Members in Compression - V

8/12/2019 Members in Compression - V

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Compression Members


2/28

COLUMN STABILITY

A.Flexural Buckling

Elastic Buckling

Inelastic Buckling

Yielding

B. Local BucklingSection E7 pp 16.1-39

and B4 pp 16.1-14

C. Lateral Torsional Buckling


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AISC Requirements

CHAPTER E pp 16.1-32

Nominal Compressive Strength

gcrn AFP

AISC Eqtn E3-1


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AISC Requirements

LRFD

ncu PP

loadsfactoredofSumuP

strengthecompressivdesignncP

0.90ncompressioforfactorresistance c


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In Summary

877.0

44.0or

71.4658.0

otherwiseF

FF

F

E

r

KLifF

F

e

ye

y

yF

F

cr

e

y

200

r

KL


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In Summary - Definition of Fe

Elastic Buckling Stress corresponding to the controlling mode of

failure (flexural, torsional or flexural torsional)F

e:

Theory of Elastic Stability (Timoshenko & Gere 1961)

Flexural Buckling Torsional Buckling

2-axis of symmetry

Flexural Torsional

Buckling

1 axis of symmetry

Flexural Torsional

Buckling

No axis of symmetry

22

/ rKLEFe

AISC EqtnE4-4

AISC EqtnE4-5

AISC EqtnE4-6


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Column Design Tables

Assumption : Strength Governed by Flexural Buckling

Check Local Buckling

Column Design Tables

Design strength of selected shapes for effective length KL

Table 4-1 to 4-2, (pp 4-10 to 4-316)

Critical Stress for Slenderness KL/r

table 4.22 pp (4-318 to 4-322)


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Design of Members in Compression

Selection of an economical shape: Find lightest shape

Usually category is defined beforehand, e.g. W, WT etc

Usually overall nominal dimensions defined in advance

because of architectural and other requirements.

USE OF COLUMN LOAD TABLES

IF NOT APPLICABLE - TRIAL AND ERROR


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EXAMPLE I COLUMN LOAD TABLES

A compression member is subjected to service loads pf 165 dead and 535

kips live. The member is 26 feet long and pinned at each end

LRFD

Calculate factored load

kips054,1)535(6.1)165(2.16.12.1 LDPu

Required Design Strength

kips054,1ncP

Enter Column Tables with KL=(1)(26)=26 ft

uPXW kips230,1:strengthdesign14514 OK


10/28

EXAMPLE I COLUMN LOAD TABLES

A compression member is subjected to service loads pf 165 dead and 535

kips live. The member is 26 feet long and pinned at each end

ASD

Calculate factored load

kips700)535()165( LDPa

Required Allowable Strength

kips700c

nP


aPXW kips702:strengthdesign13214 OK


11/28

EXAMPLE Ii COLUMN LOAD TABLES

Select the lightest W-shape that can resist a service dead load of 62.5

kips and a service live load of 125 kips. The effective length is 24 feet.

Use ASTM A992 steel

LRFD

Calculate factored load and required strength

nu PLDP ckips275)125(6.1)5.62(2.16.12.1


No Footnote: No need to

check for local buckling

kips275withW8No:8 ncPW

kips282,5410:10 c nPXWW




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IF COLUMNS NOT APPLICABLE

1. Assume a value for Fcr

ycr FF

2. Determine required areaLRFD

crc

ugugcrc

F

PAPAF

ASD

cr

ag

g

acr

F

PA

A

PF

6.06.0


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IF COLUMNS NOT APPLICABLE

3 Select a shape that satisfies area requirement

4 Compute Fcrfor the trial shape

5 Revise if necessary

If available strength too close to required value try next tabulated value

Else repeat 1-4 using Fcrof trial shape

6 Check local stability and revise if necessary


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Example

Select a W18 shape of A992 steel that can resist a service dead load of

100 kips amd a service live load of 300 kips. Effective length KL=26 ft

Calculate factored load and required strength

kips600)300(6.1)100(2.16.12.1 LDPu

Try ksi333

2 ycr FF

Required Area 2in2.20339.0

600

crc

ugF

PA


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Example



Try W 18x71

2.20in8.20

2

gA

Slenderness 2005.18370.1

1226

min

r

KLOK

OKAvailable Area

Eulers Stress ksi5.85.183

)000,29(

/2

2

2

2

rKL

E

Fe

11350

000,2971.471.4

yF

EElastic Buckling

Slenderness Limit

5.183

min

r

KL

ELASTIC BUCKLING


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Example



Critical Stress ksi455.75.8877.0877.0 ecr FF

NG

Design Strength

kips140)8.20)(455.7(9.0 gcrcnc AFP kips600


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Example



Required Area

2in3.33209.0

600

crc

ug

F

PA

Assume NEW

Critical Stress

2

455.733ksi20crF


18/28

Example



Try W 18x119

3.33in1.35

2

gA


1226

min

r

KLOK

OKAvailable Area


)000,29(

/2

2

2

2

rKL

E

Fe

11350

000,2971.471.4

yF

EElastic Buckling

Slenderness Limit

116

min

r

KL

ELASTIC BUCKLING


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Example




Design Strength

kips589)1.35)(65.18(9.0 gcrcnc AFP kips600 NG

This is very close, try next larger size


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Example



Try W 18x130

2

in2.38gA


1226

min

r

KLOK

Available Area


)000,29(

/2

2

2

2

rKL

E

Fe

11350

000,2971.471.4

yF

EElastic Buckling

Slenderness Limit

6.115

min

r

KL

ELASTIC BUCKLING


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Example




OK

Design Strength

kips646)2.38)(79.18(9.0 gcrcnc AFP kips600


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More on Effective Length Factor

A

B

IgLg IgLg

IcLc

IcLc

Assumptions

All columns under

consideration reach bucklingSimultaneously

All joints are rigid

Consider members lying in the

plane of buckling

All members have constant A

Elastic Behavior

Define:

gg

cc

ALI

LIG

gg

cc

BLI

LIG


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Effective Length Factor-Alingnment Charts

Use alignment charts (Structural Stability Research Council SSRC)

AISC Commentary Figure C-C2.3 nad C-C2.4 p 16-.1-241

Connections to foundations

(a) Hinge

G is infinite - Use G=10

(b) Fixed

G=0 - Use G=1.0

Assumption of Elastic Behavior is violated whenInelastic Flexural Buckling min

71.4r

KL

F

E

y


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Example

gg

cc

LI

LIG

Joint A

94.018/183020/1350

12/107012/833 AG

A

B

W12x120

C

W12x120

W24x68

W24x68W24x55

W24x55

12

15

12W12x96

20 18

Joint B

95.018/183020/1350

15/107012/1070

BG

Joint C

0.10CGPinned EndSway Uninhibited


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Example

AISC Commentary Figure C-C2.3 nad C-C2.4 p 16-.1-241

COLUMN AB

94.0AG

95.0BG

3.1xK

COLUMN BC

0.10cG

95.0BG

85.1xK


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More on Effective Length

Assumptions

All columns underconsideration reach bucklingSimultaneously

All joints are rigid

Consider members lying in theplane of buckling

All members have constant A

Elastic Behavior Violated


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Example

Compute Stiffness Reduction Factor per LRFD for an axial compressive stress of25 ksi and Fy=50 ksi

ksi25

g

u

A

P

y

FF

gc

uinelasticcr

F.A

PF ey6580ksi27.78

9.0

25)(

ksi61.35506580ksi27.78 50 eF F. e

23.3161.35877.08770)(

eelasticcr F.F

890023.31

28.27

)(

)(.

F

F

elasticcr

inelasticcr

a

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Members in Compression - V