Art. 04. CONCENTRATED AND UNIFORM LOADS. 



115 - 



the section at which the maximum moment occurs is not appar- 

 ent from a consideration of the loads separately. The maximum 

 shear is equal to the greater reaction, and after this has been 



determined, the section of 

 maximum moment is easily 

 gotten, because it is located 

 where the shear passes 

 through zero. If, for . ex- 

 ample, the cases of Figs. 

 101 and 96 are combined 

 as shown in Fig. 114, the 

 shear passes through zero at 14 ft. from A, and M m&JL 14000 X 

 141000X14X7 = 98000 ft. Ibs. 



In Fig. 115 the shear 



passes through zero at the soo /t> 5 per ft 



load and M max = 9000X16 A 

 -500X16X8 = 80000 ft. | 

 Ibs. 



The same rule applies 

 when there are any number of loads on the beam. With nothing 

 Imt concentrated loads, the shear must evidently pass through 

 zero at a load, and therefore the moment is a maximum under 

 some load. This is also evident if a moment diagram is drawn. 



95. Bending Moments and Shears for Beams Having 

 Fixed Ends. In order that the end of a beam may be fixed, 

 there must be a moment at the support of such magnitude as to 

 keep the elastic line horizontal at the support, as was explained 

 in Art. 89, and acting as shown in Figs. 94, 98, 99, 100, 102, 103, 



and 104. This condition is imposed by making = at the 



dx 



fixed end. In Fig. 99, for example, 



3f x <li = R& Mi J M X >1 1 = Rix Mi P (x h) 



Putting these values into the differential equation of the 



elastic line, two values of ~~ and two values of y will be gotten. 

 The conditions to be fulfilled are, y Q when x = ; y =0 when 

 x = l i+ l z . ^ = when a = 0; ^?= when = ^+^ ; at C, 

 y for one segment is equal to y for the other segment ; and at C, 

 -t for one segment is equal to - for the other. These six 



