Allowable stress and deflection on multiple-span supports

[Acob]

Does anyone knows the formula for allowable stress and deflection of a three or more span continous beam loaded with a distributed load.
Thank you

 

[SlideRuleEra]

If the spans are equal length look in AISC Manual of Steel Construction, ASD, Ninth Edition. Reaction, shear, moment, and deflection are addressed. With this information stress can be computed for any given material, not just steel:
For 3 Spans, Beam/Deflection Diagram #36, page 2-308
For 4 Spans, Beam/Deflection Diagram #39, page 2-309

 

[SmithJ]

Acob,

If you have the ninth edition of the ASD Manual for Steel Construction [Green Book], Deflection in a continuous beam with three equal spans is shown on page 2-308.

The allowable bending stress in the beam will depend on the beam section properties and laterally unbraced length. See Chapter F, Section F1 (page 5-45) of the same manual for the applicable formula. Allowable shear stress is shown in the same chapter in Section F4 (Page 5-49).

Hope this helps.

JS.

 

[Acob]

Thank you for your help.
I don't have the book and i search on the internet and the book is too expensive. The problem that I want to resolve is for three spans or more with equal length. Can you say to me what's the general formula? For the 3 spans I solve the values of the reactions but i don't have enough knowledge to go much far.

 

[hernma]

Acob:

For any beam with moments Ml and Mr, use the following expressions:

E*I*Dx = ( p*L^3/24 + L/3 ( Ml + Mr/2 )) X – mx

Where:

Dx = Deflection at a distance X from the left support

p = T/m (force/length)

mx = X^3/6 ( Rl –p*X/4 ) + Ml*X^2/2

Rl = p*L/2 – (Ml-Mr)/L

Ml ( Mr ) = Moments at the left (right) supports, positives causing traction at the lower part of the beam.


If Ml = Mr = 0 (simply supported),

E*I*Dx = p*X*L^3/24 ( 1 – 2* N^2 + N^3),

With N = X/L


I hope it helps.

 

[RockEngineer]

Try this page for online formulas for various simple and two span beams.

http://www.kmitl.ac.th/engineer/civil/civilhandbook/HTML/structural_formular.htm