Calculating Maximum Stress in a Beam - where did I go wrong?

[Saladsamurai]

!Help Please! Bending (stuck)

Homework Statement

Homework Equations

$$\sigma_{max}=\frac{Mc}{I}$$

The Attempt at a Solution

I am not sure where I am messing this up.

I am pretty I found I correctly to be 140.144.

But I think I am using the wrong internal force.

I am going with replacing the distributed load with a concentrated load and getting:

$$\sigma_{max}=\frac{4*8*w*c}{I}$$

$$\Rightarrow w=\frac{22(10^6)(140.14)}{4*8*5.3}$$

But this is off by many orders of magnitude. It is supposed to be w=1.65 kip/ft

Where am I going wrong

 

[Pyrrhus]

First off recalculate your area moment of inertia, i got about 150. Now, why do you think the moment must be equal to 4*8*w??, first off imagine the bending moment diagram. If you notice by symmetry the max positive and negative value will be equal. Now imagine how will the first max value of moment will be achieved? it'll be after the shear becomes 0 (in this case, because we don't have any couples), then the moment's slope will go negative ( $\frac{dM}{dx} = V$), therefore at 8 feet the moment will have its highest value. By using this argument, you can obtain the value of w. Also, don't forget to convert from Kip-in to Kip-ft. Good luck!

 

[elbarto]

Hi,

I have had a go at your problem, I am from Australia tho so I usually work with Metric units so I may need to you clarify a few things up with some of my workings.

Hope It helps you out in someway, If I have made any mistakes (most likely) please let me know.

Regards
Elbarto

 

[Pyrrhus]

Hi,

I have had a go at your problem, I am from Australia tho so I usually work with Metric units so I may need to you clarify a few things up with some of my workings.

Hope It helps you out in someway, If I have made any mistakes (most likely) please let me know.

Regards
Elbarto

Very well worked, i just don't feel it's good posting the complete solution.

PS:
I made a mistake the moment's slope is 0 between both distributed loads, not negative like i said above.

 

[elbarto]

Cyclovenom, can you confirm that the end result is correct? I wasn't sure on the multiplication of the units given in the problem as I have never worked with ksi, lbs, ft before (see the final section of calculations).

It might not have been the best idea to post the entire solution, but the question is a good example of statics/mechanics of material that I think others may also find useful. Of course if this is discouraged then I will change the structure of my replies in the future.

Regards Elbarto