Albert Irvin Frye.

Civil engineers' pocket book; a reference-book for engineers, contractors, and students, containing rules, data, methods, formulas and tables online

. (page 75 of 182)
Online LibraryAlbert Irvin FryeCivil engineers' pocket book; a reference-book for engineers, contractors, and students, containing rules, data, methods, formulas and tables → online text (page 75 of 182)
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length — 12 ft.; width of brace *- 14 ins.; then, reducing to inches, k »
120. p - 72. d - 7. With o as origin plot circle (1) with d as radius, fuD
sire; also lay off tangent, equation (3), intersecting the circle at T. The
point s will he a li ttle below T on the circle. Assume Xx — 6, then, equation
(2), yi - 60 - \ /3. 600 - 3 96 -> 3.40. Assume Xi - 6>i. then equation (2).
yj - 60 -vTeOO - 410.94 - 3.62.

Plot Xt Vi and X2 yal connect with line intersecting circle at s. Then,
by scale, x »> 6.09 ins., y » 3.45 ins. A s B is face of angle block. Length

of brace is

2 \/(A - y)» + (p - «)» - 22 ft. 3W ins. + . Ans.

*Table8 of Cubes and Squares. — ^The subjoined tables of cubes and sqtsares
are very useful in designing and detailing. For convenient reference they
are listed as follows:

Table 31. —Cubes of Inches, 0* to V, advancing by 64ths and S^ds.

•• 31a.— " " •• 9* to 29'. " ** 16ths.

" 81b.— " •• " 29* to lOO*. *' " 8ths.

" 32. —Squares of Inches, O'to 12* (0' to 1'). advancing by 64ths.

•• 32a.— 12* to 120* (1' to lO') " '^ Sinds.

" 32b.— " " " 120* to 624* (lO'to 6^) " " leths.

Note that the last coliimn of Table 82b. ( + A), is the average amovmt
(the amount at the center of the respective line — the half-inch column) to
be added for each 32nd of an inch. Thus, the square for 13* OA «
24472.69; and for 13' OH' is 24472.69+9.78-24482.47. The same iesu:t
can also be obtained by adding the squares of 13^ OiV' and 13^ OW
together, and dividing the sum by 2; thus, ( 24 4 72. 69 -f 24492.25) -4-2 «
24482.47. Remember that this difference for (j^) is for the H^'-column, in
middle of line; and that for the beginning of the line the tabular difference
in the last column should be decreased by 0.03, and increased by O.OS for
end of same line. This refinement, however, of modifying the amounu
given in the last column, to conform to different parts of the line, may
generally be neglected.

« ,^*P^»^*on of Uses of Tables 31 to 32 6.— These tables may be used ic

J:V^ bending moments, moments of resistance, moments oi inertia and

radu of gy ration; and in the solution of right angle triangles when two sides



PROBS, IN CUBES AND SQUARES^MOMENTS.



637



are gi'ren, and of any triangle when three sides are given. The following
examples will illustrate.

PiKDiNo Bbkdino Moments. (Table 32b.)
Example. — A girder having a span (L) of 14' 6A' supports a uniform
load (IV) of 400 lbs. per lin. ft. What is the bending moment (Af ') in tn.-lbs. ?

12 WL*
Solution. — ^Prom the well-known formula M' — — s * ^e have, if / —



span in ins. — 12L,Af'*-



WP 400 X 30080.6



8
- 126336 in.-lbs. Ans.



12X8 12X8

PiNDiNO Rbsistino Mombnts. (Table 32a.)
Example. — What is the resisting moment in inch4bs. (Af') of a rect-



angular beam (f wide (b} and 12^' deep (i). assuming the allowable fiber
■CSS per sq. ' ^
Solution .-



stress per sq. in. (/) — 1000 lbs.?

lution. — From the well-known formula Af * ■■ H / ^ <^i we have, by



substitution. M' - >000X 6X 165.766 _ ^^^^^^ j^ j^ ^^
o
Finding Radii op Gyration.
The square of the radius of gyration (r*) — the moment of inertia (/)
divided by the area (A) of the section. Thus r - Vl+A.

Finding Mombnts op Inbrtia.

