Torsion and stress on a beam question

[Confusedbiomedeng]

Homework Statement

A rectangular Cross-section beam, 20cm deep by 10cm wide, is subjected to a maximum bending moment of 360kNm
A) Calculate the second moment of area of the beam cross-section
B) what is the maximum stress in the beam under this load
C) if the value of E for the beam of material is 208x10⁹ n\M² , determine the radius of curvature for that portion of the where the bending moment is 360kNm

Homework Equations

Ina=bh³/12 σ/y=m/Ina=E/R

The Attempt at a Solution

A)Ina=(0.1)(0.2³)/12 =0.00006M³
B)σ/20/2=360x10³/0.00006 σ=6x10¹⁰
C) 360x10³/0.00006=208x10⁹/R R=0.028mjust wondering if this is correct?

 

[haruspex]

20cm deep by 10cm wide, is subjected to a maximum bending moment of 360kNm

how does the direction of bending relate to the depth/width?

 

[Confusedbiomedeng]

Thats All that the question states??

 

[haruspex]

Thats All that the question states??

Ok. Your assumption that the bending is in the plane containing the 20cm dimension looks right.
But .00006 is not rounded correctly. Isn't it nearer .000067?

 

[haruspex]

σ/20/2

Please explain the 20/2. (I gather you mean σ/(20/2).)

 

[Confusedbiomedeng]

yes i just rechecked and it comes up on the calculator as a recuring 6 so yes it would be 0.000067 or 0.00007, however keeping that error in mind is my method for the question correct? just this is a 25mark question and it seems very simple? i feel i am doing it incorrectly.

 

[Confusedbiomedeng]

im taking the neutral axis as being the centre to the top of the 20cm section. therefore it being 10. sorry i know that's not the correct terms sorry if that doesn't help.

 

[haruspex]

yes i just rechecked and it comes up on the calculator as a recuring 6 so yes it would be 0.000067 or 0.00007, however keeping that error in mind is my method for the question correct? just this is a 25mark question and it seems very simple? i feel i am doing it incorrectly.

Your methods look ok but I am suspicious of your management of units. Shouldn't the 20/2 be .02/2?
I have been looking at your other post, where I see a calculation using numbers whose units involved mm, but no obvious conversion to standard units. You may have done the conversion ok somewhere along the line, but it takes a bit of checking.

 

[Confusedbiomedeng]

yes I see that now thank you. i must really write them at the top of my page. but other then that I am good? thanks so much i will look over my conversions again.

 

[haruspex]

C) 360x103/0.00006=208x109/R R=0.028m

Check the arithmetic.