GRAPHIC STATICS 239 



If the end spans were restrained at the outer ends, the broken base 

 line would pass through points / and 8. Starting from A a line 

 is drawn upward to the vertical line through support B. This 

 broken line should pass above point 2 and below point 3, or it 

 should pass below point 2 and above point 3, or it should pass 

 through these points. In the present case it passes through 

 them. 



Passing through point 3 the line passes below point 4 and 

 strikes the vertical line through support C. It then passes above 

 point 5 and point 6 and below point 7 to close on support E. 



The broken line must be fixed by trial in all cases. It must 

 pass below (or above) one point and above (or below) the adjacent 

 point in the adjoining span to the vertical line through the sup- 

 ports. If the spans are equal the broken base line passes as far 

 below one point as it passes above the adjacent point on the 

 adjoining span. When the spans are unequal the line passes 

 above or below inversely as the length of the span. That is, on 

 the shorter span the vertical space is greater than it is on the 

 longer span; in proportion to the lengths of the spans. 



In fixing the position of the broken line the author puts over 

 the drawing a sheet of tracing paper on which to mark the several 

 trial lines. When the final line is selected the points on the ver- 

 tical lines through supports are pricked in with a needle, the 

 tracing paper is taken off, and the line drawn. The line can 

 have only one position. 



In the figure the moment diagram is shown at (a). The broken 

 line is a base line from which to scale the bending moments. All 

 the shaded portion within the parabola on each span represents 

 positive moment. All the shaded portion outside the parabola 

 between it and the vertical line through supports represents 

 negative moment. At (6) is shown graphically the system of 

 cantilever and simply supported beams into which a continuous 

 beam over several supports is divided. The ends of the can- 

 tilevers are at the point of contraflexure, the curved line at (d) 

 showing the deflection of the beam to an exaggerated scale. 



At (c) is the curve for shears and also reactions. The reaction 

 is always equal to the shear. The shear is zero at the point of 

 maximum bending moment, or, rather, it passes through zero at 

 this point, the sign for shear being positive (+) above the base 

 line and negative (-) below the line. The reaction on either 



