- #1

pd2905

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## Homework Statement

A ski pole is bent(plastic deformation) in three point bending by applying a load 2F perpendicularly to the ski pole. The forces at the end points are of magnitude F. If the pole yields due to plastic deformation at the mid point longitudinal span of the ski pole which is 90 cm long and which is a hollow tube with inner radius Ri and outer radius Ro give the formula to calculate the minimum load for which the pole will fail, given that the pole is made of an isotropic 5086 Al alloy with E=71GPa modulus of elasticity and that the yield stress of the alloy is Y=230 MPa. We assume a static load.

## Homework Equations

Stress at tip=Yield stress=Moment of cross-sectional area*Distance from the centroid/Second moment

I calculate moment of cross-section by M=F*length/2

I would like to know if any other more suitable yield criterion can be used

such as Von mises or Tresca. I think Al alloys are considered ductile materials.

So I get M=Yield stress/Distance from the centroid*Second moment

2F=4M/length=4.

## The Attempt at a Solution

Yield stress=230Mpa

Distance from centroid=9mm

Ri=16.5mm

Ro=18mm

length=900mm

2F==4*230/(900)/9*(3.14/4)*(18^4-16.5^4)=2751N is the load to necessary bend the pole.

It seems kind of ridiculous although I have never bent a ski pole.