Design of compression members-3

8/17/2019 Design of compression members-3

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Chapter 03 C

Design of CompressionMembers

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Example 3.1

Design a truss compression member

using the following three given cross-sectional shapes

1! "#s with 10 mm thic$ gusset plate an%

snug tight bolte% sta& plates!"! 'ingle angle connecte% through longer

leg!

3! (-section! )he other %ata is as un%er

*D + 110 $, *# + 1.0 $,

# + 3!. m 36 'teel" 5/9/16


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Solution:

or truss members 2+1

#u+# as there is no bracing betweenthe oints

*u+ 1!"*D 41!6*#

*u+ 1!" 110 41!6 1.0 + 356 $,

1- Double Angles

3 5/9/16


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5/9/16 .


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! )he section will be economical if it has nearl&same slen%erness ratio in both %irections! )hismeans that r an% r& shoul% be nearl& same

as the length for both %irections is e7ual8!

! )he ra%ius of g&ration r for the %ouble

section will be same as that for a single

section!C! )he ra%ius of g&ration r& for the %ouble

section will be consi%erabl& higher than for asingle section!

D! rom the above facts it is clear that to ma$e r same in both %irections une7ual leg anglesare to be use% with their longer legs

connecte% together!5 5/9/16


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:! )he proecting leg shoul% be relativel&smaller!

*u + 356 $, KLu + 3!. m

;ass + 90


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Areq for single ngle + 1"16 mm"

sel = re7

'elect section Minimum weight section

b > bmin

bmin + 3!"5% 4"6

+ ?5 mm assuming % + 15 mm8

#/.0+ @5 mm not full& applicable here8

? 5/9/16


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DiAerent options available are

1! "# @9 @9 ?!9 + "?00 mm"

"! "# 10" ?6 ?!9 + "?00 mm"

3! "# 10" ?6 9!5 + 3"00 mm"

,ote n&one out of the Brst two optionsma& be trie% Brst! owevercalculations show that these sections

are not sucient with onl& the thir%section closer to the re7uirements! )henumber of trials ma& be re%uce% b&

using the column selection tables!@ 5/9/16


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Esing the %ouble angles selectiontables of Design i%s for *u+ 356 $,

2 5#5 + 2 & + 3!. m an% sta& plateswith full& tensione% bolts followingoptions are available

9 5/9/16

'ection


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Esing the %ouble angles selectiontables of Design i%s for *u+ 356 $,

2 5#5 + 2 & + 3!. m an% sta& plateswith full& tensione% bolts followingoptions are available

10 5/9/16

'ection


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5/9/1611

1

1


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5/9/161"

1

1


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ence $eeping in view the above valuesfor full& tight sta& plates trial section for

snug tight sta& plates ma& be "#s 10" ?6 9!5! owever consi%ering snug tightsta& plates "#s 10" @9 9!5 ma&

ultimatel& be the Bnal result!

)rial 'ection1 "# 10" ?6 9!5 + " 1600 mm"

#ong legs bac$-to-bac$ connecte% to the

gusset plate!

b + 10" mm F bmin G2

#onger leg is connecte%!13 5/9/16


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G2

r5 + 3"!0 mm as for single angle

Esing Design i%s

b + " ?6 4 10 + 16" mm

r&8appr + b0!19 4s/1"?08

+ 16" 0!19 4 10/1"?08 + 3"!06mm

1. 5/9/16

7.12 7.1050.9

102=


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15 5/9/16

1070.32

34001≅

×=

x

ux x

r

L K

05.10606.32

34001≅

×=

y

uy y

r

L K

lthough r5 is lesser than r& the columnma& buc$le about &-ais if mo%iBe%slen%erness ratio in &-%irection ecee%s

2 5#u5/r5!


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ssume that snug tight bolts connect

sta& plates an% gusset plates!Esing ?5 mm long sta& plates an%treating HaI as the clear %istance

between the sta& plates an%/or gussetplates the c/c spacing of sta& plateswill be a4?5 mm!

