Chapter 5
description
Transcript of Chapter 5
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Chapter 5
Introduction to Axially Loaded Compression Members
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Compression Members
ColumnsChords of Trusses Bracing Members
Columns are straight vertical members whose lengths are considerably greater than their thicknesses
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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
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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
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• 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
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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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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
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End restraint and Effective Lengths of Columns
K is the Effective Length Factor
KL is the Effective Length of Column
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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.
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19 AISCM 14th Edition
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Stiffened Elements
Unstiffened Elements
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Limiting values for the width thickness ratioAISCS section B4 and Table B4.1a of AISCS
Control of Local Buckling
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HW # 4 : Problems 5-3 and 5-8