maximum deflection and the rest as before: see Fig. 175. Thus in the case of the beam in (654) we obtain m = (5+2)5 × 2 × 2 - 11

{25 +

2

3

= 1.5 foot from the weight, therefore

1.5 0.5 foot, or 6 inches from the centre.

As the distance of the weight from the centre increases, so does m increase, and it becomes a maximum when the weight is at the support, when z = (L), and it then becomes m = (5+5)

- {25+

5 × 5 × 2
3

251

3

4.227

= 4.227 feet from the weight (and

the support), or 5 0.773 foot from the centre, which is equal to 77351546 of the half-length of the beam. From this it appears that wherever a weight is placed, the point of maximum deflection can never be more than 0.1546 of the half-length distant from the centre.

=

(657.) Comparing the curves A and B in the Diagram, Fig. 213, we observe this remarkable fact; that the deflection at any and every point of a beam with a central load is greater than would be produced by that same weight at any other point: for example, the curve B the deflection at every point throughout the length by a given central weight, and A= the deflection at the same point by the self-same weight placed there. This of course is due to the fact that the beam is less strained by a weight out of the centre than by the same weight in the centre. When strained at every point to the same extent, or in proportion to the strength, the deflections are given by the line C.

(658.) "Laws of Deflection."-The Deflection of beams varies very much with the methods of fixing and loading (667): to simplify the matter we may take as a Standard case, that of a horizontal beam, supported at each end and loaded in the centre: other conditions may be considered afterwards. We then have the Rules

---

168

.344

⚫3368 27,028,500

224

⚫458

*4491 27,067,900

280

⚫571

336

⚫684

392

.3613 27,817,800 •7226 27,701,900|

27,477,800

27,778,500 | 27,851,000

001 1.0700 1.084 27,960,700 0021-3940 1.445 28,616,000| ⚫5614 27,139,000 003 1.7410 1 804 6737 27,186,600 003 2.1590 2 168 .800 7860 27,118,600 004 2.5065 2.529 448 ⚫916 ⚫8982 27,067,900 504 1.005 1.010 27,754,700 560 1.124 1.223 27,573,600 616 1.222 1.235 27,895,000

006 2.8015 2.890 28,478,100| 0073.1635 3.252 28,371,800 008 3.6095 3.613 27,629,000 010 3.9595 3.974 27,705,300

672 1.332 1.374 27,921,400 011 4.3370 4.336 27,593,300 728 1.434 1.459 28,096,500 ⚫017 784 1.547 1.572 28,047,700 019

840 1.693 1.684 27,459,600 019 896 1.824 1.797 27,264,200 ⚫019 952 1.933 1.909 27,256,900 020 2.044 2.02127,293,000

1008

⚫021

1064 2-165 2 133 27,199,100 022 1120 2.256 2.246 27,470,000

:::::