16 5/9/16


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'election of 'ta& *lates 'pacing

a/ri + 0!?5 larger of 2 5#u5/r5 J 2 u&/r&

+ 0!?5 10?8 + @0!"5ri + rK + 16!. mm

ama5 + @0!"5 16!./1000

+ 1!316 m

or ?5 mm long sta& plates

,umber of spaces between sta& plates +3.00/13164?58

+ "!.5 sa& 3 spaces8

1? 5/9/16


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,umber of sta& plates + "

a + 3.00/38-?5 + 105@ mm

Note: Number of stay plates may notgenerally exceed three.

a/ri + 105@/16!. + 6.!53

or snug tight plates

1@ 5/9/16

12553.6405.106 22

≅+=

m y

uy y

r

L K


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; + larger of 2 5#u5/r5 J mo%iBe% 2 u&/r&

+ 1"5

Maimum 'len%erness ;atio Chec$

; L "00 G2

Capacit& Chec$

rom table of Design i%s


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G2

r5 + 31!@ mm as for single angle

Esing Design i%s

b + " @9 4 10 + 1@@ mm

r&8appr + b0!19 4s/1"?08

+ 1@@ 0!19 4 10/1"?08 + 3?!"mm

:act calculation for r& to be ma%e onl&

for the last trial8"1 5/9/16

7.12 7.1050.9

102=


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"" 5/9/16

[ ]

( ) mmr

mm I

exact y

y

7.3917202

103.541

103.541)53.24(1720101232

4

4424

=× ×=

×=+×+××=

1078.31

34001 ≅×= x

ux x

r L K

64.857.3934001 ≅×=

y

uy y

r L K


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Esing ?5 mm long sta& plates an%treating HaI as the clear %istance

between the sta& plates an%/or gussetplates the c/c spacing of sta& plateswill be a4?5 mm!

"3 5/9/16


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'election of 'ta& *lates 'pacing

a/ri + 0!?5 larger of 2 5#u5/r5 J 2 u&/r&

+ 0!?5 10?8 + @0!"5ri + rK + 1@!5 mm

ama5 + @0!"5 1@!5/1000

+ 1!.@5 m

or ?5 mm long sta& plates

,umber of spaces between sta& plates +3.00/1.@54?58

+ "!1@ sa& 3 spaces8

". 5/9/16


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,umber of sta& plates + "

a + 3.00/38-?5 + 105@ mm

a/ri + 105@/1@!5 + 5?!19

or snug tight plates

"5 5/9/16

10319.5764.85 22 ≅+=

m y

uy y

r

L K


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or full& tightene% bolts or wel%sappropriate formula for the mo%iBe%

slen%erness ratio must be use%!; + larger of 2 #u/r J mo%iBe% 2 u&/r& +

10?

Maimum 'len%erness ;atio Chec$

; L "00 G2

Capacit& Chec$

rom table of Design i%s


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2- Single Angle !onnecte" #$%oug$ Longe%Leg

Ot is almost impossible to loa% such members

concentricall& %ue to the fact that onl& one

leg is generall& connecte% with the gusset

plate!

)heoreticall& concentric loa%ing coul% onl& beapplie% b& milling the en%s of an angle an%

loa%ing it through bearing plates igure

3!"08!

On practice the actual eccentricit& of loa%ing

is relativel& large an% neglecting it in %esign

ma& lea% to a %angerousl& un%er-%esigne%

member!"@ 5/9/16


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urther single angle can un%ergo lateraltorsional buc$ling!

'eparate O'C provisions are applicablefor such %esign!

)he proce%ure use% in this eample isapplicable for single angles with

eccentricit& epecte% in a planar truss! :7ual leg angles are generall& preferre%

for single angle columns in case the two

eAective lengths 2 # an% 2 & are e7ual! owever une7ual leg angles ma& also be

use% if the resulting section comes out to

be economical!"9 5/9/16


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5/9/1630

)he selection can also be ma%e usingthe single angle section column

selection tables!


