6 



STEEL ROOF TRUSSES AND MILL BUILDINGS . 



CHAP. I. 



where P n and P are the same as in (3) and (4), and A is the angle of inclination of the surface 

 in degrees (A being equal to or less than 45), gives results which agree very closely with Hutton's 

 formula, and is much more simple. 



Hutton's formula (3) is based on experiments which were very crude and probably erroneous. 

 Duchemin's formula (4) is based on very careful experiments and is now considered the most 

 reliable formula in use. The Straight Line formula (5) agrees with experiments quite closely 

 and is preferred by many engineers on account of its simplicity. 



The values of P n as determined by Hutton's, Duchemin's and the Straight Line formulas 

 are given in Fig. 3, for P equals 20, 30 and 40 Ib. 



It is interesting to note that Duchemin's formula with P equals 30 pounds gives practically 

 the same values for roofs of ordinary inclination as is given by Hutton's and the Straight Line 

 formulas with P equals 40 pounds. 



FIG. 



O 5 K> l& 20 5 30 35 40 45 50 55 60 65 70 . 75 60 65 90 



X^iqle Exposed Roof makes with Horizontal in Degrees, A. 

 3. NORMAL WIND LOAD ON ROOF ACCORDING TO DIFFERENT FORMULAS. 



Duchemin has also deduced the formula 



PK = P 



2 sin 2 A 



i + sin 2 A 

 where PA in (6) equals the pressure parallel to the direction of the wind, Fig. 2; and 



p p 2 sin A -cos ^4 

 ' 



i + sin 2 



(6) 



(7) 



where Pj in (7) equals the pressure at right angles to the direction of the wind, Fig. 2. PI may 

 be an uplifting, a depressing or a side pressure. With an open shed in exposed positions the 

 uplifting effect of the wind often requires attention. In that case the wind should be taken 

 normal to the inner surface of the building on the leeward side, and the uplifting force determined 



