8 LANDER, Stresses in the Main Spars of Monoplanes. 



found from the above diagram will give an equation from 

 which P x may be determined. Similarly by equating 

 moments of forces to the left of o to the moment at o as 

 found from the diagram P 2 may be deduced, and finally 

 P. A may be obtained since the moment at E is zero. 

 These values of P v P v P 3 will be very close approxima- 

 tions to their true values. The bending moment diagram 

 for the loading as actually applied may now be drawn. 

 At B (Fig. 6) set up a perpendicular equal in length to 

 P^dcosa and join the extremity of this to the point E at 

 the end of the spar. At C add to the ordinate at that 

 point a length mn equal to P„d cos /3 and join its ex- 

 tremity to E. At D add to the total ordinate at that 

 point a length op equal to P s d cos $ and again join to E. 

 This diagram will represent with considerable accuracy 

 the diagram of bending moments actually induced by the 

 approximately horizontal components of the true pulls 

 in the wires. Using the upper lines of this diagram as 

 bases, draw parabolas to represent the bending moment 

 diagrams for the spans simply supported at B, C, D, E. 

 It is necessary now to determine the position of the 

 characteristic points for figures of shape such as these 

 which consist of a parabola superposed upon a trapezium 

 or triangle. The best method is to consider separately the 

 component elementary figures, viz., rectangles, parabolas, 

 and triangles which constitute the complete diagram. 



If B be the breadth of the retangular diagram and L 

 the span under consideration, the height of the character- 

 istic point above the horizontal base line will be 



2 A X 



which reduces to B and it is therefore apparent that 

 these points lie upon the upper line of the rectangle 

 {Fig. Ja). In the case of a triangle of maximum height at 



