Hi. Been at it again.
Having learned some PHP - the web-scripting langugage.
My beam calculations written in Lisp - done as webpage version.
http://weldsmith.co.uk/cgi_my/ebbeam_rhs/230724_ebbeam_rhs.html
"Rectangular Hollow Section beam calculations"
Best wishes,
Rich S

"Richard Smith" wrote in message news:lypm4hjemg.fsf@void.com...

Hi. Been at it again.
Having learned some PHP - the web-scripting langugage.
My beam calculations written in Lisp - done as webpage version.
http://weldsmith.co.uk/cgi_my/ebbeam_rhs/230724_ebbeam_rhs.html
"Rectangular Hollow Section beam calculations"
Best wishes,
Rich S

----------------------

I try to do the math and then check it with on-line calculators. A useful
result is the deflection at maximum load or yield point, which can be used
as a gauge by placing something that high on the beam center and observing
its alignment with the two ends when the test or straightening setup is too
unstable and risky to approach or put an expensive load cell on. The 3" and
4" channel I found to build my gantry hoist and sawmill tends to twist when
near full load.

"Jim Wilkins" <muratlanne@gmail.com> writes:

> "Richard Smith" wrote in message news:lypm4hjemg.fsf@void.com...
>
> Hi. Been at it again.
> Having learned some PHP - the web-scripting langugage.
> My beam calculations written in Lisp - done as webpage version.
> http://weldsmith.co.uk/cgi_my/ebbeam_rhs/230724_ebbeam_rhs.html
> "Rectangular Hollow Section beam calculations"
> Best wishes,
> Rich S
>
> ----------------------
>
> I try to do the math and then check it with on-line calculators. A
> useful result is the deflection at maximum load or yield point, which
> can be used as a gauge by placing something that high on the beam
> center and observing its alignment with the two ends when the test or
> straightening setup is too unstable and risky to approach or put an
> expensive load cell on. The 3" and 4" channel I found to build my
> gantry hoist and sawmill tends to twist when near full load.

Check maths - be appreciated.
I was exhausted after a through-the-night and could only say it agrees
with "The Blue Book" where I spot-checked.

(I was learning a lot of programming with PHP (scripting language for
getting the web-server to do calculations and processing for you and
put the answers into the webpage being served-up) being so different
to the Lisp which is all I have used for years)

I had a warm feeling that that deflection at load would be useful to
practical designers.
* I will come back to this *

Usage - strong hint - put in the yield stress as "your stress" and you
will get the deflection at the point where any further and the section
would yield.

I've done this a couple of times in tests and it is so spot-on right -
at least once with Euler-Bernoulli beam (this calculation) and once
with Finite Element modelled "structure" (the FEA is doing essentially
the same mathematics).

I was so tired then I had to leave as-is and walk-away.

I have heard military training, especially for Sergeants and the the
like, deliberately takes you far far far into "impossible" exhaustion
so you learn what thoughts do work in that state (unfortunately I
found out about the "hallucinatory" world for the first time at a
crucial time and messed-up, having no prior experience of it - had I
known to trust my "gut instincts" still working I could have produced
the good outcome).

The one about coupling the stress and deflection.

So if you put in the yield stress and get the max. load
and the deflection for your beam at the point that is reached...

This is what I promised to come back to.

In the function which does that - a bit of algebra, obviously - a lot
of variables cross-cancel if/when you run through it on paper first.
I was most surprised.
That was during that night I couldn't sleep anyway.
You end up with a surprisingly small formula which gets the deflection
at the "aim stress" the "this is the load which would cause it"
output.

Taking three of the big formulae of beams:

M=FL (cantilever beam)
M=FL/4 ("simple" beam - it's spanning between two supports)

the massive one which combines material property and geometric
property...
M=sigma.Z
[noting "Z" = I/half-height for a symmetrical section]

and deflection
d=F_c.L^3/3EI (cantilever beam)
d=F_s.L^3/48EI (simple beam)

the equations have a lot of "substituting into each other".

Hence that which you like - you get the deflection - what you can
readily see and measure - at the point beyond which everything goes
wrong - that has a backstory which was quite delightful.

In the evening leading into the night I was there with a multi-colour
"magic pen" there writing out equations in black, arrowing where they
cross-substituted in blue, leaving notes in green and striking though
cross-cancelled variables in red.

There is a general function for beam deflection in the code, for
debugging during development, but it isn't used in the "working" code
which gives the outputs from your inputs.

What you "jumped to noticing you can do" - deflection at the point it
all goes wrong - I have tested and seen and you know already that -
what happens is not sudden disaster.

My "moment" is recorded here:
http://weldsmith.co.uk/tech/struct/201123_wssb_test/201123_weld_RHS_beam_test.html
I was doing the worst I could to a weld - but got to see the
Euler-Bernoulli beam calculations giving such accurate predictions
that you could actually use them to measure the yield stress of your
steel you have in the shop.
I did the maths in chalk on a bench-top by the way - I had half and
hour with the work held up and had to jump at the opportunity
immediately.
That's where at the instant you hit that value you are interested in,
if you go any further your section which always returned to straight
before now has a bend.

The one where I "Finite Element'ed" is here
http://weldsmith.co.uk/tech/struct/201113_u_rhs/201120_U_RHS_make_analyse_test.html
Same.

Both you see - the prediction of deflection at the point of "overload"
is accurately predicted.
What happens after is what you the individual needs to see at least
once.
The structure takes more and more bend under progressively increasing
resistance to further bend.
In a world of "Clipboard Clarence" and "Safety Sam the Management Man"
there is an edict and anything beyond what they say is "absolutely
disaster". Well it is if you get "fired" for being held to have
transgressed "Clipboard Clarence's" edict.

Hope this was a nice follow-up chat.

The one about the maths cross-cancelling - as you'll also be
commending to anyone "on the path", you can only see that by having
some sheets of paper, preferably a multicolour pen, and running
through it yourself.

