STRESSES IN ROOF TRUSSES. 



Dead Load Stresses. -The dead load is made up of the weight of the truss and the roof 

 i iivn inu.. and is usually considered a* ,i|i|.li< <! at the pam-1 points of the upper chords in computing 

 stresses in roof trusses. If the purlins do not come at the panel points, the upper chord will have 

 to be designed for direct stress and stress due to flexure. 



The stress in a Fink truss due to dead loads is calculated by graphic resolution in (a) Fig. 2. 



The loads are laid off, the reactions found, and the stresses calculated beginning at joint L<, 

 as explained in Fig. I. The stress diagram for the right half of the truss need not be drawn 

 wli-.-iv tlu- truss and loads are symmetrical as in (a) Fig. 2; however, it gives a check on the accuracy 

 >f the work and is well worth the extra time required. The loads PI on the abutments have no 

 effect on the stresses in the truss, and may be omitted in this solution. 



In calculating the stresses at joint PI, the stresses in the members 3-4, 4-5 and x-$ are 

 unknown, and the solution appears to be indeterminate. The solution is easily made by cutting 

 out members 4-5 and 5-6, and replacing them with the dotted member shown. The stresses in 

 the members in the modified truss are now obtained up to and including stresses 6-x and 6-7. 

 Sinn- the stresses 6-x and 6-7 are independent of the form of the framework to the left, as can 

 easily be seen by cutting a section through the members 6-x, 6-7 and j-y, the solution can be 

 carried back and the apparent ambiguity removed. The ambiguity can also be removed by cal- 

 culating the stress in f-y by algebraic moments and substituting it in the stress diagram. It will 

 be noted that all top chord members are in compression and all bottom chord members are in 

 tension. 



Snow Load Stresses. Large snow storms nearly always occur in still weather, and the 

 maximum snow load will therefore be a uniformly distributed load. A heavy wind may follow a 

 sleet storm and a snow load equal to the minimum given in 19, " Specifications for Steel Frame 

 Buildings," Chapter I, should be considered as acting at the same time as the wind load. The 

 stresses due to snow load are found in the same manner as the dead load stresses. 



Wind Load Stresses. The stresses in trusses due to wind load will depend upon the direction 

 and intensity of the wind, and the condition of the end supports. The wind is commonly con- 

 sidered as acting horizontally, and the normal component, as determined by one of the formulas 

 in 20, " Specifications for Steel Frame Buildings," Chapter I, is taken. 



The ends of the truss may (i) be rigidly fixed to the abutment walls, (2) be equally free to 

 move, or (3) may have one end fixed and the other end on rollers. When both ends of the truss 

 are rigidly fixed to the abutment walls (i) the reactions are parallel to each other and to the 

 resultant of the external loads; where both ends of the truss are equally free to move (2) the 

 horizontal components of the reactions are equal; and where one end is fixed and the other end 

 is on frictionless rollers (3) the reaction at the roller end will always be vertical. Either case (i) 

 or case (3) is commonly assumed in calculating wind load stresses in trusses. Case (2) is the con- 

 dition in a portal or a framed bent. The vertical components of the reactions are independent of 

 the condition of the ends. 



Wind Load Stresses: No Rollers. The stresses due to a normal wind load, in a Fink truss 

 with both ends fixed to rigid walls, are calculated by graphic resolution in (b) Fig. 2. The reac- 

 tions are parallel and their sum equals the sum of the external loads; they are found by means of 

 force and equilibrium polygons. To calculate the reactions, lay off the loads PI, Pi, PI, Pt, PI, 

 as shown, and select the pole O at any convenient point. Then at a point on line of action of P\ 

 in the truss diagram, draw strings parallel to the rays drawn through the ends of Pi in the force 

 polygon. The string drawn parallel to the ray common to forces PI and PI in the force polygon 

 will cut the force Pj in the tr^ss diagram. Through this point draw a string parallel to the ray 

 common to forces Pj and P 8 in the force polygon, and so on until the strings drawn parallel to 

 the outside rays meet on the resultant of all the loads. The closing line of the force polygon 

 connects the two points on the reactions. Through point in the force polygon draw line O-Y 

 parallel to the closing line in the equilibrium polygon, R\ and Rt are the reactions, as shown. 



The stress diagram is constructed in the same manner as that for dead loads. Heavy lines 

 in truss and stress diagram indicate compression, and light lines indicate tension. 



