10 FORCES IN THE SAME PLANE. [CHAP. I. 



to the vertical reaction at A, a b = the sum of the horizontal 

 components, or the horizontal force at A, and o b the vertical 

 reaction at the right support. This last line should close the 

 force polygon and bring us back to o. 



Now starting at the left, support, we have the vertical reac- 

 tion a c, the horizontal force a , and the wind force P l5 in 

 equilibrium with A and E. Closing the polygon by lines par- 

 allel to A and E, we obtain the strains in these pieces, E ten- 

 sion and A compression. At the next apex we have A and P 3 

 in equilibrium with 1 and B. Completing the parallelogram, 

 we find 1 compression and B compression. At the next apex 

 1 and E are in equilibrium with 2 and F, and we find F and 2 

 tension and so on. The upper flanges are in compression and 

 start from the ends of the forces p ls P 2 , etc. The lower flanges 

 radiate from b. If we were to carry out the construction for 

 the rest of the frame, the upper flanges after D would radiate 

 from o. 



A comparison of Fig. 6 (a) and (b) shows that whereas under 

 uniform load the strain in 1 is tension, for wind force the same 

 brace is in compression. In fact in the first case all the braces 

 are in tension, while in the second 1, 3, and 5 are compressed, 

 and 3 and 5 quite severely. The strains in the bracing gener- 

 ally are much greater in the second case. 



Were we to consider the wind as blowing from the other 

 side, or what is the same thing, suppose the right end fixed and 

 the left supported on rollers, then the horizontal reaction a b 

 will be applied at the right abutment. In this case the lower 

 flanges will radiate from a instead of &, and the first upper 

 flange will start from o. Supposing the first two lines of this 

 new diagram drawn, as indicated by the dotted lines, and fol- 

 lowing round from b to o, and so round to a and back to b, it 

 may easily happen that the last upper flange is in tension and 

 the last lower flange in compression that is, a complete reversal 

 of the ordinary condition of strain. 



For an excellent presentation of the above method, we refer 

 the reader to Iron Bridges and Roofs, by "W. C. Unwin, pp. 

 128-140. The above method is there referred to as "Prof. 

 Clerk Maxwell? 8 Method" and as such is known and used in 

 England.* 



* Phil. Mag. , April, 1864, and a Paper read before the British Association foi 

 the Advancement of Science, by Prof. Maxwell, in 1874. 



