How to use Table3-22b in AISC 13th edition? 3

[StructLin]

Can anybody tell me how to use Table3-22b in AISC 13th edition? I will appreciate it very much if somebody can give an example showing how the Table3-22b in AISC 13th edition is used. Thank you very much in advance.

 

[StructLin]

Table 3-22a and Table 3-22c are quite straight forward and easy to understand how to use. But Table 3-22b is not. Its title is "Beam Diagrams and Formulas, Design Properties of Cantilevered Beam-.....", but I do not see any cantilevers, all the diagrams are showing statically inderminate simply supported members.

 

[JAE]

The cantilevers are the short segments of beams between the interior supports and the pin (indicated by the small open circle).

This is a common method of construction where segments of beams span from column to column, then cantilever over the interior column to pick up the next interior beam. The next interior beam then spans from end-of-cantilever to the next column, and then cantilevers over that column.

The diagrams shown in this table show a different method where two beams cantilever toward each other and a short segment of beam within the span extends from end-of-cantilever to end-of-cantilever.

The moment diagrams below reflect a continuous beam with pins located off the columns, producing an inflection point where M = 0.

The first column of values is for a continuously loaded span.

The columns marked 2 - 5 are for equally spaced concentrated load conditions.

 

[tolchijb]

It is used in the Gerber System, also known as Drop in-Cantilever beam system.

 

[hokie66]

Who is Gerber? I have used versions of this system for years, but never knew it was named for someone.

 

[JaredS]

To use table 3-22b in AISC 13

1. Determine the number of spans that you need to, uh well, span.

2. Determine your loading condition, is n infinite, 2, 3, 4, or 5. For n equal to infinite P = w * L.

3. If you are spanning an odd number of spans you will need to choose a configuration.

4. To find the maximum positive and negative moments the diagram you selected will show M 1-5 in a little bubble. The bubble indicates an approximate location and the respective label M1 or whatever indicates the load in the respective n column.

5. The same goes for reactions and dimensions of the cantilever.

At this point I'm not really certain how to treat odd and even spans greater than eight (six and seven are given). I suspect that additional spans would be given in between the H and H support and that any cantilevering would be dimensioned to the dimension f and the the maximum moment would be M3.

If we were to consider the example

3 spans 10 feet
with a uniform load, w = 1 kip/ft

____________________________________
||||||||||||||||||||||||||||||||||||
--------o------------------o--------
/\ /\ /\ /\
A B C D E F

Then the maximum moments would be

on the span AB M1=.086*P*L=.086*1*10*10=8.6 kip ft !Remember that P = w * L
At B -M1=.086*P*L=-.086*1*10*10=-8.6 kip ft
on the span CD M4=.039*P*L=.039*1*10*10=3.9 kip ft
sym for rest of the beam

the reactions would be

At A A=.414*1*10=4.14 kip
At C E=1.086*1*10=10.86 kip

the distance of cantilever would be

distance of BC c=.22*L=.22*10=2.2 feet

To check my work we will take the cantilevers from the middle span

10' - 2 * 2.2' = 5.6'

and find the moment on CD of w*L^2/8

1 * 5.6^2 / 8 = 3.92 kip ft

QED

Jared Stewart

 

[JaredS]

*EDIT*

I accidentally left out the last support in my ASCII diagram above and the spacing is off but I hope you can interpret what I intended.

Jared Stewart

 

[lkjh345]

Star for Jared just for effort alone on that one!

 

[StructLin]

Thank you JAE and JaredS, Now I can figure out how to use this table.