I woke up this morning feeling great having slept like a log from
early, after yesterday was "different" having not slept the night
before.

Best wishes,
Rich Smith

Deriving the expression for deflection at that already-calculated Force:

Caution here is that on-paper often put "=" when mean "=="
"=" is "assign" or "are equal at this one specific instance" where
"==" means "always equal to".
What is derived has no generality - only useful in this case (?)
A stopped clock is correct twice a day.
What I derive is only right at one of those "coincidence points"...

Taking cantilever beam case.

M=FL
M=sigma.Z
[noting "Z" = I/half-height for a symmetrical section]
d=F_c.L^3/3EI

M=FL -> F=M/L into d=F_c.L^3/3EI
d=(M/L)L^3/3EI=ML^3/3EIL=ML^2/3EI

M=sigma.Z -> M=2.sigma.I/H into ML^2/3EI

(2.sigma.I/H)L^2/3EI=2.sigma.IL^2/3EIH=2.sigma.L^2/3EH

d is abtained for cantilever beam by this algebra in my program
2.sigma.L^2/3EH
Astonishingly simple!

When/if do "simple beam" remember M=FL/4

On Mon, 24 Jul 2023 20:25:43 +0100
Richard Smith <null@void.com> wrote:

>Hi. Been at it again.
>Having learned some PHP - the web-scripting langugage.
>My beam calculations written in Lisp - done as webpage version.
>http://weldsmith.co.uk/cgi_my/ebbeam_rhs/230724_ebbeam_rhs.html
>"Rectangular Hollow Section beam calculations"
>Best wishes,
>Rich S

Nifty stuff Rich👍

If you haven't found this already... you might like Marv's bunch of
little calculator programs:

https://www.myvirtualnetwork.com/mklotz/

Maybe give you some more ideas and/or another way to double check some
of your calculations.

--
Leon Fisk
Grand Rapids MI

"Leon Fisk" wrote in message news:u9oh7l$146vc$2@dont-email.me...

Nifty stuff Rich👍

If you haven't found this already... you might like Marv's bunch of
little calculator programs:

https://www.myvirtualnetwork.com/mklotz/

Maybe give you some more ideas and/or another way to double check some
of your calculations.

Leon Fisk
Grand Rapids MI

----------------------

I like spreadsheets for cutting mathematically definable shapes like
spheres. By putting the constants, multipliers and step size into fixed
cells and referencing them in the formulas it can be adjusted for roughing
and finishing cuts with steps as small as your patience allows.

It generates a pair of columns with the part's dimensions for checking, and
another pair with the machine settings to produce them, infeed and carriage
travel.

Cross-check
http://weldsmith.co.uk/cgi_my/ebbeam_rhs/230724_ebbeam_rhs.html
to
http://weldsmith.co.uk/tech/struct/201123_wssb_test/201123_weld_RHS_beam_test.html
[much detail provided of test, and has both Euler-Bernoulli beam and
Finite Element Analysis modelling - which agree and the physical
measurement agrees]

"100x50by7.8, of "S355" (nominal 355MPa)"
"The end supports for the test beam with test weld are set at 600mm
gap between these supports"

So:

RHS Height
100e-3

RHS Width
50e-3

RHS Wall-thickness
7.8e-3

RHS beam length
0.6

RHS material yield stress
355e6

RHS material Young's modulus
210e9

My new online beam calculator for RHS's agrees with
"The Second Moment of Area, "I", of a square-cornered rectangle of the
overall dimensions of the RHS = 2.443e-6 m^4"
"Section Modulus, "Z" = 2I/h = 4.886e-5 m^3"

"The central load causing the selected stress is
115644.490402Newtons"
(/ 115644.490402 9.81 1e3) ;; 11.78842919490316
That predicted is 11.8Tonnes-force
The beam did not return to straightness after 11.6Tonnes of applied
force.
Very very close prediction
[Western European steel "just" makes the yield stress - they have such
accurate control that the manufacturers can and do do that - gives a
lovely steel to work with in the workshop - punches, drills, bends in
3-point rolls, welds, etc. exactly as you'd wish]
The slightly lesser force to bend real<->predicted could be due to the
rounded corners of the real section slightly reducing the Second
Moment of Area.
The predicted elastic bending at 355MPa yield
1.014286e-03 m (Nov 2020 programme)
and
"At that maximum stress, the deflection at the middle of the beam is
0.00101428571429metres (1.01428571429mm)" (online calculator)
agree.

So that carefully checked work of Nov. 2020 with two different
theoretical treatments and physical engineering tests
and
this new online beam calculator
agree.

Both the 2020 mathematical work and the online calculator are based on
right-angled-corner sections (slight deviation from actual sections
with rounded corners).

Would be glad of any checks anyone else does.

There is the "Contact Form" on my website if you want to raise a
private query.
Seen from "root" of weldsmith.co.uk - is
http://weldsmith.co.uk/contactform/contact.html

"Richard Smith" wrote in message news:lypm4f826p.fsf@void.com...

Both the 2020 mathematical work and the online calculator are based on
right-angled-corner sections (slight deviation from actual sections
with rounded corners).

---------------

If the corner is truly a quarter circle the area reduction is pi/4 times the
wall thickness.

"Jim Wilkins" <muratlanne@gmail.com> writes:

> "Richard Smith" wrote in message news:lypm4f826p.fsf@void.com...
>
> Both the 2020 mathematical work and the online calculator are based on
> right-angled-corner sections (slight deviation from actual sections
> with rounded corners).
>
> ---------------
>
> If the corner is truly a quarter circle the area reduction is pi/4
> times the wall thickness.

Wouldn't it be a bit more complicated than that on how much metal is where?
The "square" corner is the material thickness too.
Then there is a more complicated effect on assigning where the metal
is to what it contributes to the Second Moment of Area?

In the context that
* the radius sections have at the corners / edges is a bit variable
anyway
* the wall thickness variation of the sections would make a bigger
difference than accurately representing a rounded corner compared to a
"square" corner
???

