CONTINUOUS INFLUENCE LINES F O R . SPAN MOMENTS.

BEAM OVER INFINITE NUMBER OF ELASTIC SUPPORTS.

APPENDIX C

8

i 7 6

I i

5

*r- -

4

I

' 3

J

2

>

1

0

1

0

m

1

_

2

3

e

4

I

in

t

6

t \

7 8 J

ORDINATES FOR BENDING

T MOMENT j - AT SECTION m - m DUE TO A LOAD P = l AT ANY ARBITRARY SUPPORT.

tf 0 8

OO

0.02 0 .04 0 .06 0.08

+ 0 .01321 + 0 .02313 + 0 .03130 + 0 .03839

- 0.01465 - 0. 02333 - 0.02917 - 0. 03344

+ 0. 00125 - 0 . 0 0 0 8 7 - 0 . 0 0 3 8 3 - 0 .00700

+ 0.00024 + 0 .00102 + 0 .00150 + 0 .00149

- 0 .00006 0. 00004 + 0. 00029 + 0. 00068

0 0.00004 0.00010 0.00002

+ 0.00001 - 0 . 0 0 0 0 5

0 0. 00001

0. 1 0. 2 0. 3 0. 4

+ 0.04468 + 0 .06902 + 0.08713 + 0. 10188

0.03674 0 .04 538 0. 04835 0. 04 903

0. 01015 0. 01628 0.03450 0. 04268

+ 0 .00122 + 0 .00495 - 0 . 0 0 8 1 6 - 0 .0 1384

+ 0. 00 155 + 0.00198 + 0. 00 148 + 0. 00005

+ 0.00009 + 0.00100 + 0.00187 + 0.00237

- 0.00007 + 0.00010 + 0.00062 + 0.00122

- 0 .00002 - 0 .00009

0 + 0 .00023

0 0. 00004 0.00010 0. 00010

0. 5 0 .6 0. 7 0.8 0 .9

+ 0. 11450 + 0. 12559 + 0. 13555 + 0. 14459 + 0. 15297

0.04858 0.04 743 0.04591 0.04417 0.04 198

0. 04932 0.05473 0.05593 0 .06311 0. 06640

- 0.01935 - 0. 02454 - 0.0294 1 - 0 .03395 - 0 .03819

- 0 . 00196 - 0.00428 - 0.00681 - 0.00943 - 0 . 0121 -

+ 0.00248 + 0 .00226 + 0. 00 1 78 + 0.00107 + 0.00019

+ 0.00180 + 0 .00227 + 0.00262 + 0.00286 + 0 .00297

+ 0.00057 + 0.00096 + 0.00136 + 0.00175 + 0.00211

- 0. 00002 + 0. 00023 + 0.00034 + 0 .00052 + 0. 000 77

1. 0 1. 5 2 .0 3. 0 4. 0

+ 0. 16073 + 0. 19322 + 0. 21895 + 0. 25930 + 0. 29104

- 0.04018 - 0. 02944 - 0. 01876 + 0. 00 107 + 0.01881

0. 06923 0. 07881 0. 08383 0. 08 748 0. 08705

0.04216 0.05860 0. 07094 0 .08821 0.09957

0.01478 0 .02771 0.03933 0.05869 0. 07298

0.00080 0. 00715 0.01436 0.0288 1 0. 04215

+ 0.00297 + 0.00166 - 0.00115 - 0. 00889 - 0 .01764

+ 0.00242 + 0 .00340 + 0 .00333 + 0.00092 - 0 . 0 0 3 2 8

+ 0. 001 10 + 0 .00243 + 0. 00340 + 0. 00396 + 0 .00300

5. 0 6. 0 7.0 8. 0 9. 0 10.0

+ 0. + 0 + 0. + 0. + 0

31756 34052 36139 37926 39604

+ 0. 41 154

+ 0. 03484 + 0 .04947 + 0 .06347 + 0 .07552 + O. 08728 + 0 . 098 3 5

0. 08469 0. 08 130 0.07733 0. 07302 0. 06855 0. 06394

