lecture -0008 compression members
TRANSCRIPT
-
8/13/2019 Lecture -0008 Compression Members
1/91
N.W.F.P. University ofEngineering and Technology
Peshawar
1
By: Prof Dr. Akhtar Naeem Khan
Lecture 08: Compression Members
-
8/13/2019 Lecture -0008 Compression Members
2/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 2
Compression Members
Structural elements that are subjected to axial compressive forces only are called columns.Columns are subjected to axial loads through
the centroid. The stress in the column cross-section can be
calculated as
where, f is assumed to be uniform over the
entire cross-section
A
=f
-
8/13/2019 Lecture -0008 Compression Members
3/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan
Compression Members
This ideal state is never reached. The stress-state will be non-uniform due to!Accidental eccentricity of loading with
respect to the centroid
"ember out-of #straightness $croo%edness&,or
'esidual stresses in the member cross-section due to fabrication processes
-
8/13/2019 Lecture -0008 Compression Members
4/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan !
Compression Members
Sometime they may carry bending moments as
well about one or both axis of cross-section.
The bending action may produce tension inpart
of the cross-section
(espite of tensile stresses or forces that mayproduce, columns are generally referred as)Compression "embers* because compression
stresses normally dominate their behavior.
-
8/13/2019 Lecture -0008 Compression Members
5/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan "
Compression Members
#n addition to mo$t common type of
compre$$ion mem%er$ &vertica' (em%er$
in $tructure)*compre$$ion may inc'ude the
Arch ri%$
+i,id frame mem%er$ inc'ined or otherwi$e
-ompre$$ion e'ement$ in tru$$e$
-
8/13/2019 Lecture -0008 Compression Members
6/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan
Compression Members
-
8/13/2019 Lecture -0008 Compression Members
7/91CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan /
Compression Members
-
8/13/2019 Lecture -0008 Compression Members
8/91CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 0
Compression Members
-
8/13/2019 Lecture -0008 Compression Members
9/91CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan
Compression Members
-
8/13/2019 Lecture -0008 Compression Members
10/91CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 1
Compression Members
-
8/13/2019 Lecture -0008 Compression Members
11/91CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 11
Compression Members
-
8/13/2019 Lecture -0008 Compression Members
12/91CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 12
3'enderne$$ +atio4he 'on,er the co'umn* for the $ame 56$ection*
the ,reater %ecome$ it$ tendency to %uck'e and
$ma''er %ecome$ it$ 'oad carryin, capacity.
4he tendency of co'umn to %uck'e i$ u$ua''y
mea$ured %y it$ $'enderne$$ ratio
Compression Members Vs
Tension Members
-
8/13/2019 Lecture -0008 Compression Members
13/91CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 1
Compression Members Vs
Tension Members
7ffect of materia' #mperfection$ and 8'aw$
3'i,ht imperfection$ in ten$ion mem%er$ are can
%e $afe'y di$re,arded a$ they are of 'itt'e
con$e9uence.n the other hand $'i,ht defect$ in co'umn$ are
of ,reat $i,nificance.
A co'umn that i$ $'i,ht'y %ent at the time it i$ putin p'ace may have $i,nificant %endin, re$u'tin,
from the 'oad and initia' 'atera' def'ection.
-
8/13/2019 Lecture -0008 Compression Members
14/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 1!
Compression Members Vs
Tension Members
4en$ion in mem%er$ cau$e$ 'en,thenin,
of mem%er$.-ompre$$ion %e$ide compre$$ion force$
cau$e$ %uck'in, of mem%er.
-
8/13/2019 Lecture -0008 Compression Members
15/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 1"
Compression Members Vs
Tension Members
resence of holes in bolted connection reduce
+ross area in tension members.
resence of bolts also contribute in ta%ing loadAn Ag
-
8/13/2019 Lecture -0008 Compression Members
16/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 1
WHY column more critical
than tension member?
A co'umn i$ more critica' than a %eam
or ten$ion mem%er %ecau$e minorimperfection$ in materia'$ and
dimen$ion$ mean a ,reat dea'.
