Design of Concrete Structure IDesign of Concrete Structure I

Dr. AliTayeh

First Semester 2009

Dr. AliTayeh

First Semester 2009

Lecture 12One Way Slab

Part 1

Slab – Minimum thickness

One-Way Slab DesignOne-Way Slab Design

Thickness of One-Way Slabs

Fire Rating

This is equal to the number of hours for unexposed surface to rise a set amount usually 120 o C

9.0 cm. 1 hour 12.5 cm. 2 hours 16.0 cm. 3 hours

Cover for Slab Cover for Slab ReinforcementReinforcement

ACI Sec. 7.7.1 (min. cover for corrosion protection)

( 1.) Concrete exposed to earth or weather.

( 2.) Concrete not exposed to earth or weather.

< 16 = 4.0 cm

> 16 = 5.0 cm

< 32 = 2.0 cm

Min. covers for fire ratings should also be considered.

Minimum Reinforcement

• According to ACI-Code 7.12.2.1 and for steels yielding at , the shrinkage reinforcement is taken not less than 0.0018 of the gross concrete area, or

hbA shrinkages 0018.0

Solid slab

Ribbed SlabOne-way slabTwo way slab

One-way slabTwo way slab

2L

S2

L

S

One-Way Solid Slab DesignOne-Way Solid Slab DesignReinforcement

Typical Reinforcement in a one-way slab:

One-Way Solid Slab DesignOne-Way Solid Slab Design

Cutoffs

If requirements for use of ACI Moment Coefficients:

One-Way Solid Slab DesignOne-Way Solid Slab Design

Need to confirm thickness is adequate for one-way shear. Difficult to place shear reinforcement in a slab. Minimum area of shear reinforcement required in slabs if

dbf

V

VV

wc

c

cu

6

Usual use

Moment Diagram: Approximate Method of Continuous Beams and One-Way Slabs:

More than two slabs

Two slabs

Shear Diagram: Approximate Method of Continuous Beams and One-Way Slabs:

More than two slabs

Two slabs

Summary of One-way Solid Slab Design Procedure

• Select representative 1-m wide design strip/strips to span in the short direction

• Choose a slab thickness

• Calculate the factored load by magnifying service dead and live loads according to this equation . The dead load includes own weight of the slab in addition to the covering materials it supports. The live load is dependent on the intended use of the slab.

• Draw the shear force and bending moment diagrams for the strip

Example 1Using the ACI-Code approximate structural analysis, design for a warehouse, a continuous one-way slab supported on beams 5.0 m apart as shown in Figure . Assume that the beam webs are 30 cm wide. The dead load is 3 kN/m2 in addition to the slab own weight, and the live load is 2 kN/m2. Use

Mpafc 25

Mpaf y 420

2

6

85.0

10211

85.0

dbf

M

f

f

wc

u

y

c

10@20cm

25.20

79.0

100

9.3

9.34.38618410000021.0

0021.01840001 52 .90 85.0

3.2610211

420

2585.0

.3.26moment .

10

22

2

6

use

S

Scm

cmmmAve

mKNveMax

strip

s

O.k.

0184.0

0161.0

0033.0

1000

184

max

lim

min

mmb

mmd

10@15cm

67.18

79.0

100

23.4

23.42.42318410000023.0

0023.01840001 52 .90 85.0

0.2910211

420

2585.0

.0.29moment .

10

22

2

6

use

cmS

Scm

cmmmAve

mKNveMax

strip

s

O.k.

Ribbed Slab

One-way Ribbed Slab Design Notes

• According to ACI-Code 8.11.6.1, topping slab thickness is not to be less than 1/12 the clear distance between ribs, nor less than 5.0 cm.

• According to ACI-Code 8.11.8, shear strength provided by rib concrete Vc may be taken 10 % greater than those for beams. It is permitted to increase shear strength using shear reinforcement or by widening the ends of ribs

• Ribs are designed as rectangular beams in the regions of positive moment between the supports and as T-shaped beams in the regions of negative moments at the supports. Effective flange width beff is taken as half the distance between ribs, center-to-center

Summary of One-way Ribbed Slab Design Procedure

• The direction of ribs is chosen.• The overall slab thickness h is determined

based on deflection control requirement. • The factored load on each of the ribs is

computed.• The shear force and bending moment

diagrams are drawn.• The strength of web in shear is checked.• Design positive and negative moment

reinforcement.

Example 2

Design a one-way ribbed slab to cover a 4 m x 10 m panel, shown in Figure below. The covering materials weigh 2 kN/m2, the live load is 2 kN/m2 Mpafc 25

Mpaf y 420

An Example for Ribbed slab Reinforcement