BEAMS ANALYSIS

In analyzing beams of various types, the geometric properties of a variety of cross-sectional areas are used. Figure 2.1 gives equations for computing area A, moment of inertia I, section modulus or the ratio S = I/c, where c = distance from the neutral axis to the outermost ber of the beam or other member. Units used are inches and millimeters and their powers. The formulas in Fig. 2.1 are valid for both USCS and SI units.
Handy formulas for some dozen different types of beams are given in Fig. 2.2. In Fig. 2.2, both USCS and SI units can be used in any of the formulas that are applicable to both steel and wooden beams. Note that W = load, lb (kN); L = length, ft (m); R = reaction, lb (kN); V = shear, lb (kN); M = bending moment, lb•ft (N•m); D = deflection, ft (m); a = spacing, ft (m); b = spacing, ft (m); E = modulus of elasticity, lb/in2 (kPa); I = moment of inertia, in4 (dm4); < = less than; > = greater than.
Figure 2.3 gives the elastic-curve equations for a variety of prismatic beams. In these equations the load is given as P, lb (kN). Spacing is given as k, ft (m) and c, ft (m).
CONTINUOUS BEAMS
Continuous beams and frames are statically indeterminate. Bending moments in these beams are functions of the geometry, moments of inertia, loads, spans, and modulus of elasticity of individual members. Figure 2.4 shows how any span of a continuous beam can be treated as a single beam, with the moment diagram decomposed into basic components. Formulas for analysis are given in the diagram. Reactions of a continuous beam can be found by using the formulas in Fig. 2.5. Fixed-end moment formulas for beams of constant moment of inertia (prismatic beams) for

FIGURE 2.1 Geometric properties of sections