Maximum Stress on a Beam: Solving Homework Question 2 with the M/I Formula

[eddievic]

Homework Statement

My Question paper is listed under attachement Question 2

Homework Equations

M/I = σ/y

The Attempt at a Solution

My attempt at the solution is as per Q 2 attachment.

What I am looking for is to see if I am on the right track. I'm worried that the units seem to change and therefore i may be making a mistake purely with my arithmetic .

Could a kind sole chekc I'm working in the right method and perhaps point me in the right direction for further reading on this subject as I am unsure of how to proceed with question d

Any help is greatly appreciated.

 

[SteamKing]

I don't know what you thought you were calculating, but it was not the maximum bending moment.

After determining the end reactions, draw the shear force diagram. Using this, construct the proper BM diagram. Pick the maximum BM.

 

[pongo38]

Sorry to disagree with steamking but I thought it was correct, but not well-expressed. You can check it by taking moments to the left of the 10 load, and to the right. The values should agree. To answer d, you need to consider the sensitivity of stress to the breadth and depth. If you have expressions for the bending stress that should speak for itself and you could progress.

 

[eddievic]

Thanks for your reply I'll see if I can progress with this problem.:)

 

[rev8]

Bending moment HELP

Can anyone help me to figure out this one
I have no clue
Trying to find the bending moment of this beam
is related to bending moment in cracked beams
all I know is σ=Mc/I how do I approach this
Thanks

 

[SteamKing]

First of all, how is the beam loaded? You can't determine the BM unless you know the loading.

 

[rev8]

The beam is under 3 point loading

First of all, how is the beam loaded? You can't determine the BM unless you know the loading.

 

[Carlo2986]

Ignore this

 

[Carlo2986]

And this . .

 

[Carlo2986]

Also, your answer for 2c, shouldn't it relate to stress in the beam, and not the bending moment? The diagram looks correct but the numbers don't.

I'm not an expert so any help would be appreciated :)

 

[eddievic]

can i have some advice on my original question on section(d)

I just need help understanding what the question is asking on the first bullet point is the question just asking to add 20% to the dimension of the beam and then work out the maximum bending stress?

on the second point it states the beam section is to remain a solid rectangle (what does this mean exactly?)

 

[pongo38]

If you change your formula fro stress so that, instead of y and I, you have an expression with b and d, each to some power, you will be able to see the sensitivity of stress the the parameters b and d. As the AREA can be increased by 20%, that implies that the questioner believes that b and d are not necessarily to be increased by the same percentage.
quote: "on the second point it states the beam section is to remain a solid rectangle (what does this mean exactly?)" end quote. What do you detect are the possibilities for variation of meaning?

 

[eddievic]

I think I am on the right track now. make a new cross sectional area so existing is 20000mm^2 and then add 20% so 240000mm^2

so new beam will be 240mm d * 100 mm b
and then find the maximum stress this beam can take

I increased the d as the beam is supporting a load so its better to increase the thickness.

 

[pongo38]

quote "I increased the d as the beam is supporting a load so its better to increase the thickness."
Correct to increase d but for a different reason from the one you give. The reason you give would just as equally apply to the breadth of the beam? Maybe you didn't express yourself precisely? Look again at the formula for stress. Rearrange it so that M is by itself on the left hand side. For a fixed value of maximum stress, vary d by say 20% and see how M is affected. Then vary b by 20% and see how M is affected by that. Draw conclusion.

 

[eddievic]

quote "I increased the d as the beam is supporting a load so its better to increase the thickness."
Correct to increase d but for a different reason from the one you give. The reason you give would just as equally apply to the breadth of the beam? Maybe you didn't express yourself precisely? Look again at the formula for stress. Rearrange it so that M is by itself on the left hand side. For a fixed value of maximum stress, vary d by say 20% and see how M is affected. Then vary b by 20% and see how M is affected by that. Draw conclusion.

Ok thanks for your help with this topic it was much appreciated :)

 

[mamike1515]

Hi
Am new to the forum, but as regards to the original question of the second moment of area I.
Should this be the second moment of area for a rectangle Ixx = bd^3/3?
The formula being used is for second moments of area about an axis passing through the centroid, Ixx=bd^3/12?

 

[SteamKing]

Hi
Am new to the forum, but as regards to the original question of the second moment of area I.
Should this be the second moment of area for a rectangle Ixx = bd^3/3?
The formula being used is for second moments of area about an axis passing through the centroid, Ixx=bd^3/12?

Ixx = bd^3/3 is the second moment of area for a rectangle about one of the edges of the rectangle.

In order to calculate the bending stress in a cross section, σ = My/I, the second moment of area, I, must be calculated about the centroid of the cross section, which is also the location of the neutral axis. The bending stress at the neutral axis is zero, by definition, and the variable y in the bending stress formula indicates the distance from the neutral axis at which the bending stress is calculated. The bending stress increases with distance from the neutral axis.

 

[mamike1515]

Hi Steamking

Thanks for the reply. I have had a look through my notes and realize that the formula for calculating the stress uses the second moment of area with the neutral axis, so Ixx=bd^3/12.
Again thanks for the confirmation