strength , c psi Aggregates all lightweight, lb/yd3 Sand aggregate lightweight, lb/yd3 weights range from 90 lb / ft3 (all aggregates lightweight) to 115 lb / ft3 (sand lightweight). Typically, compressive strengths range from 2500 to 4000 psi. Highstrength lightweight concretes, however, have been produced with maximum unit weights of 125 lb / ft3 and strengths from 6000 to 9000 psi. Structural lightweight concretes are defined by the ACI as concretes with a 28-day compressive strength more than 2500 psi and air-dry unit weight of 115 lb / ft3 or less. The variable amount of water absorbed in the voids of lightweight aggregates makes use of W/C difficult in design of a lightweight-aggregate mix (Table 4.5). Air entrainment of 4 to 6% is desirable to prevent segregation. Maximum size of the coarse aggregate should not exceed half the depth of cover over the reinforcing steel. Lightweight-aggregate concrete exposed to sulfates should have a compressive strength ranging from 3750 to 4750 psi (see ACI 318). For marine structures, the W/C should not exceed 0.40 and at least seven bags of cement should be used per cubic yard of concrete. The modulus of elasticity Ec of lightweight concrete generally ranges from 1,500,000 to 3,000,000 psi. It may be estimated from E  w1.5
 (4.1) c c where w  unit weight of concrete, lb / ft3

3V/2bd (10.16) V where V is the vertical shear. In calculation of V for a beam, all loads occurring within a distance d from the supports may be ignored. This is based on the assumption that loads causing the shear will be transmitted at a 45
angle through the beam to the supports. (K. F. Faherty and T. G. Williamson, Wood Engineering and Construction Handbook. McGraw-Hill Publishing Company, New York.) 10.7.2 Beam Stability Beams may require lateral support to prevent lateral buckling. Need for such bracing depends on the unsupported length and cross-sectional dimensions of the members. When buckling occurs, a member deflects in the direction of its least dimension b. In a beam, b usually is taken as the width. If bracing precludes buckling in that TABLE 10.13 Approximate Lateral-Support Rules for Lumber Flexural Members* Depth-width ratio (nominal dimensions) Rule d/b  2 No lateral support required 2  d/b  4 Hold ends in position with full-depth blocking, bridging, hangers, or other structural members 4  d/b  5 Hold ends in position and compression edge in line, e.g., with direct connection of sheathing, decking, or joists 5  d/b  6 Hold ends in position and compression edge in line, as for 5 to 1, and provide adequate bridging or blocking at intervals not

6.10.1 Compaction Fundamentals An important part of the grading of the site often includes the compaction of fill. Compaction is defined as the densification of a fill by mechanical means. This physical process of getting the soil into a dense state can increase the shear strength, decrease the compressibility, and decrease the permeability of the soil. There are four basic factors that affect compaction: 1. Soil Type. Nonplastic (i.e., granular) soil, such as sands and gravels, can be effectively compacted by using a vibrating or shaking type of compaction operation. Plastic (i.e., cohesive) soil, such as silts and clays, is more difficult to compact and requires a kneading or manipulation type of compaction operation. If the soil contains oversize particles, such as coarse gravel and cobbles, these particles tend to interfere with the compaction process and reduce the effectiveness of compaction for the finer soil particles. Typical values of dry density for different types of compacted soil are listed in Table 6.20. 2. Material Gradation. Those soils that have a well-graded grain size distribution can generally be compacted into a denser state than a poorly graded soil that is composed of soil particles of about the same size. For example, a well-graded decomposed granite (DG) can have a maximum dry density of 2.2 Mg/m3 (137 pcf), while a poorly graded sand can have a maximum dry density of only 1.6 Mg/m3 (100 pcf, Modified Proctor). 3. Water Content. The water content is an important parameter in the compaction of soil. Water tends to lubricate the soil particles thus helping them slide into dense arrangements. However, too much water and the soil becomes saturated and often difficult to compact. There is an optimum water content at which the soil can be compacted into its densest state for a given compaction energy. Typical optimum moisture contents (Modified Proctor) for different soil types