136 APPLIED MECHANICS 
22. A beam of uniform section is built into a wall at one end, and rests on a 
support at a distance of 20 feet from the wall. A load of 26 tons rests on the 
beam at a point 12 feet from the wall. Taking E=13,000 tons per square inch, 
‘and I=1000 in inch units, determine the reaction of the support on the beam 
and the deflection of the beam at the point where the load is applied. Draw 
the bending moment and shearing force diagrams for this beam. 
23. A beam of uniform section is built into a wall at one end and supported 
on a column, as shown in Fig. 181. The 
beam carries a load of 54 tons uniformly 
distributed. Find the vertical thrust on 
the column, and draw the bending moment 
and shearing force diagrams. At what 
points is the bending moment zero ? ---- ---- “HT: 
24. A beam of uniform section is rigidly ! 
fixed at its ends to two walls, which are Fig. 181. 
24 feet apart. Two loads, each of 10 tons, 
are applied to this beam at points 6 feet from the walls. Determine the bend- 
ing moments at the ends and at the centre, and find the positions of the 
points of zero bending moment. Draw the bending moment and shearing force 
diagrams, 
25. A continuous beam of uniform section covers two spans, each equal to 
L, and carries a uniform load of w per unit of length. Show that the middle 
4 
support must be below the level of the outer supports by an amount oi in 
order that the pressures on the three supports may be equal. 
26. A continuous girder of uniform section consists of two spans, each of 
50 feet, and carries over both spans a uniformly distributed load of 1 ton per 
foot run, Both ends of the girder are free. Calculate the bending moment 
over the middle support, and the maximum positive bending moment between 
the centre and one end. Find also the reactions at the supports. 
27. A continuous girder of uniform section and of two equal spans carries a 
uniformly distributed load of w tons per foot run. Find the bending moment 
over the central pier when the height of the three piers is the same, and also 
when the central pier, owing to temperature effects, is raised or lowered by an 
amount equal to x inches, [U.L.] 
28. A rolled steel joist 40 feet in length, of I section, 10 inches deep, and 
5 inches wide, has a thickness which is equivalent to } inch in both flanges and 
web. It is continuous over three supports, forming two spans of 20 feet each. 
What uniformly distributed load would produce a maximum stress of 5} tons 
per square inch? Sketch the diagrams of bending moments and shearing 
forces, [Inst.C.E.] 
29. Apply the theorem of three moments to find the reactions when there 
are three level piers supporting a continuous girder carrying a uniformly 
distributed load of 2 tons per foot run, the two spans being 200 feet and 150 
feet respectively. [U.L.] 
80. A continuous girder consists of two spans. One span of 100 feet is 
loaded with 1? tons per foot run, the second span of 80 feet is loaded with 
2} tons per foot run. Find the values of the supporting forces, and the 
maximum bending moment for the whole girder. Both ends of the girder are 
free, [Inst.C.E, ] 
31. Work out the example of Article 135, pp. 128-130, assuming that, owing to 
settlement of the pier, the support at B is + inch below the level of the other 
supports. Take H=13,000 tons per square inch, and [=432,000 in inch units. 
32. A cantilever bridge ABCD has supports at A, B, C, and D. AB=CD 
=100 feet. BC=300 feet. There are hinge joints at E and F in the centre 
span. BE=CF=100 feet. Assuming that there is a permanent dead load of 
2 tons per foot run, and a live load of 1 ton per foot run, construct the bending 
moment and shearing force diagrams for this bridge when the live load covers 
(a) the span AB only, (5) the cantilever AE only, (c) the girder EF only. 
33. A cantilever bridge has three spans, each of 200 feet. There are hinge 
joints in the side spans at points 120 feet from the shore ends. Assuming a dead 
load of 2 tons per foot run, and a live load of 1 ton per foot run, construct the 
bending moment and shearing force diagrams when the live load covers (a) one 
side span only, (6) the centre span only. 
