INTERNAL FORCES 61 



equal over the entire area. In a frame pieces are generally so 

 placed that the stresses are purely tension or compression, but a 

 beam is a solidly filled frame and the stress is greatest at top and 

 bottom, reducing to zero on the line where the compressive force 

 changes to tension. It is necessary then to find the position of 

 the center of gravity of the beam on each side of the neutral 

 plane. 



The question may be asked, " Why is the depth used as a 

 divisor? " Referring to Fig. 48 and Fig. 49 a dotted line is shown 

 from B to D. The moment is obtained by multiplying the load 

 by the horizontal distance from the wall. To resist this moment, 

 which means to prop up the member AB, there must be some 

 force exerted at a distance BD from the point B. That is, the 

 bending moment and the moment to resist it are taken about the 

 point B. The bending moment at B = 8 X 3000 = 24,000 ft. Ibs. 

 This is resisted by some force acting about the point B with an 

 arm = BD. Thus the upward pushing force in the member 

 AC must equal the downward moment divided by the length BD. 

 This upward force is a reaction and is compressive. 



To obtain a reaction multiply the loads by the distance through 

 which they act and divide by the span length between supports. 

 The obtaining of tensile and compressive stresses is the same 

 thing. First a downward bending moment is obtained and then 

 a reaction is found by dividing, not by the span of the beam, but 

 by the span between supports. There is an upper support to 

 which the tension member is fastened and a lower support against 

 which the compression member abuts. The distance between them 

 is the span between supports. This span is the distance measured 

 on the shortest line between the lines representing the direction 

 of the forces, so it is perpendicular to the direction of the inclined 

 member. For all practical purposes the lower support is at D 

 and not at C. The member is merely carried on to the point C. 



It is correct to multiply the load by the arm BA and divide 

 by the arm BD in all cases, but considerable work must be done 

 to obtain the length of the arm BD. This requires a knowledge 

 of geometry and trigonometry and the use of tables of functions 

 of angles. To obtain the length of the inclined member and use 

 this as a moment arm and then divide by the vertical distance 

 between the centers of gravity of the top and bottom members, 

 is the shortest method and commonly used, for the result is correct. 



