Calculating Bulk Earth Works Simpson's Rule. Simpsons Rule Sum of Grids Method Trapezoidal Method...
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Transcript of Calculating Bulk Earth Works Simpson's Rule. Simpsons Rule Sum of Grids Method Trapezoidal Method...
Calculating Bulk Earth Works
Simpson's Rule
Simpson’s Rule• Sum of Grids Method• Trapezoidal MethodAll assume that the land is a straight line
between the spot heights
Simpson’s Rule
• Simpson's Rule attempts to allow for the natural shape of the land.
Simpson’s Rule
Using Simpson’s Rule
Page 2
NOTE - Must be an odd Number of Spot Heights
Formation Ht Grid R.L. Cut or Fill
Mul
tiplie
r
Cut or Fill x Multiplier
Total Cross Section
x (Grid ÷ 3)
Mul
tiplie
r
A 1 100.500 100.950 -0.450 1 -0.450 B 1 100.500 100.800 -0.300 4 -1.200 C 1 100.500 100.730 -0.230 2 -0.460 D 1 100.500 100.735 -0.235 4 -0.940 E 1 100.500 100.724 -0.224 2 -0.448 F 1 100.500 100.680 -0.180 4 -0.720 G 1 100.500 100.830 -0.330 1 -0.330 -4.548 1.66667 1
A 2 100.500 1B 2 100.500 4C 2 100.500 2D 2 100.500 4E 2 100.500 2F 2 100.500 4G 2 100.500 1 4
A 3 100.500 1B 3 100.500 4C 3 100.500 2D 3 100.500 4E 3 100.500 2F 3 100.500 4G 3 100.500 1 2
A 4 100.500 1B 4 100.500 4C 4 100.500 2D 4 100.500 4E 4 100.500 2F 4 100.500 4G 4 100.500 1 4
A 5 100.500 1B 5 100.500 4C 5 100.500 2D 5 100.500 4E 5 100.500 2F 5 100.500 4G 5 100.500 1 1
Totalx Grid ÷ 3
Answer
Add
Grid
A5
to G
5 An
swer
Bel
ow
Grid
Assesment 3 Simpsons Rule Answer Sheet
-7.5
80
Add
Grid
A1
to G
1 An
swer
Bel
owAd
d G
rid A
2 to
G2
Answ
er B
elow
Add
Grid
A3
to G
3 An
swer
Bel
owAd
d Gr
id A
4 to
G4
Answ
er B
elow
Page 3
Page 3
Formation Ht Grid R.L. Cut or Fill
Mul
tiplie
r
Cut or Fill x Multiplier
Total Cross Section
x (Grid ÷ 3)
Mul
tiplie
r
A 1 100.500 100.950 -0.450 1 -0.450 B 1 100.500 100.800 -0.300 4 -1.200 C 1 100.500 100.730 -0.230 2 -0.460 D 1 100.500 100.735 -0.235 4 -0.940 E 1 100.500 100.724 -0.224 2 -0.448 F 1 100.500 100.680 -0.180 4 -0.720 G 1 100.500 100.830 -0.330 1 -0.330 -4.548 1.66667 1
A 2 100.500 100.900 -0.400 1 -0.400 B 2 100.500 100.830 -0.330 4 -1.320 C 2 100.500 100.720 -0.220 2 -0.440 D 2 100.500 100.700 -0.200 4 -0.800 E 2 100.500 100.650 -0.150 2 -0.300 F 2 100.500 100.650 -0.150 4 -0.600 G 2 100.500 100.600 -0.100 1 -0.100 -3.960 1.66667 4
A 3 100.500 1B 3 100.500 4C 3 100.500 2D 3 100.500 4E 3 100.500 2F 3 100.500 4G 3 100.500 1 2
