BEAMS AND BENDING 103 
al load, 10 tons. Scales,—Linear, } inch to 1 foot. Forces, 1 inch to 3 tons. 
ents, 1 inch to 10 foot-tons. 
. Two cantilevers, 10 feet long, carrying a beam 20 feet long, as shown in 
120, p. 91. The whole carrying a load of 40 tons uniformly distributed over 
a hl rs and beam. Scales.—Linear, 4 inch to 1 foot. Forces, 1 inch to 
tons. Moments, | inch to 50 foot-tons, 
‘18. Girder resting on su | ing 40 feet apart. Single travelling load of 2 tons. 
Wi i also the pean nt uniform dead load w in tons per foot, es.—Linear, 
inch to 8 feet. Forces, 1 inch to 1 ton. Moments, 1 inch to 8 foot-tons. 
19, Girder resting on supports 50 feet apart. A travelling uniform load of } ton 
per foot. The length of the load being not less than 50 feet. Scales.—Linear, 
4 inch to 10 feet. Forces, 1 inch to 5 tons. Moments, | inch to 50 foot-tons. 
- 20. Girder resting on supports 50 feet apart. Two travelling loads of 5 tons 
each, and at a fixed distance of 10 feet apart. Find also the equivalent uniform 
load w in tons per foot. Scales,—Linear, 1 inch to 5 feet. Forces, 1 inch 
to 5 tons. Moments, 1 inch to 40 foot-tons, 
21. Girder resting on supports 50 feet apart. ‘T'wo travelling loads, one of 8 
; “tons and the other of 4 tons, the fixed distance between the loads being 12 feet. 
Find also the equivalent uniform dead load w in tons per foot. Scales, the 
ee as in Exercise 20. 
92. Same as Exercise 21, but in addition to the travelling loads there is a 
, Swafforinly distributed load of 3 ton per foot run. Determine the portion of the 
_ girder in which the shearing force may change sign. 
23. Girder resting on supports 60 feet apart. Three travelling loads W; 
- =10 tons, W2=15 tons, and Ws=5 tons. We is’ between W; and Ws, and is 
10 feet from W) and 6 feet from Ws. Use the graphic tracing paper method. 
_ Find the equivalent uniform dead load w in tons per foot. Scales.—Linear, 
1 Lin to 10 feet. Forces, 1 inch to 10 tons. Moments, 1 inch to 100 foot-tons. 
24 An axle AB rests in swivel bearings at A and B12 feet apart. At a point 
_ 4 feet from A there is a vertical load of 600 Ibs., and at a point 4 feet from B 
there is a horizontal load of 900 lbs. at right angles to the beam. Calculate the 
bending moments on the axle, in ft.-lbs., at distances of 2, 4, 6, 8, and 10 feet 
F from A. Find also the shearing forces, in lbs., on the axle ‘at sections 2, 6, and 
10 feet from A. 
109. Stresses Induced by Bending. —At (a) Fig. 141 is shown a 
portion of a straight beam before it is subjected to bending. At (0) is 
Shown the same portion bent to a cir- 
 eular form. It is obvious that in bend- 0 
_ ing this portion of beam, the plane of | 
oes paper being the plane of bending, 
® upper part is compressed while the D 
lowe: ait is stretched, and there will F 
adams be a surface which will separ- Y, | 
_ ate the compressed and stretched parts; (qa) aa 
_ this surface is called the neutral surface J 
of the beam. Let HK be the position 
of the neutral surface. Transverse sec- 
AD and BC, which are perpen- 
h “dicular to the neutral surface, will be 
lel to one another when the beam 
is straight, but when the beam is bent 
these sections will be inclined to one 
_ another and their planes will intersect at 
0, ‘the axis of the cylindrical surfaces 
famed by longitudinal sections of the 
perpendicular to the plane : 
bending. R, the radius of the curved “yee 
surface, is called the radius of curvature of the bent beam. 
g Bx 
c 
