, LAWS OF BONE ARCHITECTURE 195 



If the load P is at the distance m from the support, the mo- 

 ment about the support is P times m, which is the bending mo- 

 ment at the support. At any point at the distance x from P, 

 between the load P and the support, the bending moment is 

 equal to P times x. These products vary uniformly from zero, 

 at the point of application of P, to a maximum P ' m at the sup- 

 port. The amount of the bending moment at any point will 

 be shown graphically, if the product P' m'l^ measured to suitable 

 scale vertically downward under the point of support, and from 

 a horizontal base line; then from the point on the base line 

 under the point of application of the force P, a line is drawn to 

 the ordinate erected under the support. The triangular figure, 

 figure 7 a, thus drawn is the bending moment diagram. Scal- 

 ing the vertical ordinate between the base line and the last drawn 

 hne will give the amount of the bending moment for the section 

 of the beam vertically above the ordinate. 



In figure 7, h is shown the bending moment diagram for a 

 simple beam on two supports, carrying the load P. 



27. The vertical shear for the single load P on the cantilever 

 remains the same for every section of the beam from the point of 

 application of this load to the support. It is represented graph- 

 ically to scale by drawing a line parallel to the horizontal 

 base line, at a distance measured to any convenient scale, as 

 one inch = 100 pounds shear. The diagram giving the values 

 of the vertical shear at all points in the beam is called the shear 

 diagram. Such a diagram is drawn for the cantilever and is 

 shown in figure 7 a. 



Figure 7 h shows a shear diagi'am constructed for the simple 

 beam resting on two supports. 



28. Relation between internal stresses and external loads. All 

 external forces acting on a beam maintain equiUbrium by means 

 of internal stresses produced in the beam by these forces. Since 

 in any section of a beam the external forces produce bending 

 moment and shear, the problem is to determine the relation 

 between these and the internal stresses in any given section. 