-
8/13/2019 Lecture -0008 Compression Members
17/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 1/
WHY column more critical
than tension member?
4he %endin, of ten$ion mem%er$
pro%a%'y wi'' not %e $eriou$ a$ the
ten$i'e 'oad$ tend$ to $trai,hten tho$emem%er$* %ut %endin, of compre$$ion
mem%er$ i$ $eriou$ %ecau$e
compre$$ive 'oad$ wi'' tend to ma,nify
the %endin, in tho$e mem%er$.
-
8/13/2019 Lecture -0008 Compression Members
18/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 10
Compression Member Failure
4here are three %a$ic type$ of co'umn fai'ure$.
ne* a compre$$ive materia' fai'ure& very $hort
and fat).
4wo* a %uck'in, fai'ure*&very 'on, and $kinny).
4hree* a com%ination of %oth compre$$ive and
%uck'in, fai'ure$.&'en,th and width of a co'umn i$in %etween a $hort and fat and 'on, and $kinny
co'umn).
-
8/13/2019 Lecture -0008 Compression Members
19/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 1
Compression Member Failure
4here are three %a$ic type$ of co'umn fai'ure$.
ne* a compre$$ive materia' fai'ure& very $hort
and fat).
4wo* a %uck'in, fai'ure*&very 'on, and $kinny).
4hree* a com%ination of %oth compre$$ive and
%uck'in, fai'ure$.&'en,th and width of a co'umn i$in %etween a $hort and fat and 'on, and $kinny
co'umn).
-
8/13/2019 Lecture -0008 Compression Members
20/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 2
Compression Member Failure
Flexural Buckling &a'$o ca''ed 7u'erBuck'in,)i$ the primary type of
%uck'in,.mem%er$ are $u%;ected to
%endin, or f'e5ure when they %ecome
un$ta%'e
-
8/13/2019 Lecture -0008 Compression Members
21/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 21
Compression Member Failure
Local Buckling4hi$ occur$ when $omepart or part$ of 56$ection of a co'umn are
$o thin that they %uck'e 'oca''y in
compre$$ion %efore other mode$ of%uck'in, can occur
-
8/13/2019 Lecture -0008 Compression Members
22/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 22
Compression Member Failure
Torsional Buckling 4he$e co'umn$ fai' %y
twi$tin,&tor$ion) or com%ined effect of
tor$iona' and f'e5ura' %uck'in,.
-
8/13/2019 Lecture -0008 Compression Members
23/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 2
Sections used or
Compression Member
#n theory numerou$ $hape$ can %e
u$ed for co'umn$ to re$i$t ,iven 'oad$.
-
8/13/2019 Lecture -0008 Compression Members
24/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 2!
Sections used or
Compression Member
-
8/13/2019 Lecture -0008 Compression Members
25/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 2"
Sections used or
Compression Member
-
8/13/2019 Lecture -0008 Compression Members
26/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 2
Sections used or
Compression Member
-
8/13/2019 Lecture -0008 Compression Members
27/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 2/
Sections used or
Compression Member
-
8/13/2019 Lecture -0008 Compression Members
28/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 20
Column !uc"lin#
Buck'in,
7'a$tic Buck'in,
#ne'a$tic Buck'in,
-
8/13/2019 Lecture -0008 Compression Members
29/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 2
Column !uc"lin#
Buck'in, i$ a mode of fai'ure ,enera''y
re$u'tin, from $tructura' in$ta%i'ity due
to compre$$ive action on the $tructura'
mem%er or e'ement invo'ved.
75amp'e$ of common'y $een and u$ed
too'$ are provided.
-
8/13/2019 Lecture -0008 Compression Members
30/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan
!uc"lin#75amp'e
-
8/13/2019 Lecture -0008 Compression Members
31/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 1
!uc"lin#75amp'e
-
8/13/2019 Lecture -0008 Compression Members
32/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 2
!uc"lin#75amp'e
-
8/13/2019 Lecture -0008 Compression Members
33/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan
!uc"lin#75amp'e
-
8/13/2019 Lecture -0008 Compression Members
34/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan !
!uc"lin#
75amp'e &a) i$ temporary or e'a$tic
%uck'in,.
75amp'e &%*c*d) are e5amp'e$ of p'a$tic
%uck'in,.
-
8/13/2019 Lecture -0008 Compression Members
35/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan "
Column !uc"lin#3tee' co'umn %uck'in,
-
8/13/2019 Lecture -0008 Compression Members
36/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan
Mechanism o !uc"lin#
=et u$ con$ider 8i, 1* 2* and $tudy themcarefu''y.
#n fi,1 $ome a5ia' 'oad P i$ app'ied to the co'umn.
4he co'umn i$ then ,iven a $ma'' def'ecion %y,ivin, a $ma'' force 8.
#f the fprce P i$ $uficient'y $ma''* when the force 8
i$ removed* the co'umn wi'' ,o %ack to it$ ori,ina'$trai,ht po$ition.
-
8/13/2019 Lecture -0008 Compression Members
37/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan /
Mechanism o !uc"lin#Fig 1
-
8/13/2019 Lecture -0008 Compression Members
38/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 0
Mechanism o !uc"lin#
4he co'umn wi'' ,o %ack to it$ ori,ina' $trai,ht
po$ition. >u$t a$ the %a'' return$ to the %ottom
of the container.?ravity tend$ to re$tore the %a'' to it$ ori,ina'
po$ition whi'e in co'umn$ e'a$ticity of co'umn
it$e'f act$ a$ a re$torin, force.
4hi$ action con$titute$ $ta%'e e9ui'i%rium.
-
8/13/2019 Lecture -0008 Compression Members
39/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan
Mechanism o !uc"lin#
4he $ame procedure can %e repeatedwith increa$ed 'oad unti'' $ome critica'
va'ue i$ reached.
-
8/13/2019 Lecture -0008 Compression Members
40/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan !
Mechanism o !uc"lin#
Fig 2
-
8/13/2019 Lecture -0008 Compression Members
41/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan !1
Mechanism o !uc"lin#
4he amount of def'ection depend$ on
amount of force 8.
4he co'umn can %e in e9ui'i%rium in an
infinite num%er of %ent po$ition.
-
8/13/2019 Lecture -0008 Compression Members
42/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan !2
Mechanism o !uc"lin#
Fig 3
-
8/13/2019 Lecture -0008 Compression Members
43/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan !
Mechanism o !uc"lin#
4he e'a$tic re$torin, force wa$ not
enou,h to prevent $ma'' di$tur%ance
,rowin, into an e5ce$$ive'y 'ar,edef'ection.
Dependin, on ma,nitude of 'oad P*
co'umn either remain in %ent po$ition* orwi'' comp'ete'y co''ap$e or fracture.
-
8/13/2019 Lecture -0008 Compression Members
44/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan !!
Mechanism o !uc"lin#
4hi$ type of %ehavior indicate$ that for a5ia''oad$ ,reater than Pcrthe $trai,ht po$ition of
co'umn i$ one of un$ta%'e e9ui'i%rium in that a
$ma'' di$tur%ance wi'' tend to ,row into ane5ce$$ive deformation.
Buck'in, i$ uni9ue from our other $tructura'e'ement$ con$ideration$ in that it re$u't$ from
$tate of un$ta%'e e9ui'i%rium.
-onc'u$ion$
-
8/13/2019 Lecture -0008 Compression Members
45/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan !"
Mechanism o !uc"lin#
Buck'in, of 'on, co'umn$ i$ not cau$ed %yfai'ure of materia' of which co'umn i$
compo$ed %ut %y determination of what wa$$ta%'e $tate of e9ui'i%rium to an un$ta%'e one.
-onc'u$ion$
-
8/13/2019 Lecture -0008 Compression Members
46/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan !
Mechanism o !uc"lin#-onc'u$ion$
Compression member
-
8/13/2019 Lecture -0008 Compression Members
47/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan !/
Compression member
!uc"lin#
Buck'in, occur$ when a $trai,ht* homo,eneou$*centra''y 'oaded co'umn $u%;ected to a5ia'
compre$$ion $udden'y under,oe$ %endin,.
