t  e    d   o   n
   2    0    1    5
   8    G    M    T
   d    l  e
   9    0    7    8    5    5    6    6    2    8
   P   u
   i  n  ,
   d
   t .   o   r  g
  u   s   e
   t  e    d   o   n
   2    0    1    5
   0    G    M    T
   d    l  e
   9    0    7    8    5    5    6    6    2    8
   P   u
   i  n  ,
   d
   t .   o   r  g
  u   s   e
   t  e    d   o   n
   2    0    1    5
   4    G    M    T
   d    l  e
   9    0    7    8    5    5    6    6    2    8
   P   u
   i  n  ,
   d
   t .   o   r  g
  u   s   e
   t  e    d   o   n
   2    0    1    5
   4    G    M    T
   d    l  e
   9    0    7    8    5    5    6    6    2    8
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   t .   o   r  g
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for
national   organization,   are   limited   to   scientific   research,
the   development   of   new   or   improved   products and
methods,   technical service,   promotion   and   educational
effort   (including   safety   work),   and are   primarily   designed
to   improve   and extend the   uses   of  port land   cement and
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 The   manifold  program   of  the   Association and its varied
services to cement users are   made  possible   by the financial support   of over  60  member   companies   in   the   United   States
and   Canada,   engaged   in   the   manufacture   and sale   of   a
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furnished   on request.
COPYR1GHT,l»47bY   PORTLaNDCEMENTaSSOC1aT1ON
 
   t  e    d   o   n
   2    0    1    5
   5    G    M    T
   d    l  e
   9    0    7    8    5    5    6    6    2    8
   P   u
   i  n  ,
   d
   t .   o   r  g
  u   s   e
NOMENCLATURE
oA   = ratio   of   length   of    haunch   at end   A   to   length
of   span
ob   = ratio   of   length   of   haunch   at end   8   to   length   of  span
b   =   ratio   of   distance from   loading point   to end   A to   length   of   span
bt   = ratio   of   distance from   loading   point   to end   B   to
length   of   span
E   = modulus   of   elasticity
U   = moment   of   inertia   of   section   of   minimum   depth
fx   = moment   of   inertia   of   any   section   distance x from
A   or X!   from   B
 JcAb   =   stiffness   factor   of   member AB at end A;   stiffness
=   kuEU
L
L   =   length   of   member
MAb   = fixed   end   moment   at end   A   of   member AB   for any type   of   loading;   used to   identify   column   of  F.E.M. coefficients   in   tables
Msa   =   fixed   end   moment   at end   B   of   member AB   for any type   of   loading;   used   to   identify   column   of  F.E.M.   coefficients   in   tables
P   =   concentrated   load
rt   =   ^c
w   = uniform   load
WA   = weight   of   haunch   per   lin.ft.   right   at   end  A
Wt   = weight   of   haunch   per   lin.ft.   right   at end   B
x   = distance   from variable   point   to end   A
X]   =   distance from variable   point   to end   B
 
   t  e    d   o   n
   2    0    1    5
   5    G    M    T
   d    l  e
   9    0    7    8    5    5    6    6    2    8
   P   u
   i  n  ,
   d
   t .   o   r  g
  u   s   e
factors and   fixed end moment   coefficients   for uni
form, concentrated   and haunch   loads are   given   for   660
members   with parabolic   haunches   (Tables   1   through
26)   and   for   660 members   with   straight   haunches
(Tables   27   through   52).   In   each   of   these tables   the
left   haunch is   kept   constant while   the   right   haunch
is   given   25   different sets   of    dimensions   with   the
exception   of Tables   26   an d 5 2   in which   there are
35   different sets   of   dimensions   for   the   right   haunches.
Lengths   of   haunches   in   terms   of   the   length   of   the
member   are 0.10, 0.20, 0.30, 0.40,   0.50,   0.75   and   1.00.
Depths   of   haunches are   given   by   the   ratio r   depth   of 
haunch   to   depth   of   shallowest   section,   and values   of  r
are   0.4, 0.6, 1.0,   1.5,   and   2.0.   Concentrated   loads   are
placed   at  points   0.1, 0.3, 0.5,   0.7, and   0.9  of  the   length
of   the   member.   Altogether,   20   coefficients are   given
for   each   of  t he   1,320   members in   Tables   1   through   52,
or a   total   of   26,400   coefficients.
 The   two   groups   of   tables,   1-26   and 27-52, are   in
layout  and   arrangement   exact   duplicates   of each   other,
the   only   basic   difference   being   that   the   general   equa
tion   for   the   variable   moment   of  inertia   is
7x=/cj^l   +  r(l   —
^)2J for   parabolic   haunches,
with   the   deck structure.   Transverse   loading   between
the   two pier   ends    i  snot   considered,   so   only   carry-over
and stiffness   factors are  included  in   the table.   Bending
moments   at   ends   of    the   piers   are assumed   to   be
applied   in   the   plane   indicated   by   the dash and   dot
lines.   Consequently,   qrepresents   the   change   in width
and   rthe   change   in   depth   of   the member.   The variable
moment   of inertia    i  s
7X-   /cd   + ff)8   u+
  «    f   )
in  which   x i  sthe distance from   avariable   point to   the
small end where    I  x=
 Table   54    i  s for   symmetrical   members   of   constant
depth   throughout   but   having   haunches   of   tapered
width at both   ends.   Table   55    i  s for   members   with
similar   haunches   at   one end   only,   the other end   being
prismatic.   In   Tables   54   and   55,   coefficients   for   fixed
end moments due   to   haunch loads have   not   been
included. Such moments are  relatively   small   compared
to   the   uniform   dead load   moments   plus   the   live   load
moments,   so   in   general they   can be   neglected.   If    i   t
   i  sdesired   to   determine the   haunch load   moments this
can   be   done   readily by   considering   the   weight   of   the
haunch as concentrated   load   applied   at   the   center   of 
gravity  of  the   haunch   for   which   the   fixed   end   moment
coefficients can be taken   directly   from the table   or obtained   by interpolation.
For   symmetrical   beams   of   prismatic   section   having infinite   moment   of inertia at   the   ends,   beam   factors
and fixed end   moment coefficients   are  given   in Table   56.
 Table   57    i  sfor members   with infinite  moment   of  inertia at   one   end,   the other   end   being   prismatic.   Tables   56
and   57   are   particularly   applicable   to   the   frame   analy sis   method   of   design   of flat   slab   construction*.
 Table   58    i  s   acalculation   schedule   illustrating   the
method   of   summations which   may   sometimes be   sub
stituted for  integration. Integrals by which   tabulated
coefficients were   computed   and   by   means   of   which the tables   may   be   extended,    i   fdesired,   are   recorded   in
 Tables   59   through   62.   Further   explanation   and des
cription of   these   integrals   are   given   in   the section
entitled Derivations.
Except  for  the   few cases  of   symmetrical members,   all data are recorded twice   in   the tables   so as   to eliminate
the   necessity   for   the user   to   transpose   left   haunch   for
right   haunch,   or   vice   versa,   which   may   be   somewhat
confusing   and   entail   an added hazard   of  making  errors.
 There   are   probably   some combinations   of    a-   and
r-values   included   in   the   tables which   rarely would   be
applicable   in   ordinary   engineering practice,   but   the
choice   of   a- and r-values    i  sone   to   be made   for   each
individual   set   of   circumstances.
tabulated   i   tmay   be  necessary occasionally   to  ascertain
fixed end moments   for   concentrated loads   at inter mediate   points   for   members   of   the   dimensions   given
or   to   determine   coefficients   for   members   not   included.
   Amethod   of   interpolating   between   tabular   values   of  fixed end   moments   for   concentrated   loads    i  sgiven   in
the section   immediately   following   the tables.
   Atypical   example   illustrating   the use   of   the tables
   i  sgiven   in   the   following   section,   which   immediately
precedes   the   tables, so,   in   general,   the   designer   need
not   concern   himself with   the discussion   following   the
tables unless he    i  sparticularly   interested in the mathe
matical   derivations.
Peabody,   Jr.,   Journal   o    fthe Boston   Society   o
   fCivil   Engineers,  July   1939,   Vol.   XXVI,   No.    3
  ; also Frame   Analysis Applied
lo   Flat   Slab   Bridges,   available free in the   United   States   and
Canada on   request   to   Portland   Cement Association.