Example. — Fig. 63
represents the section of
a steel column latticed on
two of its sides. Find the
moments of inertia about
the axes X and Y,

Solution. — ^The mom-
ent of inertia (/) of a rect-
angle about its base, is / —
W* + 3; in which 6 — width
and li» height of rectangle.
Hence. 3/-W. Now
Pig. 63 is symmetrical
about each of its axes,
hence if we find the value
of 3/ for one-quarter of the
section and then increase
this value by one-third, we
obtain the value 4/ for one-
fourth of the section — /
for the whole section. The
calculation is tabulated
below; the values of 6/r*
being made up from the
various rectangles in one-
quarter of the section.




frfc* about axis X.



bf^ about axis Y.



30



)» - -f



plate. ttX(16
173^ plate. «X(^)» - +



2320.31 15

- 16
418.70 8«4^X

- 8?^X



X(10A)» - +16450.65
X( »*8)» - -13375.00



angle. 6 X(16H)» - +20760.48 6 X(
'^ -^X(14M)» - -16386.36 - 5«h'X(
" - HX( 9H)» - - 474.88 - HX(



9h)» - +


7802.08


9 )«


6378.75


9H)> - +


5350.00


9 )«


3918.38


m)* —


29.77



Add one-third —

For the whole section. Ix



6638.25
2212.75



8851.00



+ 5900.83

^ 1966.94

Digitized by VjOC

ly - 7867.77



638 nSTRUCTURAL DETAILS.

Another Method. — Inttead of using the"rectanfl1e method*' (moedbg
case), we may use the method of "transferrence of neutral azis. Thns.
to find the moment of inertia of the 17H' X H* plate about the axis Y iw
proceed as follows: Find lo about its own neutral axis (/o — W»» -«- 12 -
17H X (H)* ■•- 12 - 0.366) and then use the formula ly » lo •¥■ Ac^, in
which A — area of plate — ITVi X H. and a — distance between the two
axes (see Pig. 68). Hence, tne moment of inertia of the plate about the
axis y - /y - /o + ila» - 0.366 + 17H X H X (»A)« - M8.88. Proceed
in like manner with the other plates, and the angles, etc. The sum of the
several moments of inertia will oe the total moment of inertia of the sectioiL

Corollary. — In the last method, above, we have the equation, ly •■
lo + Acfi. When the section of the column is unsymmetrical, it is often
necessary to assume an axis Y and find the value of Jy about this axis, and
then, from the said equation, to find the vaulea of a and lo,

SoLViNo Right Anolb Trianolbs. (Tables 83, 83a. 83b.)

Example. — ^What is the hypothenuse of a right angle triangle whose
base is 21' 741" and perpendicular Sr 9A'? (tf-6»-f?.)

Solution. — ^Prom Table 32b we have:

Por square corresponding to 21' TH* -" 67340.26

+ *' - l«-22

38* W -216616.70

-383872.17
Ans. 44' 411' - 283866.0

Corollary. — Prom the above equation, li* — 6* + ^, it is evident that
(S -/i«-//andp« - A«-6«.

Solving Any Trianolb — 3 Sidbs Givbn.

Example. — In Fig. 64 let there be given the sides H, h and B +h.
Solve the triangle.

Solution. — Drop the perpen-
dicular p upon the base B + 6.
Then, />« - //a - B« - A» - 6»;
therefore. H«- A«- B«-6«.

Whence, B - 6 - ^^-^.

ProbUm. — Given the three sides of a triangle (Pig. 64) J fc — 14' 8ft'.
H - 28^ IH", and B + 6 - 36' 6^'. Solve for the left-hand angle at the base
(which call ^)?

Solution. — Using the formulas in the solution to the above Example,
we have,

H-28' 7H': H« (ins.) -118078.1
A-14'3A': fcMins.)- 29433.7

.-. H« - A« (ins.) - 88644.4; log - 4.0476618
B +6 (ins.)- 426.60; log - 2.6280100

diff. - 2.3177328

.-. B -6 (ins.)- 207J4; log - 2.3177301

2 )634.34

.-. B (ins.)- 317.17; log - 2.6013021

H (ins.) - 343.626; log - 2.6800848

diff. -0.9653073
Ans.— 5«22° 37' 46'. from log cos »- 0.06SS076




C (-(K O*)— CI;B£S— 9* (-(K 9*).



639



■CnbM of Inches, 0* to 9*, Advancino bt d4TB8 and SSnds.



No.



