMInt = = k.

5 , = k/ in slab Slab (S2) Slab size (= 1413 c/c) = 1312 M0 = wL2Ln2/8 = = k Interior Support MInt = M0 = k, M+ = M0 = k, MInt = M0 = k L2/L1 = 13/14 = , 1L2/L1 = Total column strip moments are MCInt = MInt = k; , = k in beam, = k/ in slab MC+ = M+ = k; , = k in beam, = k/ in slab MCInt = MInt = k; , = k in beam, = k/ in slab Total middle strip moments are MMInt = = k; , = k/ in slab MM+ = = k; , = k/ in slab MMInt = = k; , = k/ in slab Slab (S3) Slab size (= 1413 c/c) = 1312 Column strip = , Middle strip = M0 = wL2Ln2/8 = = k Support (d) MExt = M0 = k, M+ = M0 = k, MInt = M0 = k L2/L1 = 13/14 = , 1L2/L1 = Total column strip moments are MCExt = MExt = k; , = k in beam, = k/ in slab MC+ = M+ = k; , = k in beam, = k/ in slab MCInt = MInt = k.

6 , = k in beam, = k/ in slab Total middle strip moments are MMExt = = k; , = k/ in slab MM+ = = k; , = k/ in slab MMInt = = k; , = k/ in slab Panel 2 Width = ; In case of Slab (S2), the Design for Panel 2 is similar to the Design for Panel 1 For Slab (S1) and Slab (S3), Moment of Inertia of edge slab, Is = 1404 in4 For these two slabs, no beam along panel length; 1 = 0 Transverse edge beam t = EcbC/2 EcsIs = 5309/(21404) = Column strip = , Middle strip = = Slab (S1) Slab size (= 1613 c/c) = 1512 M0 = wL2Ln2/8 = = k Support (d) MExt = M0 = k, M+ = M0 = k, MInt = M0 = k L2/L1 = 13/16 = , 1L2/L1 = 0 Total column strip moments are MCExt = MExt = k; , = k/ in slab MC+ = M+ = k; , = k/ in slab MCInt = MInt = k; , = k/ in slab Total middle strip moments are MMExt = = k.

7 , = k/ in slab MM+ = = k; , = k/ in slab MMInt = = k; , = k/ in slab Slab (S2) Similar to Slab (S2) of Panel 1. Slab (S3) Slab size (= 1413 c/c) = 1312 M0 = wL2Ln2/8 = = k Support (d) MExt = M0 = k, M+ = M0 = k, MInt = M0 = k L2/L1 = 13/14 = , 1L2/L1 = 0 Total column strip moments are MCExt = MExt = k; , = k/ in slab MC+ = M+ = k; , = k/ in slab MCInt = MInt = k; , = k/ in slab Total middle strip moments are MMExt = = k; , = k/ in slab MM+ = = k; , = k/ in slab MMInt = = k; , = k/ in slab Panel 3 Width = 7.

8 Moment of Inertia of edge slab, Is 71263/12 = 1512 in4 No beam along panel length; 1 = 0 t = EcbC/2 EcsIs = 5309/(21512) = Column strip = , Middle strip = 7 = Slab (S4) Slab size (= 1614 c/c) = 1513 M0 = wL2Ln2/8 = = k Simple Support MExt = M0 = k, M+ = M0 = k, MInt = M0 = k L2/L1 = 14/16 = , 1L2/L1 = 0 Total column strip moments are MCExt = MExt = k; , = k/ in slab MC+ = M+ = k; , = k/ in slab MCExt = MExt = k; , = k/ in slab Total middle strip moments are MMExt = = k; , = k/ in slab MM+ = = k; , = k/ in slab MMExt = = k; , = k/ in slab Slab (S5) Slab size (= 1414 c/c) = 1313 M0 = wL2Ln2/8 = = k Simple Support MExt = M0 = k, M+ = M0 = k, MInt = M0 = k L2/L1 = 14/14 = , 1L2/L1 = 0 Total column strip moments are MCExt = MExt = k; , = k/ in slab MC+ = M+ = k; , = k/ in slab MCExt = MExt = k.

9 , = k/ in slab Total middle strip moments are MMExt = = k; , = k/ in slab MM+ = = k; , = k/ in slab MMExt = = k; , = k/ in slab Panel 4 Similar to Panel 3. Panel 5 Similar to Panel 2. Panel 6 Similar to Panel 1. Panels in the Short Direction Panel 7 Width = ; Moment of Inertia of edge slab, Is = 1836 in4 For the edge beam along panel length; 1 = EcbIb/EcsIs = 5419/1836 = , for all the slabs For Slab (S1) and (S6), t = EcbC/2 EcsIs = 5309/(21836) = , while t = 0 for Slab (S4).

10 Slab (S1) Slab size (= 1316 c/c) = 1215 Column strip = Short span (c/c)/4 = 13/4 = , Middle strip = 8 = M0 = wL2Ln2/8 = = k Support (d) MExt = M0 = k, M+ = M0 = k, MInt = M0 = k L2/L1 = 16/13 = , 1L2/L1 = Total column strip moments are MCExt = MExt = k; , = k in beam, = k/ in slab MC+ = M+ = k; , = k in beam, = k/ in slab MCInt = MInt = k; , = k in beam, = k/ in slab Total middle strip moments are MMExt = = k; , = k/ in slab MM+ = = k; , = k/ in slab MMInt = = k; , = k/ in slab Slab (S4) Slab size (= 1416 c/c) = 1315 Column strip = Short span (c/c)/4 = 14/4 = , Middle str