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Chapter 5. Introduction to Axially Loaded Compression Members. Compression Members. Chords of Trusses. Columns. Bracing Members. Columns are straight vertical members whose lengths are considerably greater than their thicknesses. Residual Stresses.

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chapter 5

Chapter 5

Introduction to Axially Loaded Compression Members

slide2
Compression Members

Chords of Trusses

Columns

Bracing Members

Columns are straight vertical members whose lengths are considerably greater than their thicknesses

slide3
Residual Stresses

The stresses that remain in a material after the original cause of the stresses, such as external forces, heat gradient, has been removed.

  • Caused by :
    • Uneven cooling of hot rolled sections
    • Uneven cooling welded materials
    • Cambering
  • Affect strength
  • Could be 10 to 15 ksi or more

Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012

slide5
Column Failure Modes

Local Buckling

Torsional Buckling

Flexural Buckling

(Euler buckling)

slide6
Length, L

Material, E

Euler Buckling depends on

Cross section, A or I or r

End support condition

slide7
Columns are Long and slender members subjected to an axial compressive force.
  • Buckling is Lateral deflection of columns
  • Buckling result in instability of columns, and causes sudden failure.
  • Buckling occurs when load P > Pcr the critical load
column with pin support ideal
Column with Pin Support (Ideal)

Ideal column :

perfectly straight before loading

Linear-Elastic Homogeneous material

P is applied thru c.g.

The flexural differential equation

slide10
Buckling Load of an elastic column is calculated using Euler Formula

Dividing both sides by cross sectional area A

And since the radius of gyration

Euler Buckling Stress is the defined as

Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012

slide13
End restraint and Effective Lengths of Columns

K is the Effective Length Factor

KL is the Effective Length of Column

Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012

slide16
For short columns , the failure stress will equal the yield stress.

For intermediate columns , the member will fail by both yielding and buckling.

The strength of long columns is predicted by Euler formula (elastic buckling control)

Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012

slide24
Stiffened Elements

Unstiffened Elements

Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012

slide25
Control of Local Buckling

Limiting values for the width thickness ratio

AISCS section B4 and Table B4.1a of AISCS

Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012

slide41
HW # 4 : Problems 5-3 and 5-8

Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012

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