Presented byPresented by

Morales, Ma. Theresa V.Gan, Jun Patrick G.Endaya, Andrei P.

SEPTEMBER 06, 2010

Design of Two-Way Floor Slab System

DIRECT DESIGN METHOD

Lecture GoalsLecture Goals

• Direct Design Method

• Example of DDM

Direct Design Method for Two-way SlabDirect Design Method for Two-way Slab

Minimum of 3 continuous spans in each direction. (3 x 3 panel)

Rectangular panels with long span/short span 2

Method of dividing total static moment Mo into positive and negative moments.

Limitations on use of Direct Design method

1.

2.

Direct Design Method for Two-way SlabDirect Design Method for Two-way Slab

Limitations on use of Direct Design method

Successive span in each direction shall not differ by more than 1/3 the longer span.

3.

4. Columns may be offset from the basic rectangular grid of the building by up to 0.1 times the span parallel to the offset.

Direct Design Method for Two-way SlabDirect Design Method for Two-way Slab

Limitations on use of Direct Design method

All loads must be due to gravity only (N/A to unbraced laterally loaded frames, from mats or pre-stressed slabs)

Service (unfactored) live load 2 service dead load

5.

6.

Direct Design Method for Two-way SlabDirect Design Method for Two-way Slab

For panels with beams between supports on all

sides, relative stiffness of the beams in the 2

perpendicular directions.

Shall not be less than 0.2 nor greater than 5.0

Limitations on use of Direct Design method

7.

212

221

l

l

Direct Design Method for Two-way SlabDirect Design Method for Two-way Slab

Limitations on use of Direct Design method

Moment redistribution as permitted by Section 408.4 (Method of Analysis; NSCP) shall not be applied for slab systems designed by the Direct Design Method.

8.

Variations from the Limitations of Section 413.7.1 shall be permitted if demonstrated by analysis as long as requirements of Section 413.6.1 are satisfied.

9.

Direct Design Method for Two-way SlabDirect Design Method for Two-way Slab

Limitations on use of Direct Design method

A slab system shall be distinguished by procedure satisfying conditions of equilibrium and geometric compatibility, if shown that the design strength at every section is at least equal to the required strength set forth in section 409.3 (Required Strength) and 409.4 (Design Strength)

SECTION 413.6.1

Direct Design Method for Two-way SlabDirect Design Method for Two-way Slab

Limitations on use of Direct Design method

and that all serviceability conditions, including limits of deflections are met.

SECTION 413.6.1

Definition of Beam-to-Slab Stiffness Ratio, Definition of Beam-to-Slab Stiffness Ratio,

Accounts for stiffness effect of beams located along slab edge reduces deflections of panel

adjacent to beams.

slab of stiffness flexural

beam of stiffness flexural

Definition of Beam-to-Slab Stiffness Ratio, Definition of Beam-to-Slab Stiffness Ratio, mm

With width bounded laterally by centerline of adjacent panels on each side of the beam.

scs

bcb

scs

bcb

4E

4E

/4E

/4E

I

I

lI

lI

slab uncracked of inertia ofMoment I

beam uncracked of inertia ofMoment I

concrete slab of elasticity of Modulus E

concrete beam of elasticity of Modulus E

s

b

sb

cb

usedratiostiffnessallofmeanm

Definition of Beam-to-Slab Stiffness RatioDefinition of Beam-to-Slab Stiffness Ratio

2.0m

panels drop with 100mm t

panels drop without 125mm t

min

min

CASE 1:

drop panels

Definition of Beam-to-Slab Stiffness RatioDefinition of Beam-to-Slab Stiffness Ratio

:monolithicfor

smallest theis whicheverchoose*

t8b b

h2b b

fwflange

wwflange

hw

bf

bw

tf

Definition of Beam-to-Slab Stiffness RatioDefinition of Beam-to-Slab Stiffness Ratio

22.0 m

spanclear short Sn

spanclear longLn

:where

Sn

Ln

CASE 2:

)2.05 36

(fy/1500)] Ln[0.8min

m

t

Definition of Beam-to-Slab Stiffness RatioDefinition of Beam-to-Slab Stiffness Ratio

2m

spanclear short Sn

spanclear longLn

:where

Sn

Ln

CASE 3:

9 36

(fy/1500)] Ln[0.8min

t

Two-Way Slab DesignTwo-Way Slab DesignStatic Equilibrium of Two-Way Slabs

Analogy of two-way slab to plank and beam floor

Section A-A:

Moment per ft width in planks

Total Moment

ft/ft-k 8

21wlM

ft-k 8

21

2f

lwlM

Distribution of MomentsDistribution of Moments

Slab is considered to be a series of frames in two directions:

Distribution of MomentsDistribution of Moments

Slab is considered to be a series of frames in two directions:

Design ProblemDesign Problem

An interior panel 5.5m x 7.3m center-to-center is monolithically supported on beams on each side. The columns are 400mm x 400mm and the supporting beams are 300mm x 500mm. The floor live load is 5.25kPa in addition to the slab weight. f’c=27.6MPa and fy=415MPa. Using Direct Design Method:

1. Compute the thickness of the slab

2. Compute the total factored static moment in the long direction of the interior panel

3. Compute the total factored static moment in the short direction of the interior panel