A 4 100.500 1B 4 100.500 4C 4 100.500 2D 4 100.500 4E 4 100.500 2F 4 100.500 4G 4 100.500 1 4
A 5 100.500 1B 5 100.500 4C 5 100.500 2D 5 100.500 4E 5 100.500 2F 5 100.500 4G 5 100.500 1 1
Totalx Grid ÷ 3
Answer
Add
Grid
A1
to G
1 An
swer
Bel
owAd
d G
rid A
2 to
G2
Answ
er B
elow
Add
Grid
A3
to G
3 An
swer
Bel
owAd
d Gr
id A
4 to
G4
Answ
er B
elow
Grid
Assesment 3 Simpsons Rule Answer Sheet
-7.5
80
-6.6
00
Add
Grid
A5
to G
5 An
swer
Bel
ow
Formation Ht Grid R.L. Cut or Fill
Mul
tiplie
r
Cut or Fill x Multiplier
Total Cross Section
x (Grid ÷ 3)
Mul
tiplie
r
A 1 100.500 100.950 -0.450 1 -0.450 B 1 100.500 100.800 -0.300 4 -1.200 C 1 100.500 100.730 -0.230 2 -0.460 D 1 100.500 100.735 -0.235 4 -0.940 E 1 100.500 100.724 -0.224 2 -0.448 F 1 100.500 100.680 -0.180 4 -0.720 G 1 100.500 100.830 -0.330 1 -0.330 -4.548 1.66667 1
A 2 100.500 100.900 -0.400 1 -0.400 B 2 100.500 100.830 -0.330 4 -1.320 C 2 100.500 100.720 -0.220 2 -0.440 D 2 100.500 100.700 -0.200 4 -0.800 E 2 100.500 100.650 -0.150 2 -0.300 F 2 100.500 100.650 -0.150 4 -0.600 G 2 100.500 100.600 -0.100 1 -0.100 -3.960 1.66667 4
A 3 100.500 100.750 -0.250 1 -0.250 B 3 100.500 100.730 -0.230 4 -0.920 C 3 100.500 100.690 -0.190 2 -0.380 D 3 100.500 100.550 -0.050 4 -0.200 E 3 100.500 100.530 -0.030 2 -0.060 F 3 100.500 100.450 0.050 4 0.200G 3 100.500 100.400 0.100 1 0.100 -1.510 1.66667 2
A 4 100.500 1B 4 100.500 4C 4 100.500 2D 4 100.500 4E 4 100.500 2F 4 100.500 4G 4 100.500 1 4
A 5 100.500 1B 5 100.500 4C 5 100.500 2D 5 100.500 4E 5 100.500 2F 5 100.500 4G 5 100.500 1 1
Totalx Grid ÷ 3
Answer
Add
Grid
A5
to G
5 An
swer
Bel
ow
Grid
Assesment 3 Simpsons Rule Answer Sheet
-7.5
80
-6.6
00
-2.5
17
Add
Grid
A1
to G
1 An
swer
Bel
owAd
d G
rid A
2 to
G2
Answ
er B
elow
Add
Grid
A3
to G
3 An
swer
Bel
owAd
d Gr
id A
4 to
G4
Answ
er B
elow
Formation Ht Grid R.L. Cut or Fill
Mul
tiplie
r
Cut or Fill x Multiplier
Total Cross Section
x (Grid ÷ 3)
Mul
tiplie
r
A 1 100.500 100.950 -0.450 1 -0.450 B 1 100.500 100.800 -0.300 4 -1.200 C 1 100.500 100.730 -0.230 2 -0.460 D 1 100.500 100.735 -0.235 4 -0.940 E 1 100.500 100.724 -0.224 2 -0.448 F 1 100.500 100.680 -0.180 4 -0.720 G 1 100.500 100.830 -0.330 1 -0.330 -4.548 1.66667 1
A 2 100.500 100.900 -0.400 1 -0.400 B 2 100.500 100.830 -0.330 4 -1.320 C 2 100.500 100.720 -0.220 2 -0.440 D 2 100.500 100.700 -0.200 4 -0.800 E 2 100.500 100.650 -0.150 2 -0.300 F 2 100.500 100.650 -0.150 4 -0.600 G 2 100.500 100.600 -0.100 1 -0.100 -3.960 1.66667 4
