51 JOURNAIv OF THE 



the temperature afterwards rises /=25°C (45°F). If the 

 expanded horizontal bar CC is supposed in position, the 

 end bars A C and KC will each be too long- by 



1 15 t 15.52/ 

 . cos i + =:.00027()/ 



2 82500 82500 



where / = an«-le that end bar m kes with chord. 

 The tension in end rod or tie is 



15.5 (14—/)) -4 

 Twice the product of these two expressions, or, 

 {couslant—m2\M) 

 g^ives the work due to heat in the truss, neg"lectin<>- any 

 expansion of the wood. 



By the article of the writer referred to above (Section 

 6), we must add this term to the elastic work (9) of the 

 entire truss and put the derivative with respect to p 

 equal to zero. Doinof this we obtain, 



58960/)— 298625— .00214/K^O. 

 If we assume E for yellow pine, 1,600,000 pounds xwi' 

 sq. inch, or, as we n;ust substitute it here, where all 

 dimensions are in feet and loads in thousand pounds, 

 E =230400 thousand pounds per sq. foot, 



we derive, 



58960/)— 298625— 493/^0 (10), 



whence for /=4-25(C), /):=5.27 

 and ior /—25(C), /) = 4.85. 

 The rise of temperature of 25°C (45''F) above the sup- 

 posed normal of lO^C (50°F) ^ives the greatest reaction, 

 2103 ' pounds, at left abutment^ and hence the greatest 

 momemt — 2103x 15 fcot pounds at left post. This 

 moment calls for a beam 7.4 inches wide by 16 deep. It 

 was made 8 inches wide to allow somewhat for the uni- 

 form compression, which, however, is less than 300 

 pounds per square inch on account of the largfe section, of 

 the chord. At the left post, the weight of the chord 