0. 10751 0. 1 1315 0. 11722 0. 12014 0. 12221 O. 12362

0. 08641 0. 09665 0. 10526 0. 11257 0. 11855 0. 12430

0.05413 0.0648 5 0.07448 0.08317 0.09103 O.09820

- 0 .02651 - 0.03512 - 0.04335 - 0. 05117 - 0.05856 - 0. 06555

- 0. 00839 - 0. 01395 - 0. 01970 - 0 .02549 - 0 .03123 _ O. 03 688

0. 00099 0.00174 0. 00497 0 .00849 0.01223 O. O1610

TABLE 2 INFLUENCE LINES FOR SUPPORT MOMENTS.

CONTINUOUS BEAM OVER INFINITE NUMBER OF ELASTIC SUPPORTS.

APPENDIX C

to CO

0* 0. 02 0. 04 0 .06 0. 08

0. 1 0. 2 0. 3 0. 4

0. 5 0. 6 0. 7 0. 3 0. 9

1. 0 1. 5 2. 0 3. 0 4 .0

5. 0 6. 0 7. 0 8. 0 9.0

10. 0

TABLE 2 INFLUENCE LINES FOF

CONTINUOUS BEAM OVER INFINITE

Tff

3 8 7 6 5 4 3 2 1 0

t ^ ^ ^ ^ ^ ^ ^ X . 1 . e E i. |. 1 . I * C ?

ORDINATES FOR BENDING MOMENT -M_ AT SUPPORT 0 I

0 + 0.05763 + 0.08919 + 0.11111 + 0. 12800

+ 0. 14183 + 0. 18859 + 0.21870 + 0.24142

+ 0. 25989 + 0.27556 + 0. 28924 + 0. 30143 + 0. 31245

+ 0. 32254 + 0.36346 + 0. 394 70 + 0.44218 + 0.47857

+ 0. 50847 + 0. 53406, + 0.55656 + 0. 57672 + 0. 59502 + 0.61185

I - 0 .03121 - 0.04294 - 0 .04850 - 0.05128

- 0. 05257 - 0 .05056 - 0 .04445 - 0. 03 766

- 0 .03090 - 0.02438 - 0 .01814 - 0 .01225 - 0 .00651

- 0. 00108 + 0 .02297 + 0 .04319 + 0.07641 + 0. 10351

+ 0. 12664 + 0. 14698 + 0. 16522 + 0 . 18180 + 0. 19706 + C .21122

2 + 0 .00191 - 0 .00361 - 0 . 0 0 9 8 5 - 0 . 0 1 5 6 6

- 0. 02091 - 0 .04019 - 0.05224 - 0 .06040

- 0. 06625 - 0 .07049 - 0 .07368 - 0 .07609 - 0. 07791

- 0 .07927 - 0.08184 - 0 .08071 - 0.07428 - 0.06588

- 0 .05697 - 0.04804 - 0 .03927 - 0.03075 - 0 .02250

0.01452

3 + 0 .00060 + 0 .00187 + 0 .00219 + 0 .00166

+ 0 .00061 - 0 . 0 0 7 6 4 - 0 .01665 - 0 .02496

- 0 .03238 - 0 .03897 - 0 .04486 - 0 .05013 - 0 .05489

- 0 .05919 - 0 .07577 - 0 .08695 - 0. 10068 - 0. 10822

- 0. 11241 - 0. 11456 - 0 .11538 - 0 .11529 - 0. 11456

0. 11335

4 - 0. 00011 + 0. 00017 + 0. 00080 + 0.00133

+ 0.00182 + 0.00226 + 0.00034 - 0 . 0 0 2 7 2

- 0.00631 - 0.01010 - 0.01395 - 0.01776 - 0. 02149

- 0.02512 - 0.04142 - 0.05492 - 0.07573 - 0.09092

- 0. 10261 - 0. 11174 - 0. 11905 - 0. 12499 - 0. 12986 - ) . 13389

SUPPORT NUMBER OF

1 2

k. 4 i I

MOMENTS. ELASTIC

3 4

x k \ I

SUPPORTS.

