iir, 
MR. L. N. G. FILOX OX AX APPIiOXLMATE 
SOLUTIOX FOE BEXDIXG A 
base of the elastic block where it rests on the rigid plane. The ordinates represent 
the ratio of Q to 'ZW/nh —that is, the integral which has been called I. The abscissae 
represent the quantities oc/h. The diagram has been plotted from the following values 
of I, which have l)een calculated :— 
xjh. 
I. 
0 
1-4444 
■frjQ 
•7412 
i -/3 
•112.J 
I 
1 ^ 
- -0300 
i 27r/3 
- -0252 
77 
- -0030 
! 
For a value of -x/h equal to F 35 about the pressure vanishes, and is re2)laced Ijy a 
tension. This is a very remarkable residt, as it shows that an elastic block, acted 
upon by a concentrated load along a line of its upper surface transverse to its length, 
cannot have its whole base in contact with a smooth rigid plane on AAdiich it rests : at 
a certain distance from the load the body of the beam is lifted off the plane. 
It would therefore appear as though the problem treated of above were impossible 
to realise in practice. But obviously we may superimpose any uniform pressure on 
the top of the beam, sufficient to make the total pressure at every point below 
positive. This ma.y be done, in some cases, by the weight of the beam itself, 
if the weight W be not too large. 
Further, the tensions required to keep the lower surface of the block horizontal 
are, as we may see from fig. iv., very small. If we leave them out of account, 
we do not sensibly disturb the distribution of the large pressure under the load, so 
that fig. iv. still gives us an approximation if we omit the negative part of the curve 
altogether. 
This gives a maximum pressure just below the load equal to (W/h) X '920, 
or rather less than the 23 ressure due to the load W distributed uniformly over the 
vertical cross-section of the block. This pressure diminishes rapidly as we go away 
from this joomt, being very small at a distance from it equal to a,bout 1‘35 of the 
height of the block. 
We cannot tell exactly, in the actual case, where the pressure will be first 
absolutely nil. We can form a rough estimate, hov/ever, of the dimensions of the 
area in contact by taking the area over which, in the solution obtained, the stress is 
always a pressure. This area extends to a distance of 1’35 X height of block, on 
either side of the vertical through tlie load. 
