t e d o
n
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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
P u
i n ,
d
t . o
r g
u s e
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
concrete.
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
very large proportion of all port land
cement used in these
two countries. A current list of member
companies will be
furnished on request.
COPYR1GHT,l»47bY PORTLaNDCEMENTaSSOC1aT1ON
t e d o
n
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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
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P u
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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
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6 G M
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d l e
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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
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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