Maximum bending moment and radius of curvature for 125mm diameter bar

[Confusedbiomedeng]

Homework Statement

a round bar,125mm in diameter , is to be used as a beam. if youngs modulus for the material E=200x10³ N/mm²
Calculate:
i)Maximum allowable bending moment(12marks)
ii)The radius of curvature at the point of maximum bending moment(8marks)

Homework Equations

σ/y=m/I=E/R
I=πD⁴/64[/B]
y=125/2

The Attempt at a Solution

i)17.5/62.5=M/11984224
0.28x11984224=3355582.72Nmm=M
ii)0.28/200x10³=1.4mm=R

Can anyone tell me where I am going wrong ?

 

[scottdave]

Homework Equations

σ/y=m/I=E/R
I=πD⁴/64[/B]
y=125/2

The Attempt at a Solution

i)17.5/62.5=M/11984224
0.28x11984224=3355582.72Nmm=M
ii)0.28/200x10³=1.4mm=R

Can anyone tell me where I am going wrong ?

Can you put some units onto your workings out? It would be easier to follow what you are doing (for us and for you).

 

[Confusedbiomedeng]

Can you put some units onto your workings out? It would be easier to follow what you are doing (for us and for you).

in the final answers i have them put in ?? should i put them in throughout the workings??

 

[scottdave]

in the final answers i have them put in ?? should i put them in throughout the workings??

It would help me to figure out what you were doing.

 

[Chestermiller]

You left out the tensile strength in the problem statement.

 

[scottdave]

y=125/2

The Attempt at a Solution

i)17.5/62.5=M/11984224
0.28x11984224=3355582.72Nmm=M
ii)0.28/200x10³=1.4mm=R

Can anyone tell me where I am going wrong ?

So where did the 17.5 come from? I am guessing it is σ. It would be nice to eliminate guessing, when figuring out where you are going wrong.

 

[Confusedbiomedeng]

So where did the 17.5 come from? I am guessing it is σ. It would be nice to eliminate guessing, when figuring out where you are going wrong.

Yes it is stated in the question and I forgot to put it in so 17.5n/mm² then y is 125/2 because everything is in mm² so I don't need to change the diameter . I ,I worked out by ∏(125⁴)/64 but now I'm wondering should the equation for I be ∏(D⁴)/32?? So sorry for any confusion

 

[Chestermiller]

I confirm you calculation of the bending moment, and I confirm the factor of 64 in the denominator. But the equation for the radius of curvature should be $$R=\frac{Er}{\sigma}$$where r is the radius of the bar.

 

[Confusedbiomedeng]

I confirm you calculation of the bending moment, and I confirm the factor of 64 in the denominator. But the equation for the radius of curvature should be $$R=\frac{Er}{\sigma}$$where r is the radius of the bar.

Ok could you just explain why that equation and not M/I =E/R? And so I have the right answer for the allowable bending moment

 

[Chestermiller]

Ok could you just explain why that equation and not M/I =E/R?

It's that too. I just found it easier to calculate it the other way.