structure strength 3

[aljibbouri]

hi all,
I have a sold mild steel round bar of 40 mm diameter and 850 mm length. this bar is subjected to a load of 1500 kg at the middle. i have already tried the the bar and i know that it can take the load applied to it. however i need to show the calculation in order to get it load certified. can anyone help to put in correct direction.

 

[Ussuri]

Is it simply supported or fixed in at the ends?
How are the ends supported?
How was your 1.5 tonne load applied, do you have bearing along the length spreading the load?
What is your limiting deflection?

Based on the figures (assuming simple support mid span point load) above I get a bending stress of about 500MPa, which is significantly greater than the yield stress of mild steel.

 

[aljibbouri]

the ends of the bar are welded to a frame. i'm not concern about the intergrity of the frame as its already tested. its just the bending stress at mid span that i need to show. could you show me how you done the calculation?

 

[apsix]

I think it's time to consult an engineer.
Don't be suprised if they won't certify it, as Ussuri said the bending stress is very high.

 

[rb1957]

i believe ussuri assumed the kg are mass (not at all unreasonable), but maybe the kgs are weight ? (makes for a factor of 10 difference).

OP ... are the kgs mass or force (weight) ?

 

[aljibbouri]

1500 kg is the mass or the weight sitting on top of the bar, so it would be 14715 N.

 

[CTW]

If you've loaded the bar and it works, why do you need to have calcs to get it load certified? Just have a load test performed under the direction of a qualified person with 125% of the rated load.

 

[aljibbouri]

i was asked for the calculation from the company who will certify it, as they said it will not be valid without it.

 

[rb1957]

as a simple beam the max. moment is PL/4.
the bending stress is MR/I.
I = pi/64*D^4
you should get a stress of 500 MPa, which is pretty high for nominal stell, as noted above.

the simple beam is an assumption, says there's no moment transferre at the ends (into your frame). fully fixed ends (making the beam doubly cantilevered) reduces the moment to 1/2; but now some moment is loading your frame so if they're asking you for an analysis of the beam, they're probably also going to ask for an analysis of the frame.

btw, if they're fussy, they might want to see you account for the weight of the beam.

any reason you went with a bar, rather than an I-beam ? bar was what was lying around (readily assessable) ??

 

[aljibbouri]

rb1957
are you sure that the I equation is correct? because i cant manage to get the 500 MPa value. is there any chance that you could include the calculation please. so i can try it for different bar diameter to suit the load.

 

[Ussuri]

This is just simple bending theory, with 'I' being the second moment of area for a solid round bar.

I=(pi/64)*D*D*D*D

 

[TXStructural]

This is very basic structural question. Please don't ask us to do your work by providing calculations for a real project for which you seem to be the EOR. If you are not qualified to do the work, please consult with a registered engineer.

 

[BAretired]

Instead of maximum stress, you could look at the strength of the bar, i.e. Z*Fy where Z is the plastic modulus (d³/6) and Fy is the yield point of the steel bar.

M = PL/4 = 14.7*0.85/4 = 3.123kN-m

For a 40 mm bar, Z = 10,666 mm³

If Fy = 248MPa, Mp = 2.64kN-m (no good)
If Fy = 350MPa, Mp = 3.73kN-m (won't fail, but not much Safety Factor)

Try 50mm bar...Z = 20,833 mm³
Mp = 5.17 for Fy = 248 (looks okay)

As TXStructural has said, this is pretty basic stuff. The certifying company should know how to perform the calculation. Otherwise, their certification doesn't mean much.

BA

 

[rb1957]

maybe they have done their calcs, determined what you have (that 40mm is dodgy) and want to see how the OP justifies the design.

depends on (the fixity of) the supports ...

 

[BAretired]

rb1957,

Hadn't thought about that. You may be right.

BA

 

[aljibbouri]

they asked for the calculation before they even see the structure. should the testing firm do thier own calculation?

 

[aljibbouri]

i'm sorry for asking another silly question, but how come when i have done the calculations i came up with (497040.88) where the figures provided by you gentlemen is 500 MPa. i have used meter and KN throught as standard units.

 

[apsix]

I suspect your value is in kPa, which would make it 0.6% less than 500 kPa, near enough to being the same result.
Basic SI units are Newtons and Metres.

All you need now is to show that the yield strength is over 660 MPa.

 

[Ussuri]

If you need to demonstrate the adequacy of this before they certify it then your design really should at least consider more than just bending.

What design code are you checking against?
What is your deflection under load, and what is your deflection limit?
Shear check (although not a problem but your calcs should at least show you considered it and ruled it out)
How are you attaching it? Welded, if so what about the weld capacity? Slotted through holes, if so how thick is the material, do you have any bearing issues?
How is your load attached, are there any issues with the detailing that need checked? The simplification above uses a point load which I doubt you actually have.
Is the structure you are fixing to adequate. No point sizing your rod to take 1.5 tonnes if the thing it is attached to fails at 500kg.

In reality none of these may be an issue, but if someone submitted a set of calculations to me for verification and all they contained was bending check then I would start asking questions about the competency of the designer. The usual approach would be a single line stating that it is not critical and explain why.

 

[leeStruct]

If your frame on which your 40mm dia, 850mm long beam was welded to is huge enough to compare with your beam, and your end weld is solid and strong enough, then you can take it as fixed end bending beam. In that case, theoretically, the bending moment is only PL/8, then you will get maximum bending stress of 248 MPa, for AISC Code, a 1.67 safety factor is required, therefore 415 MPa yield strength steel will do. But first of all, you need to prove that consider fixed end condition is adequate.