BEAMS AND BENDING 93 
bending moment at a section where the shearing force is zero or changes 
from positive to negative is that at that section the bending moment has 
ceased to increase or ceased to decrease, but in seeking for the section 
‘where the bending moment is a maximum, the shearing force diagram is 
very useful. . 
105. Travelling Loads.—By a travelling, moving, or rolling load is 
meant one that comes on to a girder at one end, moves along the girder, 
and comes off at the other end. It is evidently necessary to know what 
_ the maximum bending moment and the maximum shearing force are at 
any section of the girder, and the bending moment and shearing force 
diagrams are constructed so as to show the maximum bending moment 
and maximum shearing force at every section. 
The first step is to find the position of the travelling load in relation 
to any section selected which will 
make the bending moment a maxi- 
mum at that section; then an ex- 
pression is found for that bending 
moment in terms of the load and the 
distance of the section from a fixed 
selected point, and from this expres- 
sion the bending moment diagram 
can be constructed. The positive 
and negative shearing force diagrams 
_ are determined in a similar manner. 
Exampte I.—A single load W 
travelling along a girder AB (Fig. 
123) supported at its ends. 
When the load W is to the right 
of a section D which is at a distance 
# from A the bending moment at : : 
D is av, and R, is greater the Fia. 123. 
nearer W isto D. Again, when W 
is to the left of D the bending moment at D is R,(/—2), and R, is 
greater the nearer W is to D. Hence the bending moment at D isa 
maximum when W is at D. 
Placing W at D, R, = vo -), and the maximum bending moment at 
) D=M="%q -2x). If D be referred to the vertical through C, the 
centre of the span, so that CD = ~,, then since x = $7 -—2,, M= ee - vt), 
which is the equation to a parabola whose axis is the vertical through C. 
= height of the vertex above the base line is the maximum value of 
ul ts — 2} ), which is obtained by putting 2,=0, then M= We. The 
bending moment for the travelling load is shown at (a). This bending 
moment diagram is the same as for a uniform dead load of w per unit of 
length, where ae, or w= * The load w per unit of length is 
called the equivalent uniform dead load. ° 