Nett - my impression is leave as right-angled corners so at least the
user knows where they stand. The simplest model.

I am missing here some simple and obvious logic I clearly haven't
grasped?

There's yet another argument to "leave as-is".
You are going to be selecting promising sections from "The Blue Book".
Which has properties which are best known by empirical testing done by
experts. Particularly the "Class" of the beam. Will it bend - but be
heavy. Or be light - but prone to buckling.
Only the designer of this structure in question can know how to
navigate that.
Obviously - "my" "simplistic" beam calculation cannot.
But the low "cost" of running calculations with my "web
server-side scripted" "beam calculator" means you can develop your
ideas - and record a trail by copy-and-pasting the output into a
"project file".

When you've found the apparent candidate - do anew the calculations
using "The Blue Book"'s tabulated
* Second Moment of Area ("I")
* Section Modulus ("Z")
* Moment capacity (in N.m)
* the statement of the section Class ("1" to "4")
* etc.
for the chosen solution and take that as "THE design case".

You get straight into the F=M/L (cantilever) and F=4M/L ("simple
beam") starting from the tabulated values - where the human can
readily see if the arithmetic looks about right
(the early stages with Second Moment of Area take a series of steps
where any one non-obvious error can give wrong output which is
difficult to intuitively spot (reason to write functions to do those
calculations - so what you did in the best of times and tested with
mathematic values which give obvious mental-arithmetic-obvious
outputs - and spot-checked "realistic" section values - serves you
machine-faultlessly when you are fraught, tired and distracted))

You must have experience of such "navigation" as a skilled
knowlegeable project driver...

Regards,
Rich Smith

On Wed, 26 Jul 2023 16:53:40 +0100
Richard Smith <null@void.com> wrote:

<snip>
>You must have experience of such "navigation" as a skilled
>knowlegeable project driver...

You ever read?

https://en.wikipedia.org/wiki/Zen_and_the_Art_of_Motorcycle_Maintenance

Quite the slog but I don't regret suffering it...

Your kinda discussions always bring it to mind😉

--
Leon Fisk
Grand Rapids MI

Leon Fisk <lfiskgr@gmail.invalid> writes:

> On Wed, 26 Jul 2023 16:53:40 +0100
> Richard Smith <null@void.com> wrote:
>
> <snip>
>>You must have experience of such "navigation" as a skilled
>>knowlegeable project driver...
>
> You ever read?
>
> https://en.wikipedia.org/wiki/Zen_and_the_Art_of_Motorcycle_Maintenance
>
> Quite the slog but I don't regret suffering it...
>
> Your kinda discussions always bring it to mind.Ÿ.‰
>
> --
> Leon Fisk
> Grand Rapids MI

Should I take that as a compliment?!?

A long time I read Pursig's "Zen and the Art of Motorcycle Maintenance".

I used to tweak and repair motorcycles.
Mechanical skill probably featured in my "unusual" Doctoral research
in science. My abilities propelled me into a lot of problems - which
then became my "story" and shaped my personality.

My Doctoral years were an almost hallucinatory experience.
I only got that because I "realised" my mind does interesting things
if I let it. All the interesting, crazy and wild things happened
when I departed on my path of being a dedicated career person.

Once at tea-break (we were in the UK) we looked around at each other
and spontaneously broke out laughing - we were all there palid,
strained, shaking hands, drawing on cigarettes like a vacuum cleaner,
etc, etc, etc.
Such is life's experience.

So - I can assure you I am fine myself with your conjecture.

Best wishes,
Rich Smith

On Wed, 26 Jul 2023 18:41:08 +0100
Richard Smith <null@void.com> wrote:

<snip>
>So - I can assure you I am fine myself with your conjecture.

Cool! and I'm not surprised :) Would have been helpful had I read it
earlier in life, maybe...

--
Leon Fisk
Grand Rapids MI

"Leon Fisk" wrote in message news:u9rkjh$1i26t$1@dont-email.me...

On Wed, 26 Jul 2023 16:53:40 +0100
Richard Smith <null@void.com> wrote:

<snip>
>You must have experience of such "navigation" as a skilled
>knowlegeable project driver...

You ever read?

https://en.wikipedia.org/wiki/Zen_and_the_Art_of_Motorcycle_Maintenance

Quite the slog but I don't regret suffering it...

Your kinda discussions always bring it to mind😉

--
Leon Fisk
Grand Rapids MI

----------------------
https://en.wikipedia.org/wiki/Robert_M._Pirsig
"Pirsig had a mental breakdown and spent time in and out of psychiatric
hospitals between 1961 and 1963. He was diagnosed with schizophrenia and
treated with electroconvulsive therapy on numerous occasions, a treatment he
discusses in Zen and the Art of Motorcycle Maintenance."

"Richard Smith" wrote in message news:lyila63bzv.fsf@void.com...

"Jim Wilkins" <muratlanne@gmail.com> writes:

> "Richard Smith" wrote in message news:lypm4f826p.fsf@void.com...
>
> Both the 2020 mathematical work and the online calculator are based on
> right-angled-corner sections (slight deviation from actual sections
> with rounded corners).
>
> ---------------
>
> If the corner is truly a quarter circle the area reduction is pi/4
> times the wall thickness.

Wouldn't it be a bit more complicated than that on how much metal is where?
The "square" corner is the material thickness too.
Then there is a more complicated effect on assigning where the metal
is to what it contributes to the Second Moment of Area?

In the context that
* the radius sections have at the corners / edges is a bit variable
anyway
* the wall thickness variation of the sections would make a bigger
difference than accurately representing a rounded corner compared to a
"square" corner
???

Nett - my impression is leave as right-angled corners so at least the
user knows where they stand. The simplest model.

----------------------

The test is how much closer to the book value that simplified correction
brings you. I agree that it may not be worth the added complexity unless the
improvement is significant, but I'd rather under than overestimate yield
strength. Usually I measure the actual dimensions of what I bought for the
CAD model and it's almost always been near the low end of the tolerance.