PAGE    3
   t  e    d   o   n
   2    0    1    5
   6    G    M    T
   d    l  e
   9    0    7    8    5    5    6    6    2    8
   P   u
   i  n  ,
   d
   t .   o   r  g
  u   s   e
haunches   is  shown   with  dimensions   in  Fig.   1.  The left
exterior   girder  is  unsymmetrical   and has the   following
characteristic   ratios:
aA   =   0.3,   rA   = \    [   ]   '   * -    1 =   1.0,  a   =   0.4,   and    3ft.    2in.
 The   coefficients   for  this  case are  given   in   the   19th line
of Table   13. Because the   group   of   three   spans    i  s
symmetrical   about   the   centerline   the   right   exterior
span   will  be   similar   to the   left   span   except   that   the
Fixed   end moment   coefficients   taken   from Tables
13  and   18   are recorded below   for uniform   load,   con
centrated   load   at 0.7-point   in   left   exterior   span,
and   for   the   parabolic   haunch   loads.   To   obtain   fixed
end  moments,   the tabular   coefficients   must  be  multi
plied  by  wlß   for uniform   load,  PL   for   concentrated
load,   and   WL2  for haunch   load in which  W    i  sthe load
per   lin.ft.  at the  deep   end  of the  haunch  due   to  which
the moments are  being   obtained   and   L   i  sthe   length of 
the   span   under   consideration.   It   must   be noted   in
selecting   coefficients   from   the tables   that  each member
   i  sconsidered   individually   and   the dimension   ratios
for   the   left   end   of   the   member are   given   in   the table
heading   and   those   for   the   right   end   are   in   the   two
columns   at  the   left  side  of   the table.
   L   :   »  ;
-0.0896wL2 -0.116SwL2 -0.0413PL   -0.2231PL -0.0067WAL4   -0.0006WaL2 -0.0008JVBL2t -0.0119Wb¿2
-0.1028ioLa   -0.1028tcL2   -0.II6810L2    0   0    0
-0.0070'1.2   -o.ooomAL2 -0.0003WBL2 -0.0070tVBL2
0.4,     =   1.5,     =   0.3  and     =   1.0.  The   coefficients
for   abeam  with   these   dimension   ratios  may  be  taken
from line   13  of  Table   19,  or   they may  be   taken from
line   19   of Table   13   by   reversing   the   subscripts   at
the heads   of   the columns.   The   center   span    i  ssym
metrical and   the   dimension   ratios   are     = aB   =   0.3
and     =   =   1.5.  The   coefficients   for the   center
span   are  given   in   the 14th   line  of  Table   18.   All  these
coefficients   together   with distribution   factors   com
puted   from   the   relative  stiffnesses*,   the   center   depths
being   the   same,   are recorded   below.
 The   design   procedure   using   beam factors   and
moment coefficients   similar to   those recorded above    i  s
illustrated in  detail in   design problems   in  Continuous
Concrete   Bridges%   in which final   moments   are deter
mined   by  means  of formulas  given   in Tables   Iand II of   that   publication.   The   use   of formulas for   deter
mination of final   moments    i  sconvenient   and   time-
saving   in  many   instances,   but   a  general   procedure    i  s
to   make an   actual   distribution   of  moments.   For  such
cases,   refer   to  One-Story   Concrete Frames   Analyzed  by
Moment   Disiribuliont, which   contains  many  numeri
cal  examples   including  vertical  and   horizontal   loading,
volume   change   and  settlement.
Carry-over   factor   -0.789   -0.615   -0.698   -0.698 -0.615 Relative  stiffness   = k/L   0.181   0 .232 0.147   0.147   0.232 Distribution   factor   1.00   0.612   0.388   0.388   0.612
*In   volume   change   calculations the absolute stiffness   must be used which can be obtained   by   substituting   the tabular   stiff  ness factors   in   the   expression   kEIc/L.
fSubscripts    Aand     in   each   span   indicate haunch   loads   at left  and   right  ends   respectively   of that  span.    L   i  salways   the
length   of   the   span   under   consideration.
   ÎFree   copies   available   in  U.S.  and Canada   on   request   to  Port land   Cement Association.
PAGE    4
   t  e    d   o   n
   2    0    1    5
   6    G    M    T
   d    l  e
 
   i  n  ,
   d
   t .   o   r  g
  u   s   e
Haunch   Carry-over
F.E.M.
Coef. X   toL' 0.1   0.3 0.5   0.7 0.9   F.E.M. Coef.X   WaL'
F.E.M. Coef.X  W,L'
'a Cab 1 Cba   kab |   kba   Mas 1Mba   Mab I  Mba Mab M ba Mab   I  Mba   Mia   M ba Mab M ba Mab Mba   Mab |  Mba
bl
he
r,ht
Note:
All   carry-over factors  and fixed  end moment coefficientsare negativeand all stiffnessfactorsare positive.
OA   =   0.4   ait   - variable   TABLE   4   rA   =   0.4   ru   =   variable
0.4   0  510  0   629 5.95   4 81 0 09980 08160.08820 00580   17870 05190   15640.120 10 07550 15240  00820.08620 01060.00120.00000.0008 0.6   0  521  0 628   6.01   4  99 0 09840 08400.08810 00600 17810   05380   15400.12400  07270 15710 00700.08820 01060.00130.00000.0008
0.1   1.0   0  536  0   627 6.10   5 23 0 09630 08750.08790 00630   17660 05630   15070.12960 06870   16380 00530.09100   01060.00130.00000.0008 1.6   0 551 0 626   6.17   5 44 0 09*50   09040.08780 00650 17540 05830   14800.13420 06540   16930  00410.09300   01050.00140.00000.0008 2.0   0  560  0   625 6.22   5 58 0  09340 09230.08770 00670   17450  05980   14610.13730 06320 17300 00330.09440   01050.00140.00000.0008
0.4   0 543 0  622   6.11 5 34   0   09670 08730.08790 00630  17620 05660 15070.130 30  06940   16340   00720.08790   01060.00140.00020.0030 0.6   0 567 0   618 6.23   5  72   0   09390 09200.08760 00670   17440   06040 14620.138 30 06420   17240 00570.09040 01050.00140.00020.0031
0.2 1.0   0 603 0 613 6.42 6 32   0  08990  09900.08730 00740 17130 0660 0  13930.15050  05650 18600 00370.09360 01040.00160.00010.0032 1.5   0 633 0   608 6.58   6  86   0   08650   10520.08700  00790   16850  07090 13330.16110 05000   19760 00240.09590 01040.00170.00010.0032 2.0   0  654  0  604   6.70 7 25 0  08420   10940.08670 00830   16660  07450   12910.168 80 04550  20570  00160.09720   01030.00180.00000.0033
0.4   0   572 0   610 6.23   5  84   0  09460 09110.08760  00680  17410  06070 14660.13830  06570 17030 00710.08790   01050.00150.00070.0063 0.6 0 609 0 603   6.41   6 48   0  09100   09770.08730  00740   17150   06630 14020.150 20 05890 18250 00560.09040 01040.00160.00050.0066
0.3   1.0   0  666  0  592   6.71   7   55   0  08540   10810.08670  00850   16660 07540   12990.169 30  04840  20160 00360.09370  01030.00180.00040.0068 1.5   0  716  0 582   6.99   8 59   0  08030  11750.08620  00950   16220  08400  12050. 18720 03940  21860 00230.09600  01020.00200.00020.0070 2.0   0  752  0   575 7.20   9 41 0  07690   12420.06580 01030  15880 09060 11370.20060  03300 23070  00150.09730   01010.00220.00020.0072
0.4   0 596 0   596 6.32   6 32   0  09340   09340.08750  00720   17300  06390 14390.14390 06390   17250 00720.08750   01050.00150.00150.0105 0.6   0 645 0 584   6.56   7 24   0  08910   10130.08700  00800  16920 07120  13590.159 00 05620   18670 00570.08990   01040.00170.00130.0110
