Compression Members

1
Compression Members
2
COLUMN STABILITY

• A. Flexural Buckling
• Elastic Buckling
• Inelastic Buckling
• Yielding
• B. Local Buckling Section E7 pp 16.1-39
• and B4 pp 16.1-14
• C. Lateral Torsional Buckling

3
AISC Requirements

• CHAPTER E pp 16.1-32

Nominal Compressive Strength
AISC Eqtn E3-1
4
AISC Requirements
LRFD
5
Design Strength
6
In Summary
7
Local Stability - Section B4 pp 16.1-14
Local Stability If elements of cross section
are thin LOCAL buckling occurs The strength
corresponding to any buckling mode cannot be
developed
8
Local Stability - Section B4 pp 16.1-14
Local Stability If elements of cross section
are thin LOCAL buckling occurs The strength
corresponding to any buckling mode cannot be
developed
9
Local Stability - Section B4 pp 16.1-14

• Stiffened Elements of Cross-Section

• Unstiffened Elements of Cross-Section

10
Local Stability - Section B4 pp 16.1-14

• Compact
• Section Develops its full plastic stress before
  buckling (failure is due to yielding only)
• Noncompact
• Yield stress is reached in some but not all of
  its compression elements before buckling takes
  place
• (failure is due to partial buckling partial
  yielding)
• Slender
• Yield stress is never reached in any of the
  compression elements (failure is due to local
  buckling only)

11
Local Stability - Section B4 pp 16.1-14
If local buckling occurs cross section is not
fully effective Avoid whenever possible
Measure of susceptibility to local
buckling Width-Thickness ratio of each cross
sectional element l
If cross section has slender elements - lgt
lr Reduce Axial Strength (E7 pp 16.1-39 )
12
Slenderness Parameter - Limiting Values
AISC B5 Table B4.1 pp 16.1-16
13
Slenderness Parameter - Limiting Values
AISC B5 Table B4.1 pp 16.1-17
14
Slenderness Parameter - Limiting Values
AISC B5 Table B4.1 pp 16.1-18
15
Slender Cross Sectional ElementStrength
Reduction E7 pp 16.1-39
Reduction Factor Q
Q B4.1 B4.2 pp 16.1-40 to 16.1-43
16
Slender Cross Sectional ElementStrength
Reduction E7 pp 16.1-39
Reduction Factor Q
QQsQa
Qs, Qa B4.1 B4.2 pp 16.1-40 to 16.1-43
17
COLUMN STABILITY

• A. Flexural Buckling
• Elastic Buckling
• Inelastic Buckling
• Yielding
• B. Local Buckling Section E7 pp 16.1-39
• and B4 pp 16.1-14
• C. Torsional, Lateral/Torsional Buckling

18
Torsional Flexural Torsional Buckling
When an axially loaded member becomes unstable
overall (no local buckling) it buckles one of the
three ways

• Flexural Buckling
• Torsional Buckling
• Flexural-Torsional
• Buckling

19
Torsional Buckling
Twisting about longitudinal axis of member Only
with doubly symmetrical cross sections with
slender cross-sectional elements
Cruciform shape particularly vulnerable
Standard Hot-Rolled Shapes are NOT susceptible
Built-Up Members should be investigated
20
Flexural Torsional Buckling
Combination of Flexural and Torsional
Buckling Only with unsymmetrical cross sections
1 Axis of Symmetry channels, structural tees,
double-angle, equal length single angles
No Axis of Symmetry unequal length single angles
21
Torsional Buckling
Eq. E4-4
Cw Warping Constant (in6) Kz Effective Length
Factor for Torsional Buckling (based on end
restraints against twisting) G Shear Modulus
(11,200 ksi for structural steel) J Torsional
Constant
22
Lateral Torsional Buckling 1-Axis of Symmetry
AISC Eq. E4-5
Coordinates of shear center w.r.t centroid of
section
23
Lateral Torsional Buckling No Axis of Symmetry
Fe is the lowest root of the Cubic equation
AISC Eq. E4-6
24
In Summary - Definition of Fe
Elastic Buckling Stress corresponding to the
controlling mode of failure (flexural, torsional
or flexural torsional)
Fe
Theory of Elastic Stability (Timoshenko Gere
1961)
Flexural Buckling
Torsional Buckling 2-axis of symmetry
Flexural Torsional Buckling 1 axis of symmetry
Flexural Torsional Buckling No axis of symmetry
AISC Eqtn E4-4
AISC Eqtn E4-5
AISC Eqtn E4-6
25
Column Strength
26
EXAMPLE

