Transcript Civil Engineering - Schilling Farms Middle School

Civil Engineering
Math Concepts
Formulas
• Efficiency = Load supported by structure ÷
Weight of structure
• Area of a square = s2
• Area of a rectangle = l × w
• Area of a circle = πr2
Basic Trigonometric Functions
• A right triangle has
one right angle and
two acute angles.
• The hypotenuse is
the side of a right
triangle opposite the
right angle. The other
two sides are called
legs.
Basic Trigonometric Functions
• There are three basic trigonometric
functions:
– Sine
– Cosine
– Tangent
Basic Trigonometric Functions
sine  A = Length of Opposite Leg
Length of Hypotenuse
hypotenuse
Opposite
Leg
A
Adjacent Leg
Basic Trigonometric Functions
cosine  A = Length of Adjacent Leg
Length of Hypotenuse
hypotenuse
Opposite
Leg
A
Adjacent Leg
Basic Trigonometric Functions
tangent  A = Length of Opposite Leg
Length of Adjacent Leg
hypotenuse
Opposite
Leg
A
Adjacent Leg
Indirect Measurement
• These functions – sine, cosine, and tangent –
can be used to find measurements.
• For example, if the measurement of Angle A is
45° and the length of the adjacent leg is 20
meters, the length of the opposite leg can be
determined using the following equation:
tangent A = Length of Opposite Leg
Length of Adjacent Leg
tangent 45° = Length of Opposite Leg
20 meters
Indirect Measurement
• The tangent of 45° can be found using a
scientific calculator or a table of known
tangent values. The tangent of 45° is 1.
1 = Length of Opposite Leg
20 meters
• 20 meters × 1 = Length of Opposite Leg
20 meters = Length of Opposite Leg
Analytical Geometry
• Weight distribution in structures is a big concern
for civil engineers.
• Think about a platform constructed with loadbearing pillars in each corner. If the platform is a
square or rectangle it would have four corners
and therefore four pillars.
• If a load of 1,000 pounds were placed on the
platform, then each of the pillars would
essentially be bearing 250 pounds of force.
Analytical Geometry
• Now, consider that instead of four straight pillars
the same platform was constructed with
triangular shaped supports in each corner.
• The 1,000 pound load would be distributed
throughout the triangle’s sides.
• Some of the force would be distributed
horizontally, and some would be distributed
vertically. This decreases the amount of force on
each of the supports.