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13-3 APPENDIX 359 Table B MAXIMUM MOMENTS IN CONTINUOUS BEAMS CONTINUOUS BEAMS OF TWO SPANS 1:1 Moments X I From g From p M Max. (+Af) Max. (-M) + o O.I + 0.0325 0.03875 0.00625 0.2 +0.0550 0.06750 0.01250 0.3 + 0.0675 0.08625 0.01875 0.4 + 0.0700 0.09500 0.02500 0.5 -|- 0.0625 0.09375 0.03125 0.6 + 0.0450 0.08250 0.03750 0.7 + 0.0175 0.06125 0.0437s 0.75 0.04688 0.04688 0.8 —0.0200 0.03000 0.05000 0.85 —0.0425 0.01523 0.05773 0.9 —0.0675 0.00611 0.07361 0.95 —0.0950 0.00138 0.09638 I —0.1250 0.12500 gp pp pp Note. — In this and the following table, in cases in which the calculations include only quiescent loads, as for roofs, it is recommended that the positive moments at centers of spans be increased to at least ^— . In computations concerning par- tial live loads p in unfavorable positions, the deficient value due to g found in. the table is overbalanced, so that the tabular values can be employed as they stand. In beams with more than four spans, the end ones can be calculated like the first one of a beam of four spans, and the other spans in the longer beam like the second span of a continuous beam of four spans. 360 CONCRETE-STEEL CONSTRUCTION Table C MAXIMUM MOMENTS IN CONTINUOUS BEAMS CONTINUOUS BEAMS OF THREE SPANS 1:1:1 Moments X T From g From p M 1 Max. (+A/) Max. (-A/) First opening — 4- o O.I + 0.035 0.005 0.040 0.2 -I-0.060 O.OIO 0.070 0.3 -1-0.075 0.015 0.090 0.4 -1-0.080 0.020 O.IOO 0.5 -h 0.075 0.025 0.100. 0.6 4-0.060 0.030 0.000 0.7 -1-0.035 0.035 0.070 0.8 0.04022 0.04023 0.85 —0.02125 0.04898 0.02773 0.9 —o. 04 500 0.06542 0.02042 0.95 —0.07125 0.08831 0.01706 I — O.IOOOO 0.11667 0.01667 Second opening — O.IOOOO O.I 1667 0.01667 0.05 —0.07625 0.09033 0.01408 0.1 —0.05500 0.06248 0.00748 0.15 —0.03625 0.05678 0.02053 0.3 —0.020 0.050 0.030 0.2764 0.050 0.050 0.3 -ho. 00s 0.050 0.055 0.4 -f-0.020 0.050 0.070 0.5 -1-0.025 0.050 0.075 J?^ pp pp APPENDIX 361 Table D MAXIMUM MOMENTS IN CONTINUOUS BEAMS CONTINUOUS BEAMS OF FOUR SPANS 1:1:1:1 X Moments 1 From g From P M Max. (-A/) Max. (+ M) First opening — + o O.l 4-0.03429 0.00536 0.03964 0.2 + 0.05857 0.01071 0.06929 0.3 + 0.07286 0.01607 0.08893 0.4 + 0.07714 0.02143 0.09857 0.5 + 0.07143 0.02679 0.09822 0.6 + 0.05572 0.03214 0.08786 0.7 + 0.03000 0.03750 0.06750 0.7857 0.04209 0.04209 0.8 -0.00571 0.04309 0.03738 0.85 —0.02732 0.05216 0.02484 0.9 -0.05143 0.06772 0.01629 0.95 —0.07803 0.09197 0.01393 I — 0.10714 0.12054 0.01340 Second opening — 0.10714 0.12054 0.01340 0.05 —0.08160 0.09323- 0. 01 163 0.1 -0.05857 0.07212 0.01455 0.15 —0.03803 0.06340 0.02537 • 0.2 —0.02000 0.05000 0.03000 0.2661 0.04882 0.04882 0.3 + 0.00857 0.04821 0.05678 0.4 + 0.02714 0.04643 0.07357 0.5 + 0.03572 0.04464 0.08036 0.6 + 0.03429 0.04286 0.07715 0-7 + 0.02286 0.04107 0.06393 0.8 • + 0.00143 0.04027 0.04170 0.8053 0.04092 0.04092 • 0.85 —0.01303 0.04754 0.03451 0.9 —0.03000 0.06105 0.03105 0.95 —0.04947 0.08120 0.03173 1 I.O —0.07143 0.10714 0.03571 1 gr" pP PP 362 CONCRETE-STEEL CONSTRUCTION Table E CONVERSION TABLE, METRIC TO ENGLISH No. Kilograms to Averdupois Pounds. Tonnes to Tons of 3000 Pounds. Centimeters to Inches. Meters to Feet. Square Centimeters to Sauare Inches. Square Meters to Square Feet. I 2.20462 1.10231 0.39370 3.280833 0.155 10.76387 2 4.40924 2.20462 0.78740 6.561667 0.310 21.52773 3 6.61387 3-30<^93 1.18110 9.842500 0.465 32.29160 4 8.81849 4.40924 1.57480 13.123333 0.620 43.05547 5 II.02311 5.51156 1.96850 16.404167 0.775 53.81934 6 13-22773 6.61387 2.36220 19.685000 0.930 64.58320 7 15.43236 7.71618 2.75590 22.965833 1.085 75.34707 8 17.63698 8.81849 3.14960 26 . 246667 1.240 86.11094 9 19.84160 9.92080 3 • 54330 29.527500 1.395 96.87481 No. ■ Cubic Meters to Cubic Yards. Hektoliters to Bushels. Kilograms per Square Centimeters to Pounds per Square Inch. Kilograms per Square Meter to Pounds per Square Foot. Kilograms per Cubic Meter to Pounds per Cubic Foot. I 1.30794 2.83774 14.22340 0.20482 0.06243 2 2.61589 5.67548 28.44680 0.40963 0.12486 3 3.92383 8.51323 42.67020 0.61445 0.18728 4 5.23177 11.35097 56.89359 0.81927 0.24971 5 6.53971 14.18871 71. I 1699 1.02408 0.31214 6 7.84766 17.02645 85.34039 I. 22890 0.37457 7 9.15560 19.86420 99.56379 1.43372 0.43700 8 10.46354 22.70194 113. 