Now, referring to Fig. 39, suppose that while the solid sash was still in the position, it were sawed clear through along the dotted line. Now what would happen? Why, since the left-hand end of one sawed part is being pushed upward by 14.4 pounds, and being pushed downward by the weight on top, which is only 8 pounds, the left-hand piece would move upward with a force of 14.4 8=6.4 pounds. The right piece has a force of 10 and 20, which is 30 pounds pushing it down, and only 23.6 pushing it up, and there fore it will go downward with a force of 30 less 23.6, which is 6.4 pounds, Fig. 40. Therefore one part will move upward, and the other part downward, as shown in Fig. 40, the parts sliding over each other along the section sawed. Be fore the material was sawed, the material at this place was strong enough to keep the pieces from sliding. In other words it was strong enough to stand the 6.4 pounds. On account of the fact that the portions slide over each other in a manner similar to being cut by a pair of shears, the action is called shearing, and the value 6.4 is called the shear. As long as the loads between the place considered and the end are less than the reaction at that end, that part will move or tend to move upward with a force equal to the difference between the reaction and the loads.
When the loads on top and between the place and the reaction are greater than the reaction, then that portion of the beam will move or tend to move downward.
In order to simplify the work of writing out certain portions of this work, the following signs will be used: x means Multiplied by; + " Added to (or positive);— " Subtracted from or taken from (or negative) ; " Is equal to, or comes to, or the amount left; " bivided by.
Thus 16+7=23 means that if 16 be added to 7, it will come to 23. Or again, 16-10=6 means that if 10 be taken away from 16 there will be 6 left, or the amount left will be 6.
From the foregoing, shear may be defined as tendency of one part of a beam to slide past the other part.
The actual value of the shear is equal to the reaction less all the loads between the sec tion (part under consideration) and the end at which R, acts.
•?/ kl 0 -., R i' 0 i 2 I ir i r . 1 ; f 1 i II I 1 I i i A ' : ' ' 1 , 1 1