Chapter 5 Introduction to Axially Loaded Compression Members
Chapter 5
Feb 23, 2016
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. - PowerPoint PPT Presentation
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Chapter 5
Introduction to Axially Loaded Compression Members
2
Compression Members
ColumnsChords of Trusses Bracing Members
Columns are straight vertical members whose lengths are considerably greater than their thicknesses
Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012
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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
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Column Failure Modes
Flexural Buckling(Euler buckling)
Local Buckling Torsional Buckling
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Euler Buckling depends on
Length, L
Material, E
Cross section, A or I or r
End support condition
• 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)Ideal column :
Linear-Elastic Homogeneous materialP is applied thru c.g.
perfectly straight before loading
The flexural differential equation
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Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012
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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
𝐹 𝑒=𝜋 2𝐸
( 𝐿𝑟 )2
𝑃𝑐𝑟=𝜋 2 𝐸 𝐼𝐿2
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Column Strength Curve
Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012
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Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012
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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
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The strength of long columns is predicted by Euler formula (elastic buckling control)
For short columns , the failure stress will equal the yield stress.
For intermediate columns , the member will fail by both yielding and buckling.
Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012
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19 AISCM 14th Edition
20 AISCM 14th Edition
21 AISCM 14th Edition
22 AISCM 14th Edition
23 AISCM 14th Edition
Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012
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Stiffened Elements
Unstiffened Elements
Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012
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Limiting values for the width thickness ratioAISCS section B4 and Table B4.1a of AISCS
Control of Local Buckling
Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012
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HW # 4 : Problems 5-3 and 5-8
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