0.4   1.0   0   723 0   567 6.96   8 89   0 08240   11430.08630 00950   16280  08390 12280.18430  04440  20870 00370.09320   01020.00200.00080.0117 1.5   0 796 0 551   7.36   1064   0 07610   12680.08550 01110   15660  09690  11040.20990 03410 22850 00240.095 60 01010.00240.00070.0120 2.0   0  852  0   540 7.67   12 11   0 07150   13620.08490 01240   15170   10730   10080.22980 02690 24260   00160.09700  01000.00260.00050.0124
0.4   0 614 0   581 6.40   6  78   0  09280   09450.08730 00760   17230 06600   14210.14720 06270 17250 00740.08700   01050.00160.00280.0152 0.6   0 674 0 561   6.66   7 98   0 08800   10320.08670 00870 16780 07460 13290.16440 05500 18780 0059 0.08930   01040.00180.00240.0159
0.5 1.0   0  774 0  537   7.17 1030   0 08020  11780.08590  01050   16000 09060   11780.19460  04220 20970 00390.09270 01020.00220.00180.0169 1.5   0  872 0 516   7.70   1297   0  07290   13260.08490  01270 152 10 10810 10270.22620 03200 23000 0025 0.09500 01000.00270.00140.0180 2.0   0 947   0 499 8.08   1540   0  06740 14430.08410  01450   14560   12290  09130.25220 02440 24480   00170.09650 00980.00310.00100.0186
= 0.5   as   =   variable   TABLE   5   rA   =   0.4   ru   =   variable
0.4   0 497  0 648   6.39 4.90   0   10080 08090.08760 00600   17940  05110   15980 11880 07830  15190  00890.08600 01530.00230.00000.0008 0.6 0 508 0 647 6.42 5 02   0 09950  08340.08760 00610   17840  05310 15730 1 2230  07530 15640   00740.08800 01530.00250.00000.00C8
0.1 1.0   0   525 0 646 6.51 5 25 0 09720  08700.08750  00640  17690  05640   15420   12790 07130 16270 00560.090 90   01520.00270.00000.0008 1.5 0  538 0  645   6.59   5 47   0  rmsfi0  nono0.08740 00660   17560 05820   15120   13240 06820 16820   00430.09290 01510.00290.00000.0008 2.0   0  645 0 644   6.64   5 60 0 09430  09160.08730 00680   17450  05880  14930 13540  06630  17200   00350.09430   01510.00310.00000.0008
0.4   0  627  0  640   6.58   5 40   0 09780   08700.08740 00650   17680 05560   15410 12860 07180 16270 00770.08770  01530.00260.00020.0030 0.6   0  552  0   636 6.69 5 77 u UH3i!u 09140.08720 0UO80 17460 05950   14940 13660  06640  17170  00600.09020 01520.00280.00020.0031
0.2   1.0 0  589 0  632 6.86 6  38  0 09110 09850.08690 00750   17130  06580   14250 14870 05850  18580   00390.09350  01500.00300.00010.0032 1.6   0 617 0  626 7.04   6   93 0 08770 10450.08660  00800   16850 07060 13600 15930 05210 19710  00250.09580   01490.00330.00010.0032 2.0   0  636 0   623 7.19   7 37 0  08520   10880.08630  00840 16690  07360   13170 16690  04700  20480   00170.09710  01480.00350.00010.0033
0.4   0   556 0  628 6.70   5  93   0 09580  09040.08720 00700   17430  05940   15000 13660 06 800   16960  00760.08770   01530.00270.00070.0063 0.6   0  593  0   620 6.88   6   55  0 09220   09730.08690 0 0750 17140 06530   14330 1 4850  06070  18200   00590.09020  01510.00300.00050.0066
0.3 1.0   0  648  0  609   7.18   7   62 0 08670  10770  08620 00860 16670 07480   13290 16740  05010   20150  00380.09360 01490.00320.00040.0068 1.6   0 694 0  600 7.46   8  65   0   08130   11700 08570  00970   16200 08340   12290   18530  04110 21810 00240.09590   01470.00360.00020.0070 2.0   0  731  0   591 7.69   9  55 0 07780 12360.08530  01050   15850 08970 11580 19870 03410 22990  00160.09720 01450.00390.00020.0072
0.4   0   581 0 614   6.78   6 40 0  09450   09280.08700 00740   17250  06270  14720 14210 06600   17230  00760.08730 01520.00280.00160.0105 0.6   0  628  0   602 7.03   7  33   0 09010   10080   08650 00820   16900 07030   13900 15730  05830   18620  00600.08970 01500.00320.00140.0109
0.4 1.0   0  703  0  586   7.43   8  95   0  08340   11370.08580  00980  16270 08330   12550 18240  04610 20800  00390.09300   01480.00360.00090.0116 1.6   0  771  0  568   7.85   10 80   0 07710 12620.08490 01130 15610  09590   11280 20800 03560   22800 00260.09550   01450.00420.00070.0120 2.0   0 827  0   556 8.19 1220   0  07230   13570.08430   01260   15120   10620 102 60 22790  02760  24200  00170.09690   01420.00470.00050.0124
0.4   0  599  0  699   6.84 6 84 0 09370   09370.08660  00760   17180  06520   14510 1 4610  06520  17180   00760.08660  01600.00300.00300.0150 0.6   0 656 0   581 7.14 8 07   0  08890 10230.08610 00870 16730  07390   13600   16220 05680  18610   00610.08920 01480.00350.00260.0158
0.3   1.0   0  753 0 554   7.66   1042 0  08110   11700.08530 01070 15950  08980   12050   19240 04420  20870   00400.09260   01450.00420.00200.0169 1.5   0  849  0   531 8.21   13 15 0 07380  13190.08430  01280 15150 10700   10520 22390 03320 22930 00260.09490  01410.00500.00140.0179 2.0   0   924 0 614 8.67 15 59  0 06820 14360.08350  01470   14490 12170 09330  24990  02560 24410  00180.09640   01380.00570.00110.0185
u   =   0 .1   i   = variable   TAB LE   6   0.6   variab le(   aj   rA   = rb   =
0.4   0.536   0.549 4.72   4  60   0.0898 0.6 0.548 0.548   4.76   4  76   0.0885
0.1   1.0   0.566   0.547   4  82   4  98   0.0867 1.5 0.580 0.546   4.87   5  17   0.0852 2.0 0.589 0.545   4.90   5 30   0.0842
0.4   0.571   0.543   4.83   5  09   0.0870 0.6   0.597   0.540   4.92 5  44   0.0846
0.2   1.0 0.634   0.535   5.05   5   98 0.0810 1.6 0.666   0.531 5.16   6   47 0.0780 2.0   0.688   0.528   6.24   6   83 0.0760
0.4   0.602   0.533   4.92   5  56   0.0851 0.6   0.641 0.527   5.05   6  14   0.0819
0.3   1.0 0.701   0.518   5.25   7   11 0.0769 1.5 0.754   0.509   5.44 8   05 0.0725 2.0   0.792 0.504   5.59   8   79 0.0695
0.4   0.628 0.521 4.96   6  00   0.0840 0.6 0.680   0.511   5.15   6  85   0.0803
0.4 1.0   0.763 0.496 5.43 8 40   0.0742 1.6   0.841   0.483 5.71 9 93 0.0687 2.0 0.899 0.474   5.93   1125   0.0647
0.4 0.647   0.508 5.02   6   42 0.0834 0.6   0.710 0.494   5.23   7 55   0.0794
0.5 1.0   0.817 0.471   5.57   9 67   0.0725 1.5   0.920   0.452   6.97 12 10   0.0660 2.0 1.001   0.439   6.30   14 25   0.0610
0.0860| 0. 0.0921 0.0950 0.0969
0885|0.0887|0 0 0  0885 0.0884
0.0919 0.0967 0.1038 0.1100 0.1142
0.0959 0.1026 0.1131 0.1226 0.1293
0.0984 10.1064 0.1196 0.1321 0.14151
0 0.0884 0.0881 0.0878 0.0877
0.0884 0.0881 0.0876 0.0872 0
0.0882 0.0879 0.0873 0.0867 0.0862
0.0056 .0058
0.09950.08800.0074 0.10860.08760.0084 0.12360.08700.0102 0.13840.08620.0121 0.14980.08550.0136>0.1311   1
'0.1605 0.1585 0.1555 0.1529 0.1511
0.1585| 0.1556 0.1510| 0.1469 0.1437
0.1571 0.1535 0.1474 0.1415 0.1370
0.1564 0.1516 0.1447 0.
0.0753 0.0850 0.1024
0.1223 0.11391 10.1008
0.0868 0.0887
30.
0.0884 0.0909 0.0940 0.0962 0.0975   0
0.0008 0.0008
0.0876; 0. 0.0932|    0  .
0.0008 0.0008 0.0008 0.0008
00000 00000
PAGE    6
   t  e    d   o   n
   2    0    1    5
   7    G    M    T
   d    l  e
   9    0    7    8    5    5    6    6    2    8
   P   u
   i  n  ,
   d
   t .   o   r  g
  u   s   e
Haunch   Carry-over
F.E.M. Coef.X  wL' 0.1   0.3 0.5   0.7 0.9   F.E.M.
Coef.X  WaL' F.E.M.
