For a column supported two-way
slab, 100% of the applied load must be carried in each
direction.
CEVE 530
Minimum Thickness of Slabs
Without Interior Beams With Beams
Table 9.5(c)
or
Computations
Equations
or
Computations
CEVE 530
Two Way Slabs: Thickness Requirements
Factors affecting deflection of a slab:� Slab thickness, h
� Clear span of the slab, Ln (long span)
� Ratio of Long to Short span, β β β β (bay size)
� Continuity of slab, ββββs
� Beam size (Moment of Inertia), Ib
� Fy of reinforcing steel� 60 ksi will require larger thickness compared to 40 ksi
� Higher strain produces more cracking and thus more deflection.
� Modulus of Elasticity of Slab, Ecs
� Modulus of Elasticity of Beams, Ecb
CEVE 530
Moment of Inertia: Flanged Section
CEVE 530
Define Stiffness Ratio:
ααααf = (Ecb . Ib) / (Ecs . Is)
� Ib = f.(b.a3)/12
� Is = (llll2.h3)/12
� h: slab thickness
� llll2 : width of slab bounded laterally by centerline of adjacent panel, if any, on each
side of beam
Moment of Inertia: Flanged Section
CEVE 530
ααααf = (Ecb . Ib)/(Ecs . Is)
ααααf = (Ecb .f.b.a3/12) / (Ecs . llll2.h3/12)
ααααf = (Ecb / Ecs ).(b/ llll2).(a/h)3.f
Factor f Chart
Observation:
� For no beams at edge:
� a/h = 1 => f = 1.0
� For interior beamless slab:
� a/h = 1 => f = 1.0
� For a/h between 1 and 5:
� f increases as a/h increases for a constant b/h
� For a/h greater than5:
� f decreases as a/h increases for a constant b/h
CEVE 530
Slab Deflection
For Square Panels:
∆∆∆∆ = ∆∆∆∆cx + ∆∆∆∆my = ∆∆∆∆cy + ∆∆∆∆mx
For Rectangular Panels:
∆∆∆∆ = [(∆∆∆∆cx + ∆∆∆∆my ) + (∆∆∆∆cy + ∆∆∆∆mx)]/2
CEVE 530
Minimum Thickness of Slabs
Without Interior Beams With Beams
Table 9.5(c)
or
Computations
Equations
or
Computations
CEVE 530
Minimum Thickness of Slabs
ααααfm : Average value of ααααf for all beams on the edges of a panel
CEVE 530
Minimum Thickness
Slab with Beams
ααααfm Use hmin (in.)
≤≤≤≤ 0.2 Sect. 9.5.3.25 (flat plates)
4 (flat slabs)
>0.2 , ≤≤≤≤2.0 Eq. (9-12) 5
> 2.0 Eq. (9-13) 3.5
CEVE 530
Example – Slab ThicknessFlat Plate (no edge beams)
� Bay Size: 25’ x 20’
� Ln = 25-1.5 = 23.5’
Panels 1,2, and 3:
� h = Ln/30 = 23.5*12/30 = 9.4”
Panel 4:
� h = Ln/33 = 23.5*12/33 = 8.55”
Use h = 9.5”CEVE 530
Example – Slab ThicknessFlat Slab (no edge beams)
� Size of Drop Panel:� 1/3*25 = 8.33’
� 1/3*20 = 6.67’
� Ln = 25-1.5 = 23.5’
Panels 1,2, and 3:
� h = Ln/33 = 23.5*12/33 = 8.55”
Panel 4:
� h = Ln/36 = 23.5*12/36 = 7.83”
Use h = 8.5”
Depth at drop panel = 8.5*1.25 = 10.6” (say 11”)CEVE 530
Example – Slab ThicknessTwo way Slab with Beams
� Size of Panel: 25’x20’
� Ln = 25-1.5 = 23.5’
Assume: h = 6.5”
Need:
ααααf and ααααf mCEVE 530
Example – Two way Slab with Beams
Typical Edge Beams: B-1, B-2, B-5, and B-6
bE = 18 + 17.5 = 35.5” <---- controls
or
bE = 18 + 4*6.50 = 44”
1. a/h = 24/6.5 = 3.69
2. b/h = 18/6.5 = 2.77
3. f = 1.35
(from chart of the
Edge beams)CEVE 530
Example – Two way Slab with Beams
Typical Interior Beams: B-3, B-4, B-7, and B-8
bE = 18 + 2*17.5 = 53” <---- controls
or
bE = 18 + 8*6.50 = 70”
1. a/h = 24/6.5 = 3.69
2. b/h = 18/6.5 = 2.77
3. f = 1.55
(from chart of the
interior beams)CEVE 530
Example – Two way Slab with Beams
Aspect Ratio, β ?β ?β ?β ?� Clear span, long direction = 25-1.5 = 23.5’
� Clear span, short direction = 20-1.5 = 18.5’
�ββββ = 23.5 / 18.5 = 1.27
CEVE 530
Example – Two way Slab with Beams
� ααααf = (Ecb / Ecs ).(b/llll2).(a/h)3.f
� ααααf = (b/llll2).(a/h)3.f (for Ecb = Ecs )
Beam b (inches) llll2 (feet) a/h f ααααf
B-1 18 13.25 3.69 1.35 7.68
B-2 18 13.25 3.69 1.35 7.68
B-3 18 25 3.69 1.55 4.67
B-4 18 25 3.69 1.55 4.67
B-5 18 10.75 3.69 1.35 9.46
B-6 18 10.75 3.69 1.35 9.46
B-7 18 20 3.69 1.55 5.84
B-8 18 20 3.69 1.55 5.84
CEVE 530
Example – Two way Slab with Beams
αfm = ?
Panel 1:ααααfm = (7.68+5.84+4.67+9.46)/4 =6.91
Panel 2:ααααfm = (4.67+5.84+4.67+9.46)/4 =6.16
Panel 3:ααααfm = (7.68+5.84+4.67+5.84)/4 =6.0
Panel 4:ααααfm = (5.84+5.84+4.67+4.67)/4 = 5.26
αααα = 5.84
αααα = 5.84 αααα = 5.84
αααα = 5.84
αα αα=
4.6
7
αα αα=
4.6
7
αα αα=
4.6
7
αα αα=
4.6
7
αααα = 9.46 αααα = 9.46
αα αα=
7.6
8
αα αα=
7.6
8
CEVE 530
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