05 compression members (1)

Civil Engineering Department – University of Lahore.
Design of Steel Structures
1
DESIGN OF COMPRESSION
MEMBERS
1/3
Department of Civil Engineering
The University of Lahore, Lahore

COMPRESSION MEMBERS
When a load tends to squeeze or shorten a
member, the stresses produced are said to be
compressive in nature and the member is
called a compression member (Figure 3.1).
2
Examples are struts (short compression
members without chances of buckling),
eccentrically loaded columns, top chords of
trusses, bracing members, compression
flanges of beams and members that are
subjected simultaneously to bending and
compressive loads.
P
P

There are two significant differences between the
behavior of tension and compression members, as
under:
1. The tensile loads tend to hold a member straight
even if the member is not initially in one line and is
subjected to simultaneous bending moments.
In contrast, the compressive loads tend to bend the
member out of the plane of the loads due to
imperfections, simultaneous bending moment or
even without all of these.
3

Tests on majority of practical columns show that they
will fail at axial stresses well below the elastic limit of
the column material because of their tendency to buckle
(which is a sudden lateral bending due to a critical
compressive force).
For these reasons, the strength of compression members
is reduced in relation to the danger of buckling
depending on length of column, end conditions and
cross-sectional dimensions.
The longer a column becomes for the same cross-
section the greater is its tendency to buckle and the
smaller is the load it will support.
4

When the length of a compression member increases
relative to its cross-section, it may buckle at a lower load.
After buckling the load cannot be sustained and the load
capacity nearly approaches zero.
The condition of a column at its critical buckling load is
that of an unstable equilibrium as shown in Figure 3.2.
5
(a) Stable (b) Neutral (c) Unstable
Figure 3.2. Types of Equilibrium States.

In the first case, the restoring forces are greater than the
forces tending to upset the system.
Due to an infinitesimal small displacement consistent
with the boundary conditions or due to small
imperfection of a column, a moment is produced in a
column trying to bend it.
At the same time, due to stress in the material, restoring
forces are also developed to bring the column back to
its original shape.
If restoring force is greater than the upsetting moment,
the system is stable but if restoring force is lesser than
the upsetting moment, the system is unstable.
6

Right at the transition point when restoring force is
exactly equal to the upsetting moment, we get neutral
equilibrium.
The force associated with this condition is the critical
or buckling load.
2. The presence of rivet or bolt holes in tension
members reduces the area available for resisting
loads; but in compression members the rivets or
bolts are assumed to fill the holes and the entire
gross area is available for resisting load.
7

CONCENTRICALLY AND ECCENTRICALLY
LOADED COLUMNS
The ideal type of load on a column is a concentric load
and the member subjected to this type of load is called
concentrically loaded column.
The load is distributed uniformly over the entire cross-
section with the center of gravity of the loads coinciding
with the center of gravity of the columns.
Due to load patterns, the live load on slabs and beams
may not be concentrically transferred to interior
columns.
8

Similarly, the dead and live loads transferred to the
exterior columns are, generally, having large eccentricities,
as the center of gravity of the loads will usually fall well
on the inner side of the column.
In practice, majority of the columns are eccentrically
loaded compression members
Slight initial crookedness, eccentricity of loads, and
application of simultaneous transverse loads produce
significant bending moments as the product of high axial
loads (P) multiplied with the eccentricity, e.
This moment, P  e, facilitates buckling and reduces the
load carrying capacity.
9

P
a) Initial
Crookedness
P
e
P
e
b) Eccentric Load
P
P
c)Simultaneous
Transverse Load
10
Eccentricity, e, may be relatively smaller, but the product
(P  e) may be significantly larger.