Coef. X  WaL' o-a   *a
Cab C ba   k ab kba Mab  1Mba   Mab   I  Mba Mab I  Mba Mab   I  Mba Mab I M«   *Cis| Mba M a  |  Mba Mab   I  Mba
& iP 1
All   carry-over factors and coeff icie ntsare  negativeandall positive.
OA   =   o.<2   Ob   =   variable   TABLE   7   rA   =  0.6   rb   =   variable
0.4 0 528 0 598 5 38   4  75 0 09810 08210.09090 00460.178 20  05250 15030  12220 07150 15380  00770 08640.00310 00010 00000  0008 0.6   0  540 0 597 5  44 4  92  0 09670 08460.09080 00470.17720 05420  14810  12610  06880 15850 00650 08840.00310  00010  00000  0008
0.1   1.0   0  557  0   595 5  51 5  15  0  09470 08810.09070 00490.17560 05660 14490 13170 06500  16520  00500 09110.00310 00010  00000 0008 1.5 0 570 0 594   5  58   5  35  0  09310  09090.09060 00510. 17470 05870  14230 13640  06200 17060  00380 09310.00310  00010  00000 0008 2.0 0 580 0 593 5 62 5 49  0  09200  09280.09050 00520.17390 06010  140 50 13950 05990  17430  00310 09440.00310  00010  00000  0008
0.4 0 562 0  591   5  52   5  26  0 09510 08780.09070  00500. 17570  05710  14490  13250  06570  16480  00670 08810.00310  00010  00020 0030 0 6 0 5B 7 0  687   5 63 5 63  0 09250 09250.09050  00530.17380  06070  14050  14050  06070  17380  00530 09050.00310  00010 00010  0031
0.2 1.0   0 624 0 582 5 80 6  21  0 08870 09950.09020  00580.17080  06630  13390  15270 05350 18720  00360 09360.00310 00020  00010  0032 15   0  655  0  578   5  94   6 74 0 08540  10560.09000 00630.16820  07110 12830 16340  04730  19870  00220  09590.00310 00020  00010  0032 2.0   0  677  0  575   6  05   7 12 0 08330  10970.08980 00660.16640  07460  12430  17100 04310 20680 00150 09720.00310 00020  00000  0033
0.4   0  593  0  580   5  63   5  76  0 09310  09170.09050  00540.17380  06110  14090  14050 06220 17170  00660  08800.00310 00010  00060  0064 0.6   0  631  0  573   5 80   6  38  0 08970 09820.09020  00590.17100 06660  13470  15240 05570  18380  00520  09050  00310 00020  00050  0066
0.3 1.0   0  689  0  563   6  06   7 42 0 08440 10840.08980 00670.16640 07560  12490 17160  04580  20280 00340 09380.00310 00020 00030  0068 1.5   0  741  0  554   6  31   8  43  0 07960 11780.08940  00750.16220  08410  11600  18950  03720  21960  00210 09600.00310 00020  00020  0071 2.0 0 779 0 548 6 49   9  23  0 07640  12440.08910  00810.15900  09060  10950  20280  03120 23160  00140 09730.00300 00020 00020  0072
0.4   0  618  0  567   5  72   6 23 0 09200  09390.09040 00570.17240 06420  13830  14620 06040  17440 00670 08760.00310 00020  00140  0105 0.6 0 669  0  556   5  93   7 13 0 08790  10180.09000  00640.16880 07150  13070  16130  05320  18810 00530  09010.00310 00020  00120  0109
0.4 1.0   0  750 0 540   6  29   8 74 0 08150  11470.08950  00750.16280 08420  11820  18690  04200  20990 00350 09330.00310 00020  00080  0118 1.5   0  826 0 526   6  64 10 44 0  07560  12700.08890  00870.15680  09680  10620 21210  03220 22950  00220 09570.00300  00020  00060  0121 2.0   0  883  0 615 6  92  1187 0 07130  13620.08850  00970.15220 10710  09710  23200  02540  24350  0015u 09700.00300 00030 00050 0124
0  4 0  636 0 562 5 77 6  69  0 09140  09520.09020  00600.17170  06640  13660  14940  05950  17460  00680 08720.00310 00020  00280  0152 0.6 0 697  0  538 6 03 7 85  0 08700  10400.08970  00690.16680  07530 12780  16680  05170  18960 00540 08970  00310 00020 00240  0159
0.5   1.0   0  803  0  515 6 45 10 10  0 07950  11830.08920  00830.16000 09170  11360 19690  04040  21100  00360  09280.00300  00020 00180  0170 1.5   0  904  0  493 6 96 1272 0 07280  13300.08840  01000.152 11010880 09920 22820  03030  23140 00230 09520.00300  00030 00130  0179 2.0   0  981 0 478 7 30   15 05 0 06780  14400.08780  01130.146l|0 12340  08790 25440 02350  24610 00160 09670.00300  00030  00100 0186
=  0.3   Ob   =   variable   TABLE   8   rA   =  0.6   ru   =   variable
0.4 0 515  0  642   6  08   4.87  0  10410 07950.09100.00450.18830.04790  16270  11690  07820 15090 00850  08610 00660  00040  00000  0008 0.6 0 527 0 641 6 14   5.05 0 10260  08190 09090.00460. 18730.04950.16040.12070 075 30  15560 0 0720  08810  00660 00040 00000  0008
0.1 1.0   0  544 0 640   6  23 5.30 0 10050 08530.09070.00480.18590.05180.15700.12620  07120  16240 00550  09080 00660  00050 00000  0008 1.5   0  557  0  638   6   31 5.51 0  09880 08820.09060.00500.18470.05370.1543 0.13070  06790  16790  00420  09300 00660  00050  00000 0008 2.0 0 566 0 637   6  36 5.65 0 09770 09010.09050.00510.18400.05510.15240.13380 06560 17160  00340  09430 00660  00050  00000 0008
0.4   0  549  0  634   6  24   5.39   0  10090  08510.09070.00490.18580.05230.15710.1269 0 07190  16190  00740 08770  00660  00050  00020  0030 0.6   0  573  0  631   6  38   5.80   0 09820  08970.09050.00520.18380.05570.15240.13470 06660  17100  00590 09 020  00660  00050  00020  0031
0.2   1.0   0  609  0  625   6   58 6.41   0 09420  09660.09020.00570.18080.06090.14550.14670 05870  18450  00390 09350  00650  00050 00010 0032 1.5 0 639  0  620   6   76 6.97   0 09070  10270.09000.00620.17820.06550.13950.1573 0  05200  19620  00250 09540  00650  00060 00010  0032 2.0   0  661 0 617   6  89   7.37   0  08840  10680.08980.00650.17640.06880.13530.16480 04740  20440  00710  09710  00650  00060  00000  0033
0.4   0  578  0  623   6  38 5.92   0 09890  08880.09050.00530.18390.05600.15290.1347 0 06820  16880  00730  08770  00660 00050  00070  0063 0.6   0  615  0  615   6  58   6  58  0 09520  09520.09020.00580.18100.06120.1464 0.14640  06120  18100  00580  09020  00650 00060  00060  0065
0.3 1.0   0  672  0  604   6  90   7  68  0 08960  10540.08980.00660.17640.06970.13600.16530 05050 20020  00380  09360  00650  00060 00040  0068 1.5   0  723  0  595   7  20 8 75  0 08450  11470.08940.00740.17210.07780.12650.1830 0 04110  21720  00240 09590 00650  00070  00030 0070 2.0   0  760 0 587 7 42 9 60 0  08100  12130.08910.00800.16890.08390.11960.19630 03450  22950  00160  09720  00640  00080  00020  0072
0.4   0  603  0 609   6  48   6  41  0 09770  09100.09040.00560.18250.05890.15020.1402 0  06630  17150  00740 08730  00660  00050 00160  0104 0.6   0  652  0  597   6 74 7  36  0 09340  09870.09000.00620.17890.0657 0.14220.15500 05850  18520  00590  08980  00650 00060 00130  0109
0.4 1.0   0  731  0  579   7 17   9 06  0 08660  11160.08940.00740.17270.07770.12890.1803 0  04630  20720  00390  09310 00650  00070  00090 0117 1.5   0  805  0  563   7  61   10 87  0 08030  12370.08880.00870.16670.08980.11620.2053 0 03570 22710  00250 09550 00640  00080  00070  0120 2.0   0 860 0 552 7 95 1239 0  07560 13290.08830.00970.16190.09960.10640.2252 0  02820 24140  00170  09690  00640  00090  00050  0123
