224 APPLIED MECHANICS 
at each end, supposing the girder to rest on stone templets. Wall plates 
1 foot 6 inches square would give a bearing area of 2} square feet at 
each end, and the actual span or the distance between the reactions would _ 
then be about 37 feet 6 inches. 
Depth and Width—The minimum depth would be 54, of 37 feet 6 
inches, say 22 inches. It would be desirable for economy to go to +; of 
37 feet 6 inches, say 37 inches. Since head room is valuable, a com- 
promise of about 30 inches will be tried, say 24 inches between the centre 
lines of rivets in the flange angles. The girder is, it may be supposed, 
fairly well supported laterally by the cross girders which bring on the 
loads, and a width of 54, to 4, of the span may be taken, say a flange 
width of not less than 12 inches. 
Weight.—Using Unwin’s formula (p. 223). W=72 tons. 1=372 ft. 
7 =373$/25=15. c=1500. f=7 tons per square inch. 
wa 12% 875 x 15 
1500 x 7-374 x 15 
As a round figure, the weight of the girder will be taken as 4 tons. 
End Bearings and Exact Span.—The total weight is 72 + 4 = 76 tons. 
Each end reaction will be 38 tons. If wall plates 18 inches by 18 inches 
be used, the bearing pressure on each stone templet will be practically 17 
tons per square foot. A hard stone will safely carry this. The actual 
span may therefore be taken as 36 +14= 374 feet. 
Bending Moment and Shearing Force Diagrams.—These can now be 
drawn, and are shown in Fig. 331, p. 227. 
The maximum bending moment is at the centre, and is 4440 inch-tons, 
and the maximum shearing force is at the ends, and is 38 tons. 
Thickness and Stiffening of Web.—The depth of the girder between 
the centre lines of the flange angles is 24 inches. The depth of the web 
plate may therefore be taken at about 28 inches, and this is constant 
throughout the span. The shear per inch of depth diagram is at once set 
ut (Fig. 330, p. 226). Its value at the extreme end is 38/28 = 1°36 tons. 
‘the loads brought on by the cross girders are at intervals of 3 feet, this 
ecides that stiffeners must be placed at 3 feet intervals under the loads, 
and it remains to be seen whether further stiffeners will be required. 
Considering the panels between the stiffeners under the loads, the 
dimension d in the formule on p. 220 is 24 inches, the vertical distance 
between the centre lines of the rows of rivets in the boom angles and the 
web. Putting d= 24 inches in the first instance, and giving ¢, the web 
thickness, the values 2 inch, 35, inch, and } inch, § from the formula 
given is 0°73, 1:07, and 1°47 tons respectively, and these are plotted on 
the shear per inch of depth diagram (Fig. 330). It is now evident that 
except at the extreme ends a ;% inch plate is of ample strength. Near 
the centre a 3 inch plate would suffice. A change of thickness however, 
entailing, as it would, two web joints, would probably cost more than the 
metal saved, unless of course many similar girders are required. If a +> 
inch plate is to be adopted, extra stiffening must be used near the ends. 
The most convenient way to carry this out is to put intermediate stiffeners 
between those under the loads, reducing d to 18 inches. A 3 inch plate 
would then stand 1:1 tons per inch of depth, and a 7% inch plate 1°54 
tons. zs inch plate will therefore serve, a $ inch plate being too weak, 
= 4:07 tons. 
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