4 LANDER, Stresses in tJie Main Spars of Monoplanes. 



acteristic points ; and thirdly, to draw a broken line such 

 that it passes over and under the characteristic points on 

 each side of every support by equal distances, or dis- 

 tances inversely proportional to the span. 



As an example this method has been used in drawing 

 the bending moment diagram, Fig. 2, for a spar of 15' 9" 

 span, supported at equal distances of 4/ 6" apart by wires 

 as shown {Fig. 1), and having a small cantilever portion 

 at the tip. The loading has been taken as amounting to 

 40 lbs. per foot run. The moment at B was calculated as 

 being that due to the cantilever loading lying to the left 

 of B. The three parabolic diagrams are drawn as though 

 the three spans were discontinuous and their maximum 

 ordinates will therefore be equal to 101 ft. lbs. To deter- 

 mine the base line, the separate spans were divided into 

 three equal parts and perpendiculars ii\jj\ kk\ 11' erected 

 equal in length to two-thirds that of the maximum height 

 of the parabolas, since this is the value of the expression 



2 A x 



IT 



when the load is uniformly distributed. The base line 

 was then drawn so as to make the bending moment at B 

 equal to the cantilever bending moment, and so as to pass 

 over and under the characteristic points z, j and k, I 

 on each side of each support by equal amounts, and 

 finally to give a value of zero for the bending moment 

 at the right extremity since a flexible attachment to the 

 fuselage is assumed at this point. This base is repre- 

 sented by the broken line abcde in the drawing. The 

 moments at C and D will be given by eg and d/i, and 

 amount to 55 ft. lbs. and 88 ft. lbs. respectively. The 

 maximum bending moment occurs at B and is equal to 

 1 01 ft. lbs. If the load had varied irregularly or had 

 decreased uniformly from the chassis to the wing tip, the 



