Draft

14.3ApproximateAnalysisof Buildings 239

14.3.1 VerticalLoads

30 Thegirdersat each
oor areassumedto be continuousbeams,andcolumnsareassumedto

resisttheresultingunbalancedmoments fromthegirders.

31 Basicassumptions

1. 
   

   Girdersat each
   oor actas continousbeamssupportinga uniformload.

   
   


2. 
   

   In
   ectionpoints areassumedto be at

   
   

(a)Onetenth thespanfrombothendsof each girder.

(b)Mid-height of thecolumns

3. Axialforcesanddeformationin thegirderarenegligiblysmall.


4. Unbalancedendmoments fromthegirdersat each joint is distributedto thecolumns

above andbelow the
oor.

32 Basedonthe rstassumption,allbeamsarestaticallydeterminateandhave a span,Ls

equalto 0.8theoriginallengthof thegirder,L. (Notethatfora rigidlyconnectedmember,the

in
ectionpoint is at 0.211L, andat thesupportfora simplysupportedbeam;hence,depending

onthenatureof theconnectiononecouldconsiderthosevaluesas upper andlower boundsfor

theapproximatelocationof thehinge).

33 Endforcesaregivenby

Maximumpositive momentat thecenterof each beamis, Fig.14.9

0.1L

L

0.1L

0.8L

V

rgt

V

lft

M

rgt

M

lft

w

Figure14.9:ApproximateAnalysisof FramesSubjectedto VerticalLoads;GirderMoments

M

+

=

1

8

wL

2

s=w

1

8

(0:8)

2

L

2

= 0: 08 wL

2

(14.29)

Maximumnegative momentat each endof thegirderis givenby, Fig.14.9

M

lef t

=M

rgt

=

w

2

(0: 1 L)

2

w

2

(0: 8 L)(0: 1 L) = 0 : 045 wL

2

(14.30)