8 147 •11 1/32
0518 i 1/16
0300 i 3/32
4414 y 1/8
7684 i 5/32
2397 U 3/16
" 7/32

»/*^
9/32

5/16
11/32
3/8
13/32
4675 B 7/16
B746 315/32
S250 i 1/2
7416 !l7/32
2473 H 9/16
1650 yi9/32
S176 i 5/8
1279 i21/32
1189 ill/16
1134 123/32
r344 I 3/4
S046 125/32
)471 gl3/16
)847 027/32
r402 i 7/8
)367 |29/32
►968 315/16
1436 |31/32
»000 [2

1/32

1/16

3/32

1/8

5/32

3/16

7/32

1/4

9/32

5/16

11/32

512 i 3/8

148 13/32

7/161

15/32 1

1/2 '

17/32

9/16

9/32

6/8

2l/32j

1/16

23/32

25/32
13/16
27/32

29/32^
15/16



Cube.



.OUOOOOl'i

09671

19946

3084411
.423821

5458071

674561

810272

953121

1033021
.260981
.426361
.599601

78091

970451 .

168427|l5/32

375000| 1/2



1/32

1/16

3/32

1/8

6/32

3/16

7/32

1/4
9/32
5/16
1/32
3/8
13/33
7/16



.590363



.814697 9/16



048187
291016
543365
805420
077362
359375
651642
954346
267670
591797
926910
273193
630829'
000000



17/32



9/32

6/8
21/82
11/16
23/32

3/4
25/32
13/16
27/32

7/8
29/32
15/16
31/32



380890 1/32



773682



178558 3/32



595703
025299
467529
922577
390625
871857
366455
874603
396484
932281
482178
046356
625000
218292
826416
449554
087891
741608,



1/16



/8

6/32

3/16

7/32

1/4

9/32

5/16

11/32

3/8

13/32

7/16

15/32

1/2
17/32
9/16
19/32
5/8
21/32
410889 11/16
095917 23/32
7968751 3/4
513947!25/3^
2473l4|l3/16
997162127/32
7636721 7/8
547028i 29/32
34741215/16



Cube.



31/32 36. 165009y31/S2il22



9J31/82|i:



.00000
.85257
,72290



61118 3/32



1/32
\0A



.51758
44229
38550
347361
3281
3279
34692
38535
44336
52115
61890
73679
87500
03372
21313
41342
63477
87735
14136
42697
73438
06375
41628
78915
18555
60464
04663
51169
00000
51175
04712
60629
18945
79678
42847
08469
76563



1/8

6/32

3/16

7/32

1/4

9/32

6/16

11/32

3/8

13/32

7/16

15/32

1/2
17/32
9/16
19/32
6/8
21/32
11/16
23/32

3/4
25/32
13/16
27/32

7/8
29/32
15/16
31/32

1/32
1/16
3/32

1/8
5/32
3/16
7/32



20239
95859
74023
54752
38062
23972
12500
03665
97485
93979
93164
95059
99683
07053
1718a
30106i
468251
643651
857421
099761



47147 9/32



5/16
11/32

3/8
13/32

7/16
15/32

1/2
17/32

9/16
19/32

5/8
21/32
11/16
23/32

3/4
25/32
13/16
27/32

7/8
29/32



Cube.



37085i'15/16
67087il31/32,



125
127
129
132
134
137
139
142
144
147
49
52
56
58
60
163
166
169
172,
75,
177
180
183
187,
190,
93
196,
199
202,
206,
209.
212.
216
219
222.
226
229.
233.
236.
240.
244
247.
251
256.
259
262.
266.
270.
274.
278
282.
286.
290
294.
299
303.
307
311
316
320.
324
329.
333
338



000001
35843
74634
16391
61133
08878
59644
13449
70313
30252
93286
59433
2871
01138
76733
55515
37500
22708
11157
02866
97852
96133
97729
02658
10938
22586
37622
56064
77980
03238
32007
64255
00000
39261
82056
28403
78320
31827
88940
49680
4063
82108
53833
29257
08398
91275
77906
68307
62500
60501
623291
68002
77639
90958
082761
29514;
54688^
83817



No,



/32

1/16

3/32

1/8

6/32

3/16

7/32

1/4

9/32

6/16

11/32

3/8

13/32

7/16

15/32

1/2
17/32
9/16
19/32
6/8
21/32
11/16
23/32

3/4

26/32

13/16

27/32

7/8

29/32

15/16

31/32

8

1/32

1/16

3/32

1/8

5/32

3/16

7/32

1/4

9/32

6/16

11/32

3/8

13/32

7/16



Cube.