Hello all

Wrote following as example of a beam calculation in a project.

Following on from creating the "beam calculator"
http://weldsmith.co.uk/cgi_my/ebbeam_rhs/230724_ebbeam_rhs.html
"Rectangular Hollow Section beam calculations"
webpage.

I have a feeling beam calculations are often like this.
Finding your way along.
Same as for the other case I made a webpage for
http://www.weldsmith.co.uk/tech/struct/210314_ebbeam_drillplat/19_drillplat_calcs.html
"Cantilever drilling platform - analysis using beam calculations"

------------------------------------------------

I didn't give any idea why you might want a beam calculator when
interested in mines...

Take for example Wheal Round
(a hypothetical case).

It's accessed from high ground and water flows from adits draining
mines in the area. So there's a good chance a lot of the workings
remain dry.

Problem - the main shaft is blocked by a boulder 30m down which is
estimated to be 3 Tonnes.

The promise of many levels and interesting finds in Wheal Round has a
project to open the main shaft. Resin-anchor in an eye-bolt and hoist
the boulder out.

The beam would span 5m across the top bank around the shaft.

Wheal Round is in that high place with a small path as only access, so
that beam needs to be very portable.

It's lifting a boulder, there's no-one underneath anything and the
hoist can be worked from a safe distance, so the consequence is just
about zero of the beam totally collapsing by local plastic buckling.

So we can look to even a "Class 4" section (it could locally buckle
and instantly collapse on overload).

Considering all, we'd like a factor of 3 safety on the beam load bear
- mainly for it if boulder jams and the load on the beam with hoisting
increases.

So that's 9 Tonnes point capacity at the middle.

Box-section - take as being S355 steel - 355MPa = 355e6Pa yield.

We'll get an estimate were to start looking for candidate sections in
"The Blue Book"

Pardon that I use "Lisp" in-line to calculate things. Using the
"emacs" text-processor, I can "fire-up" its interpreter on Lisp
expressions and it will insert its answer into the file.

M=FL/4 for a "simple beam" (end supported; central load)

M = ...

(/
(*
(* 9 1e3 9.81) ;; 88290.0 ;; N ;; (gravity - 9.81N/kg)
5 ;; m length
)
4e0 ;; ) ;; 110362.5 ;; N.m
1e3) ;; 110.3625 ;; kNm

Going straight to "The Blue Book" for hot-finished Rectangular Hollow
Section
https://www.steelforlifebluebook.co.uk/hfrhs/ec3-ukna/bending-s355/
and looking down the "Mc,y,Rd" column
plausible sections start at around 250x150x5mm - with a weight of
30.4kg/m

For squares - Square Hollow Sections
https://www.steelforlifebluebook.co.uk/hfshs/ec3-ukna/bending-s355/
plausible sections start at around 200x200x6.3mm - with a weight of
38kg/m

Going with 250x150x5mm in my beam calculator
http://weldsmith.co.uk/cgi_my/ebbeam_rhs/230724_ebbeam_rhs.html

"

Input values you provided

Variable Value (in familiar units)
Height 250e-3 (250mm)
Width / breadth 150e-3 (150mm)
Wall thickness 5e-3 (5mm)
Beam length 5 (m)
Maximum stress 355e6 (N mm^2)
Young's Modulus (E) 210e9 (N mm^2)

Beam intrinsic sectional properties
....
Derived variable Derived value (in familiar units)
Second moment of area: 3.403250e-5 (3403.25cm^4)
Section modulus: 2.722600e-4 (272.26cm^3)
Moment: 96652.3 (N.m)

Beam extrinsic properties
....
"simple beam"

The central load causing the selected stress is
77321.84Newtons

At that maximum stress, the deflection at the middle of the beam is
0.0281746031746metres (28.1746031746mm)

"

My calculation and "The Blue Book" agree - For "I" the Second Moment
of Area is 3.403250e-5m^4 = 3403.25cm^4 (my) to 3360cm^4 (Blue Book).

For what it's worth general geometric page
https://www.steelforlifebluebook.co.uk/hfrhs/ec3-ukna/section-properties-dimensions-properties/
has "Z" as 269cm^4 (Blue Book) for "my" 272.26cm^3 - same.

We expect "my" "I" and "Z" to be a bit higher because "my" section is
a rectangular-cornered hypothetical sections, whereas the real section
has rounded corners, putting a bit less metal for from the neutral
plane where it would have counted the most.
But "my" calculation is quick to use to step through the logic
processes of selecting "candidate" beams.

The force at yield the beam calculator gives:
(/ 77321.84 9.81 1e3) ;; 7.881940876656472 ;; Tonnes-force
We might seek a bit higher; were it not for seeing the weight of
plausible sections - see later.

Continuing...

So the excess load carrying capacity is still okay - in the region of
what we wanted.

Using my beam calculator alone now for other sections seen in "The
Blue Book"

If that section fell over on its side, presenting 150x250, it would
still support the boulder, with 5.95 Tonnes capacity. Not as it would
be recommended to allow that to happen, but there wouldn't be the
buckled beam, chain-block and boulder dropping back down the
mineshaft.

300x100x5mm looks plausible too.
300x100x5 if it fell over - and it is tall and narrow - would give
41932.6N -> (/ 41932.6 9.81 1e3) ;; 4.274475025484199 Tonnes
so it would likely be "game over" or best keep well clear and lower
the boulder back from whence it came.
So if contemplated 300x100x5 - which is 30.4kg/m - would have to bring
some strong "keep upright" support with "feet" - likely a steel
fabrication weighing a few kg each end.

These two - 250x150x5mm and 300x100x5mm - are looking-in at about
30.5kg/m, and the beam to span 5m is 6m long.

