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Design of Waffle Slab (without beams) by Direct Design Method
32 32 32
C1 C2 C3 C4
32
C5 C6 C7 C8
32
C9 C10 C11 C12
32
C13 C14 C15 C16
Building Plan
Assume S = (32 + x/2) , Building spans = (S, S, S) by (S, S, S)
Building Height = 4@10 = 40
Loads: LL = 40 psf, FF = 20 psf, RW = 20 psf [i.e., (40 + x/2), (20 + x/4), (20 + x/4) psf]
Material Properties: f c = 3 ksi, fs = 20 ksi [i.e., f c = (3 + x/20) ksi, fs = (20 + x/4) ksi
(S1) (S1)
(S1) (S1)
(S2) (S2)
16.5 16 16 16.5
B1 B3
B4 B5
B6 B7
B8 B9
B10 B12
16.5
16
16
16.5
16
16
16 16
(S3)
(S2)
(S2)
B2
B11
Design of Slabs and Ribs
Slabs
Assuming 10 square pans per slab; i.e., (3.2 3.2 ) c/c and (2.7 2.7 ) clear spans (with 6 ribs)
Slab thickness = 2.5 Self weight = 2.5 150/12 = 31.25 psf
Total load on slab, w = 31.25 + 20 + 20 + 40 = 111.25 psf = 0.111 ksf
Maximum Moment for an edge-supported (2.7 2.7 ) slab with Support condition Case 2
M( )
max = 0.045 wL2
= 0.045 0.111 (2.7)2
= 0.0365 k /
Modulus of rupture = 5 fc = 5 (3/1000) = 0.274 ksi; i.e., Allowable tensile stress = 0.274/2 = 0.137 ksi
Ssect = bh2
/6 0.0365 = h2
/6 0.137 hreq = (0.0365 6/0.137) = 1.26
Slab thickness, h = 2.5 is OK; i.e. d = 2 As(Temp) = 0.0025 bh = 0.0025 12 2.5 = 0.075 in2
/ft
Use appropriate wire mesh to provide the required As(Temp); i.e., 1/8 -wire diameter (2 2 ) mesh
Ribs
Maximum clear span = 31 ; Slab without edge beam and fy = 40 ksi
Slab thickness = Ln(0.8 + fy/200)/33 = 31 (0.8 + 40/200) 12/33 = 11.27
Assume 18 thickness; i.e., 13.5 below slab, with bw = 6
Average thickness without column head = 18 {(2.7 2.7) 15.5}/(3.2 3.2) = 6.97
If column head covers (5 5 = 25) square pans, average thickness of slab
= 6.97 + {25 (2.7 2.7) 15.5}/(32 32) = 9.72
Assuming the entire slab thickness to be = 9.72
Self weight = 9.72 150/12 = 121.5 psf
Total load on slab = 121.5 + 20 + 20 + 40 201.5 psf = 0.202 ksf
For design, n = 9, k = 0.378, j = 0.874, R = 0.223 ksi
d = 18 1.5 = 16.5 ; As = M/fsjd = M 12/(20 0.874 16.5) = M/24.04
Moment capacity Mc(max) = Rbd2
= 0.223 1 16.52
= 60.70 k / , or 30.35 k /rib
Also, As(Temp) = 0.0025 bt = 0.0025 12 18 = 0.54 in2
/ ; or 0.27 in2
/rib
Punching shear force in slab 0.202 {322
(16 + 2/12)2
} = 153.71 k
and in column head 0.202 {322
(12/12 + 16.5/12)2
} = 205.25 k
Stresses are = 153.71/(4(16 12 + 2) 2) = 0.099 ksi and = 205.25/(4(12 + 16.5) 16.5) = 0.109 ksi
Allowable punching shear stress, punch = 2 fc = 2 (3/1000) = 0.110 ksi OK for punching shear
Panels in the Long and Short Direction
Panel 1 (and all other panels)
Width of Panel = 16.5
No edge beam along panel length; 1 = 0, for all slabs
