88 



MOMENT AREAS. 



Art. 65. 



sections. An inscribed curve, tangent to the string polygon 

 (Fig. 63) is the string polygon for uniform load. 



In truss bridges the uniform load is transformed into con- 

 centrated loads (panel loads) at the panel points, and the apexes 

 of the string polygon will lie on a parabola. 



65. Moment Areas. In Fig. 64 the moment at any section 

 as it or ss is Hy, y being the ordinate made by the string polygon 

 in the section. The area enclosed by the string polygon is called 

 the moment area. The moments represented by the ordinates 



TTl 



Fig. 64. 



above the closing line are of opposite sign to those below the 

 closing line. Moments which make a beam concave on the upper 

 side (produce compression in the upper fibers) are usually called 

 plus moments. 



A moment area gives a graphic representation of the bend- 

 ing moment at every section of a beam and is, of course, appli- 

 cable to trusses as well as solid beams. Thus at sections through 

 points a and b, the moment is zero and at load P 4 , it is a maxi- 

 mum. Between the points c and d, the moment is positive, and 

 beyond them it is negative ; these points of zero moment are 

 dividing points of contrary flexure. The part cd of length L is 

 exactly like an ordinary beam of the same length supported at 

 its ends, because the moments at the supports are zero. The end 

 reaction of such^a beam, at c, can be gotten from the location of 

 P 3 , P 4 , and P 5 , but it is also equal to the shear at c which is 



