Mba Ebooks ! Edhole

Free Ebooks Download

Mba Ebooks


Mba Ebooks

By Edhole

Mba ebooks

Free ebooks downloadhttp://ebooks.edhole.com

2

Second order effectsSecond order effects

P

H

x

M(h) = Hh + PM(x) = Hx + P + P x / h

PH

h

x

M(h) = HhM(x) = Hx

Displacement

Frame

Load

Sway

http://ebooks.edhole.com

3

ImperfectionsImperfections

Frame imperfection

L

N

Member Imperfection

eo,d


4

ImperfectionsImperfections

Frame imperfection– always to be allowed for

Member imperfection:– only for slender members (rare) in sway

frames, otherwise it is covered in the relevant buckling curve


5

Frame imperfectionFrame imperfection

The frame imperfection is as follows:

storeys ofnumber :

planeper columnsheight full ofnumber :

1but 1

2,0

1but 1

5,0

200/1

5,0

5,0

0

0

s

c

ss

s

cc

c

sc

n

n

kn

k

kn

k

kk


6

Frame imperfectionFrame imperfection

Frame imperfection can be replaced by an equivalent closed system of horizontal forces applied at the floor levels (including the foundation level).

F1

F2

F1

F2

(F1+F2)/2 (F1+F2)/2

Equivalent forceshttp://ebooks.edhole.com

7

Methods of structural analysisMethods of structural analysis

MATERIAL PROPERTYELASTIC PLASTIC

1st ORDERGEOMETRICAL

EFFECTS2nd ORDER


8 Choice between elastic analysis and plastic analysis

Choice between elastic analysis and plastic analysis

Elastic analysis can always be used.

Plastic analysis allowed only when one meets the restrictions on steel properties, cross-section classification, restraints (at or near plastic hinges) and, if needed, on joint ductility.


9

Frame classificationFrame classification

BRACINGBRACED UNBRACED

SWAYLATERAL

DISPLACEMENTNON SWAY


10

Braced frame

(may be sway if bracing is very flexible)

Unbraced frame

(may be non-sway if it is insensitive to horizontal loads)

Braced and unbraced framesBraced and unbraced frames

A frame without bracing is unbraced. A frame with bracing is classified as braced

only when the braced structure is sufficiently stiff laterally. http://ebooks.edhole.com

11

Frame without bracing is unbraced

Frame with bracing is– unbraced when:

– braced when:

where are the lateral flexibilities of the structure with and without the bracing respectively

Braced and unbraced framesBraced and unbraced frames

Displacement

Frame without bracing

LoadSway

Displacement

Frame with bracing

LoadSway

unbrbr 2,0

unbrbr 2,0

and unbrbr


12

Sway and non-swaySway and non-sway

Non-sway frame when:

Sway frame when:

where: is the design value of the total vertical load applied to the structure

and: is the elastic critical vertical load producing sway instability of the structure

1,0cr

SdV

V

1,0cr

SdV

V

SdV

crV


13

Elastic critical loadElastic critical load

The following approach may be used:– Approximate procedure:

where:

is the sway at the top of storey ih is the height of storey iH and V are the total horizontal and

vertical reactions respectively at the bottom of storey i

icr

Sd

hH

VV

V

max


14

Frame classificationFrame classification

Decision on the use of bracing or not influences sway classification

Preliminary member sizing and estimates of column vertical loads: use to provide an indication of the sway classification using:

effectsorder 2ndfor allowmust :Sway : 1,0

analysisorder 1st usecan :sway -Non : 1,0

cr

Sd

cr

Sd

VV

VV


15

Frame classification and type of frame analysis

Frame classification and type of frame analysis

BRACINGBRACED UNBRACED

SWAYLATERAL

DISPLACEMENTNON SWAY 1st order1st order

2nd order2nd order2nd order2nd order

1st order1st order


16

Second order analysis for sway frames

Second order analysis for sway frames

“True” second order analysis includes both the sway effect (P-effect) and the P-effect (member deflection effect) by modifying the member stiffness terms. Load is applied in increments. Iteration and convergence procedures are required.

For most sway frames, only the P-effect (sway effect) needs to be allowed for. The concept of the

Equivalent Lateral Load Method may also be used.

Eurocode 3: indirect methods often possible.http://ebooks.edhole.com

17

Sway frame : 2nd order effects Sway frame : 2nd order effects

Alternatives to a “true” 2nd order analysis: 1st order analysis + “Amplified Sway

Moment” method when:

1st order analysis + “Sway Mode Buckling Length” method (20% sway moment increase)

crSdcr

Sd

crSdcr

Sd

VVVV

VVVV

11by forces allAmplify 20,0:design Plastic

11by MAmplify 25,0:design Elastic sway


18 Check for joint stiffness when rigid joints are assumed

Check for joint stiffness when rigid joints are assumed

Mj

Step a) :Frame analysis based onthe assumption Sj,app = (joint presumably rigid)

Mj

Step b) :Stiffness range for rigidjoints based on Sj,app = see Eurocode 3

Mj

Step c) :Check if actual initial stiffnessSj,ini is in range

Sj,app

Sj,ini

Joint must meet “rigid joint” classification criteriahttp://ebooks.edhole.com

19 Check of initial semi-rigid joint “good guess” stiffnesses

Check of initial semi-rigid joint “good guess” stiffnesses

M

S j,app

M

lower boundary

upper boundary

M

S j,ini

Step b) Step a) Step c)

S j,app

Frame analysis based on a design joint stiffness derived fromSj,app

Stiffness range for semi-rigid joints based on S,app

Check if actual initial stiffness Sj,ini is in range

Semi-rigid joint stiffnesses can vary within a fairly wide range without significantly altering the frame resistancehttp://ebooks.edhole.com

20 Fixity factor approach: check for joint stiffnesses

Fixity factor approach: check for joint stiffnesses

Frame Lower boundary Upper boundary

Braced (f = 0,5)

SEI

Lj,appb

b

3

SEI

Lj,inib

b

24

13

SEI

Lj,inib

b

6

Unbraced (f=0,8)

SEI

Lj,appb

b

12

SEI

Lj,inib

b

48

7

SEI

Lj,inib

b

30



Mba Ebooks


Mba Ebooks

By Edhole

Mba ebooks

Free ebooks downloadhttp://ebooks.edhole.com

Mba Ebooks ! Edhole

Education

Transcript of Mba Ebooks ! Edhole