Posted by **shane** on Saturday, August 4, 2012 at 12:51pm.

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 -
**MathMate**, Saturday, August 4, 2012 at 1:27pm
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):

loading rotation deflection

moment M ML/(EI) ML²/(2EI)

P(point load) PL²/(2EI) PL³/(3EI)

w,udl wL³/(6EI) wl^{4}/(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.

Hope you can post or describe the loading, and post your work up to this point.

## Answer this Question

## Related Questions

- statics and strengths - A cantilever beam member made from steel with hollow ...
- Statics - A cantilever beam, made of a material with a Young's modulus, E with a...
- Physic - Reaction at support and internal axial force resultant Consider two ...
- psuchics - Reaction at support and internal axial force resultant Consider two ...
- physics - Consider two straight bars of uniform cross section made of the same ...
- physics - A steel bar of length L=2 m, with modulus E=200 GPa and constant cross...
- Physic - A steel bar of length L=2 m, with modulus E=200 GPa and constant cross ...
- Physics - Steel is very stiff, and the Young's modulus for steel is unusually ...
- Physics - HW8_1: CANTILEVERED BEAM WITH TAPERED SQUARE CROSS SECTION A ...
- Physics/Mechanics - HW8_1: CANTILEVERED BEAM WITH TAPERED SQUARE CROSS SECTION A...