4 beam reaction

[Bert2]

Hi all,

been quite a while since I have been on here......

I have a problem I hope some of you can point me in the correct direction;

I have a simple beam reaction calc I need to calculate each reaction based upon one load.

I cant remember the last time I done this for four reactions.

Should I consider the it to be statically indeterminate ? will I end up with three un-knows?

please see attached FBD.

thanks
Bert.

 

[rb1957]

yes doubly redundant ... statically indeterminate or "hyper-static"

look into ...
3 moment equation,
unit force method,
moment distribution

Quando Omni Flunkus Moritati

 

[desertfox]

Hi

Try this link, my attached file 7th November it shows the three moment equation.


thread404-258455

 

[desertfox]

Hi Bert

I've worked out the reactions as follows:- Ra = -51.17KN, Rb = 2253.9KN, Rc = 744.7KN, Rd = -87.52KN

Fixed moments are Mb = -997.8, Mc = -941.8 Ma and Mb are zero.

I cannot upload a pdf of the solution at present, so I've done it as a TIFF file and hope you can open it.

desertfox

 

[msquared48]

By hand, Moment Distribution would be the simplest.

Mike McCann
MMC Engineering

 

[Bert2]

Thanks desertfox i can view your solution as the tiff.

ill run through your calc and get my bearings again with 'three moment equation' great help much appreciated

Bert

 

[desertfox]

hi Bert

Your welcome!

msquared48 is there any chance you could post a solution using the moment distribution method? it would act as a good cross check and I've never used that method so it would be interesting to see.

Regards

desertfox

 

[Bert2]

desertfox,

one question regarding your answer; have you assumed an area ie; considered it are a beam hence the 17985 and 4.95 values?

thanks bert

 

[IDS]

Both of my continuous beam spreadsheets give:
Reactions, kN:
-51.20
2254.51
743.85
-87.15

Moments at internal supports, kNm:
-998.49
-937.76


Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[desertfox]

Hi Bert2

The values on the right of the equal sign are the area's of the bending moment diagram and the 4.95 dimension is the distance from the centroid of the bending moment area diagram to the support, in the case of the 4.95 its the dimension to the support Rc.

Follow the link below its gives an example of the three moment equation and explains better the method.

http://www.roymech.co.uk/Useful_Tables/Beams/Continuous_Beams.html

 

[Bert2]

Desert Fox,

Many thanks for your efforts with this, I have gone through the equation and came to very similar bending moments for Mb and Mc (slight differences for rounding).

One last question if the regarding the '-' reactions Ra & Rb if the beam infinitely stiff would these values be positive?

Ie; what is the positive load reaction on Ra and Rb?

Thanks
Bert.

 

[desertfox]

Hi Bert2

The reactions are based on your support configuration and loadings, so no I don't think the stiffness of the beam will alter the direction of the reactions.
If you change how the beam is loaded or change a beam support to say (built in) then that might alter the reactions.

desertfox

 

[rb1957]

for my money Ra and Rd are -ve because they're restaining the upward movement of the beam ends (consider the beam supported on b and c only).

i notice you're using a "cg" symbol for the load ... is it a point load or are you showing the sum of applied loads (as a point force) ?

Quando Omni Flunkus Moritati

 

[Bert2]

rb1957;
correct the CG is for the sum of the applied loads, as this is the only info I have on the applied force.

 

[rb1957]

well that'll be a problem for the reactions ... loads on spans a-b and c-d will change the reactions.

Quando Omni Flunkus Moritati

 

[Tmoose]

I think the beam properties and even installation details (support heights) potentially might change the outermost reactions quite a bit.

 

[desertfox]

Hi Bert2

The mass of the beam would be a Udl loading which would help to reduce the negative reactions at Ra and Rd but I guess you don't know the beam size at this stage. If the external loads are actually Udl loadings then again these would produce positive reactions at Ra and Rb which I think rb1957 is alluding to.