Buck'in, i$ identified a$ a fai'ure 'imit6$tate forco'umn$. Pcr
Pcr
P
P
(a) (b)Pcr
Pcr
P
P
P
P
(a) (b)
Compression member
-
8/13/2019 Lecture -0008 Compression Members
48/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan !0
Compression member
!uc"lin#
4he va'ue of P at which a $trai,ht
co'umn %ecome$ un$ta%'e i$ ca''ed the
-ritica' =oad.
hen co'umn %end$ at critica' 'oad* it i$
$aid to have %uck'ed.
4herefore* critica' 'oad i$ a'$o ca''ed the
%uck'in, 'oad.
$lastic !uc"lin# o
-
8/13/2019 Lecture -0008 Compression Members
49/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan !
$lastic !uc"lin# o
Columns
4he critica' %uck'in, 'oad Pcrfor co'umn$
i$ theoretica''y ,iven %y
4endency of compre$$ion mem%er$ to
%uck'in, i$ ,overned %y =r
$lastic !uc"lin# o
-
8/13/2019 Lecture -0008 Compression Members
50/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan "
$lastic !uc"lin# o
Columns
The intersection point , of the two curves represents the
maximum theoretical value of slenderness of a column
compressed to the yield strength. This maximum slenderness
$sometimes called uler slenderness&
$lastic !uc"lin# o
-
8/13/2019 Lecture -0008 Compression Members
51/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan "1
$lastic !uc"lin# o
Columns
%nelastic !uc"lin# o
-
8/13/2019 Lecture -0008 Compression Members
52/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan "2
%nelastic !uc"lin# o
Columns
#n e'a$tic %uck'in,* it wa$ a$$umed that a co'umnmade of a meta' who$e $tre$$6$train curve i$'inear unti' a yie'd p'ateau reached.
8or a co'umn with intermediate 'en,th* when%uck'in, occur$ after the $tre$$ in the co'umne5ceed$ the proportiona' 'imit of the co'umnmateria' and %efore the $tre$$ reache$ the
u'timate $tren,th. 4hi$ kind of $ituation i$ ca''edinelastic buckling.
%nelastic !uc"lin# o
-
8/13/2019 Lecture -0008 Compression Members
53/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan "
%nelastic !uc"lin# o
Columns
4an,ent6(odu'u$ 4heory
%nelastic !uc"lin# o
-
8/13/2019 Lecture -0008 Compression Members
54/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan "!
%nelastic !uc"lin# o
Columns
7n,e$$er$ -onc'u$ion wa$ cha''en,ed with the
%a$i$ that %uck'in, %e,in$ with no increa$e in
'oad.
The tangent-modulus theory oversimplifiesthe inelastic buckling by using only onetangent modulus. In reality, the tangent
modulus depends on the stress, which is afunction of the bending moment that varieswith the displacement w.
4an,ent6(odu'u$ 4heory: Draw%ack$
%nelastic !uc"lin# o
-
8/13/2019 Lecture -0008 Compression Members
55/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan ""
%nelastic !uc"lin# o
Columns
4an,ent6(odu'u$ 4heory: Draw%ack$
The tangent-modulus theory tendsto underestimate the strength of
the column, since it uses thetangent modulus once the stresson the concave side exceeds the
proportional limit while the convexside is still below the elastic limit.
%nelastic !uc"lin# o
-
8/13/2019 Lecture -0008 Compression Members
56/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan "
%nelastic !uc"lin# o
Columns
+educed (odu'u$ 4heory7n,e$$er pre$ented a $econd $o'ution
to the ine'a$tic6%uck'in,* in which the
%endin, $tiffne$$ of the 56$ection i$e5pre$$ed in term$ of dou%'e modu'u$
Erto compensate for the
underestimation given by thetangent-modulus theory.