5 6

/rfff frf/f

*

DUE TO A LOAD P = |

5 0

- 0 .00009 - 0. 00023 + 0. 00004

+ 0 .00027 + 0 .00170 + 0 .00262 + 0 .00281

+ 0 .00240 + 0.00154 + 0 .00034 - 0 .00109 - 0 .00271

- 0. 00444 - 0 .01399 - 0 .02373 - 0 .04165 - 0. 05704

- 0 .07021 - 0 .08156 - 0 .09146 - 0. 10015 - 0. 10785

0. 11471

6

0 + 0 .00003 - 0 . 0 0 0 0 9

- 0 .00010 - 0 . 0 0 0 3 1 + 0 .00112 + . 0 .00192

+ 0 .00256 + 0 .00298 + 0 .00321 + 0 .00323 + 0 .00309

+ 0 .00280 - 0 . 0 0 0 3 1 - 0 . 0 0 4 9 8 - 0 . 0 1 5 9 6 - 0 .02726

- 0 .03805 - 0 .04814

' - 0 .05751 - 0 .06618 - 0 .07422

0.08168

I

APl'ENUDC C

7 8 9 X X X

I e I

AT ANY ARBITRARY SUPPORT.

7

0 - 0. 00002

- 0. 00004 - 0 .00010 + 0 .00011 + 0. 00052

+ 0. 00103 + 0 .00155 + 0 .00203 + 0 .00249 + 0 .00286

+ 0. 00314 + 0 .00363 + 0. 00268 - 0 . 0 0 1 8 1 - 0 . 0 0 8 0 3

- 0 .01496 - 0. 02209 - 0. 02920 - 0 .03616 - 0 .04291

0 .04941

8

0

0 - 0 .00007 - 0 .00012 - 0 .00006

+ 0 .00011 + 0.00037 + 0.00068 + 0.00100 + 0.00135

+ 0 .00169 + 0.00317 + 0 .00397 + 0.00364 + 0.00148

- 0 .00182 - 0. 00580 - 0 .01019 - 0 .01482 - 0 .01956

0.02434

9

0 - 0 .00001 - 0. 00008 - 0.00013

- 0.00014 - 0. 00008

+ 0.00014 + 0-. 0003 1

+ 0 .00050 + 0.00168 + 0.00283 + 0.00428 + 0.00453

+ 0 .00379 + 0 .00231 + 0.00025 - 0 . 0 0 2 1 7 - 0 . 0 0 4 90 - ( J.007B5

U l _ l _ _

CONTINUOUS

6 5 4

INFLUENCE LINES FOR REACTIONS BEAM OVER INFINITE NUMBER OF ELASTIC SUPPORTS.

3 2 I O I 2 3 4 5 6

APl'KNDIX C

I X I I

T T+.

i 7T T7l

I TT- yTftr 7*^9 T&

I I I > J

I -rr rT^

I -rr ~r*

I 7 T Tr~

I TT TTJ

I -rr T f

I -rr -rrt

I rr *?

1 I J

I

ORDINATES FOR REACTION AT SUPPORT Q DUE TO A LOAD P = | AT ANY ARBITRARY SUPPORT.