11
Figure: Typical initial deflections of stiffened panels: (a) out-of-flatness of a
subpanel; (b) out-of-straightness of a stiffener; (c) stiffener camber deflection.
(IDM, 1987)

The AISC Code of Standard Practice specifies an acceptable
upper limit on the out-of-plumbness and initial crookedness
equal to the length of the member divided by 500.
(equal to 0.002, AISC C2-2b-3).
RESIDUAL STRESSES
Residual stresses are stresses that remain in a member after
it has been formed into a finished product.
These are always present in a member even without the
application of loads.
The magnitudes of these stresses are considerably high
and, in some cases, are comparable to the yield stresses
(refer to Figure 3.4).
12

83 to 93 MPa
80 to 95 MPa
(C)
(T)
a)Rolled Shapes
(C)
(T)
(C)
80 to 95 MPa
 0.3Fy for A36
(T)
80 to 95 MPa
13

280 MPa (T)
84 MPa (C)
140 MPa (T)
140 MPa
(C)
240 MPa
(T)
140 MPa (C)
b)Welded Shapes
Weld
Weld
14

The causes of presence of residual stresses are as under:
1. Uneven cooling which occurs after hot rolling of
structural shapes produces thermal stresses, which are
permanently stored in members.
The thicker parts cool at the end, and try to shorten in
length. While doing so they produce compressive stresses
in the other parts of the section and tension in them.
Overall magnitude of this tension and compression remain
equal for equilibrium.
In I-shape sections, after hot rolling, the thick junction of
flange to web cools more slowly than the web and flange
tips.
15

Consequently, compressive residual stress exists at flange
tips and at mid-depth of the web (the regions that cool
fastest), while tensile residual stress exists in the flange
and the web at the regions where they join.
2. Cold bending of members beyond their elastic
limit produce residual stresses and strains within the
members.
Similarly, during fabrication, if some member having
extra length is forced to fit between other members,
stresses are produced in the associated members.
3. Punching of holes and cutting operations during
fabrication also produce residual stresses.
16

4. Welding also produces the stresses due to uneven
cooling after welding.
Welded part will cool at the end inviting other parts to
contract with it.
This produces compressive stresses in parts away from
welds and tensile stresses in parts closer to welds.
SECTIONS USED FOR COLUMNS
Single angle, double angle, tee, channel, W-section, pipe,
square tubing, and rectangular tubing may be used as
columns.
Different combinations of these structural shapes may also
be employed for compression members to get built-up
sections as shown in Figure 3.5. 17

Four Angles
Box Section
Two Inward
Channels Box
Section
Two Outward
Channels Box
Section
Built-Up
Box
W - Section
With Cover
Plates
Built-Up
ISection
Built-Up
Rectangular
Box
W And Channels
Built-Up Section Built-Up ISection
18
Figure 3.5: Built-up Section s for Compression Member

Built-up sections are better for columns because the
slenderness ratios in various directions may be
controlled to get nearly equal values in all the
directions.
This makes the column economical as far as the
material cost is concerned. However, the joining and
labor cost is generally higher for built-up sections.
The total cost of these sections may become less for
greater lengths.
The joining of various elements of a built-up section is
usually performed by using lacing.
19

LIMITING SLENDERNESS RATIO
The slenderness ratio of compression members should
preferably not exceed 200 (AISC E2).
This means that in exceptional cases, the limit may be
exceeded.
20
B
A
C
Figure 3.6. Local Flange
Instability.
INSTABILITY OF COLUMNS
a) Local Instability
During local instability, the
individual parts or plate elements of
cross-section buckle without overall
buckling of the column.

Width/thickness ratio of each part gives the slenderness
ratio ( = b/t), which controls the local buckling.
Local buckling should never be allowed to occur before
the overall buckling of the member except in few cases
like web of a plate girder.
An unstiffened element is a projecting piece with one
free edge parallel to the direction of the compressive
force.
The example is half flange AB in Figure 3.6.
A stiffened element is supported along the two edges
parallel to the direction of the force.
21

The example is web AC in the same figure.
For unstiffened flange of figure, b is equal to half width
of flange (bf / 2) and t is equal to tf. Hence, bf / 2tf ratio
is used to find .
For stiffened web, h is the width of web and tw is the
thickness of web and the corresponding value of  or
b/t ratio is h / tw, which controls web local buckling.
Overall Instability
In case of overall instability, the column buckles as a
whole between the supports or the braces about an axis
whose corresponding slenderness ratio is bigger.
22