78719 1.63854 0.49943 9 11.77149 25.53968 128.01059 1.84335 0.56185 INDEX TAGE A DHESION 42 proof of existence of 2 Adhesive forces, formulas for 145, 146 stresses developed 157, 161, 184, 186 Anchorage for ends of rods 148, 149 Arch bridges, examples 266-284 Arches 14 in buildings 235 "DEAMS, graphical methods of calculating 130-137 of variable depth, shear in 190, 191 Bending and tensile strengths, explanation of discrep- ancy l:)et\veen 26, 27, 28 relation of 27-29 of rods, effects of 181 , 182 strength of concrete 25 tests to determine extensibility 55> 5^ with axial compression, formula for 1 19-1 23 \vith axial stress, graphical methods for 132-137 with ajcial tension 1 27-1 29 with axial thrust 1 19-127 Beton Frette 67 Brackets 8, 9 Breaking strength of columns 63 Brick curtain walls 215 Buildings of reinforced concrete, examples of 210 /CANTILEVERS, examples 257 Cellars, Water-tight 247 Cement bins, examples 295-298 Coal pockets, examples 290 Coefficient of expansion, concrete 3 steel 3 363 364 INDEX PAGE Column tests 60, 6 1 Columns 11 breaking strength of 63 effect of ties on 62 flexure of 65 with longitudinal rods 59 with spiral reinforcement 67 Compression 59 Compressive strength of concrete 19, 20 Computation, suggested methods of 323, ^^^, 340 Concrete, bending strength of 25 compressive strength of 19 elasticity of 21 extensibility of 50 punching resistance of 31 shearing strength of 31 tensile strength of 20 torsional strength of 39, 40 Continuous bridges, examples 263-266 T-beams, experiments with 199-203 slabs 5, 6 Cooling towers, example of 3i3~3i5 Corrosion, proof of prevention of 1,2 Cracking of T-beams 188-190 stage, methods of computation for 137, 138 Cracks, safety against tension 105, 106, 107 Curtain walls of brick. 215 ■pVEFLECTION of beams 192, 193 of Isar-Grimwald arch bridge 280 Deformation 192, 193 Deformed bars, objections against 17, 18 Distributing rods 5 Domes 235 Double reinforcement, formulas for 87, 88 for slabs, with methods of figuring 94 tests of slabs with 93 "C^FFECTIVE depth, alteration of, from cracks 171 Effect of humidity on extensibility of reinforced concrete S3~5^ Elasticity of concrete 21 Elastic limit of concrete 21 Examples of methods of computation 326-333 Expanded metal, objections against 17 Expansion by heat, coefficient of, concrete 3 coefficient of, steel 3 INDEX 365 PAGB Extensibility 50 from bending tests 55? 5^, 57 of reinforced concrete 5i> 52 Euler's formula not applicable to long columns 65 "DIREPROOF quality of reinforced concrete, example of , 212 Flexure of columns 65 Floor systems 209 Footings 241 /GOVERNMENT (Prussian) regulations 233 Grain bins, examples 304-306 Graphical methods of calculating beams 130-137 Grimwald-Isar arch bridge 271-280 XJAUNCHES ' 6, 8, 9 in continuous beams, effect of 203 History 204, 205 Hooks, efifects of 158, 161, 162, 164, 178, 182 Humidity, effect of on concrete 4 TINTERIOR treatment of reinforced concrete buildings 224 Isar-Grimwald arch bridge 271-280 jr NEES 8, 9, 10 J^EITSATZE 15,317,333 Longitudinal and spiral reinforcement for columns 72, 73 rods, effects of 64 TiJ"ELAN arch bridges 281 -283 Methods of computation, suggested 323, 333, 340 Modulus of elasticity of concrete 21-25 Moments, computation of 194-197 in slabs 6 T^'EUTRAL axis, position of 95-98 I^RE pockets, examples 290, 293, 298 » ■piLE formula 255 Piles 250 Prussian government regulations for reinforced con- crete work 16 366 INDEX PAGB Pumice concrete 19 Punching resistance of concrete 31 T^ EGULATIONS of Prussian government 16 Reinforcing rods, arrangement in columns 12 arrangement of, in arches 11 arrangement of, in slabs 5, 6, 9, 10 Remant stresses 198 Reservoirs, examples 284-287 Rich mixture, necessity of 18 Roof construction 230 coverings 219-230 Rust, proof of prevention of 2 OAFE stresses, suggested 323-339 Safety against tension cracks 105-107 Sand-boxes for Isar Grimwald arch bridge 276 Scherfestigkeit 31*32 Schubfestigkeit 3^f 3^ Shearing forces, effects of 139, 141 , 147, 148 experiments concerning, by author 1 51-1 73 experiments concerning at Stuttgart Testing Laboratory 1 73, 1 74 formulas for 141-146 theory of action of 151 strength of concrete 31, 33> 34, 35» 3^, 37» 3^ from slotted beams 40, 41, 42 relation of tensile and compressive to.. 