cantilever problem

[iain glenny]

cantilever.JPG

please can some engineer help me . i hope attached drawing comes up . bit rusty but cant upload cad files . The picture is of a scaffold . Tube and fitting . i am trying to establish the formula for working out the forces exerted on a cantilevered scaffold . Forces d and e . and how do they differ with changing the angle of the support . Also if i where to change dist a and dist b how would this effect things . For maths puposes the height of diagram is 6m . the width at top 1m and base .5m . THe load at top is 10 kn .
A confused scaffolder

[PinkertonD]

Hi Iain,

A scaffold like that is a bit of a disaster waiting to happen. Is there a good reason you cannot have legs at the full width? You could calculate for that set up but the problem would come if say, six guys decided to sit together for their lunch break with their legs over outer side to watch the pretty girls go by.

Suddenly the best laid plans get screwed up instantly and people get hurt. Soooo, I would be exploring every possible avenue for an equal base before embarking on the riskier approach.

[jboggs]

Ditto to Dave!
You have a recipe here for serious injury. Ever notice that tall structures are generally wider at the bottom than they are at the top? There's a reason for that.

[iain glenny]

I have been a scaffolder for 15 yrs . The safe axial loading per standard ( Vertical member is 21.6 kn .. The scaffold is designed to hold a uniformed load of 3kn/m2 however i am looking to find out the loading onto the spur and that of the outward pressure so i can justify my tie calculation . the tie pattern at the moment is set at 12.2kn / bay .. the base is set at 750mm from wall due to boundry limitations .. the scaffold works and is up . I am looking for the maths to justify the design . I think it simple trig with the effective load .. can any one help me with the maths please

[RWOLFEJR]

I think you might be looking for this...
http://www.engineersedge.com/beam_be...flection_8.htm
If you figure the moment of Inertia of the overhanging member and plug your numbers into this calculator it'll let you know about how far you can overhang this thing. Make sure you add some safety factor. For a people holding thing I'd go 3 times what you need.

BUT...Thing is... For this situation I think you'd better look more closely at something like this...
http://www.engineersedge.com/column_...lumn_ideal.htm

I don't quite understand what you're asking in your original post but if I'm following you... chances are you'll be designing more for column strength than a cantilevered beam calculation since you said you're putting a gusset under the overhung portion. If this rig was sitting a foot off the ground you could be very comfortable with a pretty stout gusset that you're not going to buckle the stand. But once you increase the length of that column (your stand or scaffold sections) that overhung load your applying up top will have a huge effect on the column strength or resistance to buckling. The column will buckle more easily with that overhung load. So... Far as that gusset goes.... the closer the lower end gets to the ground... the stronger the rig becomes. But then you will also have the resistance to buckling on your gusset to look at. If the gusset material is a thin little bar it'll be pretty much useless.

It sounds like you know a good deal about the requirements and all for scaffolding but since in all likelihood this is a rig for people to work off of. I'd say... Do yourself a huge favor and hire an engineer to run all calculations for you and approve whatever design you two come up with. It's not worth taking the chance of taking advice from somebody on the internet (myself included) that isn't right there seeing what you are doing with this and able to pick up on any other critical design considerations that might be present.

Good luck,
Bob

[PinkertonD]

Hi, I am 100% with the others here and for a human cargo, you really need an Engineer to run through this.

If, as Bob surmises, you are asking about the blacked-out gusset, then you are only moving the failure point down by the length of one leg of the gusset. You will not be making that diagonal leg strong enough just by adding a gusset regardless of the theoretical force at the bottom.

I worry, now that you say it is all up and in use.

[zeke]

Iain,
I assume you are tying this structure to the wall on the left , How? and what do the a, b and c
represent?
what is e, the tie restraining force ?
and d the compressive force in the d link?

[iain glenny]

the structure is through securely tied through the wall at e . I am trying to establish the transferal of loads through the members . If i was too place lets say 10kn uniformally spread on the top then 50 % would be transfered straight to the floor at (a) the closest point to the building . the remainder would be transfered down the (c). This load would then be shared between d and b . However with the cantilever in place would deflect weight away from wall . creating force e . I am not looking for beam deflection calculators or formulas for bending moments . I am looking for simple physics solution for weight displacement at angles . so that i can establish compressive force d and tie restraining force e . we are getting closer .... please keep posting .. If it makes things easier take out b all together as this creates a c saw effect . thus creating a triangle effect .

[zeke]

DISCLAIMER:
The following is my inexpert opinion and is intended to give the poster some basic understanding
of the physics and should NOT be used for design purposes.
You need a licensed engineer to verify the integrity of this design. There are fundamental issues
like buckling, weld stresses, tie-down issues, safety factors, local code requirements,etc., etc.
Remember, lives are at risk if you go along with the assumption that it is up and "working"
but do you know how marginal that design is?



Assuming one tie point at e (i would NOT recommend one point only for obvious reasons) and taking
worst case of the load , W hanging on the end then
e=W*H/V (simple moment equilibrium
H=width of structure
V= height from ground to e tie point

compressive load in d
d=W/sin@
@= angle of d to horizontal

If you remove b and distribute the load, then
b=d=.5*W/sin@

[Azekial33]

Taking out the variables and breaking it down to simple trig/physiocs, you'd start at the top and divide your distributed load through each beam. So when you say "If i was too place lets say 10kn uniformally spread on the top then 50 % would be transfered straight to the floor at (a) the closest point to the building " this isn't really true as there are two members tied into point A transfering some of the load to the B member and therefore establishing a load in the x direction. I only say this to let you know that you are transferring loads between the scaffolding members through these angles.

[PinkertonD]

Cantilever: Home renovator, 20-ft up. Hmmmmmm.