Single angle sections may buckle about their weak axis
(z-axis, Figure 3.10).
Calculate Le / rz to check the slenderness ratio.
In general, all un-symmetric sections having non-zero
product moment of inertia (Ixy) have a weak axis different
from the y-axis.
Z
Z
Figure 3.10. Axis of Buckling For Single Angle Section.
23

24

25

26

27

28

29

a)Buckling about
major axis
b)Buckling about
minor axis
Figure 3.6- Buckling of a Column Without Intermediate Bracing
30

Buckling
about
minor axis
Bracing to prevent
major axis buckling,
connected to stable
structures
Lx1
Lx2
31

Minor Axis
Bracing
Ly1
Ly2
32

UNSUPPORTED LENGTH
It is the length of column between two consecutive
supports or braces denoted by Lux or Luy in the x and y
directions, respectively.
A different value of unsupported length may exist in
different directions and must be used to calculate the
corresponding slenderness ratios.
To calculate unsupported length of a column in a
particular direction, only the corresponding supports
and braces are to be considered neglecting the bracing
preventing buckling in the other direction.
33

EFFECTIVE LENGTH OF COLUMN
The length of the column corresponding to one-half sine
wave of the buckled shape or the length between two
consecutive inflection points or supports after buckling
is called the effective length.
BUCKLING OF STEEL COLUMNS
Buckling is the sudden lateral bending produced by
axial loads due to initial imperfection, out-of-
straightness, initial curvature, or bending produced by
simultaneous bending moments.
34

Chances of buckling are directly related with the
slenderness ratio KL/r and hence there are three
parameters affecting buckling.
1. Effective length factor (K), which depends on the
end conditions of the column.
2. Unbraced length of column (Lu), in strong
direction or in weak direction, whichever gives
more answer for KL/r.
3. Radius of gyration (r), which may be rx or ry
(strong and weak direction) for uniaxially or
biaxially symmetrical cross-sections and least
radius of gyration (rz) for un-symmetrical cross-
sections like angle sections.
35

Following points must be remembered to find the critical
slenderness ratio:
a. Buckling will take place about a direction for
which the corresponding slenderness ratio is the
maximum.
b. For unbraced compression members consisting
of angle section, the total length and rz are used
in the calculation of KL/r ratio.
c. For steel braces, bracing is considered the most
effective if tension is produced in them due to
buckling.
36

d. Braces that provide resistance by bending are
less effective and braces having compression are
almost ineffective because of their small x-
sections and longer lengths.
e. The brace is considered effective if its other end
is connected to a stable structure, which is not
undergoing buckling simultaneously with the
braced member.
f. The braces are usually provided inclined to
main members of steel structures starting
from mid-spans to ends of the adjacent
columns.
37

g. Because bracing is most effective in tension, it
is usually provided on both sides to prevent
buckling on either side.
h. Bracing can be provided to prevent buckling
along weak axis. KL/r should be calculated by
using Ky, unbraced length along weak axis and ry.
i. Bracing can also be provided to prevent
buckling along the strong axis. KL/r in this case
should be calculated by using Kx, the unbraced
length along strong axis and rx.
j. The end condition of a particular unsupported
length of a column at an intermediate brace is
considered a hinge.
38

The reason is that the rotation becomes free at this point
and only the lateral movement is prevented.
EFFECTIVE LENGTH FACTOR (K)
This factor gives the ratio of length of half sine wave of
deflected shape after buckling to full-unsupported length
of column.
This depends upon the end conditions of the column and
the fact that whether sidesway is permitted or not.
Greater the K-value, greater is the effective length and
slenderness ratio and hence smaller is the buckling load.
39

K-value in case of no sidesway is between 0.5 and 1.0,
whereas, in case of appreciable sidesway, it is greater
than or equal to 1.0
Le = K Lu
40
SIDE SWAY
Any appreciable lateral or sideward movement of top of
a vertical column relative to its bottom is called
sidesway, sway or lateral drift.
If sidesway is possible, K-value increases by a greater
degree and column buckles at a lesser load.

