21
Compression Members
Compression Members
Compression Members
Compression Members
Compression Members
Compression Members
Compression Members:Structural elements subjected only to axial compressive forces
APf a Stress: Uniform over entire cross section
Loads are applied along a longitudinal axis through the centroid
In reality: (a) Secondary Bending due to Load Eccentricities - Ignore(b) Computed Bending Moment - Treat as Beam Column
Types of Compression Members
ColumnsVertical Members that support vertical loads
Trusses and Bracing SystemsCompressive Forces
StrutsSmaller compression members not classified as columns
Compression Members
• Compression members are susceptible to BUCKLING
• BUCKLING – Loss of stability– Axial loads cause lateral deformations (bending-like deformations)
P is applied slowlyP increasesMember becomes unstable - buckles
Column Theory
Axial force that causes Buckling is called Critical Load and is associated to the column strength
Pcr depends on
• Length of member• Material Properties• Section Properties
Let’s Have Some Fun
Column Theory - Euler Buckling
2
22
LEInPcr
Column Theory - Euler Buckling
22
2
2
,1rLEA
LEIPn cr
gyration of radiusAIr
Elastic Buckling ya fAPf
Compression Members – Stress-Strain Behavior
Tension Test Data
Compression Members – Stress-Strain Behavior
Coupon tests different than short column tests
Compression Members – Stress-Strain Behavior
Rolled Shapes
Compression Members – Stress-Strain Behavior
Rolled Shapes
Tips of flanges and web cool down first and shorten
Hot liquid areas follow
Compression Members – Stress-Strain Behavior
Rolled Shapes
Tips of flanges and web have solidified
Hot liquid areas cool down and shorten further
Solidified flanges resist shortening
Residual Compressive stresses in flanges
Residual tensile stresses in remaining
Residual stresses 10-15 ksi
Compression Members – Stress-Strain Behavior
Column Strength
Consider a Long Slender Column
Material Behavior
2
2
LIEP t
cr
ycr F
ALEIP
2
2
A
ELASTIC BUCKLING
Column Strength
Consider a Shorter Column
Material Behavior
2
2
LIEP t
cr
ycr
pl FAPF
INELASTIC BUCKLING
Column Theory - Very Short Columns
Consider a Very Short Column
ycr FAP
PLASTIC BEHAVIOR
Yielding takes place before any instabilities
Column Theory - Column Strength Curve