(* 30.5 6) ;; 183.0 ;; kg

Thinking of the narrow path - if roped the steel beam so it just lofts
off the ground when a transverse pole at each end is lifted by two
people each side - so eight people lifting total, that's
(/ (* 30.5 6) 8) ;; 22.875 ;; kg
per person - doable.
But for a pole long enough to get 4 people on the pole, it would be
too long (wide) to fit between the trees and bushes and through gates
on the narrow path. Mind's-eye sees that as not a great option.

Path is quite straight, so look to a "tail wheel" at the back - some
compliant pneumatic tyre from eg. a trailer rolling along supporting
the back of the beam - and have a forward-sticking-out pole with four
people on it lifting and pulling.

Other lifting strategies examined:

* Longitudinal pole with four people at each end? Well to be roped
with the beam just lofting above the ground, the pole has to be 6m +
about 2 x 2.5m = 11m, which is some pole - has its own weight.

* Pole attached to each end and carry at shoulder-height - NO! Never
where if say someone tripped and everyone fell over there is a
significant risk of someone getting hurt.

"Tail wheel" - could have additional people pulling on ropes for the
steep bits (not pushing from behind - not exposed to being "run-over"
if all goes horribly wrong.

So - is doable.
Go with whichever of those sections
250x150x5mm
300x100x5mm
or even
200x200x6.3mm (38kg/m - more grunting and perspiration)
is found to be available on a blagging / cadging mission...

The reason for the beam calculator is exploring options and scenarios
easily, at negligible effort to the person.
A person can with care get through one beam calculation with its
several steps.
For several beam scenarios a person tends to get overwhelmed and lose
their way.

There has been "freestyle" use of parts of the beam calculations.

There has been use of "The Blue Book".

However, the "beam calculator" made for a good portfolio of
calculations presenting the case for the option suggested.

"Richard Smith" wrote in message news:lyjzuewgpb.fsf@void.com...

I didn't give any idea why you might want a beam calculator when
interested in mines...

Take for example Wheal Round
(a hypothetical case).

It's accessed from high ground and water flows from adits draining
mines in the area. So there's a good chance a lot of the workings
remain dry.

Problem - the main shaft is blocked by a boulder 30m down which is
estimated to be 3 Tonnes.

--------------------

That's interesting, and quite similar to my built-up 16' (4.88m) gantry beam
which I designed to lift 1.5 tons of log or boulder and move it about 3~4
meters after I've hand-carried all the parts uphill to the site by myself.
No part weighs over 25kg when completely disassembled, that's why I used
four channel sections instead of the obvious single WF beam that I couldn't
move or store under cover. It worked fine to load a 2100 Lb log onto my
sawmill, though I had to lower the log at the middle to step the central
shear legs over it.

The supports are two tripods of 2" x 10' pipe, plus shear legs at the center
splice for loads over a ton. A boat trailer winch u-bolted onto one leg of
each tripod lifts the beam and levels it on sloping ground, i.e most of my
property. Then chains suspend the beam and its load.

Raising the boulder isn't enough; you need to move it off the hole. A
modified gantry trolley might work on your rectangular tubing but in my
experience doesn't add much resistance to the beam bowing sideways and
twisting.
https://www.sip-group.eu/product/sip-1-tonne-gantry-crane-beam-trolley/03851

When assembled the ~100kg beam can be moved with two fixed caster wheels
bolted to a short plank under one end, and a trailer coupler on the other,
coupled to a trailer dolly, home-made, like this:
https://www.discountramps.com/automotive/trailer/accessories/p/TD-600-V2/

I can muscle it uphill with a block and tackle (or my tractor, if it runs)
and let it downhill with abseiling gear. A similar long and narrow trailer
for logs and cut beams is manageable by hand with a 300kg load.

It doesn't corner well, a second coupler and dolly for the tail end might
help if you are actually asked to build your sample problem. In a pinch a
long handled shovel can lever up a pretty hefty load and swivel to move it
sideways.

"Richard Smith" wrote in message news:lyjzuewgpb.fsf@void.com...
....
Thinking of the narrow path - if roped the steel beam so it just lofts
off the ground when a transverse pole at each end is lifted by two
people each side - so eight people lifting total, that's
(/ (* 30.5 6) 8) ;; 22.875 ;; kg
per person - doable.
But for a pole long enough to get 4 people on the pole, it would be
too long (wide) to fit between the trees and bushes and through gates
on the narrow path. Mind's-eye sees that as not a great option.

Path is quite straight, so look to a "tail wheel" at the back - some
compliant pneumatic tyre from eg. a trailer rolling along supporting
the back of the beam - and have a forward-sticking-out pole with four
people on it lifting and pulling.

-----------------

Trailer tongue jacks are heavy-duty swivel casters with load lifting
capability.
https://www.kendonusa.com/products/crank-down-trailer-swivel-jack-stand
That one has a short URL, they are much cheaper elsewhere.

A single-wheel one can be upgraded for soft ground with replacement wheels
on either side, on a longer axle. It won't track well and needs a steering +
towing handle, one of mine is the handle from a broken snow shovel with a
fork of steel flat stock that connects to the extended axle, another is a
pipe tee with slots milled in the ends for the flat stock. The long pipe
handle screws on to move by hand, unscrews for storage or to tow the shop
crane it's on behind the tractor. The rather high mounting plate isn't a
problem if attached to the base of a gantry hoist or mast of a crane but it
makes them inconvenient for a low riding lift platform unless you can weld.

I have the shop crane, a trailer and a log splitter that all weigh around
500 Lbs and can be moved by hand on level ground without excessive effort.
As a test I've pulled them uphill without the garden tractor by using a
block and tackle (faster) or a lever chain hoist (safer). A chain fall is
very slow and doesn't work well horizontally. First I tried cheap cable
pullers but was disappointed with how quickly they wore out and failed
despite being greased. The steel is very soft. A vehicle-mounted winch was
best, assuming you can drive to the hilltop, but then you could tow with it
instead.
https://www.amazon.com/2-Ton-Along-Puller-Heavy-Duty-Automotive/dp/B09SPT85DR
Upgrading the axles and bearings helps somewhat, if you have a lathe. On
mine the ratchets deformed when manufacturing slop allowed them to misalign.

