developmenton of structure

8/13/2019 Developmenton of structure

1/141


2/141


3/141


4/141


5/141


6/141


7/141


8/141


9/141


10/141


11/141


12/141


13/141


14/141


15/141


16/141


17/141


18/141


19/141


20/141


21/141


22/141


23/141


24/141


25/141


26/141


27/141


28/141


29/141


30/141


31/141


32/141


33/141


34/141


35/141


36/141


37/141


38/141


39/141


40/141


41/141


42/141


43/141


44/141


45/141


46/141


47/141


48/141


49/141


50/141


51/141


52/141


53/141


54/141


55/141


56/141


57/141


58/141


59/141


60/141


61/141


62/141


63/141


64/141


65/141


66/141


67/141


68/141


69/141


70/141


71/141


72/141


73/141


74/141


75/141


76/141


77/141


78/141


79/141


80/141


81/141


82/141


83/141


84/141


85/141


86/141


87/141


88/141


89/141


90/141


91/141


92/141


93/141


94/141


95/141


96/141


97/141


98/141


99/141


100/141


101/141


102/141


103/141


104/141

Comparison of One way and Two way


105/141

Comparison of One-way and Two-way

slab behavior

One-way and two-way

slab action carry load

in two directions.

One-way slabs: Generally,

long side/short side > 1.5



106/141

p y y

slab behavior

Flat slab Two-way slab with beams

Comparison between a two-way


107/141

Comparison between a two-way

slab verses a one-way slabFor flat plates and slabs the column connections

can vary between:



108/141


slab behavior

Flat Plate Waffle slab



109/141

slab behavior

The two-way ribbed slab and waffled slab system:

General thickness of the slab is 2 to 4 in.



110/141


slab behavior Economic Choices

Flat Plate suitable span 20 to 25 ft with LL= 60 -100 psf

Advantages

Low cost formworkExposed flat ceilings

Fast

Disadvantages

Low shear capacity

Low Stiffness (notable deflection)



111/141



Flat Slab suitable span 20 to 30 ft with LL= 80 -150 psf

Advantages

Low cost formworkExposed flat ceilings

Fast

Disadvantages

Need more formwork for capital and panels



112/141



Waffle Slab suitable span 30 to 48 ft with LL= 80 -150

psf

Advantages

Carries heavy loads

Attractive exposed ceilings

Fast

Disadvantages

Formwork with panels is expensive



113/141



One-way Slab on beams suitable span 10 to 20 ft with

LL= 60-100 psf

Can be used for larger spans with relatively higher

cost and higher deflections

One-way joist floor system is suitable span 20 to 30 ft

with LL= 80-120 psf

Deep ribs, the concrete and steel quantities arerelative low

Expensive formwork expected.


slab behavior


114/141

slab behavior

ws =load taken by short direction

wl = load taken by long direction

dA= dB

Rule of Thumb: For B/A > 2,

design as one-way slab

EI

Bw

EI

Aw

384

5

384

5 4l4s

ls4

4

l

s 162ABFor ww

A

B

w

w

Two-Way Slab Design


115/141

Two 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

2

1wlM

ft-k8

2

12f

lwlM

Two-Way Slab Design


116/141

Two Way Slab Design

Static Equilibrium of Two-Way Slabs

Analogy of two-way slab to plank and beam floor

Uniform load on each beam

Moment in one beam (Sec: B-B) ft-k82

221

lb

lwlM

k/ft

2

1wl

Two-Way Slab Design


117/141

Static Equilibrium of Two-Way Slabs

Total Moment in both beams

Full load was transferred east-west by the planks and then was

transferred north-south by the beams;

The same is true for a two-way slab or any other floor system.

ft-k8

2

21

lwlM


118/141

General Design Concepts

(1) Direct Design Method (DDM)

Limited to slab systems to uniformly distributed

loads and supported on equally spaced columns.

