PAPERS READ IN SECTION H. 



1.— TRUSSED BEAMS AND SIMILARLY IMPERFECTLY BRACED 

 STRUCTURES. 



By GEORGE UIGGIN.S, M.C.E.. Men,oii,-tir r-nrcsif;/. n.nl M. Inst. C.E. 



The type of structure, which it is intended to discuss in the 

 following notes, is one that is very frequently met with. Trussed 

 beams are more numerous tlian completely braced girders, and their 

 use is likely to increase. Nevertheless, so far as the writer is aware, 

 xio publication presents the theory of the stresses occuri-ing in trussed 

 beams in a manner sufficiently simple to enable the dimensions of 

 the members to be readily calculated. The subject is treated ex- 

 haustively by W. Kitter, who employs the principle of virtual work, 

 and allows in his fornmlae for such matters as possil^le changes of 

 <;ross-section in the various members aad all extensions, compressions, 

 and deflections. 



What appears to be wanted, however, is a discussion of the 

 theory of the simple trussed beam in which all but factors really 

 essential to the design are left out. No necessary ac-curacy should 

 he sacrificed ; but, seeing that the engineer does not know the 

 .strength of his material, frequently within 20 per cent, of its true 

 value, he can well afford to ignore minor modifying factors which will 

 affect his results to an extent not greater, perhaps, than 1 or 2 per 

 cent, on the whole. 



It will be assumed here that the beams have uniform cross- 

 sections from end to end, likewise each tension member and each 

 post. 



It will be assumed, further, that the structure, when built and 

 loaded with its working load, shall not undergo any defonnation 

 sei'ious enough to influence the determination of the stresses so far 

 an that detennination depends upon the relative inclinations of 

 adjacent members. This can be insured by making the beam stiff" 

 enough. 



And, lastly, it will be assumed that the members are, severally, 

 incompressible and inextensible — ^an assumption which is war- 

 ranted because in most ordinary cases any deflection, or change of 

 shape, which the structure may undergo, as a whole, owing to 

 extensions and compressions of its members, is insig-nificant in com- 

 ]>avison with the deflections that are caused to occur in the beam by 

 transverse loading. This assumption will not appreciably affect the 

 detennination of stresses. 



Let us, then, examine the eft'ects of the foregoing assumptions 

 upon the calculation of the stresses in titissed beams of the ordinary 

 forms — in those, for instance, shown in Figs. 1, 2, 2a, 3, and 3a. In 

 Fig. 1, the two ends and the middle point of the beam will remain 

 at the same level under all loads. In Figs. 2 and 2a one post will 

 rise as much as the other one drops. In Figs. 3 and 3a, there will 

 be a definite geometrical relation between the rises and falls of the 