On 01/08/2023 23:17, Richard Smith wrote:
> Hello all
>
> Wrote following as example of a beam calculation in a project.
>
> Following on from creating the "beam calculator"
> http://weldsmith.co.uk/cgi_my/ebbeam_rhs/230724_ebbeam_rhs.html
> "Rectangular Hollow Section beam calculations"
> webpage.
>
> I have a feeling beam calculations are often like this.
> Finding your way along.
> Same as for the other case I made a webpage for
> http://www.weldsmith.co.uk/tech/struct/210314_ebbeam_drillplat/19_drillplat_calcs.html
> "Cantilever drilling platform - analysis using beam calculations"
>
>
> ------------------------------------------------
>
> I didn't give any idea why you might want a beam calculator when
> interested in mines...
>
> Take for example Wheal Round
> (a hypothetical case).
>
> It's accessed from high ground and water flows from adits draining
> mines in the area. So there's a good chance a lot of the workings
> remain dry.
>
> Problem - the main shaft is blocked by a boulder 30m down which is
> estimated to be 3 Tonnes.
>
> The promise of many levels and interesting finds in Wheal Round has a
> project to open the main shaft. Resin-anchor in an eye-bolt and hoist
> the boulder out.
>
> The beam would span 5m across the top bank around the shaft.
>
> Wheal Round is in that high place with a small path as only access, so
> that beam needs to be very portable.
>
> It's lifting a boulder, there's no-one underneath anything and the
> hoist can be worked from a safe distance, so the consequence is just
> about zero of the beam totally collapsing by local plastic buckling.
>
> So we can look to even a "Class 4" section (it could locally buckle
> and instantly collapse on overload).
>
> Considering all, we'd like a factor of 3 safety on the beam load bear
> - mainly for it if boulder jams and the load on the beam with hoisting
> increases.
>
> So that's 9 Tonnes point capacity at the middle.
>
> Box-section - take as being S355 steel - 355MPa = 355e6Pa yield.
>
> We'll get an estimate were to start looking for candidate sections in
> "The Blue Book"
>
>
> Pardon that I use "Lisp" in-line to calculate things. Using the
> "emacs" text-processor, I can "fire-up" its interpreter on Lisp
> expressions and it will insert its answer into the file.
>
>
> M=FL/4 for a "simple beam" (end supported; central load)
>
> M = ...
>
> (/
> (*
> (* 9 1e3 9.81) ;; 88290.0 ;; N ;; (gravity - 9.81N/kg)
> 5 ;; m length
> )
> 4e0 ;; ) ;; 110362.5 ;; N.m
> 1e3) ;; 110.3625 ;; kNm
>
> Going straight to "The Blue Book" for hot-finished Rectangular Hollow
> Section
> https://www.steelforlifebluebook.co.uk/hfrhs/ec3-ukna/bending-s355/
> and looking down the "Mc,y,Rd" column
> plausible sections start at around 250x150x5mm - with a weight of
> 30.4kg/m
>
> For squares - Square Hollow Sections
> https://www.steelforlifebluebook.co.uk/hfshs/ec3-ukna/bending-s355/
> plausible sections start at around 200x200x6.3mm - with a weight of
> 38kg/m
>
> Going with 250x150x5mm in my beam calculator
> http://weldsmith.co.uk/cgi_my/ebbeam_rhs/230724_ebbeam_rhs.html
>
> "
>
> Input values you provided
>
> Variable Value (in familiar units)
> Height 250e-3 (250mm)
> Width / breadth 150e-3 (150mm)
> Wall thickness 5e-3 (5mm)
> Beam length 5 (m)
> Maximum stress 355e6 (N mm^2)
> Young's Modulus (E) 210e9 (N mm^2)
>
> Beam intrinsic sectional properties
> ...
> Derived variable Derived value (in familiar units)
> Second moment of area: 3.403250e-5 (3403.25cm^4)
> Section modulus: 2.722600e-4 (272.26cm^3)
> Moment: 96652.3 (N.m)
>
> Beam extrinsic properties
> ...
> "simple beam"
>
> The central load causing the selected stress is
> 77321.84Newtons
>
> At that maximum stress, the deflection at the middle of the beam is
> 0.0281746031746metres (28.1746031746mm)
>
> "
>
> My calculation and "The Blue Book" agree - For "I" the Second Moment
> of Area is 3.403250e-5m^4 = 3403.25cm^4 (my) to 3360cm^4 (Blue Book).
>
> For what it's worth general geometric page
> https://www.steelforlifebluebook.co.uk/hfrhs/ec3-ukna/section-properties-dimensions-properties/
> has "Z" as 269cm^4 (Blue Book) for "my" 272.26cm^3 - same.
>
> We expect "my" "I" and "Z" to be a bit higher because "my" section is
> a rectangular-cornered hypothetical sections, whereas the real section
> has rounded corners, putting a bit less metal for from the neutral
> plane where it would have counted the most.
> But "my" calculation is quick to use to step through the logic
> processes of selecting "candidate" beams.
>
> The force at yield the beam calculator gives:
> (/ 77321.84 9.81 1e3) ;; 7.881940876656472 ;; Tonnes-force
> We might seek a bit higher; were it not for seeing the weight of
> plausible sections - see later.
>
>
> Continuing...
>
> So the excess load carrying capacity is still okay - in the region of
> what we wanted.
>
> Using my beam calculator alone now for other sections seen in "The
> Blue Book"
>
> If that section fell over on its side, presenting 150x250, it would
> still support the boulder, with 5.95 Tonnes capacity. Not as it would
> be recommended to allow that to happen, but there wouldn't be the
> buckled beam, chain-block and boulder dropping back down the
> mineshaft.
>
> 300x100x5mm looks plausible too.
> 300x100x5 if it fell over - and it is tall and narrow - would give
> 41932.6N -> (/ 41932.6 9.81 1e3) ;; 4.274475025484199 Tonnes
> so it would likely be "game over" or best keep well clear and lower
> the boulder back from whence it came.
> So if contemplated 300x100x5 - which is 30.4kg/m - would have to bring
> some strong "keep upright" support with "feet" - likely a steel
> fabrication weighing a few kg each end.
>
> These two - 250x150x5mm and 300x100x5mm - are looking-in at about
> 30.5kg/m, and the beam to span 5m is 6m long.
>
> (* 30.5 6) ;; 183.0 ;; kg
>
> Thinking of the narrow path - if roped the steel beam so it just lofts
> off the ground when a transverse pole at each end is lifted by two
> people each side - so eight people lifting total, that's
> (/ (* 30.5 6) 8) ;; 22.875 ;; kg
> per person - doable.
> But for a pole long enough to get 4 people on the pole, it would be
> too long (wide) to fit between the trees and bushes and through gates
> on the narrow path. Mind's-eye sees that as not a great option.
>
> Path is quite straight, so look to a "tail wheel" at the back - some
> compliant pneumatic tyre from eg. a trailer rolling along supporting
> the back of the beam - and have a forward-sticking-out pole with four
> people on it lifting and pulling.
>
> Other lifting strategies examined:
>
> * Longitudinal pole with four people at each end? Well to be roped
> with the beam just lofting above the ground, the pole has to be 6m +
> about 2 x 2.5m = 11m, which is some pole - has its own weight.
>
> * Pole attached to each end and carry at shoulder-height - NO! Never
> where if say someone tripped and everyone fell over there is a
> significant risk of someone getting hurt.
>
> "Tail wheel" - could have additional people pulling on ropes for the
> steep bits (not pushing from behind - not exposed to being "run-over"
> if all goes horribly wrong.
>
> So - is doable.
> Go with whichever of those sections
> 250x150x5mm
> 300x100x5mm
> or even
> 200x200x6.3mm (38kg/m - more grunting and perspiration)
> is found to be available on a blagging / cadging mission...
>
>
> The reason for the beam calculator is exploring options and scenarios
> easily, at negligible effort to the person.
> A person can with care get through one beam calculation with its
> several steps.
> For several beam scenarios a person tends to get overwhelmed and lose
> their way.
>
> There has been "freestyle" use of parts of the beam calculations.
>
> There has been use of "The Blue Book".
>
> However, the "beam calculator" made for a good portfolio of
> calculations presenting the case for the option suggested.

