118 MECHANICS 



outline of this diagram, however, is only approximately cor- 

 rect. To find its true form, the beam should be divided into 

 an infinite number of parts, in which case the lines 0^1, c\di, 

 di&i, e\fi, and f\b would be parts of a curve, shown dotted, 

 instead of a series of short, broken lines. 



MOMENT TABLES 



The methods of finding the shear and maximum moment 

 occurring in simple and in cantilever beams have been 

 explained. In these calculations the weight of the beam 

 itself, if of wood or steel, is often omitted. The various 

 unusual loadings were also considered, and the method of 

 finding the maximum bending moment was explained. 

 These methods will be found useful if such cases ever arise. 

 However, in practice the loads on the beams are often more 

 uniform, and if the weight of the beam itself is neglected, 

 the formulas given in the accompanying table may be used. 



Beams with fixed ends or even with one end fixed and one 

 simply supported are also given in the table. 



In each case in the table, the total load on the beam, in 

 pounds, is denoted by W. If there are two separate and 



W 

 equal loads on the beam, each one is called , so as to make 



the total load W. If the load is uniformly distributed over 

 the entire length of the beam, the load per foot will be 

 W -5- length of beam, in feet. The length of the beam is 

 denoted by /. If / is taken in inches, the moment will be in 

 inch-pounds; but if taken in feet, the moment will be in 

 foot-pounds. 



The usual method of indicating loading is adopted. A 

 simple support under a beam is shown by the conventional 

 arrow, while a cantilever or a beam fixed at the ends is 

 shown as in Case I or XVII, respectively. Cases XV and 

 XVI indicate a beam fixed at one end and supported at the 

 other. 



The maximum shear on a cantilever or on a beam fixed 

 at the end depends somewhat on the method of holding it in 

 the wall and the length that extends into the wall. How- 

 ever, the maximum shears given in the table are correct 