Also no transverse beam t = 0, for all slabs
Column strip = Short span (c/c)/4 = 32/4 = 8 , Middle strip = 16 8 = 8 (i.e., 2.5 pans per strip)
Slab (S1)
Slab size (= 32 32 c/c) = 31 31
M0 = wL2Ln
2
/8 = 0.202 16.5 312
/8 = 399.48 k
Support (c) MExt = 0.26 M0 = 103.87 k , M+
= 0.52 M0 = 207.73 k , MInt = 0.70 M0 = 279.64 k
L2/L1 = 32/32 = 1.0, 1L2/L1 = 0
Total column strip moments are
MCExt = 1.00 MExt = 103.87 k ; i.e., 103.87 k /8 = 12.98 k / ; AsCExt = 12.98/24.04 = 0.54 in2
/
MC
+
= 0.60 M+
= 124.64 k ; i.e., 124.64 k /2.5 rib = 49.86 k / ; ACExt
+
= 49.86/24.04 = 2.07 in2
/rib
MCInt = 0.75 MInt = 209.73 k ; 209.73 k /8 = 26.22 k / ; AsCInt = 26.22/24.04 = 1.09 in2
/
Total middle strip moments are
MMExt = 103.87 103.87 = 0 k ; i.e., 0 k /8 = 0 k / ; AsMExt = 0/24.04 = 0.0 in2
/
MM
+
= 207.73 124.64 = 83.09 k ; i.e., 83.09 k /2.5 rib = 33.24 k /rib; AM
+
= 33.24/24.04 = 1.38 in2
/rib
MMInt = 279.64 209.73 = 69.91 k ; i.e., 69.91 k /8 = 8.74 k / ; AMInt
+
= 8.74/24.04 = 0.36 in2
/
Slab (S2)
Slab size (= 32 32 c/c) = 31 31
M0 = wL2Ln
2
/8 = 0.202 16.5 312
/8 = 399.48 k
Interior Support MInt = 0.65 M0 = 259.67 k , M+
= 0.35 M0 = 139.82 k , MInt = 0.65 M0 = 259.67 k
L2/L1 = 32/32 = 1.0, 1L2/L1 = 0
Total column strip moments are
MCInt = 0.75 MExt = 194.75 k ; i.e., 194.75 k /8 = 24.34 k / ; AsCInt = 24.34/24.04 = 1.01 in2
/
MC
+
= 0.60 M+
= 83.89 k ; i.e., 83.89 k /2.5 rib = 33.56 k /rib; AsM
+
= 33.56/24.04 = 1.40 in2
/rib
MCInt = 0.75 MInt = 194.75 k ; i.e., 194.75 k /8 = 24.34 k / ; AsCInt = 24.34/24.04 = 1.01 in2
/
Total middle strip moments are
MMInt = 259.67 194.75 = 64.92 k ; i.e., 64.92 k /8 = 8.11 k / ; AsMInt = 8.11/24.04 = 0.34 in2
/
MM
+
= 139.82 83.89 = 55.93 k ; i.e., 55.93 k /2.5 rib = 22.37 k /rib; AsM
+
= 22.37/24.04 = 0.93 in2
/rib
MMInt = 259.67 194.75 = 64.92 k ; i.e., 64.92 k /8 = 8.11 k / ; AsMInt = 8.11/24.04 = 0.34 in2
/
Denoting slab reinforcement by in2
/ ( ve) and rib reinforcement by in2
/rib (+ve highlighted)
Ribs within Column Strip
Ribs within Middle Strip
0.54 2.07 1.09 1.01 1.40 1.01 1.09 2.07 0.54
0.00 1.38 0.36 0.34 0.93 0.34 0.36 1.38 0.00
0.54 2.07 1.09 1.01 1.40 1.01 1.09 2.07 0.54
0.54 2.07 1.09 1.01 1.40 1.01 1.09 2.07 0.54
0.00 1.38 0.36 0.34 0.93 0.34 0.36 1.38 0.00
0.54 2.07 1.09 1.01 1.40 1.01 1.09 2.07 0.54
0.54 2.07 1.09 1.01 1.40 1.01 1.09 2.07 0.54
0.00 1.38 0.36 0.34 0.93 0.34 0.36 1.38 0.00
0.54 2.07 1.09 1.01 1.40 1.01 1.09 2.07 0.54
1 #4 extra top between
alternate #4 bars
2 #9 through
#4 @ 4.5 c/c within slab
2 #8 through
#4 @ 7.5 c/c
A
A
Section A-A
3.2
2 #9
#4@ 4.5 c/c
B
B
Section B-B
3.2
2 #9
#4@ 4.5 c/c
+ extra top

