direct design method_final copy

Presented byPresented by

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

SEPTEMBER 06, 2010

REINFORCED REINFORCED CONCRETE DESIGNCONCRETE DESIGN

RATE RATE US !! US !!

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.



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.



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.


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


7.

212

221

l

l



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.



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



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:


:monolithicfor

smallest theis whicheverchoose*

t8b b

h2b b

fwflange

wwflange

hw

bf

bw

tf


22.0 m

spanclear short Sn

spanclear longLn

:where

Sn

Ln

CASE 2:

)2.05 36

(fy/1500)] Ln[0.8min

m

t


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


Analogy of two-way slab to plank and beam floor

Uniform load on each beam

Moment in one beam (Sec: B-B) ft-k 82

221

lb

lwlM

k/ft 2

1wl


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-k 8

22

1

lwlM

Basic Steps in Two-way Slab DesignBasic Steps in Two-way Slab Design

Choose layout and type of slab.

Choose slab thickness to control deflection. Also, check if thickness is adequate for shear.

Choose Design method– Equivalent Frame Method- use elastic frame

analysis to compute positive and negative moments

– Direct Design Method - uses coefficients to compute positive and negative slab moments

1.

2.

3.

Basic Steps in Two-way Slab DesignBasic Steps in Two-way Slab Design

Calculate positive and negative moments in the slab.

Determine distribution of moments across the width of the slab. - Based on geometry and beam stiffness.

Assign a portion of moment to beams, if present.

Design reinforcement for moments from steps 5 and 6.

Check shear strengths at the columns

4.

5.

6.

7.

8.

Minimum Slab Thickness for two-way Minimum Slab Thickness for two-way constructionconstruction

Maximum Spacing of Reinforcement

At points of max. +/- M:

Max. and Min Reinforcement Requirements

7.12.3 ACI in. 18 and

13.3.2 ACI 2

s

ts

balsmaxs

S&Tsmins

75.0

13.3.1 ACI 7.12 ACI from

AA

AA

Distribution of MomentsDistribution of Moments

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

Distribution of MomentsDistribution of Moments

Total static Moment, Mo

3-13 ACI 8

2n2u

0

llwM

cn

n

2

u

0.886d h using calc. columns,circular for

columnsbetween span clear

strip theof width e transvers

areaunit per load factored

l

l

l

wwhere

Column Strips and Middle Column Strips and Middle StripsStrips

Moments vary across width of slab panel

Design moments are averaged over the width of column strips over the columns & middle strips between column strips.


Column strips Design w/width on either side of a column centerline equal to smaller of

1

2

25.0

25.0

l

l

l1= length of span in direction moments are being determined.

l2= length of span transverse to l1


Middle strips: Design strip bounded by two column strips.

Positive and Negative Moments in PanelsPositive and Negative Moments in Panels

M0 is divided into + M and -M Rules given in ACI sec. 13.6.3

Moment DistributionMoment Distribution

Positive and Negative Moments in PanelsPositive and Negative Moments in Panels

M0 is divided into + M and -M Rules given in ACI sec. 13.6.3

8

2n2u

0avguu

llwMMM

Longitudinal Distribution of Longitudinal Distribution of Moments in SlabsMoments in Slabs

For a typical interior panel, the total static moment is divided into positive moment 0.35 Mo and negative moment of 0.65 Mo.

For an exterior panel, the total static moment is dependent on the type of reinforcement at the outside edge.

Distribution of MDistribution of M00

Moment DistributionMoment Distribution

The factored components of the moment for the beam.

Transverse Distribution of Transverse Distribution of MomentsMoments

The longitudinal moment values mentioned are for the entire width of the equivalent building frame. The width of two half column strips and two half-middle stripes of adjacent panels.

Transverse Distribution of Transverse Distribution of MomentsMoments

Transverse distribution of the longitudinal moments to middle and column strips is a function of the ratio of length l2/l1,1, and t.

Transverse Distribution of MomentsTransverse Distribution of MomentsTransverse distribution of the longitudinal moments to middle and column strips is a function of the ratio of length l2/l1,1, and t.

torsional constant

3

63.01

2

3

scs

cbt

scs

bcb1

yx

y

xC

IE

CE

IE

IE

Distribution of MDistribution of M00 ACI Sec 13.6.3.4

For spans framing into a common support negative moment sections shall be designed to resist the larger of the 2 interior Mu’s

ACI Sec. 13.6.3.5

Edge beams or edges of slab shall be proportioned to resist in torsion their share of exterior negative factored moments

Factored Moment in Column Strip Factored Moment in Column Strip

Ratio of flexural stiffness of beam to stiffness of slab in direction l1.

Ratio of torsional stiffness of edge beam to flexural stiffness of slab(width= to beam length)

t

Factored Moment in an Interior Factored Moment in an Interior Strip Strip

Factored Moment in an Exterior Factored Moment in an Exterior PanelPanel

Factored Moment in Column Strip Factored Moment in Column Strip

Ratio of flexural stiffness of beam to stiffness of slab in direction l1.

Ratio of torsional stiffness of edge beam to flexural stiffness of slab(width= to beam length)

t

Factored MomentsFactored Moments

Factored Moments in beams (ACI Sec. 13.6.3)

Resist a percentage of column strip moment plus moments due to loads applied directly to beams.

Factored MomentsFactored Moments

Factored Moments in Middle strips (ACI Sec. 13.6.3)

The portion of the + Mu and - Mu not resisted by column strips shall be proportionately assigned to corresponding half middle strips.

Each middle strip shall be proportioned to resist the sum of the moments assigned to its 2 half middle strips.

ACI Provisions for Effects of Pattern LoadsACI Provisions for Effects of Pattern Loads

The maximum and minimum bending moments at the critical sections are obtained by placing the live load in specific patterns to produce the extreme values. Placing the live load on all spans will not produce either the maximum positive or negative bending moments.

ACI Provisions for Effects of Pattern LoadsACI Provisions for Effects of Pattern Loads

The ratio of live to dead load. A high ratio will increase the effect of pattern loadings.

The ratio of column to beam stiffness. A low ratio will increase the effect of pattern loadings.

Pattern loadings. Maximum positive moments within the spans are less affected by pattern loadings.

1.

2.

3.

Reinforcement Details LoadsReinforcement Details Loads

After all percentages of the static moments in the column and middle strip are determined, the steel reinforcement can be calculated for negative and positive moments in each strip.

2uysu

2 bdR

adfAM

Reinforcement Details LoadsReinforcement Details Loads

Calculate Ru and determine the steel ratio , where =0.9. As = bd. Calculate the minimum As from ACI codes. Figure 13.3.8 is used to determine the minimum development length of the bars.

c

yu

ucuu

59.01

f

fw

wfwR

Minimum extension for reinforcement Minimum extension for reinforcement in slabs without beams(Fig. 13.3.8)in slabs without beams(Fig. 13.3.8)

direct design method_final copy

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