Analysis of Tapered Cantilever Beam

[piygar]

Hi All,
I am analyzing a cantilevere beam which is tapered only at the lower edge. (Please see attached image)
Please look at the image. I have following questions:

1. Isn't the neutral axis of a beam will be midline of upper and lower edges of beam which makes the applied vertical load to be inclined wrt neutral axis.

2. if neutral axis is inclined,do i need to resolve the applied vertical load ,normal and parallel to neutral axis? and only vertical component of load be considered (for me) to apply the classical beam bending theory. (is it anywhere mentioned in classical beam theory that vertical load be perpendicular to neutral axis)

i derived vertical deflection expression from deflection equation, for above case by considering the variable sectional inertia of beam but then i think that doesn't take in inclined NA of the beam.

basically i intend to find the vertical deflection of this beam and this is all what i think is going here.
Any more suggestion to solve the above problem?

 

[Illmatic1]

Thanks in advance.The neutral axis of the beam would still be the midline of the upper and lower edges of the beam. However, since the beam is tapered, the neutral axis will be inclined with respect to the vertical load. To account for this, you would need to resolve the applied vertical load into components that are normal and parallel to the neutral axis. Then, you can use the classical beam bending theory to calculate the vertical deflection of the beam.