Art. 98. PRACTICAL USES OF CONTINUOUS BEAMS. 



= - 



Multiplying this value by 





The reactions may now be determined from the following 

 equations . 



Ril P(l kl)= M B Rd( +nl) P(l M + nl) + R*nl= M c 

 RJ = M G Rt(l -f nl} R^nl =M R 



In this case, as in the case of Fig. Ill, there must be one 

 negative reaction if the beam is to be continuous. 



When there is a partial uniform load on any span, it may be 

 divided into a number of equal parts and each part treated as a 

 concentrated load. 



98. Practical Uses of Continuous Beams. Continuous 

 beams are avoided, when practical, on account of the uncertainty 

 of the stresses. This uncertainty is due to the difficulty of 

 making the supports fit the unstrained outline of the beam, to 

 the elasticity of the supports, and to the possible settlement of 

 supports. When the supports do not fit the unstrained outline 

 of the beam, they are said to be ' ' out of level. ' ' A slight change 

 in the "level" of the supports, may cause marked changes in 

 the stresses (96). If the exact level of the supports were fixed, 

 the stresses could be calculated by means of modifications of 

 equations (43) and (44). These modified equations are obtained 

 by taking the axis of x so that the elevations of the supports will 

 be 2/ q , 2/ r , and y a ; then there will appear in the second members 



of equations (43) and (44), the term +6^7 r ~ yq + 



Swing bridges rest upon three or four supports when in the 

 "closed" position, and one of the limiting conditions for which 

 stresses are calculated is that of a continuous beam. This is the 

 most important application of the above formulas 1 . Sometimes 

 the track of a railway bridge is supported directly by the top 

 chord of a deck-truss bridge, in which case the top chord is a 

 continuous beam with elastic supports ; the bending stresses are, 



*See Merriman and Jacoby's Roofs and Bridges, Part IV, Wright's 

 The Designing of Draw-Spans, and Johnson's Modern Framed Struc- 

 tures. 