%nelastic !uc"lin# o
http://www.efunda.com/formulae/solid_mechanics/columns/inelastic.cfmhttp://www.efunda.com/formulae/solid_mechanics/columns/inelastic.cfm -
8/13/2019 Lecture -0008 Compression Members
57/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan "/
%nelastic !uc"lin# o
Columns
+educed (odu'u$ 4heory
8or a co'umn with rectan,u'ar cro$$
$ection* the reduced modu'u$ i$ defined %y:
4he corre$pondin, critica' $tre$$ i$*
%nelastic !uc"lin# o
-
8/13/2019 Lecture -0008 Compression Members
58/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan "0
%nelastic !uc"lin# o
Columns
+educed (odu'u$ 4heory: Draw%ack$
The reduced-modulus theory tends
to overestimate the strength of thecolumn, since it is based on stiffnessreversal on the convex side of thecolumn.
%nelastic !uc"lin# o
-
8/13/2019 Lecture -0008 Compression Members
59/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan "
%nelastic !uc"lin# o
Columns
+educed (odu'u$ 4heory: Draw%ack$
The reduced-modulus theory
oversimplifies the inelastic bucklingby using only one tangent modulus.In reality, the tangent modulusdepends on the stress which is afunction of the bending moment thatvaries with the displacement w.
%nelastic !uc"lin# o
-
8/13/2019 Lecture -0008 Compression Members
60/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan
%nelastic !uc"lin# o
Columns
3han'ey$ 4heoryThe critical load of inelastic buckling is in
fact a function of the transversedisplacement w
Practically there are manufacturingdefects in mass production and geometricinaccuracies in assembly.
This is the reason why many designformulas are based on the overly-conservative tangent-modulus theory.
%nelastic !uc"lin# o
-
8/13/2019 Lecture -0008 Compression Members
61/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 1
%nelastic !uc"lin# o
Columns
3han'ey$ 4heory
Factors eectin# !uc"lin#
-
8/13/2019 Lecture -0008 Compression Members
62/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 2
Factors eectin# !uc"lin#
1. 7nd -onnection$
2. 7ccentricity of 'oad$-rookedne$$
. +e$idua' $tre$$e$
Factors eectin# !uc"lin#
-
8/13/2019 Lecture -0008 Compression Members
63/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan
1. 7nd -onnection$
Factors eectin# !uc"lin#
+otation of end$ of co'umn$ in %ui'din,frame$ i$ u$ua''y 'imited %y %eam$
connectin, to them.
Factors eectin# !uc"lin#
-
8/13/2019 Lecture -0008 Compression Members
64/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan !
1. 7nd -onnection$: 7ffective 'en,th
Factors eectin# !uc"lin#
KL i$ ca''ed effective lengthof co'umn and K
effective length factor.
Factors eectin# !uc"lin#
-
8/13/2019 Lecture -0008 Compression Members
65/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan "
1. 7nd -onnection$: 7ffective 'en,th
Factors eectin# !uc"lin#
A column with fixed ends can support four times as much load asa column with pinned ends
This benefit decrease with decreasing L/r until Fcr finally
becomes virtually independent of K
Factors eectin# !uc"lin#
-
8/13/2019 Lecture -0008 Compression Members
66/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan
2. 7ffect of initia' crookedne$$
Factors eectin# !uc"lin#
4he initia' out6of6$trai,htne$$ i$ a'$o termed Cinitia'crookedne$$C or Cinitia' curvatureC.
#t cau$e$ a $econdary %endin, moment a$ $oon
a$ any compre$$ion 'oad i$ app'ied* which in turn'ead$ to further %endin, def'ection and a ,rowth inthe amp'itude of the 'ever arm of the e5terna' endcompre$$ion force$.
Factors eectin# !uc"lin#
-
8/13/2019 Lecture -0008 Compression Members
67/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan /
2. 7ffect of initia' crookedne$$
Factors eectin# !uc"lin#
A $ta%'e def'ected $hape i$ po$$i%'e a$
'on, a$ the e5terna' moment* i.e. theproduct of the 'oad and the 'atera'def'ection* doe$ not e5ceed the interna'moment re$i$tance of any $ection.
