EXTERNAL FORCES 29 



with a value of 1, and X divided into 10 equal parts, the following 

 values are obtained, numbering the spaces from the bottom up. 



Points on X Ordinates (Y) 



1 . 0.949 



2 0.894 



3 0.837 



4 0.775 



5 0.707 



6 0.633 



7 - 0.548 



8 0.447 



9 0.317 



Assuming X and Y each with a value of 1, with X divided 

 into 8 equal parts, the following values are obtained : 



Points on X Ordinates (Y) 



1 0.936 



2 0.866 



3 0.791 



4 0.707 



5 0.612 



6 0.50 



7 0.353 



To construct a parabola by using a table of ordinates erect a 

 perpendicular at the middle of the span having a height equal 

 to the bending moment, using any convenient scale. Divide the 

 line into 8 or 10 equal parts and through the division points draw 

 horizontal lines parallel with the beam. Multiply the half span 

 by the value of the ordinate for any line and set off to scale the 

 length of the ordinate. Connect the ends by means of a French 

 curve and thus obtain the parabola. In this method the scale for 

 all horizontal lines is the scale used in drawing the beam. 



In Fig. 23 another method is shown. Divide the span of the 

 beam into any number of equal parts, numbering from each end 

 as shown. Multiply the maximum moment by the product of 

 the two figures under any line and divide by the product of the 

 two equal figures under the maximum moment line. The result 

 is the length of the perpendicular at the two numbers. Connect- 

 ing the upper ends of the perpendiculars by using a French curve, 

 the parabola is drawn. The scale used in drawing the perpendicu- 

 lar lines is the scale used in setting off the value of the bending 

 moment at the middle of the span. 



