Table I. Values of Constants C✶ and H* to be Used in Equations for Different Systems of Loads Loads not symmetrical about middle of member Load varying uniformly from zero at one end to a maximum at the other end 10 B 1 Load varying uniformly from zero at any point to a maximum at one end 12 22 (5u+3ml) (5u+2ml) (15u+8ml) -(15u+7ml) 60 60 120 120 E 10 15 *For explanation of notation, see pages 123 and 124. F is the area of the moment-diagram of a simple beam having the same length and carrying the same load as the member in question. F Values of for different loads are given in Table II. 10. Determination of Moments in Fixed and Continuous Beams by the Slope Deflection and Area-Moment Method. Before proceeding with numerical examples illustrating the application of these methods of analysis, it MBA MBA MBA Fig. 21. Single-Span Beams with assumed to be fixed, the angle ports are on the same level, R By Formula (25) should be noted that the connections between monolithic members are assumed to be rigid, the lengths of the members are considered to be unchanged by axial stresses, and the shearing-deformations assumed to be zero. The examples deal only with members the supports of which are assumed to be on the same level throughout the process of loading. This is practically the usual condition in well-designed buildingframes, except when there is an appreciable settlement. In such cases the value R, a function of the settlement, is introduced in the general Formulas on page 123. (a) Single-Span Beam with Fixed Ends. If a beam is restrained at both ends, that is, if there is any condition other than simple support, Formulas (25) and (26) apply. Since in this case both ends are A =0B0 (Fig. 15). Also, since both supОв = 0. Values of CAB and CBA, equal in this case to the two required moments are then taken from Table I or II for any usual system of loading, or they can be computed as explained on page 127 for cases not included in these tables. Example 3. Let it be required to find the bending moments at the supports for the three fixed beams with the dimensions and loads shown in the three diagrams of Fig. 21. |