BEAMS AND BENDING 99 
loads AB, BC, and CD, at fixed distances apart, travel. If instead of 
the loads travelling over the beam in one direction while the beam is 
stationary, the beam and its supports are moved under the loads in the 
site direction while the loads are stationary, the resulting maximum 
a moment diagram would be the same. On the drawing paper 
jo the beam MN and show the loads in one position. Still working 
on the drawing paper draw (Art. 56) the funicular polygon H123K, 
which will also be the bending moment diagram (Art. 75) for the 
position of the loads assumed. Draw a horizontal line XX’ under MN 
to serve as a base line for the required diagram of maximum bending 
moments. ‘Transfer the ordinates of the points 1, 2, and 3 of the 
bending moment diagram H123K to the lower diagram ; thus F2 in 
“the lower diagram is made equal to F2 in the upper diagram, XF being 
_ equal to the horizontal distance of F in HK from MX, 
___On a sheet of tracing paper TP make a tracing of the beam MN 
and the lines of the reactions of the supports. Let the tracing paper 
_ be moved into another position T,P,, the beam MN coming into the 
a _ position M “ae For clearness in the figure M,N, is not at the same 
a MN, but M,N, is parallel to MN, The bending moment 
: diagram for the altered ‘position of the beam in relation to the loads 
4 now be H,123K,, and this should be drawn on the tracing paper, 
or, at all events, the points such as F, and 2 should be clearly marked 
_ on the tracing paper. 
’ Next transfer the tracing paper so that F, is on XX’, and M,H, is 
on the vertical through X. If the point 2 on the tracing paper be now 
pricked through on to the drawing paper, the point 2 under F, on the 
_ lower diagram is obtained, and this gives the bending moment under the 
~ load BC when the latter is at F, in XX’. The points 1 and 3 are to be 
_ similarly dealt with. 
_ The tracing paper is next moved into another position T,P,, and the 
- eorresponding bending moment diagram is H,23K,. Points such as F, 
and 2 are to be clearly marked on the tracing paper, and transferred to 
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4 
Fig. 127. 
__ the lower diagram as before. Proceeding in this way until a sufficient 
_ number of points have been fixed under XX’, a fair curve drawn to 
enclose them all all and pass through the outer ones is the required diagram 
of maximum bending moments on the base XX’. 