t 0 8 0. 02 0.04 0.06 0. 08

+ 0 . 8 2 2 3 2 + 0. 73571 * 0 . 68078 + 0. 6 4 1 4 4

+ 0 . 12196 * 0 . 17146 + 0 . 19826 + 0 . 2 1490

0. 0 3 4 4 3 0. 0 3 3 8 5 0. 0 2 6 6 1 0 . 0 1 8 3 0

+ 0.00060 - 0 . 0 0 7 1 8 - 0 . 0 1 3 4 3 - 0 . 0 1 7 6 5

+ 0 . 0 0 0 8 2 + 0 . 0 0 1 4 4 + 0 . 0 0 0 3 6 - 0 . 0 0 0 9 6

- 0. 00011 + 0. 0 0 0 3 5 + 0 . 0 0 1 2 9 + 0. 0 0 1 1 6

- 0.00009 - 0.00029 + 0. 00020

+ 0.00003 -0.00005

0 0

- 0.00002

0. 1 0. 2 0. 3 0.4

+ 0. 61 120 + 0 . 5 2 1 7 0 + 0 . 4 7 3 6 8 + 0 . 4 4 1 8 3

+ 0 . 2 2 6 0 6 + 0 . 2 4 9 5 1 + 0 . 2 5 5 3 7 + 0 . 2 5 6 3 4

- 0 . 0 1 0 1 3 + 0 . 0 2 2 1 9 + 0 . 0 4 3 3 7 + 0 . 0 5 8 1 9

- 0 . 0 2 0 3 2 - 0 . 0 2 2 6 6 - 0 . 0 1 8 5 3 - 0 . 0 1 3 2 1

0 . 0 0 2 7 6 0 . 0 1 0 4 6 0 . 0 1 4 7 1 0 . 0 1 6 7 0

+ 0. 001 18 - 0 . 0 0 0 8 3 - 0. 00379 - 0. 0 0 6 4 2

+ 0 . 0 0 0 4 3 + 0 . 0 0 0 9 8 + 0 . 0 0 0 5 0 - 0 . 0 0 0 5 0

- 0. 00002 + 0.00044 + 0.00078 + 0.00082

- 0 . 0 0 0 0 4 + 0 . 0 0 0 0 3 + 0. 0 0 0 2 7 + 0 . 0 0 0 5 1

0. 5 0. 6 0. 7 0 . 8 0 . 9

+ 0 . 4 1 8 4 2 + 0 . 4 0 0 1 3 + 0. 3 8 5 2 4 + 0 . 3 7 2 6 4 + 0 . 362C3

+ 0 . 0 2 5 5 5 + 0 . 2 5 3 8 2 + 0 . 2 5 1 8 4 + 0 . 2 4 9 9 8 + 0 . 2 4 7 5 6

+ 0 + 0. + 0 + 0 + 0.

