# Simple Mechanical Questions

1. Apr 18, 2012

### Apple&Orange

1. The problem statement, all variables and given/known data

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?

2. Relevant 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 $\frac{∏d}{64}$

3. The attempt at a solution

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

$\frac{314}{$\frac{∏d}{64}$}$=200×106

d=0.0752m

B) M=413Nm
E=100GN/m2
σ=200MN/m2

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

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

2. Apr 18, 2012

### LawrenceC

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

3. Apr 18, 2012

### Apple&Orange

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 = $\frac{d}{2}$

4. Apr 19, 2012

### LawrenceC

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.