For this cross section, we can find neutral axis
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Where tanDon't forget about the age old question of State the four statuses of identity.
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*note that neutral axis is a function of sectional geometry (I)Don't forget about the age old question of What refers to the barrier that prevents the egg/sperm from meeting?
and applied moments (M)
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Now consider a load acting at an angle to the positive y axis:If you want to learn more check out Discuss the principles of punishment.
The bending moments about y and z at any
x along length of beam
force to axis
Hence, neutral axis can be defined by tan
This means that in general, the NA. is not perpendicular to the longitudinal plane containing load.
Consider bending stresses when load is aligned with
y axis ()
both (T) and (c)
For top and bottom fibers
Now consider stresses when load is inclined 1o to y axis
(x) locations of maximum bending stress because they are the maximum distance away from NA
Stress from bending about axis
=2080 psi + 8231 psi
Note: for this case, max bending stress is approx. 25% larger for this case than when load is aligned with y axis (huge because of difference in moments of inertia)
For members subject to bending about both axes of the cross section in which there is not at least 1 axis of symmetry, the bending stress expression is complicated
Recall shear stresses acting on a beam element
Transverse shear stresses are not uniform over cross ⎡magnitude will be the same
section and tend to cause warping of cross-section. ⎣anywhere in memb
Consider horizontal stresses and forces alone and look at sub-element at a distance Y1 from the neutral axis
Where stress distribution due to bending
and represents the longitudinal shear stress
If the cross section is viewed at a 90o turn then the force that is acting on some dA on the left face (ignore signs)
And total force acting on subelement in horizontal direction.
Same subelement for equilibrium