ElvISHA MITCHBLI^ SCIENTIFIC SOCIETY. 44 



called W. At the upper joint, this vertical load W is 

 decomposed by the parallelogram of forces method into 

 components acting* down the main brace and along" the 

 upper chord respectively. The resulting" push along" the 

 upper chord is decomposed at the next joint into compon- 

 ents acting- along- the other main brace and vertical. The 

 triang-le of forces at this second joint is necessarily the 

 same as that at the first joint, as the horizontal com- 

 ponent is the same and the rafters are equally inclined to 

 the vertical. Therefore the stresses in the vertical and 

 rafter at the second joint are precisely the same in char- 

 acter and amount as at the first joint. Hence there will 

 be a tension W, in the vertical rods at the second joint 

 and this tension, pressing" the suspended beam upwards 

 ag'ainst the lower chord, tends to bend it upward. The 

 lower chord is thus in the condition of a beam of length 

 equal to the span and subjected to a sing'le upward force 

 W, acting- at one third of its leng-th from one end for equal 

 panel leng-ths. The force W, causes the lower chord to 

 press upwards ag-ainst the feet of the rafters, with a force 

 I W at the nearest rafter and JW at the furthest. As we 

 found the vertical component of the stress in both rafters 

 = W, acting- dovvnwards, the resultant pressures on the 

 abutments are, W— fW = JW and W— iW = |Was should 

 be, by the law of theLver, for the orig-inal load W acting" 

 at the first joint, the larg-er reaction occurring* at the 

 abutment nearest the load. 



The lower chord must be made of sufficient dimensions 

 to act as a beam to safely sustain a vertical force W act- 

 ing- upwards and placed a panel length from one end. The 

 moment is g"reatest at the force and equals | W (its re- 

 action at foot nearest rafter) multiplied by one-third the 

 span or length of lower chord from foot of one rafter to 

 that of the other. In addition, the section of the lower 

 chord must be made larg-e enoug-h to provide for the hor- 

 izontal component H. of the stress in a rafter at its foot. 

 This thrust generally acts at h inches above the center gf 