Method uses a set of coefficients to determine the

design moment at critical sections. Two-way slab

system that do not meet the limitations of the ACI

Code 13.6.1 must be analyzed more accurateprocedures


119/141

General Design Concepts

(2) Equivalent Frame Method (EFM)

A three dimensional building is divided into a

series of two-dimensional equivalent frames by

cutting the building along lines midway between

columns. The resulting frames are considered

separately in the longitudinal and transverse

directions of the building and treated floor byfloor.


120/141

Equivalent F rame Method (EFM )

Longitudinalequivalent frame

Transverse equivalentframe


121/141

Equivalent F rame Method (EFM )

Elevation of the frame Perspective view

M h d f A l i


122/141

Method of Analysis

(1) Elastic Analysis

Concrete slab may be treated as an elastic

plate. Use Timoshenkos method of analyzingthe structure. Finite element analysis

Method of Analysis


123/141

(2) Plastic Analysis

The yield methodused to determine the limit state of

slab by considering the yield lines that occur in the

slab as a collapse mechanism.

The str ip method, where slab is divided into strips

and the load on the slab is distributed in two

orthogonal directions and the strips are analyzed as

beams.The optimal analysispresents methods for

minimizing the reinforcement based on plastic

analysis

Method of Analysis


124/141

(3) Nonlinear analysis

Simulates the true load-deformation characteristics

of a reinforced concrete slab with finite-element

method takes into consideration of nonlinearities of

the stress-strain relationship of the individualmembers.

Column and M iddle Str ips


125/141

p

The slab is broken

up into column

and middle strips

for analysis

Minimum Slab Thickness for two-way

construction


126/141

construction

The ACI Code 9.5.3 specifies a minimum slab thicknessto control deflection. There are three empirical

limitations for calculating the slab thickness (h), which

are based on experimental research. If these limitations

are not met, it will be necessary to compute deflection.


construction


127/141

construction

22.0 m(a) For

2.0536200,000

8.0

m

y

n

fl

h

fyin psi. But not less than 5 in.


construction


128/141

construction

m2 (b) For

936

200,000

8.0 y

n

fl

h

fyin psi. But not less than 3.5 in.


construction


129/141

construction

2.0m (c) For

Use the following table


construction


130/141

Slabs without interiorbeams spanning

between supports and

ratio of long span to

short span < 2

See section 9.5.3.3

For slabs with beams

spanning between

supports on all sides.


construction


131/141

construction

The definitions of the terms are:

h = Minimum slab thickness without interior beams

ln =

m=

Clear span in the long direction measured face toface of column

the ratio of the long to short clear span

The average value of for all beams on the sides

of the panel.

Definition of Beam-to-Slab Sti f fness Ratio,


132/141

Accounts for stiffness effect of beams located alongslab edge reduces deflections of panel

adjacent to beams.

slabofstiffnessflexural

beamofstiffnessflexural

Definition of Beam-to-Slab Sti f fness Ratio,


133/141

With width bounded laterally by centerline of

adjacent panels on each side of the beam.

scs

bcb

scs

bcb

EE

/4E/4E

II

lIlI

slabuncrackedofinertiaofMomentI

beamuncrackedofinertiaofMomentI

concreteslabofelasticityofModulusE

concretebeamofelasticityofModulusE

s

b

sb

cb

Beam and Slab Sections for calculation of


134/141



135/141



136/141

Definition of beam cross-section

Charts may be used to calculate Fig. 13-21



137/141

construction

Slabs without drop panels meeting 13.3.7.1 and 13.3.7.2,

tmin= 5 in

Slabs with drop panels meeting 13.3.7.1 and 13.3.7.2,

tmin= 4 in

Example


138/141

Example

A flat plate floor system with panels

24 by 20 ft is supported on 20 in.

square columns. Determine theminimum slab thickness required

for the interior and corner panels.

Use fc= 4 ksi and fy= 60 ksi

Example


139/141

Example

The floor system consists of solid

slabs and beams in two directions

supported on 20 in square columns.Determine the minimum slab

thickness required for an interior

panel. Use fc= 4 ksi and fy= 60 ksi

Example


140/141

The cross-sections are:

Example


141/141

The resulting cross section:

developmenton of structure

Documents