A 3 100.500 100.750 -0.250 1 -0.250 B 3 100.500 100.730 -0.230 4 -0.920 C 3 100.500 100.690 -0.190 2 -0.380 D 3 100.500 100.550 -0.050 4 -0.200 E 3 100.500 100.530 -0.030 2 -0.060 F 3 100.500 100.450 0.050 4 0.200G 3 100.500 100.400 0.100 1 0.100 -1.510 1.66667 2
A 4 100.500 100.550 -0.050 1 -0.050 B 4 100.500 100.470 0.030 4 0.120C 4 100.500 100.330 0.170 2 0.340D 4 100.500 100.320 0.180 4 0.720E 4 100.500 100.350 0.150 2 0.300F 4 100.500 100.600 -0.100 4 -0.400 G 4 100.500 100.290 0.210 1 0.210 1.240 1.66667 4
A 5 100.500 1B 5 100.500 4C 5 100.500 2D 5 100.500 4E 5 100.500 2F 5 100.500 4G 5 100.500 1 1
Totalx Grid ÷ 3
Answer
Add
Grid
A1
to G
1 An
swer
Bel
owAd
d G
rid A
2 to
G2
Answ
er B
elow
Add
Grid
A3
to G
3 An
swer
Bel
owAd
d Gr
id A
4 to
G4
Answ
er B
elow
Grid
Assesment 3 Simpsons Rule Answer Sheet
-7.5
80
-6.6
00
-2.5
17
2.06
7
Add
Grid
A5
to G
5 An
swer
Bel
ow
B 1 100.500 100.800 -0.300 4 -1.200 C 1 100.500 100.730 -0.230 2 -0.460 D 1 100.500 100.735 -0.235 4 -0.940 E 1 100.500 100.724 -0.224 2 -0.448 F 1 100.500 100.680 -0.180 4 -0.720 G 1 100.500 100.830 -0.330 1 -0.330 -4.548 1.66667 1
A 2 100.500 100.900 -0.400 1 -0.400 B 2 100.500 100.830 -0.330 4 -1.320 C 2 100.500 100.720 -0.220 2 -0.440 D 2 100.500 100.700 -0.200 4 -0.800 E 2 100.500 100.650 -0.150 2 -0.300 F 2 100.500 100.650 -0.150 4 -0.600 G 2 100.500 100.600 -0.100 1 -0.100 -3.960 1.66667 4
A 3 100.500 100.750 -0.250 1 -0.250 B 3 100.500 100.730 -0.230 4 -0.920 C 3 100.500 100.690 -0.190 2 -0.380 D 3 100.500 100.550 -0.050 4 -0.200 E 3 100.500 100.530 -0.030 2 -0.060 F 3 100.500 100.450 0.050 4 0.200G 3 100.500 100.400 0.100 1 0.100 -1.510 1.66667 2
A 4 100.500 100.550 -0.050 1 -0.050 B 4 100.500 100.470 0.030 4 0.120C 4 100.500 100.330 0.170 2 0.340D 4 100.500 100.320 0.180 4 0.720E 4 100.500 100.350 0.150 2 0.300F 4 100.500 100.600 -0.100 4 -0.400 G 4 100.500 100.290 0.210 1 0.210 1.240 1.66667 4
A 5 100.500 100.394 0.106 1 0.106B 5 100.500 100.330 0.170 4 0.680C 5 100.500 100.300 0.200 2 0.400D 5 100.500 100.200 0.300 4 1.200E 5 100.500 100.190 0.310 2 0.620F 5 100.500 100.140 0.360 4 1.440G 5 100.500 100.040 0.460 1 0.460 4.906 1.66667 1
Totalx Grid ÷ 3
Answer
Add
Grid
A5
to G
5 An
swer
Bel
ow
8.17
7 -7
.580
-6
.600
-2
.517
2.