Sidesway in a frame takes place due to:-
a) Lengths of different columns are unequal.
b) When sections of columns have different cross-sectional
properties.
c) Loads are un-symmetrical.
d) Lateral loads are acting.
41
2I
I
I
(a) (b) (c) (d)
Figure 3.11. Causes of Sidesway in a Building Frame.

Sidesway may be prevented in a frame by:
a. Providing shear or partition walls.
b. Fixing the top of frame with adjoining rigid
structures.
c. Provision of properly designed lift well or
shear walls in a building, which may act like
backbone of the structure reducing the
lateral deflections.
Shear wall is a structural wall that resists
shear forces resulting from the applied
transverse loads in its own plane and it
produces frame stability.
42

d. Provision of lateral bracing, which may be of
following two types:
i. Diagonal bracing, and
ii. Longitudinal bracing.
Unbraced frame is defined as the one in which the
resistance to lateral load is provided by the
bending resistance of frame members and their
connections without any additional bracing.
43

K-Factor for Columns Having Well Defined
End Conditions
Theoretical K=1.0
Practical K = 1.0
No Sidesway
Theoretical K = 0.5
Practical K = 0.65
No Sidesway
Inflection
Points
Le = L
Le = KL
44
 Check the K-value for various end condition at Page 103
on Refernce-1 (LRFD Steel Design Aids)

Theoretical K=2.0
Practical K = 2.10
Sidesway Present
Theoretical K=2.0
Practical K = 2.0
Sidesway Present
Le = KL
Theoretical K = 0.7
Practical K = 0.8
No Sidesway
Theoretical K=1.0
Practical K = 1.2
Sidesway Present
Le = KL
Le = KL
45

46
Simple or hinge Connection
Moment or Fix Connection

PARTIALLY RESTRAINED COLUMNS
Consider the example of column AB shown in Figure 3.13.
The ends are not free to rotate and are also not perfectly
fixed. Instead these ends are partially fixed with the fixity
determined by the ratio of relative flexural stiffness of
columns meeting at a joint to the flexural stiffness of
beams meeting at that joint.
This ratio is denoted by G or  and is determined for each
end of the columns using following expression.
47

 or G at each end =
 
 
EI of columns
EI of beams




A
B
B
GB or B
A
GA or A
Columns
Beams
Part-X
Column AB of Part-X
Figure 3.13. Partially restrained Columns
48

49
Figure 3.14. Determination of K-value for partially Restrained Columns
The effective length factor of column is determined using
the charts given in the Figure 3.14 expression.
(check Page- 104 on Reference - 1)
Note: The charts does not give the actual values.

K-Values For Truss And Braced Frame Members
The effective length factor, K, is considered equal to 1.0 for
members of the trusses and braced frame columns.
In case the value is to be used less than one for frame
columns, detailed buckling analysis is required to be
carried out and bracing is to be designed accordingly.
50
ELASTIC BUCKLING LOAD FOR LONG
COLUMNS
A column with pin connections on both ends is considered
for the basic derivation, as shown in Figure 3.15.

51
P =
Pcr
P =
Pcr
umax.
u
D
y
C
B
A
Buckled
Shape
L / 2
L / 2
The column has a length equal to L
and is subjected to an axial
compressive load, P.
Buckling of the column occurs at a
critical compressive load, Pcr.
The lateral displacement for the
buckled position at a height y from
the base is u. The bending moment
at this point D is: Figure 3.15. Buckled Elastic
Curve for Long Columns
M = Pcr  u (I)

This bending moment is function of the deflection unlike
the double integration method of structural analysis where
it is independent of deflection.
The equation of the elastic curve is given by the Euler-
Bernoulli Equation, which is the same as that for a beam.
EI =  M (II)
d u
dy
2
2
or EI + Pcr u = 0
d u
dy
2
2
or + u = 0 (III)
2
2
dy
u
d
EI
Pcr
52

