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Simpson’s Rule Simpson's Rule attempts to allow for the natural shape of the land.
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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
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5 An
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Grid
Assesment 3 Simpsons Rule Answer Sheet
-7.5
80
Add
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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
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Grid
A1
to G
1 An
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Bel
owAd
d G
rid A
2 to
G2
Answ
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elow
Add
Grid
A3
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3 An
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4 to
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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
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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
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Bel
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d G
rid A
2 to
G2
Answ
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elow
Add
Grid
A3
to G
3 An
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Bel
owAd
d Gr
id A
4 to
G4
Answ
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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
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Grid
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to G
5 An
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8.17
7 -7
.580
-6
.600
-2
.517
2.
067
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Grid
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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
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Bel
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d Gr
id A
2 to
G2
Answ
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elow
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Grid
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Answ
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-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.
![[5261]-11collegecirculars.unipune.ac.in/sites/examdocs/September 2017/M.C.A... · ... State and prove Simpson's 3 8 th rule for numerical integration. (b) ... x dx by Simpson's 1](https://img.dokumen.tips/doc/110x75/5b4831cd7f8b9a824f8c686b/5261-2017mca-state-and-prove-simpsons-3-8-th-rule-for-numerical.jpg)