343
347
352
366
361
366
371
376
381
386
391
396
401
406
411
416
421
427
432
437
443
448
454
459
465
471
476
482,
488
494
500,
506
512,
518
524
530,
536,
542,
548.
555.
561.
567.
574.
580
687
594
600.



16919
54013.
951171
402501
89429|
42673



15/321607

1/2 614.
17/32620.

9/16'627.
19/321634.

5/8 641.
21/32648
11/16655
23/32 662.

3/4 669.
25/32 677.
13/16684.
27/32 691.

7/8 699.
29/321706.
15/16>713
31/32721



.00000
.61429
26978
.96664
70608
.48526
30737
17160
.07813
.02713
.01880
.05331
.13086
.25162
.41577
.62350
.87500
.17044
.51001
.89389
.32227
79532
31323
87619
48438
13797
83716
58212
37305
21011
09351
02341
00000
02347
09399
21176
37695
58975
85034
15891
51563
92068
37427
87656
42773
02798
67749
37643
2500
92337
77173
67026
61914
61856
66870
76974
92188
12527
38013
68661
04492
45523
91772
43269



t
t



ft



r



f^

*.'»



t:






47^.0000038147.



d by Google



640 83.— STRUCTURAL DETAILS,

31a. — Cubes of Inches, 9* to 29*. Advancing by IOtbs.



d by Google



d by Google



842



S&.— STRUCTURAL DETAILS,



31b.-



of Inches, 69* to 109*, Advancing by 8ths. — Concluded.



Cube.



No.



Cube.



No.



Cube.



Cube.



«9



1/8
1/4
3/8
1/2
5/8
3/4
7/8



70



73



76



1/8
1/4
3/8
1/2
5/8
3/4
7/8
I
1/8

M^
3/8

1/2

5/8

3/4

7/8

1/8
1/4
3/8
1/2
5/8
3/4
7/8

3
1/8
1/4
3/8
1/2
6/8
3/4
7/8

4
1/8
1/4
3/8
1/2
5/8
3/4
7/8

5
1/8
1/4
3/8
1/2
5/8
3/4'
7/8

1/8
1/4
3/8
1/2
6/8
3/4
7/8



828509.
330297.
332092.
333894.
335702.
337567.
339338.
341165.
343000.
344840.
346688.
348542.
350402.
352269.
354143.
356024.
357911.
359804.
361705.
363612.
365525.
367446.
369373.
371307.
373248.
375195.
377149.
379110
381078.
383052.
385033.
387022.
389017.
391018>
393027.
395043.
397065.
399094.
401130.
403174.
405224.
407281.
409344.
411415.
413493.
415578.
417670.
419769.
421875.
423987.
426107.
428234.
430368.
432510.
434658.
436813.
438976.
441145.
443322.
446506.
447697,
449895
452100
454313



77



/8
1/4
3/8
1/2
6/8
3/4
7/8
78
1/8
1/4
3/8
1/2
6/8
3/4
7/8



5



79

7 1/8^

1 - "
V
9



5

4

7
9



9
8
6
5
3
1
083



U



1/4
3/8
1/2
5/8
3/4
7/8


1/8
1/4
3/8
1/2
5/8
3/4
7/8

1
1/8
1/4
3/8
1/2
5/8
3/4

//«

\^A

3/8
1/2
5/8
3/4
7/8

1/8
1/4
3/8
1/2
5/8
3/4
7/8

1/8
1/4
3/8
1/2
5/8
3/4
7/8



456533
458760
460994
463235
465484
467740
470003
472274
474552
476837
479129
481429
483736
486051
488373
490702
493039
495383
497734
500093
502459
504833
507215
509603
512000
514403
616815
519233
521660
524094
526535
528984
531441
533905
536377
538856
541343
543838
546340
548850
651368
553893
556426
558967
561515
564071,
566635,
569207
671787
574374,
576969,
579572
582182
584801
587427
590061
592704
595353
598011
600677
603351
606032
608722
611419



85



1/8
1/4
3/8
1/2
5/8
3/4
7/8

6
1/8
1/4
3/8"
1/2
6/8
3/4
7/8

7
1/8
1/4
3/8
1/2
5/8
3/4

1/8
1/4
3/8
1/2
5/8
3/4
7/8
89
1/8
1/4
3/8
1/2
6/8
■ 3/4
7/8
90
1/8
1/4
3/8
1/2
6/8
3/4
7/8