"David Billington" wrote in message news:uadmpg$38en$1@dont-email.me...

Sounds like a large tyre piano moving dolly would be suitable for the
task. I was impressed by how easily the piano movers removed my mother's
piano with one and how well it coped with multiple 6" - 7" steps.

-------------------
They appear to use hand truck wheels on 5/8" axles. I bought a batch of used
solid tire wheels with needle bearings for 3/4" axles that have served well
for loads as large as an 1100 Lb boulder but I haven't found anything
similar for sale new.

"Jim Wilkins" <muratlanne@gmail.com> writes:

> ...
>
> Raising the boulder isn't enough; you need to move it off the hole. A
> modified gantry trolley might work on your rectangular tubing but in
> my experience doesn't add much resistance to the beam bowing sideways
> and twisting.
> ...

Yes you are right...

"Wheal Round" is imaginary, of course, but yes you would need to move
the boulder sideways away from the shaft.

I kept the "Wheal Round" case as short as possible and about beams.

It proves the minimum strength beam to lift the boulder is the maximum
weight beam you could move.

[you could make a truss structure from much smaller lighter sections
to span the mine-shaft (the dimensions are about what you find in
Cornwall, where the mining areas are littered with such shafts) -
but, again, I didn't want to go away from beams - so ignoring all
this...]

So the safety case is that no-one approaches the lift and its
equipment during the lift. Given this...

I took it that, lifted above the shaft, you could drag a couple of
beams across the shaft with ropes, and onto the beams you land the
boulder.

You've already tied a "tag-line" to the strop suspending the
(chain?)block from the beam...

Load off it, you pull the strop a quarter-metre (10 inches) along the
beam then lift the boulder again, which will drift the boulder
sideways by that quarter-metre. Repeat, repeat, repeat, ... until the
boulder is on the berm. Maybe more steel sections as a slide-way and
use a "Tirfor" to haul the boulder up and over the berm and bring it
down to level ground.

???

"Jim Wilkins" <muratlanne@gmail.com> writes:

> "Richard Smith" wrote in message news:lyjzuewgpb.fsf@void.com...
> ...
> Thinking of the narrow path - if roped the steel beam so it just lofts
> off the ground when a transverse pole at each end is lifted by two
> people each side - so eight people lifting total, that's
> (/ (* 30.5 6) 8) ;; 22.875 ;; kg
> per person - doable.
> But for a pole long enough to get 4 people on the pole, it would be
> too long (wide) to fit between the trees and bushes and through gates
> on the narrow path. Mind's-eye sees that as not a great option.
>
> Path is quite straight, so look to a "tail wheel" at the back - some
> compliant pneumatic tyre from eg. a trailer rolling along supporting
> the back of the beam - and have a forward-sticking-out pole with four
> people on it lifting and pulling.
>
> -----------------
>
> Trailer tongue jacks are heavy-duty swivel casters with load lifting
> capability.
> https://www.kendonusa.com/products/crank-down-trailer-swivel-jack-stand
> That one has a short URL, they are much cheaper elsewhere.
>
> A single-wheel one can be upgraded for soft ground with replacement
> wheels on either side, on a longer axle. It won't track well and needs
> a steering + towing handle, one of mine is the handle from a broken
> snow shovel with a fork of steel flat stock that connects to the
> extended axle, another is a pipe tee with slots milled in the ends for
> the flat stock. The long pipe handle screws on to move by hand,
> unscrews for storage or to tow the shop crane it's on behind the
> tractor. The rather high mounting plate isn't a problem if attached to
> the base of a gantry hoist or mast of a crane but it makes them
> inconvenient for a low riding lift platform unless you can weld.
>
> I have the shop crane, a trailer and a log splitter that all weigh
> around 500 Lbs and can be moved by hand on level ground without
> excessive effort. As a test I've pulled them uphill without the garden
> tractor by using a block and tackle (faster) or a lever chain hoist
> (safer). A chain fall is very slow and doesn't work well
> horizontally. First I tried cheap cable pullers but was disappointed
> with how quickly they wore out and failed despite being greased. The
> steel is very soft. A vehicle-mounted winch was best, assuming you can
> drive to the hilltop, but then you could tow with it instead.
> https://www.amazon.com/2-Ton-Along-Puller-Heavy-Duty-Automotive/dp/B09SPT85DR
> Upgrading the axles and bearings helps somewhat, if you have a
> lathe. On mine the ratchets deformed when manufacturing slop allowed
> them to misalign.