0.4   0  620  0  593   6 55 6 88  0 09730  09220.09020.00590.18200.06070.14850.1433 0 06530 17140 00750  08690  00660  00050  00300  0151 0.6   0 680 0  577   6  85 8  07  0 09250  10070.08980.00670.17740.06900.1392 0.16030 05690  18660  00600  08940  00650  00060 00260 0158
0.5 1.0   0  784  0  551   7  35 1047  0 08480  11500.08900.00820.1697 0.08420.12410.19010 04460  20830 00400  09260 00640 00080  00200 0168 1.5 0 880 0 528   7  96 1322 0 07740  12920.08830.01000.16220.10070.10880.2212 0 03370  22880 00260  09500 00640  00090  00140 0178 2.0   0  957  0  512 8 40 1565 0  07160 14050.08750.01140.15590.11460.09660.2473 0 02610  24400  00180 09660  00630  00100 00110 0185
OA   = 0.4   (Ib   =   variable   TABLE   9   rA   =  0.6   rb -   variable
0.4   0  500  0  681 6.78   4  97 0 10800  07780 09050  00460.19210  04520 17200  11310 08380 14870  00910 08580  01110 00100 00000 0008 0.6   0  511  0   680 6.85 5 15 0 10640  08030 09040  00470.19170  04720 16950  11680 08070  15350 00780  08790  01100 00110 00000  0008
0.1   1.0   0  528  0   678 6.96   5 41  0  10420 08360 09030 00490.19020  04960  16600 12230 07630  16020 00590  09070  01100  00110  00000  0008 1.5 0  541 0 677   7.05   5  63  0  10240 08650 09020 00510.18900 05130  16310 12670 07240  16590  00450 09280  01100  00120  00000  0008 2.0 0 550  0  676 7 11 5  78  0  10120  08840  09010 00530.18830  05260  16120  12980 06980  16950 00370  09420  01090  00120  00000 0008
0.4 0  533  0  673 6 97   5  52  0  10470  08330  09030 00500.19000  04941016610  12290 07710 15970  00800  08750 01100  00110  00020  0030 0.6   0  556  0  669   7 13   5  93  0  10180  08790  09010 00530.18810  05320  16130  13070 07150  16880 00640 09000  01090  00120  00020  0031
0.2   1.0   0  591  0  663 7  36   6  57 0 09750  09490  08980  00580.18490  05840 15400  14260 06300  18250  00420  09340  01090  00130  00010  0032 1.5   0  621  0  657   7  57   7  15  0 09380  10090  08950  00630.18230  06270  14770  15300  05560  19440 00270  09560  01080 00140 00010 0032 2.0   0  641  0  654   7  72   7  58  0 09140  10500  08930 00670.18040 06600  14320  16050  05050  20260 00180 09710  01080 00150  00010  0033
0.4   0  561  0  660   7  13   6  06  0  10260  08700  09010  00540.18820  05340  16180  13060  07320  16660 00790  08750  01100 00120  00070  0063 0.6   0  597  0  652   7  36   6  74  0 09870  09340  08980  00590. 18520  05850  15500  14220 06570  17890  00620  09000  01090 mi 3 0  00060 0065
0.3   1.0 0  652  0  640   7  73   7  88  0 09280  10350  08930  00680.18020  06690  14410  16090 05430  19820  00410  09340  01080  00150  00040  0068 1.5   0  701  0  629   8 08   9  01  0 08740  11290  08880 00760.17600  07470  13410  17850  04410  21550  00260 09570 01070  00170  00030  0070 2.0   0  737  0  621   8  34   9  89  0 08370  11950  08840 00820.17270  08070  12680  19180  03700  22800 00170  09720 01060  00190  00020 0072
0.4   0  584  0  645   7  24   6  56  0  10130  08910  08990 00570.18700  05620  15900  13590  07120  16920  00800  08700 01100 00130 00170  0104 0.6   0  632  0  632   7  54   7  54  0  09680  09680  08950  00640.18310  06290  15060  15060  06290  18310  00640  08950  01080  00140  00140  0108
0.4   1.0 0  708  0  612   8  04   9  30  0  08960  10950  08880  00760.17670 07490  13670  17560  05000  20490  00420  09290  01070  00170  00090  0117 1.5 0  780  0  595   8  55  11 20  0 08290  12170  08820  00890.17050 08640  12330  20070  03850  22540  00270  09530  01050  00200 00070  0120 2.0   0  833  0  583   8 95   12 79  0  07800  13100  08760  01000.16550 09610 11300  22050 03050  23990  00180  09680 01040.00220  00050  0123
0.4   0  602  0  628   7  33   7  03  0  10080  09010  08970  00600.18620 05830  15730  13900  07030  16900  00820  08650 01090.00140  00320 0150 0.6   0  660  0  611   7  65   8  29  0 09560 09850 08920  00680.18130 06630  1475015570 06180 1 8400 00650.08900  01080.00160.00270  0157
0.5 1.0   0  759  0  583   8  28  10 80  0  08740  11280  08830  00840.17380 0809013170 18530  04820  20610  00430 09240  01070  00190  00200 0167 1.5   0  851  0  557   8  92   13 68 0  07960  12720  0875001020.16570  09700 115502165003640 22690 00280  09480  01040 00220  00160  0178 2.0   0  926  0   541 9  48   16 30 0 07380  13880 0867|001180  15900  11050  10270 24250  02830 242010 00190 09640 0102|0.00250 00120 0185
PA.GE   7
   t  e    d   o   n
   2    0    1    5
   8    G    M    T
   d    l  e
 
   i  n  ,
   d
   t .   o   r  g
  u   s   e
Right Haunch   Carry-over
Factors Stiffness Factors
HaunchLoadat
Left
"a    | Cba   Mab   I Mba    | Mba Mab   I   1w-   \Mba
Cab   Mab   Mba   Mab   Mba Mab Mba Mab Mba Mab Mab
  «   =   0.3   ob   =   variable   TABLE   13   r,   = - - 1.0   rb   =   variable
0.4   0506   0702   703   507 0.1147 00746 009410.00290.20690.03920.1824 010790.08840.14630.0096 00856 000690.00030.00000.0008    0 6   518   0701   711   825 0.1131 00769 009400.00300.20600.04060.1799  011150.08520.15100.00820.0876 000690.00030.00000.0008
0.1   1.0   0534   0699   723   652   0.1108 00803 009390.00310.20470.04250.1764 011680.08060.15780.00630.09050.00690.0003  00000   00008 1.5   i   °547   0698   733   675 0.1090 00831 009380.00330.20360.04410.1735  012120.07700.16340.00480.0927 0.0068 000030.00000.0008 2.0 .656   740   691 0.1078 00849 00938 000330.20290.04530.1715  012420.07460.16720.00390.09410.00680.00030.0000   0 0697 0.0008
.639 .693 28   664   0.1113 00799 00939 000320.20460.04290.1765  011740.08150.15730.00840.08730.00680.0003000020. 00300.4   0 0   7    0 6 0563   0689   742   606 0.1084 00844 00938 000340.20280.04580.1716 012490.07560.16640.00670.08980.00680.00030.00020.003i
0.2   1.0   0598   0683   768   673 0.1042 00911 00936 000370.20000.05020.1643 013650.06690.18010.00440.09320,00680.00040.00010.0031 .678   7 7   00970 00934 000400.19750.05420.1579 14671.5   0628   0   92 33 0. 100 4   0   0.05940.19200.00290.09560.00680.00040.00010.0032
.649 . 674 08   777 0.0980 01010 0932 000420.19570.05710.15342.0   0   0   8   0   015410.05420.20030.00190.09700.00680.00040.00010.0032
568 .661   743   619   0.1093 00834   00938 000340.202S0.04600.1722 012480.07740.16400.00840.08720.0068 0.00630.4   0 0   0.00030.0008 0.6   0604   0672   768   690   0.1054 00896 00936 000380.20020.05050.1653 013600.06970.17640.0066  008980.00680.0004  000060.0065
0.3   1.0   0660   0660   810   810   0.0994 00994 00932 000430.19580.05780.1543 015430.05780.19580.00430.09320.00680.00040.00040.0068 1.5   0710   0649   849   928   0.0940 01085   00929 000490.19170.06480.1442 017160.04730.21330.00270.09570.00680.00050.00030.0070
746   .642   879   .22   0.0903   1149 00927 000530.18860.07020.1366   0.0399   2 0   0 0   10   0   01846   0.22590.00180.09710.00670.00050.00020.0071