Let = C2 where C is constant (IV)
EI
Pcr
 + C2 u = 0 (V)
2
2
dy
u
d
The solution of this differential equation is:
u = A cos (C  y) + B sin (C  y) (VI)
where, A and B are the constants of integration.
Boundary Condition No. 1:
At y = 0, u = 0
0 = A cos(0) + B sin (0)  A = 0
53

 u = B sin (C  y) (VII)
Boundary Condition No. 2:
At y = L, u = 0
From Eq. VII: 0 = B sin (C L)
 Either B = 0or sin (C L) = 0 (VIII)
If B = 0, the equation becomes u = 0, giving un-deflected
condition. Only the second alternate is left for the
buckled case.
sin (C L) = sin = 0 (IX)








L
EI
Pcr
54

sin  = 0 for  = 0, , 2, 3, … (radians)
Or n where n = 0, 1, 2, … (X)
Hence, from Eq. IX: = n
L
EI
Pcr
Pcr = (XI)
2
2
2
L
EI
n 
The smallest value of Pcr is for n = 1, and is given below:
Pcr = (XII)
2
2
L
EI

55

For other columns with different end conditions, we
have to replace L by the effective length, L e = K L.
Pcr = (XIII)
 2
2
KL
EI

Pcr =
 2
2
2
KL
Ar
E

Pcr = = Fe A (XIV)
 2
2
r
L
K
A
E

and Fe = (XV)
 2
2
r
L
K
E

56

It is important to note that the buckling load determined
from Euler equation is independent of strength of the steel
used.
The most important factor on which this load depends is
the KL/r term called the slenderness ratio.
Euler critical buckling load is inversely proportional to
the square of the slenderness ratio.
With increase in slenderness ratio, the buckling strength
of a column drastically reduces.
57
In the above equations:
= slenderness ratio
r
KL

Pcr = Euler’s critical elastic buckling load
Fe = Euler’s elastic critical buckling stress
Long compression members fail by elastic buckling and short
compression members may be loaded until the material yield
or perhaps even goes into the strain-hardening range.
However, in the vast majority of usual situations failure
occurs by buckling after a portion of cross-section has
yielded.
This is known as inelastic buckling. This variation in column
behaviour with change of slenderness ratio is shown in
Figure 3.16.
58

Elastic Buckling
Fy
Fcr
200
C
D
B
A
Rc
Euler’s Curve
(Elastic Buckling)
Compression Yielding
0.44 Fy
Approximately
Short
Columns
Intermediate
Columns
Long Columns
Inelastic Buckling (Straight Line Or
a Parabolic Line Is Assumed)
KL / r (R)
(KL / r)max
 20 to 30
59

TYPES OF COLUMNS DEPENDING ON
BUCKLING BEHAVIOUR
Elastic Critical Buckling Stress
The elastic critical buckling stress is defined as under:
Fe = Elastic critical buckling (Euler) stress
= 2
2






r
KL
E

The critical slenderness ratio dividing the expected elastic
and the inelastic buckling is denoted by Rc and is given
below:
60

Rc =  133 for A36 steel
y
F
E
71
.
4
Long Columns
In long columns, elastic buckling is produced and the
deformations are recovered upon removal of the load.
Further, the stresses produced due to elastic buckling
remains below the proportional limit.
The Euler formula is used to find strength of long columns.
Long columns are defined as those columns for which the
slenderness ratio is greater than the critical slenderness
ratio, Rc.
61

Elastic Buckling
c Fy
Maximum
Compressive
Stress (c Fcr)
200
C
Rc
Short
Columns
Intermediate
Columns
Long Columns
Inelastic Buckling
No Buckling
KL / r
(KL / r)max
 20 to 30
62

Short Columns
For very short columns, when the slenderness ratio is less
than 20 to 30, the failure stress will equal the yield stress
and no buckling occurs. In practice, very few columns
meet this condition.
For design, these are considered with the intermediate
columns subjected to the condition that failure stress
should not exceed the yield stress.
63
Intermediate Columns
Intermediate columns buckle at a relatively higher load
(more strength) as compared with long columns.

The buckling is inelastic meaning that part of the section
becomes inelastic after bending due to buckling.
The columns having slenderness ratio lesser than the critical
slenderness ratio (Rc) are considered as intermediate
columns, as shown in Figure 3.16.
64
COLUMN STRENGTH FORMULAS
The design compressive strength (cPn) and the allowable
compressive strength (Pn / c) of compression members,
whose elements do not exhibit elastic local instability
(only compact and non-compact sections), are given
below:

c = 0.90 (LRFD) : Pn = Fcr Ag
c = 1.67 (ASD) : Pn = Fcr Ag
Fcr = critical or ultimate compressive strength based on the
limit state of flexural buckling determined as under:
65
Elastic Buckling
When KL / r > Rc or Fe < 0.44Fy
Fcr = 0.877 Fe (AISC Formula E3-2)
where Fe is the Euler’s buckling stress and 0.877 is a
factor to estimate the effect of out-of-straightness of
about 1/1500.

Inelastic Buckling and No Buckling
When KL / r  Rc or Fe > 0.44Fy
Fcr = Fy (AISC Formula E3-3)








e
y
F
F
658
.
0
66
TYPES OF COLUMN SECTIONS FOR
LOCAL STABILITY
Compact Sections
A compact section is one that has sufficiently thick
elements so that it is capable of developing a fully plastic
stress distribution before buckling.
The term plastic means stressed throughout to the yield
stress.

For a compression member to be classified as compact, its
flanges must be continuously connected to its web or webs
and the width thickness ratios (b/t) of its compression
elements may not be greater than the limiting ratios p
give in AISC Table B4.1 and reproduced in Table 3.1.
Element p p For A36
Un-stiffened: Defined only for
flexure

Stiffened: Flanges of hollow
sections subjected to
compression.
31.8
y
F
E
12
.
1
67

Non-Compact Sections
A non-compact section is one for which the yield stress
can be reached in some but not all of its compression
elements just at the buckling stage.
It is not capable of reaching a fully plastic stress
distribution.
In AISC Table B4.1, the non-compact sections are
defined as those sections which have width-thickness
ratios (b/t) greater than p but not greater than r.
Values of limiting b/t ratios (r) are given in Table 3.2.
68

Element
Width-
Thickness
Ratio
r
r For A36
Steel
Unstiffened
1. Flanges of I-shaped sections in pure compression,
plates projecting from compression elements,
outstanding legs of pairs of angles in continuous
contact, and flanges of channels in pure
compression.
15.9
2. Legs of single angle struts, legs of double angle
struts with separators and other un-stiffened
elements supported along one edge.
12.8
3. Stems of tees.
21.3
4. Flanges of built-up I-sections with projecting
plates or angles.
t
b
t
b
t
d
t
b
y
F
E
56
.
0
y
F
E
45
.
0
y
F
E
75
.
0
y
c
F
E
k
64
.
0
c
k
1
.
18
69

Element
Width-
Thickness
Ratio r
r For
A36 Steel
Stiffened
1. Flanges of rectangular hollow sections of uniform
thickness used for uniform compression.
39.7
2. Flexure in webs of doubly symmetric I-shaped
sections and channels.
161.8
3. Uniform compression in webs of doubly
symmetric I-shaped sections and uniform
compression in all other stiffened elements.
42.3
4. Circular hollow sections in axial compression.
d / t 0.11 (E / Fy) 88.6
t
b
w
t
h
t
b
y
F
E
40
.
1
y
F
E
70
.
5
y
F
E
49
.
1
70

Slender Compression Sections
These sections consist of elements having width-thickness
ratios greater than r and will buckle elastically before the
yield stress is reached in any part of the section.
A special design procedure for slender compression sections
is provided in Section E7 of the AISC Specification.
However, it will not be covered in detail here.
71
Width Of Un-stiffened Elements
For un-stiffened elements, which are supported along
only one edge parallel to the direction of the
compression force, the width shall be taken as follows:

a. For flanges of I-shaped members and tees, the width
b is half the full nominal width (bf /2).
b. For legs of angles, the width b is the longer leg
dimension.
c. For flanges of channels and zees, the width b is the
full nominal dimension (bf).
d. For plates, the width b is the distance from the free
edge to the first row of fasteners or line of welds.
e. For stems of tees, d is taken as the full nominal
depth.
72