06916 07763 08436 08980 09443

- 0 . 0 0 7 7 7 - 0. 0 0 2 6 5 + 0 . 0 2 0 9 0 + 0 . 0 0 6 4 1 + 0 . 0 1 0 3 8

0. 0 1 7 3 6 0 . 0 1 7 2 3 0. 0 1 6 6 2 0 . 0 1 5 7 1 0 . 0 1 4 6 2

0. 0 0 8 5 5 0. 0 1 0 1 9 0 . 0 1 1 0 8 0. 0 1 2 3 5 0. 0 1298

- 0.00169 - 0.00288 - 0.00405 - 0. 0 0 5 0 6 - 0. 0 0 6 0 2

+ 0 . 0 0 0 6 0 + 0 . 0 0 0 2 5 - 0 . 0 0 0 1 7 - 0 . 0 0 0 7 5 - 0 . 0 0 1 2 9

+ 0.00067 + 0.00074 + 0.00067 + 0.00062 + 0.00047

1. 0 1. 5 2 . 0 3. 0 4. 0

+ 0.35276 + 0. 31901 + 0.29700 + 0. 26847 + 0.24988

+ 0 . 2 4 5 4 3 + 0 . 2 3 5 6 9 + 0 . 2 2 7 6 0 + 0 . 2 1 5 0 7 + 0 . 2 0 5 6 8

+ 0 . 0 9 8 2 7 + 0 . 11087 + 0 . 11766 + 0 . 12430 + 0 . 12705

+ 0 . 0 1400 + 0 . 0 2 8 2 9 + 0 . 0 3 8 2 6 + 0 . 0 5 1 3 5 + 0 . 0 5 9 6 4

- 0. 01340 - 0 . 0 0 6 9 2 - 0 . 0 0 0 8 4 + 0. 0 0 9 1 2 + 0 . 0 1 6 5 7

- 0. 0 1 3 4 4 - 0. 0 1 3 7 5 - 0. 01243 - 0. 00838 - 0. 00409

0. 0 0 6 9 0 0 . 0 0 9 7 3 0. OHIO 0 . 0 1 1 5 3 0 . 0 1 0 5 6

0 . 0 0 178 0 . 0 0 4 4 1 0 . 0 0 6 3 7 0 . 0 0 8 7 1 0 . 0 0 9 7 2

+ 0.00026 - 0 . 0 0 1 0 3 - 0 . 0 0 2 4 3 - 0 . 0 0 4 8 1 - 0 . 0 0 6 4 6

5. 0 6.0 7-0 8.0 9.0

10. 0

+ 0 . 2 3 6 3 3 + 0 . 2 2 584 + 0 . 2 1 7 3 0 + 0 . 2 1 0 1 6 + 0 . 2 0 4 0 8 + 0 . 19875

+ 0 . 19823 + 0. 19206 + 0 . 18686 + 0 . 18236 + 0. 17840 + 0. 17488

+ 0 . 12817 + 0 . 12849 + 0 . 12831 + 0 . 12802 + 0 . 12750 + 0 . 12691

+ 0.06523 + 0.06935 + 0.07244 + 0.07485 + 0.07676 + 0.078 30

+ 0 . 0 2 2 6 1 + 0 . 0 2 7 3 6 + 0 . 0 3 1 2 7 + 0 . 0 3 4 5 4 + 0 . 0 3 7 3 2 + 0 . 0 3 9 7 1

- 0 . 0 0 0 2 5 + 0 . 0 0 3 2 4 + 0. 0 0 6 3 6 + 0. 00913 + 0 . 0 1 1 6 1 + 0 . 0 1 3 8 5

0. 0 0 9 0 6 0. 0073 7 0. 0 0 5 6 5 0 . 0 0 3 9 5 0 . 0 0 2 3 2 0. 0 0 0 7 6

0.00996 0.00976 0.00929 0.00868 0. 00796 0.00720

- 0 . 0 0 7 5 3 - 0. 008 19 - 0 . 0 0 8 5 7 - 0 . 0 0 8 70 - 0 . 0 0 8 6 9 - 0 . 0 0 8 58

D I A G R A M N9. I APPENDIX B

EFFECTIVE WIDTH OF THE ORTHOTROPIC DECK PLATE. d o AND Co = EFFECTIVE WIDTH OF THE DECK PLATE.

OL AND IDEAL SPANS OF T - R I B S . BOX-RIBS OR FLOOR BEAMS.

h g o C L * OR e0 1.100 1.050 1.000 0.9 50 0.900 0.8 50 0.800 0.7 50 0.700 0.6 50 0.600 0.5 50 0.500 0.450 0.4OO 0.350 0.300 0.250 0.200 0.1 50 0.100 0.050 0.000

960'

1

-

680'1 1.08

5

1.05

9

- -

1.04

3

-

\ .

0.98

9

0.95

6

0.93

0

- -

0.89

2

0.8

70

_ 5

0.82

6 0.

798

--

0.76

2

-

0.73

2

-

0.69

8

^

0.68

3

-

0.64

3

0.61

8

0.59

1 0.

560

-

0.54

0

0.52

0

\

0.50

5

0.48

5

0.46

8 0.

448

0.43

0 0.

420

0.40

5

a

a

e D

sea* jcL* 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Q7 0.8 0.9 1.0 I.I 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 OR e, b

.

I

. . . . . . . . .

.

T o

-L q

IT o 10

d

- j r > 0.95

0.90

0.85

0.80

0.75

0.70

0.65

0.60

0.55

0.50

0.45

0.40

0.35

0.30

0.25

0.20

0.15

0.10

0.05

0.00 0

D I A G R A M No. 2 LOADING DISTRIBUTION

CO 0 1 0> o

0.60

0

0

0,99

3 ^

0.59

9

0

0,98

4 0.

598

-

2

I*: N 0!

d m t n i n

6

-

-

0

0.95

9 0.

