This section is from the book "The English And American Mechanic", by B. Frank Van Cleve. Also available from Amazon: The English And American Mechanic.
The conditions of the stress borne or to be provided for by them are as follows:
Header or Trimmer beams support 1/2 of the weight of and upon the tail beams inserted into or attached to them.
Trimmer Beams support, in addition to that borne by them directly as a floor beam, each 1/2 the weight on the headers.
The stress, therefore, upon a header is due directly to its length, or the number of tail beams it supports; and the stress upon the trimmer beams is that of their own stress as a floor beam, and 1/2 of the weight upon the header supported by them.
The distance bet ween the support of the trimmer-beams and the point of connection with the header does not in anywise affect the stress upon the trimmer-beams; for In Just proportion as this distance is Increased, and the stress upon them consequently Increased, by the suspension of the header from them nearer to the middle of their length, so is the area of their surface supported by the header reduced, and, consequently, the load to be borne by it.
 
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