# statics

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A cantilever beam member made from steel with hollow circular cross section experiences an axial load of 300 KN (F1), and a vertical load of 200 kN (F2) as shown in the following figure.
The outside diameter of the beam is 50mm and the uniform wall thickness of the cross section is 4mm. Beam is made out of AISI 1040 Cold-drawn steel. The beam is fixed on one end and the beam has a length of 300mm

For the given system:
a. Draw the Free-Body-Diagram of the beam.
b. Compute the reaction forces and bending moment on the beam.
c. Compute the maximum normal stress, minimum normal stress and maximum shear stress.
d. Compute the maximum axial deformation on this member (x).
e. Compute the maximum vertical deflection of the tip of the beam due to the bending moment (y).
f. Will the member experience permanent deformation or complete failure due to this applied load? Draw your conclusions based on the strength values of the beam material.

• statics -

First, we do not see the loading diagram, but that does not stop me from giving a response.

Also, for "f", you will need the properties of AISI 1040 cold drawn steel (yield stress).

A cantilever is a statically determinate structure, so finding bending moments is a matter of taking moments about the appropriate points.

Deflections and rotations are a matter of getting the correct formulae.

The book Strength of Materials by den Hartog of MIT gave the rotations and deflections of the free end of a cantilever (usual E, I, L, P, w for properties and loading):
moment M ML/(EI) ML²/(2EI)
w,udl wL³/(6EI) wl4/(8EI)

It's easy to memorize by the number
1-2-2-3-6-8.

axial stress=P/A
bending stress=My/I
where y is the maximum distance from the neutral axis of the cross section.

Take care that axial force will change the location of the neutral axis even for a symmetrical cross section.

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