 L10P)(p)(p  L2L,L2B β

1. For beams on the elastic half-space (the Gorbunow-Posadow procedure) calculate:

[m]

E B

EI

L 3 2

s P

G  

  (probably, you will get 4m …) and also

P G P

G 2 L

, L L 2 β B



  

 

2. First check if the beam belongs to a category of „long beams”. The Gorbunov-Posadov charts can be used only for such beams („short beams” have other charts).

One of the three conditions must be fulfilled:

0,01 <  ≤ 0,15 &  > 1,0 either 0,15 <  ≤ 0,30 &  > 2,0 either 0,30 <  ≤ 0,50 &  > 3,5.

3. Define  = d/LG-P where the symbol d means distance from the force to the closest end of the beam. The charts are prepared for either doubly infinite beams (=+; >0 starts from the force position, dashed line) or for one-side finite beams (<+; >0 starts from this end).

4. For the value of  just calculated, select one interval to which it belongs, for example  = 0.18 belongs to Beta 0.1-0.2 (as a matter of fact, you will be using the charts for  = 0.15 which are not very different). Read only from 4 charts grouped for Beta 0.1-0.2.

Ignore all clusters of charts M, Q, p, y for other intervals of  which are not applicable here.

5. For each cross section , read dimensionless coefficients of influence (over-lined) and then use the following expressions:

 beam moments:

100 L ) P ( M ) (

M  ^GP









 beam shearing forces:

P ) ( Q ) (

Q    

 subsoil reactions:

P

LG

10 ) P ( p ) ( p

 









 beam settlements:

P G

s L

P E ) 1 ( Y ) ( y



 







 .

6. If  > 0 is „very large” (out off charts), assume simply that there is no influence, so take a zero value. Sometimes the chart is continued on the next page.

7. For all cross sections situated on the left from the force, change the sign of Q which is an odd function.

No such change is necessary for even functions M, p , y.

8. Correct the final moments at the beam ends if they are not zero.

Apply a linear correction on an interval ^:

^ = 1.2 for 0.01<   0.15

^ = 1.6 for 0.15<   0.50

^ = 2.0 for 0.50 < .

9. The Bleich method is not allowed here.

details on: www.ib.pwr.wroc.pl/brzakala in STUDIA II-go stopnia (magisterskie),

go to uzupełnienia , select wykresy Gorbunowa-Posadowa.

Example: for =0.18 read moments from Beta 0.10-0.20@M:

2 3 2 1. ) . (ξ= =

M for =+.