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EAS209 L03_General state of stress-spring 11

EAS209 L03_General state of stress-spring 11 - EAS 209...

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EAS 209 – Spring 2011 Instructor: Christine Human 1/18/2011 1 03- Stress on Oblique Planes/3D stress state/FS Lecture 3 –Stresses on Oblique Planes On plane perpendicular to the member axis: Lecture objective: To understand that both normal stress and shear stress can exist on a plane that are not perpendicular to the member axis (oblique plane) Consider components of stress under general (3D) loading conditions Discuss use of factor of safety in design Homework: shear (transverse) force results in shear stress axial load results in normal stress EAS 209 – Spring 2011 Instructor: Christine Human 1/18/2011 2 03- Stress on Oblique Planes/3D stress state/FS Stresses on oblique planes Consider a two-force member under axial loading On a plane at angle to the normal plane, the force P can be resolved into components parallel and perpendicular to the plane Therefore the oblique plane has both normal and shear stresses Since cos 0 A A sin cos P V P F 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 – Spring 2011 Instructor: Christine Human 1/18/2011 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 stress and max. shear stresses occur? Maximum normal stress occurs at θ =0 (cos 2 0=1) Maximum shear stress occurs when =±45 o cos sin cos 0 2 0 A P A P 0 0 0 m A P m m A P A P A P 45 cos 2 45 cos 45 sin 2 0 45 0 0 EAS 209 – Spring 2011 Instructor: Christine Human 1/18/2011 4
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