Taking Moments Propped Cantilever

[MatthewMansfield]

Hello all

I was hoping someone could shed some light on the following question:-

I have a propped cantilever beam as shown below:-

https://files.engineering.com/getfi...8951-4719-8660-5cd38e42a5f3&file=Question.png

I want to work out the vertical reactions at support A and B.

I have been told to work out the vertical reactions I need to take moments about support B and by doing so the reactions at support B "disappear" - my question is if I take moments about support B do ALL of the reactions disappear and if not which ones remain and which ones disappear?

I hope this makes sense.

Thank you.

 

[WARose]

I have been told to work out the vertical reactions I need to take moments about support B and by doing so the reactions at support B "disappear" - my question is if I take moments about support B do ALL of the reactions disappear and if not which ones remain and which ones disappear?

Taking the moment at "B"....the only reaction in the equilibrium equation (from "B") would be the moment at "B".

EDIT: By the way, I came out with:

M[sub]B[/sub]= 38.67 kN-m

R[sub]B[/sub]= 16.08 kN

R[sub]A[/sub]= 13.91 kN

 

[wrxsti]

indeterminacyyyyyyyyyyy

you need to take out the prop reaction
and get your deflection

a= 5
b = 3
F = 30

δA = (F a3 / (3 E I)) (1 + 3 b / 2 a) = 2375/EI

then get the deflection for reaction at A (R_a)

F = R_a
L = 8

δB = F L3 / (3 E I) = 170.66 * R_a /EI

δA+δB = 0
R_a = 13.92 kN

 

[dik]

The solution is indeterminate with statics. You have to treat it as a cantilever with a point load at a location and determine the deflection of the end and then you have to apply a unit load at the end and determine the deflection of the unit load. By dividing the original deflection by the unit load deflection, you have the reaction at the free end. You can then use statics with this reaction to calculate the balance of the reactions... as noted by wrx...

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[wrxsti]

dik i cant download the first smath file for the moment connection for some reason from the link
only the weld one works
could you try repost it thanks

 

[WARose]

The solution is indeterminate with statics. You have to treat it as a cantilever with a point load at a location and determine the deflection of the end and then you have to apply a unit load at the end and determine the deflection of the unit load.

Why go to all that trouble? I got it with the tables in the steel manual (9th ed).

 

[IDS]

Why go to all that trouble? I got it with the tables in the steel manual (9th ed).

Because plugging the numbers into a spreadsheet:
- is quicker
- gives more information
- will handle more complex load cases
- will handle more complex support conditions
- can be cross checked against the table, if you want to

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[BAretired]

Another method is to treat it as a simple span, determine the rotation at support B, then calculate M[sub]b[/sub] required to reduce the rotation to zero. Finally, add and subtract M[sub]b[/sub]/L to the simple span reaction at B and A respectively.

The handbook lookup is probably the easiest way, but can't be used if you don't have the handbook.

BA

 

[WARose]

Because plugging the numbers into a spreadsheet:
- is quicker
- gives more information
- will handle more complex load cases
- will handle more complex support conditions
- can be cross checked against the table, if you want to

Yeah except the post I was replying to (and the OP) didn't mention anything about a spreadsheet. If this is a one time deal (for this propped cantilever).....you can get those reactions I posted in about 5 minutes. (With the steel manual.)

 

[dik]

Done... This one or the End Plate connection?

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[dik]

You need to develop an understanding of what you are doing... the spreadsheet comes next.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[dik]

Moment connection attached... I should have read the message first... just skimmed it...

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik