FIGURE 12.1 Built-up roofing over two layers of preformed insulation board. Three plies of asphalt-impregnated glass-fiber felt, embedded in a continuous application of hot asphalt, overlay a base sheet adhered with asphalt to the insulation. Aggregate surfacing, about 3/8 in in diameter, is spread in the top flood coat of asphalt. (NRCA Roofing and Waterproofing Manual.) FIGURE 12.2 Protected-membrane roof with aggregate and insulation placed over, instead of under, the built-up membrane. Bitumen may be asphalt or coal tar. Roofing asphalt is a derivative of petroleum. It is described in ASTM Standard D312, which includes specifications for Types I, II, III, and IV. Each type has a different softening-point range, which should be considered by the specifier when specifying the type of asphalt to be used. Coal tar, described in ASTM D450, is a derivative of the production of coke from coal. Type I is referred to as old-style pitch. Type II is used for below-grade waterproofing. Type III, or coal-tar bitumen, was developed to be less of an irritant during application than Type I; however, Type III is no longer produced. Felts are sheet materials used to reinforce waterproofing and roofing membranes. The predominant type of felt used is glass fiber although organic felts are still commonly used in the construction of coal-tar systems. Polyester is an alternative type of felt. Asbestos felts were used in the past but are no longer produced in the

1b Extreme torsional irregularityto be considered when diaphragms are not flexible D Extreme torsional irregularity shall be considered to exist when the maximum story drift, computed including accidental torsion, at one end of the structure transverse to an axis is more than 1.4 time the average of the story drifts at the two ends of the structure. C and D (this irregularity not permitted in E or F) 2 Re-entrant corners D Plan configurations of a structure and its lateral force-resisting system contain re-entrant corners, where both projections of the structure beyond a re-entrant corner are greater than 15% of the plan dimension of the structure in the given direction. E and F 3 Diaphragm discontinuity D, E, and F Diaphragm with abrupt discontinuities or variations in stiffness, including those having cutout or open areas greater than 50% of the gross enclosed diaphragm area, or changes in effective diaphragm stiffness of more than 50% from one story to

 (6.17) z v 2(r 2  z2)5 / 2 If there is a uniform line load Q (force per unit length), the vertical stress increase at a depth z and distance r from the line load would be: 2Qz3  (6.18) z v (r 2  z2)2 In 1935, Newmark performed an integration of Eq. (6.18) and derived an equation to determine the vertical stress increase ( z) under the corner of a loaded area. Convenient charts have been developed based on the Newmark (1935) equation. For example, Figure 6.15 shows the pressure bulbs (also known as isobars) beneath a square footing and a strip footing. To determine the change in vertical stress (i.e., z or  v) at any point below the footing, multiply the value from Figure 6.15 times qo, where qo  uniform applied footing pressure. FIGURE 6.14 Definition of terms for Eqs. (6.17) and Figure 6.16 can be easily used to determine the pressure at the edge of a footing or can be used to determine the pressure under the center of the footing as described below. The values of m and n must be calculated. The value m is defined as the width of the loaded area (x) divided by the depth to where the vertical stress increase