Civil Engineering Math Concepts Formulas Efficiency Load supported

Civil Engineering Math Concepts

Formulas • Efficiency = Load supported by structure ÷ Weight of structure X 100% • Area of a square = s 2 • Area of a rectangle = l × w • Area of a circle = πr 2

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 Opposite Leg hypotenuse A Adjacent Leg

Basic Trigonometric Functions cosine A = Length of Adjacent Leg Length of Hypotenuse Opposite Leg hypotenuse A Adjacent Leg

Basic Trigonometric Functions tangent A = Length of Opposite Leg Length of Adjacent Leg Opposite Leg hypotenuse 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.