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*u + 356 $,

;ass + 1"5


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sel = re7

'elect section Minimum weight sectionb > bmin + ?5 mm

:7ual legs will be preferre% as 2 # an%

2 & are e7ual! )rial 'ection

# 15" 15" 1"!?0 rK + 30 mm r& +

.?!" mm + 3?10 mm"

b + 15" F bmin G$3" 5/9/16


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3. 5/9/16

MPa F cr c 98.96=φ

Ok kN356kN80.3591000371098.96 A F sel cr c >=×=φ

#oa%ing c&cles are lesser than "0000!

inal 'election L 12 x 12 x 12.&


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3 '-Section

*u + 356 $,

;ass + 90


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sel = re7

'elect section Minimum weightsection

b > bmin + ?5 mm

% L 360mm

Esing the (-shape selection table of

Design i%s for *u + 356 $, 2 & + 3!.

m following option is obtaine% giving


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#%ial Section: ' 10 x 22.

2 &8e7 + 3!./1!?5 + 1!9. m not critical8

r5 + 65 r& + 3?!1 mm + "@60 mm"

3? 5/9/16

Ok 762

152

2 minbmm

b f

>==

Ok 15.8 5.112

r =


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Final Section: ' 10 x 22.

3@ 5/9/16

MPa F cr c 66.143=φ

Ok 3564111000286066.143 kN kN A F sel cr c >=×=φ

Ok 002 921.37

3400

min


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:ample 3!" (embe%s un"e% St%ess)e*e%sal

Design a bri%ge truss compressionmember 2+18 that is 3!5m long!

*D+ @0 $, C8

*#+ "?0 $, C8 )#+ "?0 $, )8!

'elect following two t&pes of sections

i8 "#s with 15 mm thic$ gusset platewel%e% connections but snug bolte%sta& plates!

ii8 (-section wel%e% connections!39 5/9/16


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'olution

*u+ 1!"*D 4 1!6*# + 1!" @0 4 1!6

"?0 + 5"@ $, )u+-1!"*D 4 1!6)# +-1!" @0 4 1!6

"?0 + 336 $,

*u F )u Design as compression

member for *u an% then chec$ as

tension member for )u!

.0 5/9/16


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!omplete t$e Example

+ou%sel,

.1 5/9/16


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EAL S#)E/# !L(/

:7ual strength column is %eBne% as a

column having same critical buc$lingstrength along both strong an% wea$aes!

On other wor%s for an e7ual strengthcolumn 2#/r ratio along both the aesshoul% approimatel& be the same!

)he material of the column is use%more ecientl& if this criterion issatisBe% which results in the moreeconomical column %esign!

." 5/9/16

LK


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or an e7ual strength column ratio of

ra%ii of g&ration in the two %irectionsshoul% be e7ual to the ratio of eAectivelength in the two %irections!

racing is provi%e% in such a wa& that the

above e7uation is approimatel& satisBe%!

)he ratio r/r& is the main criterion for

%esign of bracing!

.3 5/9/16

y y

x x

y

x

y

y y

x

x x

L K

L K

r

r

r

L K

r

L K

=

=


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2nowing 2 # an% r/r& ratio the re7uire%

eAective un-brace% length along &-ais

ma& be %etermine% as follows

ase% on the above information the#;D 'peciBcations provi%es a metho%with which a (-section can be selecte%from the column selection tables withlittle trial an% error when the un-brace%lengths in the two %irections are$nown/%eci%e% earlier!

.. 5/9/16

y x

x x y y

r r

L K L K =


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)he %esigner enters the appropriatetable with 2 & selects a section ta$es

the r5/r& value given at the bottom ofthe table for that shape an% calculates2 &8e7 as follows

Of 2 &8e7 is greater than 2 & buc$ling

is epecte% about -ais an% the%esigner will re-enter the table with2 &8e7 an% will select the Bnal

selection!.5 5/9/16

( ) y x

x x

eq y y

r r

L K L K =


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Example 3.3

9 m long column in a frame structure

is to resist an aial factore%compressive loa% of 1600 $,! ssumethe bottom en% of the column to bepinne% an% the top en% to be Be% inboth %irections! )he column is brace%at its thir% points along wea$ ais!

ssume that there is no si%eswa&between the top an% bottom points!Design a wi%e Pange section using 36steel an% O'C 'peciBcations!

