Open expansion joints are sometimes used for interior locations where the opening is not objectionable. When exposed to water from above, as in parking decks, open joints may be provided with a gutter below to drain away water. The engineer should show all necessary vertical and horizontal joints on design drawings. All pertinent details affecting reinforcement, water stops, and sealers should also be shown. Construction joints should be designed and located if possible at sections of minimum shear. These sections will usually be at the center of beams and slabs, where the bending moment is highest. They should be located where it is most convenient to stop work. The construction joint is often keyed for shearing strength. If it is not possible to concrete an entire floor in one operation, vertical joints preferably should be located in the center of a span. Horizontal joints are usually provided between columns and floor; columns are concreted first, then the entire floor system. FIGURE 9.9 Types of construction joints. Circled numbers indicate order of casting. Various types of construction joints are shown in Fig. 9.9. The numbers on each section refer to the sequence of

v  (5.50) J where b is the thickness of the web or the flange of the member. Maximum shear will occur at the center of one of the long sides of the rectangular part that has the greatest thickness. (A. P. Boresi, O. Sidebottom, F. B. Seely, and J. O. Smith, Advanced Mechanics of Materials, 3d ed., John Wiley & Sons, Inc., New York.) Beams are the horizontal members used to support vertically applied loads across an opening. In a more general sense, they are structural members that external loads tend to bend, or curve. Usually, the term beam is applied to members with top continuously connected to bottom throughout their length, and those with top and bottom connected at intervals are called trusses. See also Structural System, Art. 5.5.1 Types of Beams There are many ways in which beams may be supported. Some of the more common methods are shown in Figs. 5.11 to 5.16. FIGURE 5.11 Simple beam. FIGURE 5.12 Cantilever beam. FIGURE 5.13 Beam with one end fixed. FIGURE 5.14 Fixed-end beam. FIGURE 5.15 Beam with overhangs. FIGURE 5.16 Continuous beam. The beam in Fig. 5.11 is called a simply supported, or simple beam. It has supports near its ends, which restrain it only against vertical movement. The ends of the beam are free to rotate. When the loads have a horizontal component, or when change in length of the beam due to temperature may be important, the supports may also have to prevent horizontal motion. In that case, horizontal restraint at one support is generally sufficient. The distance between the supports is called the span. The load carried by each support is called a reaction. The beam in Fig. 5.12 is a cantilever. It has only one support, which restrains it from rotating or moving horizontally or vertically at that end. Such a support is called a fixed end. If a simple support is placed under the free end of the cantilever, the propped beam in Fig. 5.13 results. It has one end fixed, one end simply supported. The beam in Fig. 5.14 has both ends fixed. No rotation or vertical movement can occur at either end. In actual practice, a fully fixed end can seldom be obtained. Some rotation of the beam ends generally is permitted. Most support conditions are intermediate between those for a simple beam and those for a fixed-end beam. In Fig. 5.15 is shown a beam that overhangs both is simple supports. The overhangs have a free end, like cantilever, but the supports permit rotation. When a beam extends over several supports, it is called a continuous beam

The allowable compressing bending stress Fb for plate girders must be reduced from that given in Art. 7.20 where h/ t exceeds 760/
F . For greater values of this b ratio, the allowable compressive bending stress, except for hybrid girders, becomes A h 760 F  F 1  0.0005 w    (7.27) b b A t
F b where Aw  the web area, in2 and A  the compression flange area, in2. For hybrid girders, not only is the allowable compressive bending stress limited to that given by Eq. (7.24), but also the maximum stress in either flange may not exceed 12  (A /A )(3

3) w F  F   (7.28) b b 12  2(A /A ) w where a  ratio of web yield stress to flange yield stress. Flange Limitations. The projecting elements of the compression flange must comply with the limitations for b/ t given in Art. 7.21. The area of cover plates, where used, should not exceed 0.70 times the total flange area. Partial-length cover plates (Fig. 7.33b) should extend beyond the theoretical cutoff point a sufficient distance to develop their share of bending stresses at the cutoff point. Preferably for welded-plate girders, the flange should consist of a series of plates, which may differ in thickness and width, joined end to end with complete-penetration groove welds (Fig. 7.33a). Bearing Stiffeners. These are required on girder webs at unframed ends. They may also be needed at concentrated loads, including supports. Set in pairs, bearing stiffeners may be angles or plates placed on opposite sides of the web, usually normal to the bending axis. Angles are attached with one leg against the web. Plates are welded perpendicular to the web. The stiffeners should have close bearing against the flanges through which they receive their loads, and should extend nearly to the edges of the flanges. These stiffeners are designed as columns, with allowable stresses as given in Art. 7.19. The column section is assumed to consist of a pair of stiffeners and a strip of girder web with width 25 times web thickness for interior stiffeners and 12 times web thickness at ends. In computing the effective slenderness ratio Kl/ r, use an effective length Kl of at least 0.75 the length of the stiffeners. Intermediate Stiffeners. With properly spaced transverse stiffeners strong enough to act as compression members, a plate-girder web can carry loads far in excess of its buckling load. The girders acts, in effect, like a Pratt truss, with the stiffeners as struts and the web forming fields of diagonal tension. The following formulas for stiffeners are based on this behavior. Like bearing stiffeners, intermediate stiffeners are placed to project normal to the web and the bending axis, but they may consist of a single angle or plate. They may be stopped short of the tension flange a distance up to 4 times the web thickness. If the compression flange is a rectangular plate, single stiffeners must be attached to it to prevent the plate from twisting. When lateral bracing is attached to stiffeners, they must be connected to the compression flange to transmit at least 1% of the total flange stress, except when the flange consists only of angles. The total shear force, kips, divided by the web area, in2, for any panel between stiffeners should not exceed the allowable shear Fv given by Eqs. (7.29a) and