Engineering Timber Beam Stress Calculation Help

[S2026]

Homework Statement

Context: I'm trying to prove that legs for a captain's style bed are strong enough

Vertical wooden beams= 4x4 inches and 1.8m long
Timber grade = C16
load on each beam ( there are 5 identical ones) = 50kg or 490.33N, so combined max weight is 250kg
using Mmax=(w x l^2)/8, I got the max moment as 110.32Nm
then using sigma(max)= (M x c) / I, I got the max bending stress as 91.54 PSI, but this seems very low compared to its permisable bending stress of 1,600 PSI, so I think I may have done something wrong here?

Even using the total weight of 250kg, the Max moment is 551.61 Nm, so that would mean that the max stress is 457.7 PSI, but this is still relativley low compared to it's permissable rating, so I'm a bit confused here.
dont know if i should use the compression stress formula for this one, sigma=axial load/cross sectional area, but that gave me 67.5 PSI, and that did not seem sensible as its rating is 1,600, although maybe this is right?

Please can anyone help as i need to prove this for an upcoming presentation in an interview on a project I built?

If you need any more information please ask and ill try to provide it.
Thanks!

Relevant Equations

sigma(max)= (M x c) / I
Mmax=(w x l^2)/8
sigma=axial load/cross sectional area

Context: I'm trying to prove that legs for a captain's style bed are strong enough

Vertical wooden beams= 4x4 inches and 1.8m long
Timber grade = C16
load on each beam ( there are 5 identical ones) = 50kg or 490.33N, so combined max weight is 250kg
using Mmax=(w x l^2)/8, I got the max moment as 110.32Nm
then using sigma(max)= (M x c) / I, I got the max bending stress as 91.54 PSI, but this seems very low compared to its permisable bending stress of 1,600 PSI, so I think I may have done something wrong here?
dont know if i should use the compression stress formula for this one, sigma=axial load/cross sectional area, but that gave me 67.5 PSI, and that did not seem sensible as its rating is 1,600, although maybe this is right?

Even using the total weight of 250kg, the Max moment is 551.61 Nm, so that would mean that the max stress is 457.7 PSI, but this is still relativley low compared to it's permissable rating, so I'm a bit confused here.

Please can anyone help as I need to prove this for an upcoming presentation in an interview on a project i built?
Thanks!

 

[berkeman]

Welcome to PF.

Do you have any diagrams or pictures of this bed? I'm not familiar with the term Captain's Bed, so I did a Google Images search and found beds like this:

https://www.pbteen.com/products/cleary-captains-bed/

Is that what you are asking about?

 

[S2026]

Hello,
Thank you!

No, not excactly! If you imagine an elevated 3/4 length bed on legs with ladders up to it; a bunk bed without the bottom bunk if you will. Attatched are some pics!

 

[berkeman]

Even using the total weight of 250kg,

Holy smokes! You have a 550 pound load on top of that bunk bed? At the very least, your anti-racking bracing looks pretty inadequate to me (but I'm an EE with just a basic ME understanding who has built my fair share of furniture and cabinets that are sturdy).

 

[S2026]

Holy smokes! You have a 550 pound load on top of that bunk bed? At the very least, your anti-racking bracing looks pretty inadequate to me (but I'm an EE with just a basic ME understanding who has built my fair share of furniture and cabinets that are sturdy).

No, dont worry! that's a highly exadurated maximum weight for if a few people were on there (and practically jumping!) , just to prove that its extra safe!

 

[Chestermiller]

Homework Statement: Context: I'm trying to prove that legs for a captain's style bed are strong enough

Vertical wooden beams= 4x4 inches and 1.8m long
Timber grade = C16
load on each beam ( there are 5 identical ones) = 50kg or 490.33N, so combined max weight is 250kg
using Mmax=(w x l^2)/8, I got the max moment as 110.32Nm
then using sigma(max)= (M x c) / I, I got the max bending stress as 91.54 PSI, but this seems very low compared to its permisable bending stress of 1,600 PSI, so I think I may have done something wrong here?

Even using the total weight of 250kg, the Max moment is 551.61 Nm, so that would mean that the max stress is 457.7 PSI, but this is still relativley low compared to it's permissable rating, so I'm a bit confused here.
dont know if i should use the compression stress formula for this one, sigma=axial load/cross sectional area, but that gave me 67.5 PSI, and that did not seem sensible as its rating is 1,600, although maybe this is right?

Please can anyone help as i need to prove this for an upcoming presentation in an interview on a project I built?

If you need any more information please ask and ill try to provide it.
Thanks!
Relevant Equations: sigma(max)= (M x c) / I
Mmax=(w x l^2)/8
sigma=axial load/cross sectional area

Context: I'm trying to prove that legs for a captain's style bed are strong enough

Vertical wooden beams= 4x4 inches and 1.8m long
Timber grade = C16
load on each beam ( there are 5 identical ones) = 50kg or 490.33N, so combined max weight is 250kg
using Mmax=(w x l^2)/8, I got the max moment as 110.32Nm
then using sigma(max)= (M x c) / I, I got the max bending stress as 91.54 PSI, but this seems very low compared to its permisable bending stress of 1,600 PSI, so I think I may have done something wrong here?
dont know if i should use the compression stress formula for this one, sigma=axial load/cross sectional area, but that gave me 67.5 PSI, and that did not seem sensible as its rating is 1,600, although maybe this is right?

What are the parameters in your equations, and what criterion are you using for failure?

 

[Lnewqban]

Hello,
Thank you!

No, not excactly! If you imagine an elevated 3/4 length bed on legs with ladders up to it; a bunk bed without the bottom bunk if you will. Attatched are some pics!

Welcome!
You are showing us many photos of the same corner, but we will need to see different angles, in order to provide you with an answer.

Also, it seems that you are calling beams the five 4x4 legs, for which you try to calculate maximum moment?