Civil Engineering - Surveying - Discussion

Slope means= just an inclined line. always 1st value indicates vertical distance & 2nd indicates horizontal distance...So h=1.5 how?

see h=(V/H.), where V=vertical distance H=Horizontal distance.

So, first Given(1 V/20 H)=(1/20)=0.05 this value in meter (we calculated slope length for 1 meter but given(30m), h=height between two endpoints of the slope.

We have to calculate for 30 m) so just multiply =0.05*30=1.5 m Now, don't use (h^2/2L) formula it's approx.

By using the formula, we get 0.03752346684 in meter now in option all value in cm.

So just convert in cm = 3.75234668427 answer.

h=height between two endpoints of the slope, hope this concept is clear.

Let me clearly explain this for those who are confused.

The formula for slope correction is;
C=h^2/2L.

Now since grade is given is 1 in 20.

That means for 20 m horizontal movement there will be a movement of 1m vertical..therefore accordingly for 30 m it will30/20 =1.5m.

Now, put this into the formula and you will get 3.75 as answer.

In ABC triangle,

AC = l = 30m.
Slope = 1 : 20.

1 in20 so in 30 = (1/20) * 30 = 1.5

Therefore BC = 1.5m.

And AB extends to BB'.
And meet to points A as arc & B as a straight line.
Here BB'= correction of line,
= AC - AB.

AB = (30^2 - 1.5^2)^1/2
= 29.962m.

BB' = 30 - 29.962
= 0.0375m or 3.75cm.

Here, l= 30 m.
Gradient= 1 in 20, i.e h= 30/20= 1.5
We know, slope correction (Ch)= - h^2/2l
= - (1.5)^2/(2*30) m.
= -3.75 cm.

In 1 in 20 means, 20m = 1m.

So total 30m length = 1.5m.

In Gradient 1 in 20 Means.

Imagine Triangle, length-30m & Height-1.5m.

Use Pythagoras theorem.

X2 = 302+1.52.
X = 30.0375m.

Change length = 30.0375-30.

= 0.0375m.
= 3.75cm.

Hypotenusal allowance.

Slope correction will be 75/(n^2)links (for 30 m chain) , where 1:n is the slope.
Cs = 75/(20 ^2) links,
= 0.1875 links of 30 m chain,
= 0.1875*20 (one links =20cm),
= 3.75 cm => Answer.

(H2/2L)+(H4/8L3) as gradient is 1 in 20. i.e For 20 m, h = 1 m.

So for 30 m, h = 1.5 m which is less than 3 m.

Therefore second term of equation should be neglected.

Answer is (1.5)2/2x3000 = 3.75 cm.

Here h= 1.5, it is not correct because here 30 m is hypotenuse (i.e. equals to L , which is also used in slope correction formula ) but why use as a base or horizontal for finding h? Please explain me.

Let me clearly explain,
tanθ = height/ base.
=> tanθ = 1/20,
=>θ = 2.86.

Now actual slop correction = l(1-cosθ).
=> 30(1-cos2.86) = 0.0373m.
=> 3.73 cm.

Slope Correction Formula=h^2/2l ---> (1)
Slope=1:20 =1/20 = 0.05.

h= slope * l= (1/20)(30) = 1.5m.

Now eq(1) becomes,
(1.5)^2/2(30) = 0.0375m.
1m = 100cm.
So,
0.0375(100cm) = 3.75cm.