Structural Steel Design
CHAPTER
Third Edition
LRFD Method
DESIGN OF AXIALLY
LOADED COMPRESSION
MEMBERS
• A. J. Clark School of Engineering •Department of Civil and Environmental Engineering
Part II – Structural Steel Design and Analysis
6b
FALL 2002
By
Dr . Ibrahim. Assakkaf
ENCE 355 - Introduction to Structural Design
Department of Civil and Environmental Engineering
University of Maryland, College Park
CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS
Slide No. 1
ENCE 355 ©Assakkaf
Built-Up Columns with Components
in Contact with Each Other
Q
Q
If a column consists of two equal size
plates as shown in Fig. 1, and if those
plates are not connected together, each
plate will act as a separate column, and
each will resist approximately half of the
total column load.
This means that the total moment of
inertia of the column will equal two
times the moment of inertia of one plate.
1
Slide No. 2
CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS
ENCE 355 ©Assakkaf
Built-Up Columns with Components
in Contact with Each Other
Figure 1. Column consisting of two plates not
connected to each otherP P
 bd 3  bd 3
 =
I = 2
6
 12 
b
u
u
2 2
Plates deform
equal amounts
d d
(a) Column cross section
Pu Pu
(b) Deformed shape of Columns
2 2
CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS
Slide No. 3
ENCE 355 ©Assakkaf
Built-Up Columns with Components
in Contact with Each Other
Q
Q
Q
The two “columns” will act the same and
have equal deformation, as shown in
part (b) of Fig. 1.
If the two plates are connected together
sufficiently to prevent slippage on each
other, they will act as a unit as shown in
Fig. 2.
Their moment of inertia may be
computed for the whole built-up section.
2
CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS
Slide No. 4
ENCE 355 ©Assakkaf
Built-Up Columns with Components
in Contact with Each Other
Figure 2. Column consisting of two plates
fully connected to each other
Pu
b(2d )
I=
12
b 8d 3
=
12
4 3
= bd
6
3
( )
Plates deform
equal amounts
Pu
CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS
Slide No. 5
ENCE 355 ©Assakkaf
Built-Up Columns with Components
in Contact with Each Other
Q
Q
The moment of inertia for this built-up
section will be four times as large as it
was for the column of Fig 1, where
slipping between plates was possible.
Also, the column of Fig 2 will deform
different amounts as the column bends
laterally.
3
Slide No. 6
CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS
ENCE 355 ©Assakkaf
Built-Up Columns with Components
in Contact with Each Other
Q
Q
Should the plates be connected in a few
places, the strength of the resulting
column would be somewhere in
between the two cases just described.
The greatest displacement between the
two plates in Fig 1 tend to occur at the
ends and the least displacement tends
to occur at middle depth.
Slide No. 7
CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS
ENCE 355 ©Assakkaf
Built-Up Columns with Components
in Contact with Each Other
Q
Greatest Strength of Built-up Column
As a result, connections placed at column
ends which will prevent slipping between
the parts have the greatest strengthening
effect, while those at middepth have the
least effect
4
CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS
Slide No. 8
ENCE 355 ©Assakkaf
Built-Up Columns with Components
Not in Contact with Each Other
Q
Q
The following example presents the
design of member built up from two
channels that are not in contact with
each other.
The parts of such members need to be
connected or laced together across their
open sides.
CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS
Slide No. 9
ENCE 355 ©Assakkaf
Built-Up Columns with Components
Not in Contact with Each Other
Q
Example 1
Select a pair of 12-in standard channels for
the column and load shown using Fy = 50
ksi. For connection purposes, the back-toback distance of the channels is to be 12
in.
5
CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS
Slide No. 10
ENCE 355 ©Assakkaf
Built-Up Columns with Components
Not in Contact with Each Other
Q
Example 1 (cont’d)
Pu = 580 k
20 ft
12 in
Pu = 580 k
CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS
Slide No. 11
ENCE 355 ©Assakkaf
Built-Up Columns with Components
Not in Contact with Each Other
Q
Example 1 (cont’d)
KL
= 50
r
Then from Table 3.50 of the LRFD Manual,
φc Fcr = 35.40 ksi
Assume
Arequired =
Pu
580
=
= 16.38 in 2
φc Fcr 35.40
Try 2C12 × 30’s (for each channel, A = 8.81
in2, Ix = 162 in4, Iy = 5.12 in4, x = 0.674 in )
6
CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS
Slide No. 12
ENCE 355 ©Assakkaf
Built-Up Columns with Components
Not in Contact with Each Other
Q
LRFD Manual Design Tables (P. 16.I-145)
CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS
Slide No. 13
ENCE 355 ©Assakkaf
Built-Up Columns with Components
Not in Contact with Each Other 6 in
Q
Example 1 (cont’d)
I x = 2 × 162 = 324 in 2
[
]
I y = 2 5.12 + 8.81(5.326) = 510 in 4
2
distance of channels
Note that 5.326 =
−x
2
12
= − 0.674 = 5.326 in
2
x
7
CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS
Slide No. 14
ENCE 355 ©Assakkaf
Built-Up Columns with Components
Not in Contact with Each Other
Q
Example 1 (cont’d)
rx =
ry =
Ix
=
A
324
= 4.29 in
(2 × 8.81)
Iy
510
= 5.38 in
(2 × 8.81)
A
=
Controls
∴ rx = 4.29 in to be used
K = 1.0(From Table 1, pinned ends )
CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS
Slide No. 15
ENCE 355 ©Assakkaf
Built-Up Columns with Components
Not in Contact with Each Other
Table 1
8
CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS
Slide No. 16
ENCE 355 ©Assakkaf
Built-Up Columns with Components
Not in Contact with Each Other
Q
Example 1 (cont’d)
KL = (1.0 )(20 ) = 20 ft
KL KL 12 × 20
=
=
= 55.94
4.29
r
rx
From Table 3.50 of the Manual and by interpolation :
φc Fcr = 33.82 ksi
Therefore, φc Pn = φc Fcr Ag = 33.82(2 × 8.81) = 596 k > 580 k
Thus,
OK
USE 2C12 × 30
CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS
Slide No. 17
ENCE 355 ©Assakkaf
Built-Up Columns with Components
Not in Contact with Each Other
Q
LRFD Manual Design Tables (P. 16.I-145)
9
Slide No. 18
CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS
ENCE 355 ©Assakkaf
Built-Up Columns with Components
Not in Contact with Each Other
Q
Example 1 (cont’d)
Checking width/thickness ratios:
 d = 12.0 in, b f = 3.17 in, t f = 5.12 in 


C12 × 30
1


 t w = 0.51 in, k = 1 in = 1.125 in
8


Slide No. 19
CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS
ENCE 355 ©Assakkaf
Built-Up Columns with Components
Not in Contact with Each Other
Q
bf
tf
Example 1 (cont’d)
=
3.17
29 × 103
E
= 6.33 < 0.56
=
= 13.49
0.501
50
Fy
OK
29 × 103
h 12.0 − 2(1.125)
E
=
= 19.12 < 1.49
= 1.49
= 35.88
0.510
50
tw
Fy
OK
∴ USE 2C12 × 30, Fy = 50 ksi
10
CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS
Built-Up Columns
Q
Figure 4. Limiting Width-Thickness Ratios for
Compression Elements
CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS
Built-Up Columns
Slide No. 21
ENCE 355 ©Assakkaf
Figure 4. (cont’d) Limiting Width-Thickness
Ratios for Compression Elements
Stiffened Elements
Q
Slide No. 20
ENCE 355 ©Assakkaf
11