Use of a Standard Parahola for Drawing Diagrams of Bending Moment. . 665 
These abscissa readings are shears ; they are set oif on the perpendiculars 
through the points of support, and the shear diagrams completed by joining 
consecutive pairs. 
This gives the pressures in order as 16"2, 40-6, 13*9, and 9*3 units, i. e. 
1620, 4060, 1390, and 930 lbs. 
The calculated values are 1630, 4043, 1391, 935 lbs. 
(2) A concrete beam, 20' long weighing 60 lbs. per foot, is supported at 
the ends and at the middle point, the points being at the same level, and 
carries a weight of 300 lbs. halfway between the middle point and one end. 
If we reduce to 1 lb. per foot run, the added weight should be 5 lbs. 
Let be the droop of the point to which the weight is attached, then 
3000 + 5a, =: - ijlOOO + 125| - 6K • 1^ 
50-2 + 2003 = - i|l25 + 125| + 6K '"^^ 
iOo - |0, + i • 10 =r - 5 
. 275 ^ 525 
whence O^, = Gr^ = ^ ' 
The spans here are 5' and 10', too small to show well on the scale used 
in (1). 
Take the scale 1 div. — ^ so that n = I', then Oo and O..^ will be 
represented on the figure as — 27*5 and +26*25 respectively. 
The drawing of the diagram proceeds as before. 
The final scales are shear 1 div. = {wn) lbs., i. e. 15 lbs. 
Bending moment 1 div. = lOwn- ft.-lbs., i. e. 37| ft.-lbs. 
The pressures are 13'0, 63-8, -19-8, 23-0 units, i.e. i95, 957, -297, 
345 lbs. 
The calculated values are 196|-, 956 J, -300, 346^. 
The figures in the cases shown have been drawn on squared paper ; but 
it should be observed that this is not essential. Blank drawing paper will 
suffice, but a scale must be used to set off lengths which agrees with the 
scale on which the standard parabola is drawn : e. g. with the parabola used 
above, it will be sufficient to have blank paper and a scale graduated in 
millimetres. 
The method holds for supports at different levels, and also for parts 
which cut at so small an angle that the thrust along the length of the beam 
may be neglected. 
§ 5. One case where the diagrams can be drawn without any heavy 
calculation is where the points of support are so arranged that the pressures 
on all are equal, or have given ratios. Each pressure can be obtained at 
once by division, and from these the shear diagrams drawn. Starting from 
the left we have zero moment at the end, and the abscissa value of the end 
point known ; thus the parabola is placed in position for the first span and 