.6 5/9/16

S l ti


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Solution:

uc$ling of the column withbraces results in rotation of

the main member at thebrace points an% lateralbracing %oes not prevent thisrotation!

ence brace point ma& beconsi%ere% ust li$e a hingefor that %irection igure3!""8!

owever lateral translationor swa& of the brace point isalmost Kero!

.? 5/9/16

igure 3!"" uc$ling ofColumn along wea$ ais


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5/9/16.@

#/3

a8 )op alf Column uc$les in (ea$ Direction


49/62

5/9/16.9

#/3

a8 )op alf Column uc$les in (ea$ Direction

#/3

8 Mi%%le J ottom Column uc$ling in (ea$ Direction


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5/9/1650

#u+ 9 m

c8 Column uc$ling in Maor is Direction

:Aective #engths for uc$ling of Column

* 1600 $,


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*u + 1600 $,

;ass + 90


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urther O'C 'peciBcationsrecommen%s 2 + 1!0 for brace%

columns!2 5 + 0!@ Bgure 3!"3c8 Ese 2 5 + 1!0

2 u& + 1!0 9/3 + 3!0 m2 5#5 + 1!0 9 + 9!0 m

ence r5/r& of the selecte% section

closer to 3!0 will be preferre%!5" 5/9/16

33

9

== y y x x

L K

L K

ll i ti il bl


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ollowing options are available

1! ( 360?" + 9100 mm" r/r& + 3!06

"! ( 36091 + 11500 mm" r/r& + "!..3! ( 310@6 + 11000 mm" r/r& + "!10

.! ( 3109? + 1"3"3 mm" r/r& + 1!?5

5! ( "00@6 + 11000 mm" r/r& + 1!?. )he Brst option has area less than theassume% re7uire% value but r/r& is close

to 3!0! )his ma& be trie% as Brst option! )heother options although have greater

area ma& fail!53 5/9/16

) i l ' ti ( 360 ?"


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)rial 'ection ( 360?"

+ 9100 mm" r5+ 1.9 mm r&+ .@!5

mm

5. 5/9/16

Ok t

b

f

f 15.8 7.6

2r =


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,ote In this example area of qualifying example


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,ote In this example, area of qualifying examplesection is lesser than the assumed requiredarea. his is only because of selecting the

equal strength column. !urther, by using thecolumn selection tables, the criterion of equalstrength is automatically satis"ed.

Example 3.4:

Design a (-section column in a buil%ing frameof .m stor& height for an aial factore%compressive loa% of 9?5 $,! )he frame is

brace% against si%eswa& along its wea$ aisbut si%eswa& is allowe% along the maor ais2+"8! ssume the en%s of the column to bepinne% at the base an% Be% at the top!

56 5/9/16

'olution


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'olution

*u + 9?5 $,

;ass + 90


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2 5 + "!0

2 & + 1!0

#u5 + #u& + .m 2 5#u5 + @!0 m

2 u& + .!0m

or *u+ 9?5 $, an% 2 & + .!0m the

selecte% section using the columnselection tables is ( "50 .9!1!

5@ 5/9/16

preferred e!ill2.0t"cl"#e 0.2 y

x

uy y

ux x

r r

l K l K ⇒=

rx 162


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ence 2 &8e7 is not critical with

respect to 2 &!

)rial 'ection ("50.9!1

595/9/16

( ) mr r l K

l K

r r

y x

x xeq y y

y

x

7.316.20.8

16.2

===

=

or * 9?5 $, an% 2 # . 0m


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or *u + 9?5 $, an% 2 &+ .!0m

)rial 'ection ("50.9!1

+ 6"60 mm" r5/r& + "!15 % + ".?mm

bf + "0" mm tf + 11!0 mm tw +

?!. mm r5 + 106 mm r& + .9!3 mm

605/9/16

Ok

t

b

f

f 15.8 1.9

2r =


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Maimum 'len%erness Chec$;+ @" "00 G$


62/62

inal 'election ' 20 x 49.1

Ok kN kN P nc 9759861000626054.157 >=×=φ

Documents

Design of compression members-3