If I know the deflection (w) of a beam subjected to a point load in the middle, can I calculate the stress in that beam by calculating the shear force or moment ?
or use a 2d plane strain state ?
deflection of beam as a function of (P,L,E,I)
bending stress of beam as a function of moment.
shear stress of beam as a function of shear.
Then you need to add the two stresses together, but they almost always don't add linearly. Bending stress is varies with the height, y, within the section; ie: high at both top and bottom fibers, and zero at the mid section. Shear stress is parabolic, with its maximum at the mid section. A bit of reading will reveal what shear stress engineers usually use at the extreme fibers (it is not zero).
This is all in most books on "Mechanics of Materials".
Ok.
So the bending stress sigma_B = M_max *Z/I , right? I=moment of inertia.
What about the stress due to shear then? With the equation for deflection I could integrate and get the shear force, but how do I get the shear stress ?
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