Table XIX. Concrete Columns. Moments of Inertia of Cross-Sections of Column- NOTE. For calculation of the moment of inertia the bars are assumed to be transformed into a continuous cylinder having a sectional area equivalent to the sum of the areas of the bars. Table XX. Concrete Columns. Moments of Inertia of Cross-Sections of Bars and Rods, in Inches 4 The moments of inertia are computed about the axis AA Arm in Side of SQUARE BAR in inches In 5% 2 22 24579 Diameter of ROUND ROD in inches 11/8 114 6 10 14 90 141 203 276 361 457 564 71 111 160 217 338 441 558 689 87 135 195 265 346 438 541 484 613 756 95 148 214 291 380 481 594 132 206 298 405 529 670 827 104 162 234 318 416 526 649 144 225 324 441 576 729 900 113 177 254 346 452 573 707 791 977 123 192 276 376 491 621 767 856 1 056| 133 207 299 407 531 672 830 25 34 44 36 49 20 25 54 71 60 79 66 87 110 135 64 87 113 143 177 133 168 208 87 118 154 195 241 99 135 177 224 276 79 113 154 99 143 195 255 201 255 314 227 287 355 322 398 CHAPTER IX FOOTINGS 1. Loads on Footings. The LOAD used in determining the AREA OF A FOOTING is the load used in the design of the column in the story immediately above the footing considered (which load has already been subjected to any allowable live-load reductions, see page 165), plus any live or dead load in that story, plus the weight of the pedestal, if there is one, plus the weight of the footing itself. The load from a basement-floor resting on the material of the foundation-bed need not, ordinarily, be considered as an added weight on the footings. The DESIGN-LOAD, used in determining the THICKNESS AND REINFORCEMENT OF THE FOOTING-SLAB, is the load as defined above, less the weight of the footing. For a footing resting on the foundation-bed this load, or reaction, is assumed to be uniformly distributed over the area of the footing; and for pile-footings to be uniformly distributed over and evenly divided among all the piles. Pilereactions are treated as concentrated loads, each acting at the center line of a pile, and equal to the safe bearing-capacity of the pile. * 2. Proportionment of the Areas of the Footings. The PURPOSE OF FOOTINGS is to distribute loads, and the character of a footing-design is governed by the weights to be distributed and the bearing power of the materials of the foundation-bed. In order to equalize varying settlements of different parts of a structure resting on a compressible foundation-bed, the UNIT SOIL-PRESSURE should be the same for all footings of the building wherever the soil-conditions are similar. When the footings rest on piles, the safe resistance or bearing power of each pile should be computed from the pile-driving record, and an AVERAGE VALUE taken for the bearing power of the piles of each group. The SETTLEMENT OF A BUILDING † is usually gradual and often continues for a long time, and it is the result of the constant or dead loads rather than the occasional or live loads; and a close approach to a UNIFORMITY OF SETTLEMENT is effected by proportioning footing-areas on the more rational basis of the probable maximum live loads instead of the assumed maximum live loads for which the other parts of the building are designed. It must be clearly under *Although the word "soil," in the classification of materials composing foundationbeds, means definitely earthy material capable of supporting vegetable life and generally limited to material containing decayed vegetable and animal matter, it has come to be used in engineering to mean any compressible foundation-bed. † For a full discussion of the subject of Proportioning Supporting Areas for Equal Settlement on Compressible Foundation-Beds, the reader is referred to Chapter II on Foundations, by Daniel E. Moran, in the Kidder-Nolan Architects' and Builders' Handbook. stood, however, that this concerns the PROPORTIONMENT only, and that the maximum unit pressure resulting from the loads as above defined should never exceed the assumed safe value of the bearing power of the foundation-bed or pile-group. Knowing the purpose of the building, an assumption should be made in regard to the percentage of live load representing the PROBABLE CONDITION OF OCCUPANCY (Table III, Chapter I), and this percentage of the live load combined with the dead load should be used as a BASIS OF PROPORTIONMENT. This is expressed in the following rule: Compute the footing-area required, for the full assumed load, for the footing, or one of the footings, which has the largest ratio of live load to dead load, and divide by this area the sum of the dead load and the assumed percentage of the live load. This determines an AVERAGE UNIT PRESSURE which is then used in finding the size of all the remaining footings, in each case based on its dead load plus the assumed percentage of its live load. The following example illustrates this method. Table I. Ratios of Live Loads to Dead Loads in Illustrative Example In this table the loads have been determined as described in Paragraph 1. Loads on Footings, of this chapter. Footing 1 has the largest ratio, 1.4, of live load to dead load, and assuming a safe bearing power of 3 tons for the foundation-bed, its area is On the assumption that 50% of the live load represents the probable condition of occupancy, the AVERAGE UNIT PRESSURE is Area of footing 4 = 92 sq ft |