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perhitungan waffle slab

  • 1. Design of Waffle Slab (without beams) by Direct Design Method 32 32 32 C1 C2 C3 C4 32 C5 C6 C7 C8 32 C9 C10 C11 C12 32 C13 C14 C15 C16 Building Plan Assume S = (32 + x/2) , Building spans = (S, S, S) by (S, S, S) Building Height = 4@10 = 40 Loads: LL = 40 psf, FF = 20 psf, RW = 20 psf [i.e., (40 + x/2), (20 + x/4), (20 + x/4) psf] Material Properties: f c = 3 ksi, fs = 20 ksi [i.e., f c = (3 + x/20) ksi, fs = (20 + x/4) ksi (S1) (S1) (S1) (S1) (S2) (S2) 16.5 16 16 16.5 B1 B3 B4 B5 B6 B7 B8 B9 B10 B12 16.5 16 16 16.5 16 16 16 16 (S3) (S2) (S2) B2 B11
  • 2. Design of Slabs and Ribs Slabs Assuming 10 square pans per slab; i.e., (3.2 3.2 ) c/c and (2.7 2.7 ) clear spans (with 6 ribs) Slab thickness = 2.5 Self weight = 2.5 150/12 = 31.25 psf Total load on slab, w = 31.25 + 20 + 20 + 40 = 111.25 psf = 0.111 ksf Maximum Moment for an edge-supported (2.7 2.7 ) slab with Support condition Case 2 M( ) max = 0.045 wL2 = 0.045 0.111 (2.7)2 = 0.0365 k / Modulus of rupture = 5 fc = 5 (3/1000) = 0.274 ksi; i.e., Allowable tensile stress = 0.274/2 = 0.137 ksi Ssect = bh2 /6 0.0365 = h2 /6 0.137 hreq = (0.0365 6/0.137) = 1.26 Slab thickness, h = 2.5 is OK; i.e. d = 2 As(Temp) = 0.0025 bh = 0.0025 12 2.5 = 0.075 in2 /ft Use appropriate wire mesh to provide the required As(Temp); i.e., 1/8 -wire diameter (2 2 ) mesh Ribs Maximum clear span = 31 ; Slab without edge beam and fy = 40 ksi Slab thickness = Ln(0.8 + fy/200)/33 = 31 (0.8 + 40/200) 12/33 = 11.27 Assume 18 thickness; i.e., 13.5 below slab, with bw = 6 Average thickness without column head = 18 {(2.7 2.7) 15.5}/(3.2 3.2) = 6.97 If column head covers (5 5 = 25) square pans, average thickness of slab = 6.97 + {25 (2.7 2.7) 15.5}/(32 32) = 9.72 Assuming the entire slab thickness to be = 9.72 Self weight = 9.72 150/12 = 121.5 psf Total load on slab = 121.5 + 20 + 20 + 40 201.5 psf = 0.202 ksf For design, n = 9, k = 0.378, j = 0.874, R = 0.223 ksi d = 18 1.5 = 16.5 ; As = M/fsjd = M 12/(20 0.874 16.5) = M/24.04 Moment capacity Mc(max) = Rbd2 = 0.223 1 16.52 = 60.70 k / , or 30.35 k /rib Also, As(Temp) = 0.0025 bt = 0.0025 12 18 = 0.54 in2 / ; or 0.27 in2 /rib Punching shear force in slab 0.202 {322 (16 + 2/12)2 } = 153.71 k and in column head 0.202 {322 (12/12 + 16.5/12)2 } = 205.25 k Stresses are = 153.71/(4(16 12 + 2) 2) = 0.099 ksi and = 205.25/(4(12 + 16.5) 16.5) = 0.109 ksi Allowable punching shear stress, punch = 2 fc = 2 (3/1000) = 0.110 ksi OK for punching shear