59 2

-

-

4

OJ 1 01

a

0.58

9

-

-

1

0

t o OJ o i

d

0.58

4

-

-

-

6

0.90

2 0.

57 9

-

-

-

0

0.87

9 0.

57 3

-

-

8

0.85

4 0.

567

-

1

0 62

8 0.

56

1

-

0

0.80

1 0.

553

--

'

0.77

3 0.

546

-

(

2

0.74

4 10

.534

-

(1=1

1

0.7

14 _

0.52

7

J

4

0.67

8

m 6

1.

0.65

4

1 O

6

I -

-

6

m OJ ID

6

0.49

4

-

-

'

0.59

6 0.

482

-

-

N

-

8

0.56

7 0.

471

-

2.

0.53

9 0,

459

0

0.5

12

0.44

7

-

2

0.48

6 0.

436

_

m

2

r o IS 1

6 OJ r j T

6

2

0 d

0.41

1

4

0.4

17

en 01 r o

-

-

2

CO 0 1 t o

d

CO t o

o

-

-

6

0.37

9

lO

6

-

2

0.36

1

t o t o t o

d

-

8

m t o

O

o IO

6

-

3

t o

O

t o t o O

-

-

0

m t o

6

0.32

6

-

-

3.

0.30

2

CO

t o

o

-

2

o> (M O

CO O t o

6

3

O CO (\> O CO 0 1 OJ

o

"

-

4

0.27

1

CO CO

2

-

5

-

3.

t o CO OJ

O

0.27

7

-

-

6

0.25

5

0 1 CD OJ O

-

3.

CO OJ

O

0,26

0 8

OJ

6 t o i n OJ

6

1 B

inn >

APPENDIX B

P ^

i i i 3 2 1 0 1 2 3 1 * 1 < - - 1 1 I 1

L U R. R R. V

1 1 _a__

1 i i i

.a 1 a l a j

u B . P 1 1 s~ r

1 i mw

1 1 1 1 1 1 1 1 3 2 1 0 0 1 2 3 | . | . | , * . | a . | , a , | . a , | . a , |

R. R. R. R.

1 1 1 , ., I , . | .

a | a I a ' " '

1 1 a 1 a 1

B 4.0 a

to CO

ct a

D I A G R A M No. 3 IDEAL SPACING OF FLEXIBLE RIBS.

2.00

0 1=1

1.

700

2 . 0 0

1.90

1.80

1 7 0

1.60

1 5 0

1 4 0

1 3 0

1 2 0

1 10

1,00

0 . 9 0

0 .80

0 .70

0 6 0

0 5 0

0 30

0 2 0

O.OO

1.99

8

o o

1.99

3

8691

1.98

4 1.

696

01

o ei 10

01 m 01

1.68

4 1.

941

1.92

0 1

1.67

8 1.

668

1.89

7 1.

658

1.87

1 1.

646

CM 0 * CO CO CO N

1.63

4 O to CM O to to

1.74

4 1.

592

(

1.70

7 1.

568

1=1

1.66

7 1.

554

f"-

)

IO

1.52

8 1.

582

1.50

8 1.

539

1.48

8

I

1.49

4 1.

464

1.44

8 1.

442

o

1.4

18

in

1.39

4 1.

309

1.37

0

to 10 cy

1.34

4

-'

1.22

3 1.

322

CO

1.29

8 1.

135

! 1.

274

O o

1.24

0

O

1.22

6

(O o

1.20

0

in

o

ID

0.9

59

1.15

2 0.

928

1.13

2 0

.90

2 0.

87 5

0.00 I I I I I 1 I I I I 11 1 I 11 I I I I I I I . 0.0 0.2 0.4 0.6 0.B 1.0 1.4 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0

D I A G R A M No. 4 A P P E N D I X B

ORDINATES FOR INFLUENCE LINES FOR CONTINUOUS BEAM OVER MULTIPLE RIGID. SUPPORTS.

[-0

Cn

n =i Tt = O -n. = i

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