Deflection of a double span with single point load

[flyingdebris]

Does anyone know the deflection formula for a single point load at mid span of a double span beam? That is, point load is in the middle of one span only. Thanks.

 

[rb1957]

google three moment equation, that'll get you the reactions; then step through the integration for displacement.

an alternative is to use superposition ...
1) remove the middle support, solve the SS beam with a point load, get the deflecte shape;
2) apply a unit load at the middle support, opposing the defelection above, solve as a SS beam is a single point load (at mid-span), get the defelcted shape;
3) get the deflection at the mid-span from both 1) and 2), call them d1 and d2;
4) the middle reaction is d1/d2 (*1) lbs;
5) multiply the deflections in 2) by this factor;
6) sum 1) and 5), you should get zero at the middle support, this is the deflected shape you weere looking for.
(this is called the unit force method. in your case, solving simple SS beams will get your answer)

if you want others to do this ...
1) spans, equal ? or L1 and L2 ??
2) MoI, constant ? or I1 and I2 ??

if you want a near enough (conservative) answer, consider it as a single span (ie neglect the unloaded span).
ask yourself why this approach is conservative ?

Quando Omni Flunkus Moritati

 

[briancpotter]

How exact a value do you need? If it's a pin connection at each support, you can infer that it'll be between PL^3/(48EI) (the deflection of a simply supported beam) and PL^3(48EI*SQRT(5)) (the deflection of a beam simply supported on one end and fixed at the other).

Brian C Potter

http://simplesupports.wordpress.com

 

[briancpotter]

Found the equation in my Civil Engineering Reference Manual (11th Edition, pg. A-88).

Max deflection for a 2 span beam with a single point load in the center of one of the spans is 0.96PL^3/(64EI)

Brian C Potter

http://simplesupports.wordpress.com

 

[rb1957]

that'd assume constant I and same spans, yes?

Quando Omni Flunkus Moritati

 

[briancpotter]

Correct.

Brian C Potter, PE

http://simplesupports.wordpress.com

 

[flyingdebris]

Briancpotter, that's great. Much appreciated. Thank you. Hang onto that book. Thank you to all for your posts.

 

[BAretired]

It is Case 35 of "Beam Diagrams and Formulae" in the 2004 CISC Handbook. Delta_max occurs at 0.48L from the exterior reaction of the loaded span.

BA