Width Of Stiffened Elements
a. For webs of rolled or formed sections, h is the clear
distance between the flanges less the fillet or
corner radius at each flange and hc is twice the
distance from the centroidal axis to the inside face
of the compression flange less the fillet or corner
radius.
b. For webs of built-up sections,
h is the clear distance between the inner lines of
fasteners on the web or the clear distance between
flanges when welds are used.
73

hc is twice the distance from the centroidal axis to the
nearest line of fasteners at the compression flange or
the inside face of the compression flange when welds
are used, and
hp is twice the distance from the plastic neutral axis to
the nearest line of fasteners at the compression flange
or the inside face of the compression flange when
welds are used.
74

MODIFIED SLENDERNESS RATIO
Snug Tight Connections
Snug tight connection is defined as the type in which the
plates involved in a connection are in firm contact with
each other but without any defined contact prestress.
It usually means the tightness obtained by the full effort
of a man with a wrench or the tightness obtained after a
few impacts of an impact wrench.
Obviously there is some variation in the degree of
tightness obtained under these conditions. The tightness
is much lesser than tensioning of the high-strength bolts.
75

Turn-of-Nut Method: After the tightening of a nut to a snug
fit, the specified pre-tension in high-strength bolts may be
controlled by a predetermined rotation of the wrench.
This procedure is called turn-of-nut method of fixing the
bolts. Slip is allowed in turn-of-nut method.
76
Turn of the nut method (Table 8 –CSA-S16)
 1/3 turn for Lb < 4db
 1/2 turn for 4db < Lb < 8db (or 200 mm)
 2/3 turn for longer bolts

Built-up compression members composed of two or more
hot rolled shapes shall be connected to one another at
intervals by stay plates (shear connectors) such that the
maximum slenderness ratio a / ri of individual element,
between the fasteners, does not exceed the governing
slenderness ratio of the built-up member, that is, the greater
value of (KL / r)x or (KL / r)y for the whole section.
Shear connectors are also required to transfer shear
between elements of a built-up member that is produced
due to buckling of the member.
77
Shear Connections / Stay Plates Between
Elements Of A Built-Up Member

Following notation is used in further discussion of the
effect of spacing of shear connectors:
a = clear distance between connectors
ri = minimum radius of gyration of individual component
a / ri = largest column slenderness of individual component
rib = radius of gyration of individual component relative to
its centroidal axis parallel to member axis of buckling
= column slenderness of built-up member acting as a
unit
= modified column slenderness of the built-up member
as a whole
78
0






r
KL
m
r
KL







 = separation ratio = h / (2 rib) , and
h = distance between centroids of individual components
perpendicular to the member axis of buckling
79
Modified Slenderness Ratio Depending
On Spacing Of Stay Plates
If the buckling mode of a built-up compression member
involves relative deformation that produces shear forces in
the connectors between individual parts, the modified
slenderness ratio is calculated as follows:
(a) For snug-tight bolted connectors:
=
m
r
KL





 2
2
0















i
r
a
r
KL

(b) for welded connectors and for fully tightened bolted
connectors as required for slip-critical joints:
=
m
r
KL





 2
2
2
2
0 1
82
.
0 















ib
r
a
r
KL


(KL / r)m should only be used if buckling occurs about
such an axis such that the individual members elongate by
different amounts. (always considered about minor axes)
For example for double angles in Figure 3.17, if buckling
occurs about x-axis, (KL / r)m is not evaluated as both the
angles bend symmetrically without any shear between the
two.
80

However, if buckling occurs about y-axis, one of the
angle sections is elongated while the other is
compressed producing shear between the two and
consequently (KL / r)m is required to be evaluated.
At the ends of built-up compression members bearing
on base plates or milled surfaces, all components in
contact with one another shall be connected by a weld
having a length not less than the maximum width of the
member, or
by bolts spaced longitudinally not more than four
diameters apart for a distance equal to 1.5 times the
maximum width of the member.
81

x
y
The slenderness ratio of individual component between
the connectors (Ka / ri) should not exceed 75% of the
governing slenderness ratio of the built-up member.
Because we do not want local buckling before overall
buckling.
82

83
Fy
Fcr
200
C
D
B
A
KL / r (R)

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