• Compute the compressive strength of a WT12x81 of
  A992 steel.
• Assume (KxL) 25.5 ft, (KyL) 20 ft, and (Kz L)
  20 ft

FLEXURAL Buckling X axis
WT 12X81
OK
Ag23.9 in2
Inelastic Buckling
rx3.50 in
ry3.05 in
27
EXAMPLE
FLEXURAL TORSIONAL Buckling Y axis (axis of
symmetry)
WT 12X81
OK
Ag23.9 in2
rx3.50 in
ry3.05 in
y2.70 in
tf1.22 in
Ix293 in4
Iy221 in4
J9.22 in4
Cw43.8 in6
28
EXAMPLE
FLEXURAL TORSIONAL Buckling Y axis (axis of
symmetry)
WT 12X81
Ag23.9 in2
rx3.50 in
ry3.05 in
y2.70 in
tf1.22 in
Ix293 in4
Iy221 in4
J9.22 in4
Cw43.8 in6
29
EXAMPLE
FLEXURAL TORSIONAL Buckling Y axis (axis of
symmetry)
WT 12X81
Ag23.9 in2
rx3.50 in
ry3.05 in
y2.70 in
tf1.22 in
Ix293 in4
Iy221 in4
J9.22 in4
Cw43.8 in6
30
EXAMPLE
FLEXURAL TORSIONAL Buckling Y axis (axis of
symmetry)
WT 12X81
Elastic or Inelastic LTB?
Ag23.9 in2
rx3.50 in
ry3.05 in
y2.70 in
tf1.22 in
Ix293 in4
Iy221 in4
J9.22 in4
Cw43.8 in6
31
EXAMPLE
FLEXURAL TORSIONAL Buckling Y axis (axis of
symmetry)
WT 12X81
Ag23.9 in2
rx3.50 in
ry3.05 in
y2.70 in
tf1.22 in
Ix293 in4
Iy221 in4
Compare to FLEXURAL Buckling X axis
J9.22 in4
Cw43.8 in6
32
Column Design Tables
Assumption Strength Governed by Flexural
Buckling Check Local Buckling
Column Design Tables Design strength of selected
shapes for effective length KL Table 4-1 to 4-2,
(pp 4-10 to 4-316) Critical Stress for
Slenderness KL/r table 4.22 pp (4-318 to 4-322)
33
EXAMPLE

• Compute the available compressive strength of a
  W14x74 A992 steel compression member. Assume
  pinned ends and L20 ft. Use (a) Table 4-22 and
  (b) column load tables

(a) LRFD - Table 4-22 pp 4-318
Fy50 ksi
Table has integer values of (KL/r) Round up or
interpolate
34
EXAMPLE

• Compute the available compressive strength of a
  W14x74 A992 steel compression member. Assume
  pinned ends and L20 ft. Use (a) Table 4-22 and
  (b) column load tables

(b) LRFD Column Load Tables
Tabular values based on minimum radius of gyration
Fy50 ksi
35
Example II

• A W12x58, 24 feet long in pinned at both ends and
  braced in the weak direction at the third points.
  A992 steel is used. Determine available
  compressive strength

Enter table 4.22 with KL/r54.55 (LRFD)
36
Example II

• A W12x58, 24 feet long in pinned at both ends and
  braced in the weak direction at the third points.
  A992 steel is used. Determine available
  compressive strength

Enter table 4.22 with KL/r54.55 (ASD)
37
Example II

• A W12x58, 24 feet long in pinned at both ends and
  braced in the weak direction at the third points.
  A992 steel is used. Determine available
  compressive strength

CAN I USE Column Load Tables?
Not Directly because they are based on min r (y
axis buckling)
If x-axis buckling enter table with
38
Example II

• A W12x58, 24 feet long in pinned at both ends and
  braced in the weak direction at the third points.
  A992 steel is used. Determine available
  compressive strength

X-axis buckling enter table with