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MBD Chapter 5

MBD Chapter 5 - Uniaxial stress = = = = = =-σ1 Eϵ1 σ2...

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Chapter 5: Elastic Strain, Deflection and Stability 5.3 Analysis of Strain – Equiangular Rosettes , = + + ±( - - ) +( + ) ϵ1 2 ϵ0 ϵ120 ϵ2403 2ϵ0 ϵ120 ϵ240 29 ϵ120 ϵ240 23 = ( - ) - - tan2α 3 ϵ120 ϵ240 2ϵ0 ϵ120 ϵ240 5.4 Analysis of Strain – Rectangular Rosettes , = + ±( - ) +( - ) ϵ1 2 ϵ0 ϵ902 ϵ0 ϵ45 2 ϵ45 ϵ90 22 = tan2α - + - ϵ0 2ϵ45 ϵ90ϵ0 ϵ90 5.5 Elastic Stress-Strain Relationships and Three-Dimensional Mohr Circles = - + = - + = σ1 E1 ν2ϵ1 νϵ2 σ2 E1 ν2ϵ2 νϵ1 σ3 0 = - = - =- ( + ) ϵ1 1Eσ1 νσ2 ϵ2 1Eσ2 νσ1 ϵ3 νE σ1 σ2 Uniaxial stress:
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Unformatted text preview: Uniaxial stress: = = = = = =-σ1 Eϵ1 σ2 σ3 0 ϵ1 σ1E ϵ2 ϵ3 νσ1E Look at Tabbed Sections 5.6, 5.7, 5.8 5.10 Column Buckling – Elastic Instability = = = ( ) = ( ) Pcr π2EILe2 Scr PcrA π2E Leρ 2 or ScrE π2 Leρ 2 5.12 Column Design Equations – J.B. Johnson Parabola = =-( ) ≫ = Scr PcrA Sy Sy24π2E Leρ 2 Scr Sy2 = Leρ 2π2ESy 5.14 Equivalent Column Stresses = ≫ = = ( ) Scr Syα α SyScr Sy Leρ 2π2E Euler = =-( ) α SyScr 4π2E4π2E Sy Leρ 2 Johnson...
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