0.4   0692   0666   755   671   0.1081 00854 00937 000360.20160.04840.1693 012990.07540.16660.00850.08670.00680.00040.00180.0103 0.6   0640   0652   788   773   0.1035 00928 00934 000410.19820.05430.1609 014410.066 90.18020.00680.08930.00680.00040.00150.0108
0.4   1.0   0717   0632   848   958 0.0963 01050 00929 000490.19240.06460.1468 016850.05330.20270.00450.09270.0068 0.00050.00100.0116 15   0789   0615   903   11 58 0.0896 01168 00925 000570.18660.07510.1332  019310.04130.22310.00290.09520.00670.0006 0.00080.0119 2.0   0843   0603   950   13 28   0.0846 01258   00921 000640.18200.08380.1226 021270.03290.23790.00200.09670.00670.00070.0006 0.0123
0.4   0609   0648   762   718   0.1077 00867 00936 000380.20150.05010.1674  013290.074 80.16670.00860.08620.00680.00040.00320.0149 0.6   0669   0630   800   860   0.1024 00944 00932 000440.19670.05700.1678 014890.065 50.18170.00690.08880.00680.00040.00280.0156
0.5   1.0   0766   0603   874   11 12   0.0943 01085   00926 000550.18990.07030.1414  017790.051 50.20360.00460.09220.00670.0005 0.00220.0167 1.5   0861   0578   950   14 15   00863 01219 00920 000660.18210.08430.1251 020840.03920.22450.00300.09470.0067 000070.00160.0177 2.0   0930   0560 10  16   16 90   0.0803 01329   00915 00076 017600.09680.1122 023390.03060.23990.00210.09630.00660.00080.00130.0184
= 0.4   as   =   variable   TABLE   14   rA   =   1.0   ra   =   variable
0.4   0485   0764   825   523   0.1213100718 00937 000300.21360.03580.1982 010160.0979|0.14260.01070.08510.0118l000070.00000.0008 0.6   0496   0763   840   543   0.1196 00742 00936 000310.21320.03710.1956  010520.0945|0.14740.00920.08730.0118 00007 000000.0008
0.1   1.0   0512   0761   861   572   0.1172 00775 00935 000320.21180.03890.1919  011030.08950.15420.00700.09020.01180.00070.00000.0008 1.5   0525   0760   8S3   597   0.1152 00803 00934 000340.21070.04050.1888  011460.08550.15980.00540.09240.01180.00080.00000.0008 2.0   0533   0758   872   613   0.1139 00821 00933 000350.20990.04150.1867  011750.082 70.16370.00430.09390.01180.00080.00000.0008
0.4   0517   0755   852   584   0.1178 00771 00935 000330.21160.03930.1920  011080.09050.15360.00950.08680.01180.00070.00030.0030 0.6   0540   0750   874   629   0.1147 00815 00933 000350.20990.04200.1869 011820.084 20.16280.00750.08950.01180.00080.00020.0031
0.2 1.0   0574   0743   907   700 0.1100 00882 00931 000390.20700.04620.1791 012950.074 50.17660.00500.0930 0.01170.00080.00010.0031 1.5   0602   0737   936   765   0.1060 00941 00928 000420.20450.05000.1723 013950.066 20.18870.00320.09540.01170.00090.00010.0032 2.0   0622   0733   968   813   0.1033 00981 00927 000440.20260.05270.1674 014680.06050.19720.00220.09690.0116 0.00100.00010.0032
0.4   0544   0740   873   642 0.1156 00805 00933 000350.21000.04220.1874  011800.08610.16030.00940.08670.0118 0.00080.00090.0062 0.6   0579   0731   906   717 0.1116 00866 00931 000390.20720.04630.1803  012890.077 70.17270.00740.08940.0117  000090.00070.0065
0.3   1.0   0632   0717   958   845 0.1050 00963 00927 000450.20270.05330.1685  014680.06460.1924  000490.09290.01160.0010 000050.0068 1.5   0680   0705 1009   973   0,0991 01054   00923 000510.19850.06000.1677  016390.05300.21010.00310.09550.01150.00110.00030.0070 2.0   0714   0696   1047 1074 0.0951  01118   00920 000550.19530.06520.1496  017690.04480.22310.00210.09690.01150.00120.00020.0071
0.4   0567   0723   889   696   0.1143 00824 00932 000370.20870.04440.1843  012280.0S390.16280.00950.08630.01170.00080.00200.0102    0 6   0612   0708   930   804   0.1095 00896   00929,000420.20490.05000.1756  013670.07490.17670.00760.0888 0.01170.00090.00170.0107
0.4   1.0   0686   0686   1002   1002 0.1017 01017 00924 000510.19920.05970.1607  016070.05970.19920.00510.09240.01160.00110.00110.0116 1.5   0755   0667 1075   12 17   0.0944 01136 009181000600.19320.06980.1460  018500.04650.22000.00330.0950 0.01140.0013 000090.0119 2.0   0807   0653   11 34   1401 0.0891 01226   00914 000670.18840.07820.1346  020450.03710.23520.00220.09650.01140.00150.00070.0122
0.4   0586   0703   896   743 0.1137 00834 00930 000390.20800.04610.1824  012550.08330.16270.00980.08580.01160.00090.00360.0148 0.6   0639   0681   943   888   0.1083 00908 00926 000450.20390.05260.1724  014100.07320.17780.00770.08820.01150.00120.00310.0165
0.5   1.0 0731   0653 1037   11  62 0.0994 01050   00920 000560.19650.06520.1551  016980.05780.19990.00520.09180.01140.00130.00240.0165 1.5   0823   0624 1128   14 95   0.0911 01185   00913 000680.18880.07850.1374 019960.04410.22130.00340.09440.01120.00150.00180.0176 2.0   0895   0606  12 10 17 90   0.0847 01295 00907 000790.18230.09060.12330.22510.03460.23710.0024 0.09600.01110.00180.0014 0.0183
OA   =   0.5   as   =   variable   TABLE   15   rA   =   1.0   rn   =   variable
0.4 0.458   0818   956   536   0.1253 00698 00932 000310.21520.03400.2085 009710.10600.13980.0120 0.08460.01710.00170.00000.0008 0.6   0471   0817   967   657   0.1236 00725 00932 000320.21400.0357  02059   010080.10240.14470.01020.08700.01700.00180.00000.0008
0.1   1.0   0489   0816   984   688 0.12150 0757 00931 000330.21290.03780.2023 010570.09750.15120.00770.0899 0.01700.00180.00000.0008 1.5   0499   0814   100 0 6. 11   0.11920 0787 00930 000350.21180.03920.19900. 10990.092 80.16710.00590.0922 0.01690.0019 000000.0008 2.0   0506   0812   10.10   630 0.1175 00805 00928 000370.21150.03960.1968 0.11270.09000.16100.00470.09370.01680.00190.00000.0008
0.4   0488   0807   968   697   0.1214 00753 00929 000340.21310.03710.20210. 10610.09790.15060.01050.08630.0171 0.00170.00030.0030 0.6   0515   0803 10  10   645   0.1183 00795 00928 000360.21100.04040.1969 011360.09170.16000.00830.08920.01700.00180.0002 0.0030
0.2   1.0   0547   0796  10 51   722   0.11380 0865 00926 000400.20790.04480.1890 012450.08090.17400.00560.09280.01680.00200.0001 0.0031 1.5   0571   0786 1090   790 0.1093 00922 00923 000430.20550.04850.18180. 13440.07190.18620.00350.09510.01670.00210.0001 0.0032 2.0   0590   0784   n   17   840   0.10630 0961 30922 000460.20410.05060.17640.14170.06610.19480.00250.09680.0166 0.00220.00010.0032
0.4   0513   0793 10 08   655   0.1191 00786 00928 000370.21110.04000.19740. 11320.09320.15760.01030.0863 0.01700.00180.00090.0062 0.6   0551   0784   10 47   735   0.11500 0848   00926 000400.20830.04460.19010. 1241 008420.16970.00820.08900.01680.00200.00080.0064
0.3   1.0   0603   0766 11 12   874   0.1085 00943   009220.00460.20360.05150.17790. 14140.07030.18990.00550,09260.0167 000220.0005  00067 1.5   0642   0751  11 74   10 08   0.1021 010360. 0917  000530.19950.05810.16650.15830.05760.20790.00350.09530.01650.00240.00030.0069 2.0   0677   0744  12 26 11.16 0. 09770.11000. 09140. 00570.19650.06280.15780.17140.04850.22080.0024 0.09690.01630.00260.00030.0071
0.4   0537   0774 10 30   7. 17   0.1178  0  .
08020. 0927  0  .