  • 3. Panels in the Long and Short Direction Panel 1 (and all other panels) Width of Panel = 16.5 No edge beam along panel length; 1 = 0, for all slabs Also no transverse beam t = 0, for all slabs Column strip = Short span (c/c)/4 = 32/4 = 8 , Middle strip = 16 8 = 8 (i.e., 2.5 pans per strip) Slab (S1) Slab size (= 32 32 c/c) = 31 31 M0 = wL2Ln 2 /8 = 0.202 16.5 312 /8 = 399.48 k Support (c) MExt = 0.26 M0 = 103.87 k , M+ = 0.52 M0 = 207.73 k , MInt = 0.70 M0 = 279.64 k L2/L1 = 32/32 = 1.0, 1L2/L1 = 0 Total column strip moments are MCExt = 1.00 MExt = 103.87 k ; i.e., 103.87 k /8 = 12.98 k / ; AsCExt = 12.98/24.04 = 0.54 in2 / MC + = 0.60 M+ = 124.64 k ; i.e., 124.64 k /2.5 rib = 49.86 k / ; ACExt + = 49.86/24.04 = 2.07 in2 /rib MCInt = 0.75 MInt = 209.73 k ; 209.73 k /8 = 26.22 k / ; AsCInt = 26.22/24.04 = 1.09 in2 / Total middle strip moments are MMExt = 103.87 103.87 = 0 k ; i.e., 0 k /8 = 0 k / ; AsMExt = 0/24.04 = 0.0 in2 / MM + = 207.73 124.64 = 83.09 k ; i.e., 83.09 k /2.5 rib = 33.24 k /rib; AM + = 33.24/24.04 = 1.38 in2 /rib MMInt = 279.64 209.73 = 69.91 k ; i.e., 69.91 k /8 = 8.74 k / ; AMInt + = 8.74/24.04 = 0.36 in2 / Slab (S2) Slab size (= 32 32 c/c) = 31 31 M0 = wL2Ln 2 /8 = 0.202 16.5 312 /8 = 399.48 k Interior Support MInt = 0.65 M0 = 259.67 k , M+ = 0.35 M0 = 139.82 k , MInt = 0.65 M0 = 259.67 k L2/L1 = 32/32 = 1.0, 1L2/L1 = 0 Total column strip moments are MCInt = 0.75 MExt = 194.75 k ; i.e., 194.75 k /8 = 24.34 k / ; AsCInt = 24.34/24.04 = 1.01 in2 / MC + = 0.60 M+ = 83.89 k ; i.e., 83.89 k /2.5 rib = 33.56 k /rib; AsM + = 33.56/24.04 = 1.40 in2 /rib MCInt = 0.75 MInt = 194.75 k ; i.e., 194.75 k /8 = 24.34 k / ; AsCInt = 24.34/24.04 = 1.01 in2 / Total middle strip moments are MMInt = 259.67 194.75 = 64.92 k ; i.e., 64.92 k /8 = 8.11 k / ; AsMInt = 8.11/24.04 = 0.34 in2 / MM + = 139.82 83.89 = 55.93 k ; i.e., 55.93 k /2.5 rib = 22.37 k /rib; AsM + = 22.37/24.04 = 0.93 in2 /rib MMInt = 259.67 194.75 = 64.92 k ; i.e., 64.92 k /8 = 8.11 k / ; AsMInt = 8.11/24.04 = 0.34 in2 /
  • 4. Denoting slab reinforcement by in2 / ( ve) and rib reinforcement by in2 /rib (+ve highlighted) Ribs within Column Strip Ribs within Middle Strip 0.54 2.07 1.09 1.01 1.40 1.01 1.09 2.07 0.54 0.00 1.38 0.36 0.34 0.93 0.34 0.36 1.38 0.00 0.54 2.07 1.09 1.01 1.40 1.01 1.09 2.07 0.54 0.54 2.07 1.09 1.01 1.40 1.01 1.09 2.07 0.54 0.00 1.38 0.36 0.34 0.93 0.34 0.36 1.38 0.00 0.54 2.07 1.09 1.01 1.40 1.01 1.09 2.07 0.54 0.54 2.07 1.09 1.01 1.40 1.01 1.09 2.07 0.54 0.00 1.38 0.36 0.34 0.93 0.34 0.36 1.38 0.00 0.54 2.07 1.09 1.01 1.40 1.01 1.09 2.07 0.54 1 #4 extra top between alternate #4 bars 2 #9 through #4 @ 4.5 c/c within slab 2 #8 through #4 @ 7.5 c/c A A Section A-A 3.2 2 #9 #4@ 4.5 c/c B B Section B-B 3.2 2 #9 #4@ 4.5 c/c + extra top