1

Prepared & Compiled by Engr. Qamar uz Zaman, qamaruzzaman@msn.com

LAYOUT—ONE WAY JOIST/RIBBED SLAB

TOP SLAB

JOIST / RIB

Refer to Section 8.13 of ACI 318-08 for

Joist Construction

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Prepared & Compiled by Engr. Qamar uz Zaman, qamaruzzaman@msn.com

Design of One Way Joist Slab

Design of Top Slab

Assume thickness, t (inches) Not < S/12 or 2”

ACI Sec 8.13.6.1

Calculate Loads and Load Effects

Wu = 1.2(Wself + WSDL) + 1.6 x Wlive

Mu = WuS2/12

Where:

Wu = Factored Load (ACI Section 9.2)

Mu = Factored / Ultimate / Design Moment

Wself = t/12 x ɣconcrete (For NSC, ɣconcrete = 150 lbs/ft3)

S = Clear Spacing between Ribs

WSDL = Superimposed dead load

Wlive = Refer to ASCE-7 2010, Table 4-1

Design of Top Slab Tensile Strength of Concrete will be considered and checked that the Moment Capacity of Un-cracked

Section is > Mu

Where:

ft = tensile strength of concrete, psi

f’c = Compressive strength of concrete, psi

I = 2nd Moment of Area about axis of bending, in4

Y = Depth of centroid of the section, in

M = Moment capacity of un-cracked section

If M > Mu (No need to calculate Reinforcement, Concrete is providing sufficient resistance.

But provide temperature and shrinkage reinforcement as per ACI 7.12.2.

'5 ct ff =

y

IfM t=

Continued on next page…..

Temperature & Shrinkage Reinforcement, As,sh • Will be provided to meet the requirements of Section 7.12 of ACI Code.

• Work out As,sh

• Find c/c spacing between the bars using Equation S = 12 Ab/As,sh

• Comply to spacing requirements of reinforcing bars as mentioned in Section 7.12.2.2

Where:

Ab = Area of bar, in2

Designed as a continuous beam

supported by the ribs.

A more conservative calculation can be done as:

Where:

If Top Slab thickness is calculated using

above relationship then there is no

requirement of design the slab for flexure.

Provide Temperature and Shrinkage rein-

forcement as per Sec 7.12.2 of the Code

12/

22

3

'

tb

tM

ff

w

u

ctφ

==

'

3

cw

u

fb

Mt

φ=

3

Prepared & Compiled by Engr. Qamar uz Zaman, qamaruzzaman@msn.com

Design of Joist/Ribs

Calculate Span Length, Ln Refer to ACI Section 8.9

Calculate Joist thickness, h Refer to ACI Table 9.5(a)

Calculate Loads and Load Effects Wu = Top Slab Load + 1.2 x Wself

Bending Moment: Mu = WuLn

2/12 (Single Span, Integral Support) or

Mu = WuLn2/8 (Single Span, Simple Support) or

Mu = Use ACI Moment Coefficient for Multi Span

Shear Force:

Vu, at Support = WuLn/2 (Simple Support/Integral Support) or

Vu = Use ACI Shear Coefficient for Multi Span

Where:

Vu = Factored / Ultimate Shear Force

Calculate Reinforcement, As • Remember that member has been proportioned (b, h), material properties (f’c, fy) are

known.

• Assume Bar # to calculate d

• d = h - concrete cover - 1/2 db

• ɸMn = ɸ x 0.85 fc’ x a x b (d-a/2) Eq (1)

• ɸMn = ɸ x As x fy (d-a/2) Eq (2)

• a = As fy / (0.85 fc’ x a x b) Eq (3)

• Calculate As using Eq (2) and (3), assuming steel is yielding (it will be confirmed later)

• Find out a, using Eq (3)

• a = β1c Eq (4)

Where β1 = For fc′ between 2500 and 4000 psi, β1 shall be taken as 0.85. For fc′ above 4000 psi, β1 shall be reduced line-

arly at a rate of 0.05 for each 1000 psi of strength in excess of 4000 psi, but β1 shall not be taken less than 0.65.

ACI Section 10.2.7.3 • Find c, the depth of Neutral Axis from extreme compression fiber

• Find c/dt , if c/dt < 0.375, Section is Tension Controlled and assumption confirmed

• if c/dt > 0.375, Increase the depth of the Joist to design a Tension Controlled Section Where:

d = Depth from top compression fiber to centroid to tension reinforcement

db = Dia of bar

Mn = Nominal Moment Capacity of the Section

a = Depth of Whitney Stress block

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Prepared & Compiled by Engr. Qamar uz Zaman, qamaruzzaman@msn.com

Perform Checks

• Reinforcement Ratios:

⇒ Calculate ϼmax = 0.75 ϼbal, Where

But not < 200/fy

ϼactual = As / bd

ϼmax > ϼactual > ϼmin

Where:

ϼmax = Maximum reinforcement ratio

ϼmin = Minimum reinforcement ratio

ϼactual = Reinforcement ratio being provided in section

• Reinforcement Spacing: ⇒ Maximum: ACI Section 10.6.4 but not <

⇒ Minimum: ACI Section 7.6 (db but not < 1”)

• Check for Shear: ⇒ Draw Shear Force diagram

⇒ Calculate Vu at critical Section i.e at distance ’d’ from face of support

⇒ Calculate

⇒ If ɸVc > Vu (OK), otherwise increase slab thickness or provide Shear reinforcement.

+=

yy

c

balff

f

87000

8700085.0

'

ζ

y

c

f

f '

min 3=ζ ACI Section 10.5

dbfV wcc'

21.1 λφφ = ACI Section 8.13.8 & 11.2.1.1

cC

sfS 5.2

4000015 −

=

=

sfS

4000012