Civil Engineering - Railways - Discussion

@All.

U= (a+b)/2 - d.

Where a and b are the absolute levels of the 2 end axles and d is the absolute level of the middle axle.
Now the problem here is that the question here has given incorrect data. The book that this question has been copied from had actually given the middle value as 100.580 which has been misprinted as 100.530 here.

If you put the middle value as 100.580 in the above formula you will get the answer exactly.
Take a=100.505.
b=100.525.
d=100.580.
Now solve you will get 0.065 m as the answer exactly.

The unevenness of the rails is determined by comparing the level of two consecutive points and dividing the difference by the distance between them, representing the slope of the rail.

For points A and B, the unevenness is;

# Calculate for A and B:
Level at A = (100.505m).
Level at B = (100.530m).
Distance = (1.8m).
Unevenness = (100.530m-100.505m)/1.8m.
Unevenness = 0.025m/1.8m = 0.0139m.

For points B and C, the unevenness is;
#Calculate for B and C:
Level at B = (100.530m).
Level at C = (100.525m).
Distance = (1.8m).
Unevenness = (100.525m-100.530m)/1.8m.
Unevenness = (-0.005m/1.8m = -0.0028m.

For points A and C, the unevenness is;
#Calculate for A and C:
Level at A = (100.505m).
Level at C = (100.525m).
Distance = (3.6m).
Unevenness = (100.505m-100.530m)/3.6m.
Unevenness = (-0.02m)/3.6m = -0.0055m.

For points A, B and C, the unevenness is;
#Calculate for A, B and C.
Unevenness = (Unevenness of points A & B + Unevenness of points B & C)/2.
*Divided by 2 since between A, B & C there are 2 gaps.
Unevenness = [0.0139+(-0.0028)+(-0.0055)]/2.
Unevenness = (0. 01307)/2.
Unevenness = 0.06535,
Unevenness ≈ 0.065.