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INCLINED BENDING. z. z. z. . y. y. y. . If bending moment does not coincide with any of principal central axis of cross-section inertia we have to deal with inclined bending. Direction of bending moment vector. Plane of load acting. +. z. z. z. z. z. . y. y. y. y. y.
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z z z y y y If bending moment does not coincide with any of principal central axis of cross-section inertia we have to deal with inclined bending. Direction of bending moment vector Plane of load acting +
z z z z z y y y y y We use superposition principle Jy>Jz For neutral axis: Jy<Jz Neutral axis
z y is represented by the equation of the plane Stress distribution: This plane cuts thorough cross-section plane at the neutral axis Tension zone Compression zone Neutral axis
Animation of neutral axis movement dependent on bending moment direction
z Angle 80o 70o 60o 50o 40o y 30o 20 10o h/b=1,41 00o Loading plane Jy/Jz =2 Neutral axis Bending moment vector
z 80o 70o 60o 50o 40o y 30o 20 10o h/b=1,41 00o Jy/Jz =2 Loading plane Neutral axis Bending moment vector
z 80o 70o 60o 50o 40o y 30o 20 10o b/h=1,41 00o Jy/Jz =1/2 Loading plane Neutral axis Bending moment vector
z z z y y y Zmax =a/2=0,5a Zmax =a/2½=0,7a h=b=a Ideal shape: independent of plane of loading angle maximum stress is the same! Jy/Jz =1 Płaszczyzna obciążenia Oś obojętna Wektor momentu
z Angle 80o 70o 60o 50o 40o y 30o 20 10o h/b=1,41 00o Loading plane Jy/Jz =2 Neutral axis Bending moment vector
z Angle 80o 70o 60o 50o 40o y 30o 20 10o h/b=1,41 00o Loading plane Jy/Jz =2 Neutral axis Bending moment vector
z z y y α=45° Zmax =a/2=0,5a Zmax =a/2½=0,7a h=b=a Ideal shape: independent of plane of loading angle maximum stress is the same! Jy/Jz =1 Płaszczyzna obciążenia Oś obojętna Wektor momentu