067
Add
Grid
A1
to G
1 An
swer
Bel
owAd
d Gr
id A
2 to
G2
Answ
er B
elow
Add
Grid
A3
to G
3 An
swer
Bel
owAd
d Gr
id A
4 to
G4
Answ
er B
elow
CUT 7.580 CUT 6.600
CUT 2.517 FILL 2.067
FILL 8.177
A B C D E F G1 -0.450 -0.300 -0.230 -0.235 -0.224 -0.180 -0.3302 -0.400 -0.330 -0.220 -0.200 -0.150 -0.150 -0.1003 -0.250 -0.230 -0.190 -0.050 -0.030 0.050 0.1004 -0.050 0.030 0.170 0.180 0.150 -0.100 0.2105 0.106 0.170 0.200 0.300 0.310 0.360 0.460
Cross Sectional Area-7.580-6.600-2.5172.0678.177
AN ISOMETRIC VIEW
B 1 100.500 100.800 -0.300 4 -1.200 C 1 100.500 100.730 -0.230 2 -0.460 D 1 100.500 100.735 -0.235 4 -0.940 E 1 100.500 100.724 -0.224 2 -0.448 F 1 100.500 100.680 -0.180 4 -0.720 G 1 100.500 100.830 -0.330 1 -0.330 -4.548 1.66667 1
A 2 100.500 100.900 -0.400 1 -0.400 B 2 100.500 100.830 -0.330 4 -1.320 C 2 100.500 100.720 -0.220 2 -0.440 D 2 100.500 100.700 -0.200 4 -0.800 E 2 100.500 100.650 -0.150 2 -0.300 F 2 100.500 100.650 -0.150 4 -0.600 G 2 100.500 100.600 -0.100 1 -0.100 -3.960 1.66667 4
A 3 100.500 100.750 -0.250 1 -0.250 B 3 100.500 100.730 -0.230 4 -0.920 C 3 100.500 100.690 -0.190 2 -0.380 D 3 100.500 100.550 -0.050 4 -0.200 E 3 100.500 100.530 -0.030 2 -0.060 F 3 100.500 100.450 0.050 4 0.200G 3 100.500 100.400 0.100 1 0.100 -1.510 1.66667 2
A 4 100.500 100.550 -0.050 1 -0.050 B 4 100.500 100.470 0.030 4 0.120C 4 100.500 100.330 0.170 2 0.340D 4 100.500 100.320 0.180 4 0.720E 4 100.500 100.350 0.150 2 0.300F 4 100.500 100.600 -0.100 4 -0.400 G 4 100.500 100.290 0.210 1 0.210 1.240 1.66667 4
A 5 100.500 100.394 0.106 1 0.106B 5 100.500 100.330 0.170 4 0.680C 5 100.500 100.300 0.200 2 0.400D 5 100.500 100.200 0.300 4 1.200E 5 100.500 100.190 0.310 2 0.620F 5 100.500 100.140 0.360 4 1.440G 5 100.500 100.040 0.460 1 0.460 4.906 1.66667 1
Totalx Grid ÷ 3
Answer
Add
Grid
A1
to G
1 An
swer
Bel
owAd
d Gr
id A
2 to
G2
Answ
er B
elow
Add
Grid
A3
to G
3 An
swer
Bel
owAd
d Gr
id A
4 to
G4
Answ
er B
elow
-37.617
-7.5
80
-6.6
00
-2.5
17
2.06
7
Add
Grid
A5
to G
5 An
swer
Bel
ow-22.570 1.667
8.17
7
Trapezoid Rule
• If there were an even amount of spot heights the next best options would be to use the Trapezoid rule to finish of the calculation as show on the next page.