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Compression Members

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**Compression Members Compression members are susceptible to BUCKLING**

BUCKLING – Loss of stability Axial loads cause lateral deformations (bending-like deformations) P is applied slowly P increases Member becomes unstable - buckles

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**Column Theory Pcr depends on Length of member Material Properties**

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

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**Column Theory - Euler Buckling**

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**Column Theory - Euler Buckling**

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**Column is perfectly straight The load is axial, with no eccentricity **

Assumptions Column is perfectly straight The load is axial, with no eccentricity The column is pinned at both ends No Moments Need to account for other boundary conditions

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**Other Boundary Conditions**

Free to rotate and translate Fixed on top Free to rotate Fixed on bottom Fixed on bottom Fixed on bottom

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**Other Boundary Conditions**

In general K: Effective Length Factor LRFD Commentary Table C-C2.2 p

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**Effective Length Factor**

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**Column Theory - Column Strength Curve**

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**AISC Requirements CHAPTER E pp 16.1-32 Nominal Compressive Strength**

AISC Eqtn E3-1

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AISC Requirements LRFD

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AISC Requirements ASD

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AISC Requirements ASD – Allowable Stress

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Design Strength

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Alternatively Inelastic Buckling

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In Summary

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LOCAL BUCKLING A. Flexural Buckling Elastic Buckling Inelastic Buckling Yielding B. Local Buckling – Section E7 pp and B4 pp C. Lateral Torsional Buckling

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**Local Stability - Section B4 pp 16.1-14**

If elements of cross section are thin LOCAL buckling occurs The strength corresponding to any buckling mode cannot be developed

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**Local Stability - Section B4 pp 16.1-14**

If elements of cross section are thin LOCAL buckling occurs The strength corresponding to any buckling mode cannot be developed

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**Local Stability - Section B4 pp 16.1-14**

If elements of cross section are thin LOCAL buckling occurs The strength corresponding to any buckling mode cannot be developed

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**Local Stability - Section B4 pp 16.1-14**

Stiffened Elements of Cross-Section Unstiffened Elements of Cross-Section

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**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)

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**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 - l> lr Reduce Axial Strength (E7 pp )

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**Slenderness Parameter - Section B5 pp 16.1-12**

Cross Sectional Element Slenderness l Stiffened Unstiffened b t h tw l=h/tw l=b/t=bf/2tw

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**Slenderness Parameter - Limiting Values**

AISC B5 Table B4.1 pp

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**Slenderness Parameter - Limiting Values**

AISC B5 Table B4.1 pp

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**Slenderness Parameter - Limiting Values**

AISC B5 Table B4.1 pp

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**Slenderness Parameter - Limiting Values**

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**Slenderness Parameter - Limiting Values**

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**Slender Cross Sectional Element: Strength Reduction E7 pp 16.1-39**

Reduction Factor Q: Q: B4.1 – B4.2 pp to

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**Slender Cross Sectional Element: Strength Reduction E7 pp 16.1-39**

Reduction Factor Q: Q=QsQa Qs, Qa: B4.1 – B4.2 pp to

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**Flange is not slender, OK**

Example I Investigate a W14x74, grade 50 in compression for local stability W14x74: bf-10.1 in, tf=0.785 in FLANGES - Unstiffened Elements Flange is not slender, OK

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**Example I Web is not slender, OK**

Investigate a W14x74, grade 50 in compression for local stability W14x74: bf-10.1 in, tf=0.785 in WEB - Stiffened Element Web is not slender, OK

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Example I Investigate a W14x74, grade 50 in compression for local stability W14x74: bf-10.1 in, tf=0.785 in PART 1 – Properties: Slender Shapes are marked with “c”

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Example II Determine the axial compressive strength of an HSS 8x4x1/8 with an effective length of 15 ft with respect to each principal axis. Use Fy=46 ksi. HSS 8x4x1/8 7.652 in 8 in 1.5 t = Ag=2.70 in2 h/t=66.0 rx=2.92 in2 b/t=31.5 ry=1.71 in2

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**Example II Maximum OK Inelastic Buckling Nominal Strength HSS 8x4x1/8**

Ag=2.70 in2 rx=2.92 in2 ry=1.71 in2 h/t=66.0 b/t=31.5 Maximum OK Inelastic Buckling Nominal Strength

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**Example II Local Buckling SLENDER HSS 8x4x1/8 Ag=2.70 in2 rx=2.92 in2**

ry=1.71 in2 h/t=66.0 b/t=31.5 Local Buckling SLENDER

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**Example II Local Buckling**

HSS 8x4x1/8 Ag=2.70 in2 rx=2.92 in2 ry=1.71 in2 h/t=66.0 b/t=31.5 Local Buckling Stiffened Cross-Section – Rectangular w/ constant t Qs=1.0 AISC E7.2 Case (b) applies provided that Code allows f=Fy to avoid iterations Aeff: Summation of Effective Areas of Cross section based on reduced effective width be

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Example II Aeff: be

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Example II Aeff: be 7.652 in 8 in 1.5 t = Loss of Area

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Example II Loss of Area Reduction Factor

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**Example II Local Buckling Strength Inelastic Buckling Same as before**

Nominal Strength

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**Example II Local Buckling Strength Nominal Strength CONTROLS**

Lateral Flexural Buckling Strength LRFD ASD

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**Assumption : Strength Governed by Flexural Buckling**

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)

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