 . 0118
2.0 764  0. 13.28 14. 0.1894 0.0161   0   698   56 0.0915 01206   009070. 0070 0.07560.14200.19870.04030.23300.00240.0963 0.00300.00080.0122
   0554   753 7. 0. 0. 0.20870.04420.19240. 12050.08980. 15950.0107 0.01690.0020   3.01450.4   0   10 42 66   0.1170   0811 09260.0040   0.0853   0.0042 0.6   0606   0730   1096   9. 12   0.11150.0889   009220.00460.20450.05060.18200.13600.07910.1738,000860.08780.01670.0022  000363.0152
0.5   1. 0 0. 694  0.   12. 0.   0.1970   0.19700.0057 3.0164694 12 03   03  0.10250. 1025 09150.0057 0.06260.16390.16390.0626 0.09150.01640.00280.0028 1. 5 0. 781 664  13.12   0
 . 0.18910,0759   0.04790.21870.0039   0.00340.00213.0174   0   1547   0.0937 11630.09080.0070 0.14560.1939   0.09400.0160
2. 0 0. 850   642 14.09   0.   00820.18250.0877 0.23480.0027 3.01810. 18 64 0.0870 1275   009010. 0.13070.21930.0376 0.09570.01570.00390.0016
PAGE   9
   t  e    d   o   n
   2    0    1    5
   9    G    M    T
   d    l  e
 
   i  n  ,
   d
   t .   o   r  g
_   u   s   e
Conce ntratedLoad F.E.M.— Coef. X   PL   HaunchLoadat Right
Haunch   Carry-over
Unif.Load b   Left   Right
F.E.M. Coef .  X  wL' 0.1 0.3   0.5   0.7   0 9   F.E.M.
Coef.X   WaL' F.E.M.
Coef.X   WbL'
Cab 1 C ba *ab   \   *n.<   Mab 1Mba   Mab   I  Mba   Mab   I Mba Mab I  Mba Mab   I  Mba MAn   | Mba Mab   I  Mba Mab Mba
OA   =   0.1   Ob
0.4   0.534 0.580   5.12   4.71 0.6 0.546 0.580   5.17 4.87
0.1   1.0   0.563   0.578 5.24   5.11 1.5   0.577 0.577   5.30 5.30 2.0 0.587 0.576 5.34 5.44
0.4 0.569 0.574   5.25   5.21 0.6 0.594 0.570 5.35 5.58
0.2 1.0 0.631 0.566 5.51   6.15 1.5 0 663 0.562 5.64 6.66 2.0   0.685  0.558   5.74   7.04
0.4   0.600 0.564 5.36 5.70 0.6 0.638  0.557   5.51 6.31
0.3 1.0 0.698 0.547   5.75   7.33 1.5 0.750 0.539 5.98 8.33 2.0 0.788 0.532 6.15 9.11
0.4   0.626   0.551   5.44   6.17 0.6   0 677 0.541 5.63   7.05
0.4   1.0   0 760 0.525 5.97 8.63 1.5   0.837 0.511 6.30 10.31 2.0   0.895 0.501 6.56 11.71
0.4 0.645   0.538   5.47 6.59 0.6 0.708 0.523 5.71 7.76
0.5 1.0 0.814 0.499 6.11 10.00 1.6 0.915  0.481   6.57 12.55 2.0 0.998 0.462   6.90   14.90
as   =   variable   TABLE   16   rA   =   15   as   "   variable
.0950 0.0827 0.0852 0.0886 0.0915
0.090510.0934
0.093410.0884 0.09090.0931
0.09040 0.08650 0.08030 0.07450. ,0.07040.
0923 0988 1090 1183 1249
0945 1024 1152 1274 1366
0.09000.0956[ 0.0852 0.0787 0.0720 0.0670I
0. 1045 0.1192 0.1336 0.1448
0.1750 0.1740 0.1726 0.1715 0.1707
0.05360.14590.12390.0691 0.05530.143710.12780.0665 0.057810.1406|0.13350.0628 0.0599I0. 13810.13810.0599 0.061310.13640.14130.0578
0.15470.00740.0865 0.15940.00630.0885 0.16610.00480.0912 0.1715(0.00370.0932 0.17520.00300.0945
0039I0 00420 00480 00540
17070.06230.1368 16790.06790.1307[ 16340.07700.1212 15920.08550.1125 15620.092010.1062
0.1682' 0.1639| 0.1571 0.1498l 0.1428
0.0682 0.0766 0.0928 0.1100 0.1245,
0.1146 0.1030l 0.0941
0.1726 0.1847 0.2036
0.0064 0.0050 0.0033
0  0066 0.0052 0.0035 0.0022 0.0015'
0.0874 0.0898 0.09300 0.0953 0.0967
0.0008 0.0008; 0.0008, 0.00081 0.0008
0.0008 0   0008 0.0008 0 0008 0.0008
0.0000 0.00001 0. 0. 0
0, 0.0008 0 0008 0.0008 0.0008
0.0008  j0.0008
0.00020.0030
.00000
.00000
0006 0.0005
0003 0002
0.0029 0.0025 [0.00191 0.0013| 0.0010
0.0031 0.0032 0.0032 0.0033
aA   =   0.2   as   =   variable   TABLE   17   tb   =   variable
0.4   0  519  0  667   6   39   4  98  0 1119I007540 09610 00190   20270.0406lo17370 mo'o 08280 14820 00900  08570  00320 00010  00000 0008 0.6 0 531  0  666   6 47 6   16  0 11000 07800  09610 00200   20180.04200 17140   11470   08020  15290 00760 08780  00320  00010 00000  0008
0. 1   1.0 0 548  0   664 6 57   8  42 0  10790  08130 09600   00210   20100.04400  16800 12000  07590 15970   00580   09060 00320  00010  00000   0008 1.5 0 562 0  663   6   66 5 64 0 10610 08410 09600   00220 19950.04570   16520 12450  07240 16520  00450   09280   00320  00010  00000   0008 2.0 0 571 0  662   6 72 6 80 0 10500  08590 09600 00220 19880.04690.16330   12760 07010   16900   00360 09420 00320 00010  00000  0008
0.4 0 553  0  659   6   as 6 53   0   10830 08100 09600 00210   20050.04440 16800 12070 07670 15920 00790 08750 00320  00010 00020  0030 0.6   0 578 0  655'   6  74   5 94   0   10560 08540 09590  00220   19870.04730   16340 12830 07110   16820 00630   09000 00320  00010 00020  0031
0.2 1.0   0 614   0 649 6  97   6  59   0  10150 09210   09580 00250   19620.05180  15630   13990   06280   18190   00410 09330 00320 00010 00010 0032 1.5   0 645 0 645 7   17 7 17   0 09800 09800 09570  00270  19360.05580   15020  15020  05580  19360 00270 09570 00320   00010 00010  0032 2.0   0 666 0  641 7  32 7  60   0  09570 10200 09560   00280 19190.05870 14590 15760 0510 0  20190  00180 09710 00320 00010  00010   0033
0.4   0 583 0 647 6   74 6 07   0   10640 08450 09590 00230 19880.04760   16390 12820 07280   16590 00780 08740  00320 00010 00070 0063 0.6   0 620 0 639 6  97 6   76 0 10270  09070 09540   00250 1 9620.05200  15730 13950 06550 17820 00620 09000  00320 00010   00060 0065
0   3   1.0   0 678  0  628   7 33 7  92   0   09700   10040  09560 00290  19200.05940  14670 15790   05420 19750 00400 09340  00320 00010  00040   0068 1.5   0  729  0  618   7 68   9 06   0  09190   10940  09540  00320 18810.06650   13700 17520 04430 21480   00250 09580 00320 00010  00030   0070 2.0   0  766  0  611   7  94   9 96   0 08840   11580 09530 00350   18510.07180 12990 18830 03740  22730 00170 09710 00320 00010 00020 0072
0.4   0 608  0  633   6 88   6  58   0   10520  08650 09590 00240  19760.05000  16110  13330  07090   16850 00790   08700   00320 00010   00170 0104 0.6   0 657  0  621   7   15 7 57   0  10090 09380 09560 00270 19440.0556 0   15300   14770 062 70  18230 00630   08950  00320  0001c  00140 0108
0 4 1.0   0  737  0  602   7 65 9  36   0 09410 10600 09540 00320 18870.0662 0   13950   17230  05000   20450 00420   09280 00320  00010 00090  0117 1.5   0  811  0  586   8  16   11 29   0  08770 11770 09510 00380  18310.07690  12650 19690 03870 22460  00270 09530 00320 00010  00070   0120 2.0   0  867  0  575   8  57   12 93   0  08310   12660 09490 00420   17870.08550  11650  21640 03070  23920 00180  09680  00320 00010 00050 0123
0.4   0 626 0 617   6 93   7 04   0   10450  08770 09580 00250 19710.05210 15930 13600 07060   16850 00800 08660 00320 00010  00330  0149 0.6   0 686  0 600 7 30 8 35   0  09980  09590  09540 00290 19270.05890  14990 15260 06190 18350 00641008900 0032 0 00010   0028,00156
