02lecture 6 (dai minh)

7/25/2019 02Lecture 6 (Dai Minh)

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Design of concrete structures based on ACI 318

Lecture note No6

Presented by Dr Nguyen Dai Minh PhD PEng

IBST, Hanoi, Dec 2011

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Lecture note 6

Short columns under compression and

biaxial bending and analysis and design ofslender columns

(based on ACI 318)


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Contents of the lecture

1. Short columns under biaxial bending

2. Load contour method

3. Reciprocal load method

4. Slender columns introduction

5. Concentrically loaded columns

6. Compression and bending

7. ACI criteria for neglect of slenderness

8. ACI criteria for non-sway versus sway frames

9. ACI moment magnifier method for non-sway frames

10. ACI moment magnifier method for sway frames

11. Second-order analysis for slenderness effects12. Summary

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1. Short columns under biaxial bending

Fig 8.15 shows the column under biaxial bending. It is called

column as the compression load is dominated.


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Failure surface: Failure curve for each angle can constructthe strength interaction curve P-M as shown in Fig 8.15d. The

series of these curves shall be the failure surface. If the point

of (Pu, Mux, Muy) outside of this failure surface the column will

fail.

Constructing of the failure surface is an extension of

uniaxial bending of the column. In Fig 8.15c, for a given angle, the strength interaction curve of compression and uniaxialbending can be built using for various value of c, the strain

compatibility and equilibrium equations can be established,

then ultimate capacities of the column (Pn and Mn) can be

determined for the given angle . Hence, the failure surfacecan be constructed.


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For design practice, more simple methods are used in the

analysis for columns under biaxial bending.

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The load contour method is based on the representing the failure

surface by a family of curves corresponding to constant values of Pn.

2. Load contour method

Fig 1: Load

contour, plane of

constant Pn.


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General form of these curves can be approximated by a

nondimensional interaction equation:

)18.8(1

2

0

1

0

ny

ny

nx

nx

M

M

M

M

ACI recommends value of is between 1.15 and 1.55 ( 1.19).

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Design procedure:

For given Pu, Mux, Muy , b, h, fc and Ast to check the column will be

failed or not ?

- Let Pn = Pu => determine Mnx0 and Mny0 based on the uniaxial

bending strength curve.

- Choose value of between 1.15 and 1.55 (

1.19).- Check equation (8.19) to be satisfied or not?

)18.8(100

ny

ny

nx

nx

M

M

M

M

This method is of course an approximate method and trial

design needs to be carried out.


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BS 8110 for biaxial bending of columns

Fig 7.3-5a, Kong and

Evans (1995)

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Kong and Evans (1995)


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(fig 7.3-5 (c))


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(a)

(b)

(c)Where: corresponding to N to find Mux and Muy as

for unaxial bending of column


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N => Mux

N => Muy

End of BS 8110

N= 0.8*Nuz

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3. Reciprocal load method (phng php ti trng nghcho)

Point C: P0, ex=ey=0

Point N: Pn,exact, ex, ey

Point B: Pnx0, ex=0, ey

Point A: Pny0, ex, ey=0,

N

Point M: Pn,approx, ex, ey

N


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4. Slender columns - introduction

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5. Concentrically loaded columns

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Bracing by shear walls, cores etc.

to prevent the lateral displacement

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6. Compression plus bendinga) Simply supportedcase

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Eq. (9.4) can be written in other form (Johnson 1976):

Where = -0.2 to +0.2 (for most practical cases) is a coefficientdepending on type of loading. Pc is the critical load.

As P


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Simply supported

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b) Two ends are fixed 2 curvatures


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c) Fixed portal frame, laterally unbraced

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d) Fixed portal frame, laterally braced


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Maximum moment and moment magnification factor considering

the column slenderness is:

where:

e) General case

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7. ACI criteria for neglect of slenderness


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braced frame

Phn 8 bi

ging


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8. ACI criteria for non-sway versus sway frames

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First way:

Second way:


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To calculate and Q:

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9. ACI moment magnifier method for non-sway

frames

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M2 >= M2,min

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EI to determine Pc in Eq. (9.13):


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Determination of k:

Degree of end restraint at each end is:

membersflooroflEI

columnsoflEI

/

)/

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Outline of the procedure for non-sway frames (braced frames):

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10. ACI moment magnifier method for sway frames

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TO BE REPLACED BY

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ACI code 10.13.4 provides 3 methods for calculating the magnifiedsway moments sMs:

- First method: the column end moments are caculated using the 2-nd

order analysis based on the member stiffness given in Point 8 (or

9.5 in the book) ACI criteria for non-sway versus sway frames:

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- The second method: The magnified sway moments are calculated by

- The thirst method:


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Note:


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Previous method using eq. (9.20) is complicated.

11. Second-order analysis for slenderness effects

a

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12. Summary

This is a hard lecture on column design. Braced and un-

braced frames should be carefully considered in design oftall buildings. Instability of the members or of the structures

will always lead to fatal failure of the building.

The lecture has discussed on:

Short columns under biaxial bending

Load contour method

Reciprocal load method

Slender columns introduction

Slender columns under concentrically loadingSlender columns under compression and bending

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ACI criteria for neglect of slenderness

ACI criteria for non-sway versus sway frames

ACI moment magnifier method for non-sway frames

ACI moment magnifier method for sway frames

Second-order analysis for slenderness effects

In the next lecture, analysis and design of column using SAP

2000 or ETABS and design of shear walls and cores will be

discussed.


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Thank you very much for attention !

Questions and answers !

02lecture 6 (dai minh)

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