Calculating Bending Moments for a Round Bar: E=200x103 N/mm2, D=125mm

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SUMMARY

The discussion focuses on calculating the maximum allowable bending moment and the radius of curvature for a round bar with a diameter of 125mm and Young's modulus of 200x103 N/mm2. The correct formula for the moment of inertia (I) is I=πD4/64, and the radius of curvature (R) should be calculated using the formula R=Er/σ, where r is the radius of the bar. The maximum allowable bending moment was confirmed to be 3,355,582.72 Nmm, and the radius of curvature was calculated to be 1.4mm.

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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 ?
 
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Confusedbiomedeng said:

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).
 
scottdave said:
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??
 
Confusedbiomedeng said:
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.
 
You left out the tensile strength in the problem statement.
 
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Confusedbiomedeng said:
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.
 
scottdave said:
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
 
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.
 
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Chestermiller said:
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
 
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Confusedbiomedeng said:
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.
 

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