0 s 1.0   0 786 0  571   7   90 10 90   0 09220   10930  09510  00350   18620.07190 13440 18180  04850  20550   0043|009230  00320  00010 00210 0167 1.5   0 883  0   548   8   67 13 85 0 08490 12320  09480   0042|017910.08621011910   2122i003720 22550 00280 09490 003210  00010 00160 0177 2.0 0 963 0   529 9   16 1660   0  07930   13400 09450  00490   17330.09870 1069|02375|00289J024070   0019,009650 00320  00010 00120 0184
aA   =   0.3   as   =   variable   TABLE   18   'a-   1.5   tb   =   variable
0.1
0.2
0.3
0.4 0.6 1.0 1.6 2.0
0.4 0.6 10 1.a 2 0
0.4 0.6 1.0 1.5 20
0.498 0.509 0.526 0.539 0.548
0.531 0.554 0.589 0.618 0.638
0.559 0.595 0.649 0.698 0.733
0.582 0.629 0 705 0.775 0.829
0.600 0.654 0.751 0  843 0.920
0.755 0.754 0.752 0.750 0.749
0.745 0.741 0.735 0.729 0.726
0.732 0.723 0.710 0.698 0.690
0.716 0.701 0.680 0.661 0.648
0.694 0.673 0.642 0.616 0.598
7.95 8.05 8.20 8.33 8.41
8.22 8.43 8.76 9  06 9.27
8.43 8.75 9.28 9.78
5.85 6.31 7.02 7.68 8.17
6.44 7.20 8.49 9.78
0.1187 0.1147 0.1085 0.1028
0.0961 0.0960| 0.0959 0.0958
0.00180.223310.03170.20050.099810.0978,0.14210.01070.0851 0.0019 0.2225;0.03290. 19800. 1033'0.094410. 146910.0091l0.0872| 0.0020'0.221310.03450.19430.10830.08950.15380.00700.0901 0.00210 .22030.03590.19130. 11250.08550.1592:0.0054:0. 09241 0.00 21:0.2197,0.03690. 18930.11540. 0828;0.16310.0043,0.0938
0.095710.0026 0.09550.0031 0.09510.0037 0.094910.0041
|0.0948I0.0042|0.2009 09440.00480.1955,
0,00710.0002 0.00700   0003
0.08341 0.07341 0 0581 0.0448 0..03530
0 1620 0.1769 0.1995 0.2200
2359
0.0857| 0 0 0
0.0070 0.0070 0.0070
   00000   00008    00000   00008    00000   00008    00000   00008    00000   00008
   00002   00030    00002   00031    00001   00031    00001   00032    00001   00032
   00009   00062    00007   00065    00005   00068    00003   00070    00002   00071
   00020   00102    00017   00107    00011   00115    00009   00119    00007   00122
   00036   00147    00031   00154    00024   00165    000180 0175    00014   00182
PAG   E 10
   t  e    d   o   n
   2    0    1    5
   9    G    M    T
   d    l  e
 
   i  n  ,
   d
   t .   o   r  g
  u   s   e
Haunch   Carry-over
F.E.M. Coef.  X tat' 0.1   0.3   0 5   0.7   0.9
  F.E.M. Coef.X   WaV
F.E.M. Coef.X   rFflL'
tiA   =   0.4   as   =   variable   TABLE   19   -   1.5   ra   =   variable
Mab |  Mba Mab   |  Mba Ma b Mba   Af^s Mba   ^«   | MM   Mab I  Afua Mab I  Mba Mab M ba
bL
he
B
All   carry-over factors and fixed end   moment coeffici entsare negativeand all stiffnessfactorsare positive.
0.4 0  472   0 842 9  79   5  49 0 13390 06640  0959|0  00190  2330*002730 22380 09080   11210 13680 01240 08440 01210   00050 00000 0008 0.6   0  483  0  841   9 93 5   71 0 132 10 06870  09590 00200   23230 02830 22110   09411010820 1415I001060 08670 01210   00050 00000 0008
0.1   1.0   0  499   0 839 1014   6  03   0   12960 07190 09580 00210 23120   02980  21720  09900 10280  14841000810 08970 01210 00060 00000   0008 1.5   0 511 0  837   10 3 1 6 30  0 12740 07450 09570   00210   23020   03101021410  10301009830  1540000620   09200 01210   00060 00000 0008 2.0   0  520  0  835 1042 6  48   0  12600 07630 09570   00220 22950 03190 21190   10570 09520   15790  00500 09350  01210 00060  00000  0008
0.4   0  503  0 831   10 1 5 6 16   0 13030   07130   09580 00210 23110  0300021740 0994010390 14760 01100 08620  01210 00060  00030 0030 0.6 0  526  0  826   10 4 4 6 64   0 12700   07560  09570  00220  22950  03220  21210   10620  0968'0  15680 00870   08890  01210 00060   00020   0030
0.2   1.0   0  558  0   818 1089   7 43   0  12200  08200  09550 00250   22690 03560   20400  11690 08610  17090 00580   09250  01200 00070   00020 0031 1.5   0  586  0 811   11 29 8   16 0 11770 08770 09530 00270  22460  03870   19690   12650 07690  18310 00380 09510  01200  00070 00010  0032 2.0 0 606 0  806   11 58 8  70   0   11490   09160 09520 00280 2229o  04090   19180   13340 0 7040   19180 00260 09670  01190  00080  oooi 0  0032
0.4   0  530 0  815   10 43 6  78   0   12800 07440  09570   0022022960 03230   21290   10590   09920  15420 01090  08610  01210  00060   00100 0062 0.6   0  563 0  805   10 87   7  61   0   12370   08030 09550 00250  22710 03570  20530   11620 08980   16670  00870  08880  01200 00070  00080 0064
0.3   1.0   0  615 0 789   11 58   9 03   0 11680   08960 09520 00290  22310 04130   19310  13320   07510  18660 00570 09250  01190 00080 00060 0067 1.5   0 661  0  775   1227   10  47 0 1106:009830  09490  00330   21920 04680 18160 14950 06210 2048J000370 09510  01190   00090 00040 007 0 2.0   0  695  0  766   12 80   11 62 0   10620 10460 09470 00360 21630  05110   1730,016211005270 21810  00250 09670  01180  00100  00030 0071
0.4   0  551  0  796   10 64   7 38  0 12680 07610  09560 00240  22850 03411020990   11040   09690 15660 0 1110  08550  01200 00070 00240  0101 0.6   0  595  0  780   11 20 8   55 0 12170 08290 09530 00270  22540 03850  20070   12330  08640   1705'000890   08820 01200 00070 0020'00105
0.4   1.0   0 667 0 755   12 17 10 75   0 11360  09440 0950,0 00330 22000 04650 18500  14600   06980 1932|000600 09180   01190 00090  0013.00114 1.5   0 733 0 733   13 18   13  18 0 10580 10580 09460   00390 21450   05480 16940 16940  05480 21450 00390 09460   01180 00110  00110  0118 2.0   0 783  0  718   1400   16 28   0   10010 11450  09420  00440 21000  06180   15710 18850 04410  23020  00270  09620 01170  00120 00080  0121
0.4   0   568 0   771 1080 7 85   0  12620 07710  09550 00260  22800 03560 20800 11280 09590   15610 01130   08490 01200   00070 00420 0145 0.6   0 619 0 749   11 41   9 43   0   1206,008430 09520   00300 22400   04090   19750   12750 08480 17110 00910  08760 01190   00090 00360 0152
0.6 1.0   0  710  0  717   1260  12 50   0   1117|009710  09480 00370 217 80 05060 17920   15430 06770 19410   00620  09110 01180   00100 00270  0163 1.5   0  797  0   683 1392   16 23 0 10240 11080  09420  00450 21070 06190 16050.18320   05230   21530   00410  09400 01170  00120 00220  0173 2.0 0  868 0 661   15 05 19.70  0  09610 12120 09370 0 0520   20470  07200 14520.20810 04140 23160  00290   09570   01160 00150 00160 0180
oa   =   0.5   as   =   variable   TABLE   20   rA   = &nb