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L03_General state of stress-fall 10

# L03_General state of stress-fall 10 - EAS 209 Fall 2010...

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EAS 209 – Fall 2010 Instructor: Christine Human 8/24/2010 1 03- Stress on Oblique Planes/3D stress state/FS Lecture 3 –Stresses on Oblique Planes Axial loading results in normal stresses on the plane perpendicular to the member axis. Lecture objective: To understand that both normal and shear stresses can exist on planes that are not perpendicular to the member axis (oblique planes) Consider components of stress under general (3D) loading conditions Discuss use of factor of safety in design Homework: Transverse forces on bolts and pins result in shear stresses on the plane perpendicular to bolt or pin axis EAS 209 – Fall 2010 Instructor: Christine Human 8/24/2010 2 03- Stress on Oblique Planes/3D stress state/FS Stresses on oblique planes Consider again a two-force member under axial loading On a plane at angle θ to the normal plane, the force P can be resolved into components parallel and perpendicular to the plane The oblique plane has both normal and shear stresses Since θ θ cos 0 A A = θ θ sin cos P V P F = = θ θ θ θ τ θ θ θ σ θ θ θ θ cos sin cos sin cos cos cos 0 0 2 0 0 A P A P A V A P A P A F = = = = = =

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EAS 209 – Fall 2010 Instructor: Christine Human 8/24/2010 3 03- Stress on Oblique Planes/3D stress state/FS Maximum normal and shear stresses due to axial loading On what planes do the maximum normal and shear stresses occur? Maximum normal stress occurs at θ =0 (cos 2 0=1) Maximum shear stress occurs when θ =±45 o θ θ τ θ σ θ θ cos sin cos 0 2 0 A P A P = = 0 0 0 m = = τ σ A P m m A P A P A P τ σ τ = = = = 45 cos 2 45 cos 45 sin 2 0 45 0 0 EAS 209 – Fall 2010 Instructor: Christine Human 8/24/2010 4
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L03_General state of stress-fall 10 - EAS 209 Fall 2010...

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