Mechanical Bending Moment and Rod Deformation Calculations

[Apple&Orange]

Homework Statement

A) A circular rod is subjected to a bending moment of 315Nm. What is the minimum diameter of the rod required so that the maximum stress does not exceed 200N/mm²?

B) If the Modulus of Elasticity for the material from which the rod is made of is 100kN/mm², what radius will the rod be deformed to when stressed to the maximum allowable?

Homework Equations

A) $\frac{M}{I}$ = σ

B) $\frac{M}{σ]}$ = $\frac{ρ]}{E]}$

Second moment of Area for a circle of diameter d, about its Neutral Axis is $\frac{∏d}{64}$

The Attempt at a Solution

A) M=314N/m
σ=200MN/m²
I=$\frac{∏d]}{64}$

[itex]\frac{314}{$\frac{∏d}{64}$}[/itex]=200×10⁶

d=0.0752m

B) M=413Nm
E=100GN/m²
σ=200MN/m²

$\frac{314}{200×10⁶}$=$\frac{ρ}{100×10⁹}$

ρ=157,000m (Ridiculous answer, I know)

I haven't done mechanics in a while, so I was wondering if someone could double check that I'm on the right track.

Chuur Chuur

 

[LawrenceC]

Bending stress is Mc/I not M/I. Check your units.

 

[Apple&Orange]

Bending stress is Mc/I not M/I. Check your units.

But how would that formula work though?

I wouldn't be able to solve for c, since I'm asked to find the diameter. If I substitute that in, then I'd have $\frac{M\frac{d}{2}}{\frac{∏d}{64}}$=σ

where c = $\frac{d}{2}$

 

[LawrenceC]

But how would that formula work though?

I wouldn't be able to solve for c, since I'm asked to find the diameter. If I substitute that in, then I'd have $\frac{M\frac{d}{2}}{\frac{∏d}{64}}$=σ

where c = $\frac{d}{2}$

You are provided with the bending moment and the maximum stress. You can easily determine diameter from that information. The formula you have above is missing an exponent.