Factors eectin# !uc"lin#
-
8/13/2019 Lecture -0008 Compression Members
68/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 0
2. 7ffect of initia' crookedne$$
Factors eectin# !uc"lin#
Factors eectin# !uc"lin#
-
8/13/2019 Lecture -0008 Compression Members
69/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan
2. 7ffect of initia' crookedne$$
Factors eectin# !uc"lin#
hen $trai,ht co'umn %uck'e$* it
a$$ume$ a $ta%'e* %ent e9ui'i%rium* %ut
with $'i,ht'y 'ar,er 'oad.#n -rooked co'umn def'ection increa$e$
from %e,innin, of 'oadin, and co'umn i$
in un$ta%'e condition when it reache$ toma5imum 'oad.
Factors eectin# !uc"lin#
-
8/13/2019 Lecture -0008 Compression Members
70/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan /
. 7ffect of +e$idua' 3tre$$e$
Factors eectin# !uc"lin#
#n ten$ion mem%er$ +e$idua' $tre$$e$ cau$e$the $ection to yie'd at a $tre$$ 'ower than the
yie'd point of the materia'.A$ a re$u't* the e'on,ation for a ,iven 'oad i$
,reater than wou'd %e ca'cu'ated form e'a$ticpropertie$.
Factors eectin# !uc"lin#
-
8/13/2019 Lecture -0008 Compression Members
71/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan /1
. 7ffect of +e$idua' 3tre$$e$
Factors eectin# !uc"lin#
-omp'ete yie'din, of 56$ection did not occur unti'app'ied $train e9ua'$ the yie'd $train of %a$e
materia'.4he re$idua' $tre$$e$ doe$ not affect the 'oad
corre$pondin, to fu'' yie'd of 56$ection.
Factors eectin# !uc"lin#
-
8/13/2019 Lecture -0008 Compression Members
72/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan /2
. 7ffect of +e$idua' 3tre$$e$
Factors eectin# !uc"lin#
Factors eectin# !uc"lin#
-
8/13/2019 Lecture -0008 Compression Members
73/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan /
. 7ffect of +e$idua' 3tre$$e$
Factors eectin# !uc"lin#
#f the ma5imum $tre$$ n
reache$ the yie'd $tre$$ fy*
yie'din, %e,in$ to occur in
the cro$$6$ection. 4heeffective area a%'e to re$i$t
the a5ia' 'oad i$* therefore*
reduced.
Factors eectin# !uc"lin#
-
8/13/2019 Lecture -0008 Compression Members
74/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan /!
. 7ffect of +e$idua' 3tre$$e$
Factors eectin# !uc"lin#
7ffect of re$idua' $tre$$e$ in cau$in,weak a5i$ %uck'in, at 'oad$ $ma''er
than tho$e for $tron, a5i$ %uck'in,.4hi$ $u,,e$t two co'umn formu'a$
for the $tee' W.
Tests carried on W shapes
Structural Stability Research
Council (SSRC)proposed a single
forula to siplify the deign
procedure
Factors eectin# !uc"lin#
-
8/13/2019 Lecture -0008 Compression Members
75/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan /"
. 7ffect of +e$idua' 3tre$$e$: 33+- 8ormu'a
Factors eectin# !uc"lin#
!esign procedure be siplified by using Parabolabeginning "ith a #erte$ at Fcr%Fy"here &'r and
terinating at Fcr%Fy'2 "here it intersects and tangent to
uler yperbola*
Factors eectin# !uc"lin#
-
8/13/2019 Lecture -0008 Compression Members
76/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan /
-om%ined 7ffect of -rookedne$$ E +e$idua' 3tre$$e$
Factors eectin# !uc"lin#
An initia' out6of6$trai,htne$$ eo* produce$ a
%endin, moment ,ivin, a ma5imum %endin,
$tre$$ $B
#f $ma5i$ ,reater than the yie'd $tre$$ the fina'
di$tri%ution wi'' %e part p'a$tic and part of the
mem%er wi'' have yie'ded in compre$$ion.
Factors eectin# !uc"lin#
-
8/13/2019 Lecture -0008 Compression Members
77/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan //
-om%ined 7ffect of -rookedne$$ E +e$idua' 3tre$$e$
Factors eectin# !uc"lin#
Code &e'uirements
-
8/13/2019 Lecture -0008 Compression Members
78/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan /0
A3D 8ormu'a
Code &e'uirements
=Cc
r
KL
rKL
rKL
E
Ccr
KL
Cc
rKL
Cc
rKL
CcFy
Fa
rKL
22
2
3
2
1+,---
23
12
.
