Steel Design - Compression Member - Ari Wibowo, Ph.D
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Steel Design- Compression Member -
Ari Wibowo, Ph.D
Compression Members
• Compression Members: Structural elements that are
subjected only to axial compressive forces.
• The stress can be taken as:
fa = P/A
where fa is considered to be uniform over the entire
cross section.
• This ideal state is never achieved in reality, because
some eccentricity of the load is inevitable.
Columns: are the most common type of compression members occurring in buildings
and bridges.
Sometimes members are also called upon to resist bending, and in these cases the
member is a beam column.
Compression Members
• Column Theory:
– Consider the long, slender compression
member.
– If the axial load P is slowly applied. it will
ultimately become large enough to cause
the member to buckle/become unstable.
– Assume the shape indicated by the dashed
line. The member is said to have buckled.
– The load at which buckling occurs is a
function of slenderness, and for very
slender members this load could be quite
small.
Compression Members
Column Theory:
• The critical buckling load Pcr :
– the load that is just large enough to deflect the column
without subjected to transverse load.
– If the member is so slender, the stress just before
buckling is below the proportional limit - and the
member is still elastic - the critical buckling load is given
by:
Compression Members
Compression Members
• For example, case n=1,
this equation can be rewritten as :
Where:
– A is the cross-sectional area .
– r is the radius of gyration with respect to the axis of
buckling.
–The ratio L/r is the slenderness ratio .
•If the critical load is divided by the cross-sectional area,
the critical buckling stress is obtained:
A WI2 x 50 is used as a column to support an axial compressive load
of 145 kips. The length is 20 feet, and the ends are pinned. Without
regard to load or resistance factors, Investigate this member for stability.
Example 1
Because the applied load of 145 kips is less than Pcr the
column remains stable and has an overall factor of safety
against buckling of 278.9/145 = 1.92
Effective Length
2
2
2
2
4)2( L
EI
L
EIPcr
• Fixed and Free Ends
• Both Fixed Ends
• Fixed and Pinned Ends
• Fixed and Fixed Roller Ends
2
2
2
2 4
)5.0( L
EI
L
EIPcr
2
2
)7.0( L
EIPcr
2
2
)5.0( L
EIPcr
Braced Columns
Column (a)
Top : KL = 2 0.7L = 1.4 L (largest governs)
Bottom : KL = 1 0.3 = 0.3 L
Column (b)
Top : KL = 0.7 0.5 L = 0.35 L (largest governs)
Middle : KL = 1 0.3 L = 0.3 L
Bottom : KL = 0.7 0.2 L = 0.14 L
Example
• Column W12 65, 12 ft, with beam constructed at x-x
axis. Determine which axis govern for compression
member calculation.
in
tft
r
LK ftin
x
x
28.5
)12(24
02.3
)12(4.8
x
x
r
LK
• X axis (major/strong axis)
Kx = 2 12 = 24 ft
= 54.55
Hence, x-x axis controls since it has the biggest slenderness
ratio
• Y axis (minor/weak axis)
Ky = 0.7 12 = 8.4 ft
= 33.38
Compression Members
• LRFD METHOD :
Factored load ≤ factored strength
Pu ≤ Øc Pn
Where
Slenderness parameter is used instead of Fcr as a function of
the slenderness ratio KL/r
= Sum of factored LoadsPu
= Nominal compressive strength =Ag FcrPn
C= ritical buckling stressFcr
= Resistance factor for compression member = 0.85Øc
AISC REQUIRMENTS
– Critical buckling stress will be summarized as:
– Also, Graphically can be summarized as:
SNI 03-1729-2002
• Nominal Load:
• Critical stress:
y
gcrgn
fAfAP ..
y
cr
ff
1
c
67.06.1
43.1
225.1 c
where:
• For c 0.25 :
(SNI 03-1729-2002 pers. 7.6-5a)
• For 0.25 < c < 1.2 :
(SNI 03-1729-2002 pers. 7.6-5b)
• For 0.25 1.2 :
Compression Members
ExExample:4.2ample 4.2:
Compute the design compressive strength of a W14 x 74 with a length of 20 feet and pinned ends.
