146 Mechanics of Materials §6.5 6.5.Advantages and disadvantages of built-in beams Provided that perfect end fixing can be achieved,built-in beams carry smaller maximum B.M.s (and hence are subjected to smaller maximum stresses)and have smaller deflections than the corresponding simply supported beams with the same loads applied;in other words built-in beams are stronger and stiffer.Although this would seem to imply that built-in beams should be used whenever possible,in fact this is not the case in practice.The principal reasons are as follows: (1)The need for high accuracy in aligning the supports and fixing the ends during erection increases the cost. (2)Small subsidence of either support can set up large stresses. (3)Changes of temperature can also set up large stresses. (4)The end fixings are normally sensitive to vibrations and fluctuations in B.M.s,as in applications introducing rolling loads (e.g.bridges,etc.). These disadvantages can be reduced,however,if hinged joints are used at points on the beam where the B.M.is zero,i.e.at points of inflexion or contraflexure.The beam is then effectively a central beam supported on two end cantilevers,and for this reason the construction is sometimes termed the double-cantilever construction.The beam is then free to adjust to changes in level of the supports and changes in temperature (Fig.6.5). Pin joints Points of inflexion Fig.6.5.Built-in beam using"double-cantilever"construction. 6.6.Effect of movement of supports Consider a beam AB initially unloaded with its ends at the same level.If the slope is to remain horizontal at each end when B moves through a distance 6 relative to end A,the moments must be as shown in Fig.6.6.Taking moments about B RAXL=MA+MB and,by symmetry, M=Ma=M 2M RA二L 2M Similarly, RB in the direction shown.146 Mechanics of Materials $6.5 6.5. Advantages and disadvantages of built-in beams Provided that perfect end fixing can be achieved, built-in beams carry smaller maximum B.M.s (and hence are subjected to smaller maximum stresses) and have smaller deflections than the corresponding simply supported beams with the same loads applied; in other words built-in beams are stronger and stiffer. Although this would seem to imply that built-in beams should be used whenever possible, in fact this is not the case in practice. The principal reasons are as follows: (1) The need for high accuracy in aligning the supports and fixing the ends during erection (2) Small subsidence of either support can set up large stresses. (3) Changes of temperature can also set up large stresses. (4) The end fixings are normally sensitive to vibrations and fluctuations in B.M.s, as in These disadvantages can be reduced, however, if hinged joints are used at points on the beam where the B.M. is zero, i.e. at points of inflexion or contraflexure. The beam is then effectively a central beam supported on two end cantilevers, and for this reason the construction is sometimes termed the double-cantilever construction. The beam is then free to adjust to changes in level of the supports and changes in temperature (Fig. 6.5). increases the cost. applications introducing rolling loads (e.g. bridges, etc.). oints of inflexion Fig. 6.5. Built-in beam using “doubleantilever” construction. 6.6. Effect of movement of supports Consider a beam AB initially unloaded with its ends at the same level. If the slope is to remain horizontal at each end when B moves through a distance 6 relative to end A, the moments must be as shown in Fig. 6.6. Taking moments about B RA x L = MA+ MB and, by symmetry, MA= Mg= M 2M L .. RA=- Similarly, 2M L RB=- in the direction shown