1
.
3
3
/
2
11
Code &e'uirements
-
8/13/2019 Lecture -0008 Compression Members
79/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan /
=+8D 3pecification$
Code e'u e e ts
4he de$i,n $tren,th of co'umn$ for the f'e5ura'%uck'in, 'imit $tate i$ e9ua' to
cP
n
here* cF .0" &+e$i$tance factor for compre$$ion mem%er$)
PnF A
,8
cr
8or cG 1." 8
crF 8
y
8or cH 1." 8crF 8y
c/01.2
c
133.2
-
4
r
56 y
Code &e'uirements
-
8/13/2019 Lecture -0008 Compression Members
80/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 0
=+8D 3pecification$
'
c
,-
4
r
56 y
4cr74y
8.2
8.0
2.9: 4cr
, 4y
c
133.2
4cr
, 4y( )c/01.2
c
,-
4
r
56 y
c
,-
4
r
56 y
4cr74y
8.2
8.0
2.9: 4cr
, 4y
c
133.24cr
, 4y
c
133.2
4cr
, 4y( )c/01.2 4cr, 4y( )c/01.2
Local !uc"lin#
-
8/13/2019 Lecture -0008 Compression Members
81/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 01
#
;f the column section is made of thin$slender& plate elements, then failure canoccur due to local buckling of theflanges or the webs in compression well
before the calculated buc%ling strength
of the whole member is reached.
hen thin p'ate$ are u$ed to carrycompre$$ive $tre$$e$ they areparticu'ar'y $u$cepti%'e to %uck'in,
a%out their weak a5i$ due $ma''moment of #nertia.
Local !uc"lin#
-
8/13/2019 Lecture -0008 Compression Members
82/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 02
#
Local !uc"lin#
-
8/13/2019 Lecture -0008 Compression Members
83/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 0
#
Flange Buckling
Laterally buckled beams
-
8/13/2019 Lecture -0008 Compression Members
84/91
Local !uc"lin#
-
8/13/2019 Lecture -0008 Compression Members
85/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 0"
#
;f local buckling of the individual plate elementsoccurs, then the column may not be able to develop its
buc%ling strength.
Therefore, the local buc%ling limit state must beprevented from controlling the column strength.
Local !uc"lin#
-
8/13/2019 Lecture -0008 Compression Members
86/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 0
#
5ocal buc%ling depends on the slenderness $width-to-thic%ness b/t ratio& of the plate element and the yieldstress $4y& of the material.
ach plate element must be stoc%y enough, i.e., have ab/t ratio that prevents local buc%ling from governingthe column strength.
Local !uc"lin#
-
8/13/2019 Lecture -0008 Compression Members
87/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 0/
#
4he critica' $tre$$ for rectan,u'ar p'ate$ with
variou$ type$ of ed,e $upport$* and with'oad$ in the p'ane of the p'ate di$tri%uted
a'on, the ed,e$ in variou$ way$ i$ ,iven %y
0% Constant depends on
-
8/13/2019 Lecture -0008 Compression Members
88/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 00
#
The coefficient k has a minimum value of 4 for
a/b=1!" etc.The error in using k=4 #ecreases $ith increasing a/b
an# for a/b= 1% or more it is extremel& small.
Local !uc"lin#
-
8/13/2019 Lecture -0008 Compression Members
89/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan 0
#
-ritica' $tre$$e$ for p'ate %uck'in, can %eeva'uated %y determination of e9uiva'ent
$'enderne$$ ratio for which a co'umn wi''
%uck'e at $ame $tre$$* u$in,
Local !uc"lin#
-
8/13/2019 Lecture -0008 Compression Members
90/91
CE-409: Lecture 08 Prof. Dr Akhtar Naeem Khan
#
The A;SC specification provides the
slenderness $b7t& limits that the individual plate
elements must satisfy so that local bucklingdoes not control.
Consult table >-> of +aylord
-
8/13/2019 Lecture -0008 Compression Members
91/91
Than"s