A992 steel is used.
Local Buckling
• If local buckling of the individual plate elements occurs, then the
column may not be able to develop its buckling strength.
• Therefore, the local buckling limit state must be prevented from
controlling the column strength.
• Two types of elements must be considered:
– unstiffened elements, which are unsupported along one edge
parallel to the direction of load, and
– stiffened elements, which are supported along both edges.
• The strength must be reduced if the shape has any slender elements.
20
Local Buckling
Local buckling depends on the slenderness (width-to- thickness b/t ratio) of the plate element and the yield stress (Fy) of the material.
Each plate element must be stocky enough, i.e., have a b/t ratio that prevents local buckling from governing the column strength.
21
Local Buckling
Local Buckling
Flange Buckling
Laterally buckled beams
23
Local Buckling
Local Buckling- AISC
Cross-sectional shapes are classified as compact, non compact, or
slender, according to the values of the width-thickness ratios. If λ is
greater than the specified limit, denoted λr the shape is slender.
• Unstiffened Element
– For I- and H-shapes, the projecting flange is considered to be an
unstiffened element, and its width can be taken as half the full
nominal width
– where bf and tf are the width and thickness of the flange.
– The upper limit is (AISC)
Local Stability - AISC
• Stiffened Elements
–The webs of I- and H-shapes are stiffened elements. and the
stiffened width is the distance between the roots of the flanges.
–The width thickness parameter is
–Where h is the distance between the roots of the flanges, and tw
is the web thickness.
–The upper limit is (AISC)
AISC
Steel shape profile and value of r according to AISC
Compression Members
•Local Stability:
Compression Members•Local Stability:
Compression Members
•Local Stability:
Local Stability - SNI 03-1729-2002
This critical stress formula applies if the ratio of width to the thickness
() is smaller than r on Table 7.5-1 SNI 03-1729-2002. Ratio can
be h/tw or b/tf, depending on the element, such as : (Note: fy in Mpa)
f
ff
t
b
t
b
t
b
2
2/
yf
250
wt
h
yf
665
• Unstiffened element : without stiffener along one side parallel
to load direction.
e.g.: flange on I or H profile shape
= ; Upper limit : r =
• Stiffened Element.
e.g.: web on I or H profile shape
= ; Upper limit: r =
SNI 03-1729-2002
Steel shape profile and value of r according to SNI 03-1729-2002
Compression Members•Local Stability:
Example 4.3:
–Investigate the column in example 4.2 for local stability.
Compression Members
•DESIGN:
–Example 4.5:
A compression member is subjected to service loads of 165 kips
dead load and 535 kips live load. The member is 26 feet long and
pinned at each end. Use A992 steel
Answer
Compression Members
•DESIGN:
–Example 4.6:
Compression Members
•DESIGN:
–Example 4.7:
Answer
Compression Members•DESIGN:
Compression Members
•DESIGN:
Compression Members
Slenderness Ratio
The longer the column, for the same x-section,
the greater becomes its tendency to buckle and
smaller becomes its load carrying capacity.
The tendency of column to buckle is usually
measured by its slenderness ratio
Compression Members Vs
Tension Members
40
Compression Members Vs
Tension Members
Effect of material Imperfections and Flaws
Slight imperfections in tension
members are can be safely disregarded
as they are of little consequence.
On the other hand slight defects in
columns are of great significance.
A column that is slightly bent at the time
it is put in place may have significant
bending resulting from the load and
initial lateral deflection.
41
Tension in members causes lengthening of members.
Compression beside compression forces causes buckling of member.
Compression Members Vs
Tension Members
42
Presence of holes in bolted connection reduce Gross area in tension members.
Presence of bolts also contribute in taking load An = Ag
Compression Members Vs
Tension Members
43
WHY column more critical
than tension member?
A column is more critical than a
beam or tension member because
minor imperfections in materials
and dimensions mean a great
deal.
The bending of tension members
probably will not be serious as the
tensile loads tends to straighten
those members, but bending of
compression members is serious
because compressive loads will tend
to magnify the bending in those
members.
WHY column more critical
than tension member?
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