TWO WAY SLAB

TWO WAY SLAB

CEVE 530

For a column supported two-way

slab, 100% of the applied load must be carried in each

direction.

CEVE 530

Two-way slab with Beams

� SLAB THICKNESS ?

� ACI, Section 9.5.3

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Minimum Thickness of Slabs

Without Interior Beams With Beams

Table 9.5(c)

or

Computations

Equations

or

Computations

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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

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What is Ib?

� Monolithic Construction

� What part of slab should be included?

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Stiffness Ratio, ααααf

CLCL llll2

h

a

b

bE = b + 2(a – h) ≤≤≤≤ b + 8h

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Stiffness Ratio, ααααf

CLllll2

h

a

b

bE = b + (a – h) ≤≤≤≤ b + 4h

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Moment of Inertia: Flanged Section

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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


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 for an Edge Beam

CEVE 530

Factor f for an Interior Beam

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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

Deflection

Calculation?

CEVE 530

Deflection Calculation

CEVE 530

Slab Deflection

For Square Panels:

∆∆∆∆ = ∆∆∆∆cx + ∆∆∆∆my = ∆∆∆∆cy + ∆∆∆∆mx

For Rectangular Panels:

∆∆∆∆ = [(∆∆∆∆cx + ∆∆∆∆my ) + (∆∆∆∆cy + ∆∆∆∆mx)]/2

CEVE 530

Deflection Control

ACI Provisions

Section 9.5.3

CEVE 530


Without Interior Beams With Beams

Table 9.5(c)

or

Computations

Equations

or

Computations

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Drop Panels

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Flat plates Flat slabs

For Fy = 60 ksi

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ααααfm : Average value of ααααf for all beams on the edges of a panel

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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

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


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


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


� 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


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


� Panel 1: h = 23.5 *12 (0.8+60,000/200,000)/(36+9*1.27) = 6.54”

� Panel 2: h = 6.54”

� Panel 3: h = 6.54”

� Panel 4: h = 6.54”

h required = 6.54”

h assumed = 6.50” ok!

CEVE 530

TWO WAY SLAB

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