91

31 1/8
3 '
2,



1/4
3/8
1/2
5/8
3/4
7/8
3
1/8
1/4
3/8
1/2
5/8
3/4
7/8



614125.
616838,
619559.
622289.
625026.
627771.
630625.
633286.
636056,
638833.
641619.
644412.
647214.
650024,
652842.
655668.
658503,
661345.
664196.
667054.
669921.
672797.
675680.
678672.
681472.
684380.
687296.
690221.
693154.
696095.
699044.
702002.
704969.
707943.
710926.
713917.
716917.
719925.
722941.
725966.
729000.
732041.
735091.
738150.
741217.
744293.
747377.
750469,
753571.
756680.
759798.
762925.
766060.
769204.
772367.
775518.
778688,
781866.
785063
788248,
791453
794666
797887
801118



93

1/8

*//
3/8

1/2

5/8

8/4

7/8
94

1/8

1/4

3/8

1/2

5/8

3/4

7/8
95

1/8

1/4

3/8

1/2

5/8

3/4

7/8
96

1/8

1/4

8/8

1/2

6/8

3/4

7/8
97

1/8

1/4

3/8

1/2

6/8

3/4

7/8
98

1/8

1/4

8/8

1/2

5/8

3/4

3/8
1/2
6/8
3/4
7/8
100
1/8
1/4

8/8101
1/2 "
5/8



804357
807604
810861
814126
817400
820683
823974
827274
830584
833901
837228
840564
843908,
647261,
850624
853995,
857375
860768
864161,
867568
670988
874408
877842
881284,
884736,
888196
891666
895144,
898632,
902128,
905634
909149.
912673,
916205,
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643



32.'-S4iMres of InchM, if to ^ (0" if to V tT), Advancino
BY 64ths.