I could learn a lot coming to visit and doing some projects with you!

David Billington <djb@invalid.com> writes:

>
> Sounds like a large tyre piano moving dolly would be suitable for the
> task. I was impressed by how easily the piano movers removed my
> mother's piano with one and how well it coped with multiple 6" - 7"
> steps.

Yes.
When you are lost in the detail of something you can lose your way.
A two-wheeled dolly just aft the centre would do very well.
Then it becomes purely a wheeling exercise.
You'd still want to keep the weight down, but you could go up a bit to
a common stock beam size with a wall thickness which means in overload
it will only plastically bend - never buckle.

I've been busy learning about building regulations, snuck-through the
programming / beam-calculator as a "naughty treat" - but been quite
frazzled. And lost in the brain-burn of the details of the project.

Thanks, David, Jim, everyone.

On Wed, 2 Aug 2023 10:04:04 -0400
"Jim Wilkins" <muratlanne@gmail.com> wrote:

<snip>
>They appear to use hand truck wheels on 5/8" axles. I bought a batch of used
>solid tire wheels with needle bearings for 3/4" axles that have served well
>for loads as large as an 1100 Lb boulder but I haven't found anything
>similar for sale new.

You can buy "wheel bearings" now for autos and such that include the
hub. As you probably already know... they are throw away pieces
nowadays. Anyway... if I was building a small trailer or similar I'd be
tempted to buy a couple for a small vehicle. Maybe pick something you
already have tires/rims for. Something like this:

https://www.amazon.com/WJB-WA513044-Assembly-Reference-BR930083K/dp/B00B7ROENY/

I've a couple that came off a RAM 3500 front, one was making noises.
For something to be used around your property and not on the road
they'd still work okay...

--
Leon Fisk
Grand Rapids MI

Leon Fisk <lfiskgr@gmail.invalid> writes:

> On Wed, 2 Aug 2023 10:04:04 -0400
> "Jim Wilkins" <muratlanne@gmail.com> wrote:
>
> <snip>
>>They appear to use hand truck wheels on 5/8" axles. I bought a batch of used
>>solid tire wheels with needle bearings for 3/4" axles that have served well
>>for loads as large as an 1100 Lb boulder but I haven't found anything
>>similar for sale new.
>
> You can buy "wheel bearings" now for autos and such that include the
> hub. As you probably already know... they are throw away pieces
> nowadays. Anyway... if I was building a small trailer or similar I'd be
> tempted to buy a couple for a small vehicle. Maybe pick something you
> already have tires/rims for. Something like this:
>
> https://www.amazon.com/WJB-WA513044-Assembly-Reference-BR930083K/dp/B00B7ROENY/
>
> I've a couple that came off a RAM 3500 front, one was making noises.
> For something to be used around your property and not on the road
> they'd still work okay...
>
> --
> Leon Fisk
> Grand Rapids MI

Yes.
We use all sorts of dollys for moving beams around fab.shops and on
construction sites. Having a moron moment forgetting all about that.
Been a while out of fab.shops.

"Leon Fisk" wrote in message news:uae706$748g$1@dont-email.me...

On Wed, 2 Aug 2023 10:04:04 -0400
"Jim Wilkins" <muratlanne@gmail.com> wrote:

<snip>
>They appear to use hand truck wheels on 5/8" axles. I bought a batch of
>used
>solid tire wheels with needle bearings for 3/4" axles that have served well
>for loads as large as an 1100 Lb boulder but I haven't found anything
>similar for sale new.

You can buy "wheel bearings" now for autos and such that include the
hub. As you probably already know... they are throw away pieces
nowadays. Anyway... if I was building a small trailer or similar I'd be
tempted to buy a couple for a small vehicle. Maybe pick something you
already have tires/rims for. Something like this:

https://www.amazon.com/WJB-WA513044-Assembly-Reference-BR930083K/dp/B00B7ROENY/

I've a couple that came off a RAM 3500 front, one was making noises.
For something to be used around your property and not on the road
they'd still work okay...

Leon Fisk
Grand Rapids MI

----------------------
Thanks, that is cheaper than the trailer parts I've seen.

I wish my Honda was made that way, replacing the wheel bearings requires
completely disassembling the front suspension to press the hub and then the
bearings out of the knuckle. I thought I might have to when I heard grinding
noises in the front so I took both sides apart as far as is easy, pulling
the brake rotors, and found the noise was only rust particles being ground
up in the narrow gap between the hub and knuckle. It's silent now to full
lock turning in both directions, nearly free of rust and all sliding
surfaces have been thinly coated with hi temp brake caliper grease.

I mentioned the beam because I had gone through the same process, using the
4" pallet rack shelf channel that I bought for the job when I saw it instead
of the rectangular tubing that the program calculates. With the
hand-carrying limitation and a center support I came up with half the
lifting capacity.

The most difficult purely manual steel erection I've participated in was
carrying a 600 Lb beam (20' of 10x30) into a house being renovated and
hoisting it to support the second floor (two above the basement), then
fitting 4" square columns under it. I'm glad I wasn't around for Stonehenge.