Calculating Bulk Earth Works Simpson's Rule. Simpson’s Rule Sum of Grids Method Trapezoidal Method All assume that the land is a straight line between.

Slides:



Advertisements
Similar presentations
HW: Finish Problem 1.2 pg 10 #1-6 Do Now4/2/14 Find the area of this composite figure (a figure made up of other shapes). 208cm².
Advertisements

Session 9 AREA MEASUREMENT Course: S0663 – Land Surveying Year: 2007.
Wes Marshall, P.E. University of Connecticut March 2007
Section 5.7 Numerical Integration. Approximations for integrals: Riemann Sums, Trapezoidal Rule, Simpson's Rule Riemann Sum: Trapezoidal Rule: Simpson’s.
ERT252/4 GEOMATICS ENGINEERING
Geology and Surveying (Part B - Surveying) Volumes and DTMs
Numerical integration continued --- Simpson’s rules - We can add more segments OR - We can use a higher order polynomial.
(a) (b) (c) (d). What is (1,2,3)  (3,4,2)? (a) (1, 2, 3, 4) (b) (1,2)  (3,4) (c) (1,3,4,2) (d) (3,1)  (4,2)
11 and 6 3 and 9 2, 5, 10 and 4, 8 Divisibility Rules.
Numerical Integration Lesson News from Space A new species has been trapped … the rare zoid Math students have long known of efforts of "trapezoid"
Area of a single trapezoid = h
Numerical Integration
Numerical Integration Approximating Definite Integral.
Lecture 19 – Numerical Integration 1 Area under curve led to Riemann sum which led to FTC. But not every function has a closed-form antiderivative.
4.6 Numerical Integration Trapezoid and Simpson’s Rules.
4.6 Numerical Integration. The Trapezoidal Rule One method to approximate a definite integral is to use n trapezoids.
1 Numerical Integration Section Why Numerical Integration? Let’s say we want to evaluate the following definite integral:
Areas and Volumes Introduction Faculty of Applied Engineering and Urban Planning Civil Engineering Department 2 nd Semester 2008/2009 Surveying.
Trapezoid Base 1: Base 2: Height: Rectangle Length: Height:
Shapes and Angle Rules 80 + ? = = 180.
11-1 Areas of Rectangles and squares. Formulas 1) Area of rectangle = base x height or length X width 2) Area of square = (side) 2 or base X height 3)
Area Measurements.
In Pairs: 1.Estimate the area of each trapezoid 2.Use the matching sticker to make a parallelogram. Find the area of the parallelogram 3.Use what.
10.2 Area of a Triangle and Trapezoids. Definition: Area of a Triangle h b Height Base h b Height Base h b Height Base The area of a triangle is one half.
What is Volume?. What is Volume? Volume is the amount of space inside an object.
Area of Triangles and Quadrilaterals Basic equations and applying to irregular polygons.
Mechanics revision Q3. During the construction of a building, a long beam was lifted into place using a crane.  Calculate the work done in lifting the.
Divisibility Rules Outcome A6 – Develop and apply divisibility rules for 3, 4, 6, 9.
Source Page US:official&tbm=isch&tbnid=Mli6kxZ3HfiCRM:&imgrefurl=
Warm up 10/16 (glue in). Be seated before the bell rings DESK homework Warm-up (in your notes) Agenda : go over hw Finish Notes lesson 4.5 Start 4.6.
AREA Ch. 5.3 EQ: HOW CAN YOU FIND THE AREA OF VARIOUS SHAPES? I WILL FIND THE AREA OF VARIOUS SHAPES.
Equations of Straight Line Graphs. Graphs parallel to the y -axis All graphs of the form x = c, where c is any number, will be parallel to the y -axis.
Areas of Trapezoids, Rhombuses, and Kites Chapter 10 Section 2.
10-2 Areas of Trapezoids, Rhombuses, and Kites. You will find the area of a trapezoid, a rhombus, and a kite.
Geometry Section 11.2 Areas of Trapezoids, Rhombuses, and Kites.
Geometry 7-4 Area of Trapezoids, Rhombuses, and Kites.
Путешествуй со мной и узнаешь, где я сегодня побывал.
Lesson 11-3 Areas of Trapezoids (page 435) Essential Question How can you calculate the area of any figure?
Area of Trapezoid.
Lecture 19 – Numerical Integration
Clicker Question 1 What is ? A. x tan(x2) + C
Midpoint and Trapezoidal Rules
More Approximations Left-hand sum: use rectangles, left endpoint used for height Right-hand sum: use rectangles, right endpoint used for height Midpoint.
NUMERICAL INTEGRATION
MTH1170 Numeric Integration
5.5 Trapezoidal Rule.
Calculating Cut and Fill
2-D Measurement Chapter 5.
Trapezoid rule for integration
Area of a single trapezoid = h
Page 1. Page 2 Page 3 Page 4 Page 5 Page 6 Page 7.
Numerical Integration
Long sections eg road cuttings Deep sections eg basement excavations
Numerical Integration
Objective: To find the area of a trapezoid.
Applications of Integration
Area of a single trapezoid = h
Divisibility Rules.
Visit for more Learning Resources
Unit 3 Review (Calculator)
AREAS AND VOLUMES.
AREAS AND VOLUMES.
Area of a single trapezoid = h
Starter Questions Calculate the area of the following shapes :- a. 12m
Question 13.
Calculate 9 x 81 = x 3 3 x 3 x 3 x 3 3 x 3 x 3 x 3 x 3 x 3 x =
Methods of computing area
Chapter 6 Construction Quantity Measurement
Can you work out the area of each shape?
Investigation 1 Building Smart Boxes Rectangular Prisms
Presentation transcript:

Calculating Bulk Earth Works Simpson's Rule

Simpson’s Rule Sum of Grids Method Trapezoidal Method All 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

Page 3

CUT CUT CUT FILL FILL 8.177

AN ISOMETRIC VIEW

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.