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3


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1.0314941


4.0000000
4.0627441


9.000000
9.093994


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1.0634766


4.1259766


9.188477


16.250977


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1.0959473


4.1896973


9.283447


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.00390625


1.1289063


4.2539063


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1.1623535


4.3186035


9.474854


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1.1962891


4.3837891


9.571289


16.758789


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4.4494629


9.668213


16.886963


26.105713


7/64




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1.2656250


4.5156250


9.765625


17.015625


26.265625


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1.3010254


4.5822754


9.863552


17.144775


26.426025


9/64




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1.3369141


4.6494141


9.961914


17.274414


26.586914


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11/64




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1.8732910


4.7170410


10.060791


17.404541


26.748291


11/64




3/16


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1.4101563


4.7851563


10.160156


17.535156


26.910156


3/16


13/64




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1.4475098


4.8537698


10.260010


17.666260


27.072510


13/64




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1.4853516


4.9228516


10.360352


17.797852


27.235352


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1.52S6816


4.9924316


10.461182


17.929932


27.898682


16/64




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1.5625000


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6.1330566


10.664307


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27.726807


17/64




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1.6416016


5.2041016


10.766602


18.329102


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1.6818848


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19/64




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5.3476563


10.972656


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28.222656


.6/16


21/64




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1.7639160


5.4201660


11.076416


18.732666


28.388916


21/64




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1.8056641


5.4931641


11.180664


18.868164


28.555664


11/32


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1.8479004


5.6666504


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19.004150


28.722900


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8/8


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1.8906250


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6.7150879


11.496338


19.277588


29.058838


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5.7900391


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19.415039


29.227539


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27/64




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2.0217285


5.8654785


11.709229


19.552979


29.396729


27/64




7/16


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2.0664063


5.9414063


11.816406


19.691406


29.566406


7/18


29/64




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2.1115723


6.0178223


11.924072


19.830322


29.736572


29/64




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2.1572266


6 0947266


12.032227


19.969727


29.907227


15/32


31/64




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2.2033691


6.1721191


12.140869


20.109619


30.078369


31/64




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33/64




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2.2971191


6.3283691


12.359619


20.390869


30.422119


38/64




17/32


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2.3447266


6.4072266


12.469727


20.532227


30.594727


17/32


35/64




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2.3928223


6.4865723


12.580322
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20.674072


30.767822


35/64




9/16


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2.4414063


6.5664063


20.816406


30.941406


9/16


37/64




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2.4904785


6.6467285


12.802979


20.959229


31.115479


37/64




19/3^


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2.5400391


6.7275391


12.915039


21.102539


31.290039


19/32


39/64




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2.5900879


6.8088379


13.027588


21.246338


31.465088


39/64




5/8


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2.6406250


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13.140625


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5/8


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21.535400


31.816650


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2.7431641


7.0556641


13.368164


21.680664


31.993164


21/33


48/64




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2.7951660


7.1389160


13.482666


31.826416


82.170166


43/64




11/16


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2.8476563


7.2226563


13.597656


21.972636


32.347656


11/16


45/64




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2.9006348


7.3068848


13.713135


22.119385


32.525635


45/64




38/32


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2.9541016


7.3916016


13.829102


22.266602


32.704102


23/32


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3.0080566


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22.414307


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7.5625000


14.062500


22.562500


33.062500


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3.1174316


7.6486816


14.179932


22.711182


33.242432


49/64




25/32


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3.1728516


7.7353516


14.297852


22.860352


33.422852


25/32


51/64




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3.2287598


7.8225098


14.416260


23.010010


33.603760


51/64




13/16


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3.2851563


7.9101563


14.535156


23.160156


33.785156


13/16


53/64




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3.3420410


7.9982910


14.654541


23.310791


33.967041


63/64




27/32


.71191406


3.3994141


8.0869141


14.774414


23.461914


34.149414


27/32


55/64




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3.4572754


8.1760254


14.894775


23.613525


34.332275


65/64




7/8


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3.5156250


8.2656250


15.015625


23.76.1625


34.515625


7/8


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3.6744629


8.3557129


15.136963


23.918213


34.699463


67/64




29/32


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3.6337891


8.4462891


15.258789


24.071289


34.883789


29/33


59/64




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3.6936035


8.5373535


15.381104


24.224854


35.068604


69/64




15/16


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8.7539063


8.6289063


16.503906


24.378906


35.253906


15/16


61/64




.90844727


3.8146973


8.7209473


15.627197


24.533447


35.439697


61/64




81/32


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3.8759766


8.8134766


15.750977


24.688477


35.625977


31/32


63/64




.96899414


8.9377441


8.9064941


15.876244


24.843994


35.812744
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63/64



Digitized by



Google



644



9B.— STRUCTURAL DETAILS,



32.— Squares of InchM, 6" to ir (Cd* to I'O*), Advamcino
BY 64ths. — Concluded.



la.


6


7


8


9


10


n


la.




36.000000
36.187744


49.000000
49.218994


64.000000
64.250244


81.000000
81.281494


100.00000
100.31274


121.00000
121.84399




'i'/u




i/ii




1/32


36.875977


49.438477


64.500977


81.563477


100.62598


121.68848


1/32


S/64




36.564697


49.658447


64.752197


81.845947


100.93970


122.03345


3/64




1/16


36.753906


49.878906


65.003906


82.128906


101.25391


122.37891


1/1«


6/64




36.943604


50.099854


65.256104


83.412354


101.56860


122.72485


5/64




3/32


87.133789


50.321289


66.608789


82.696289


101.88379


123.07129


8/32


7/64




37.324463


30.543213


65.761963


82.980713


102.19946


123.41821


7/64




1/8


37.515625


60.765625


66.015625


83.265635


102.51563


123.76663


1/8


«/64




37.707275


50.988525


66.269775


83.551025


102.83228


124.11353


9/64




5/32


37.899414


51.211914


66.524414


83.836914


103.14941


124.46191


S/32


11/64




38.092041


51.435791


66.779541


84.123291


103.46704


124.81079


11/64




8/16


38.285156


61.660156


67.035156


84.410156


103.78516


125.16016


3/16


13/64




88.478760


51.885010


67.291260


84.697510


104.10376


125.51001


13/64




7/32


38.672852


62.110352


67.547852


84.985352


104.42285


125.86035


7/32


15/64




38.867432


52.3361821 67.804932


85.273682


104.74243


126.21118


15/64




1/4


39.062500


52.562500


68.062500


85.662500


105.06250


126.56250


1/4


17/64




39.258057


52.789307


68.820557


85.851807


105.38306


126.91431


17/64




9/32


39.454102


53.016602


68.579102


86.141602


105.70410


127.26660


9/32


19/64




39.650635


53.244385


68.838135


86.431885


106.02563



Online LibraryAlbert Irvin FryeCivil engineers' pocket book; a reference-book for engineers, contractors, and students, containing rules, data, methods, formulas and tables → online text (page 75 of 182)