Bridge Design part 2 Note: have worksheets of triangles for using trig functions ready By Alan Pennington, materials taken from and adapted West Point Bridge Design

Learning Objectives Explore simple trigonometry functions related to bridges Calculate the components of a force vector.

Structural analysis Structural analysis is calculating the parts of a structure and how it relate to the whole structure. The main parts of a structural analysis are (1) reactions, (2) internal member forces, (3) deflections—how much the structure bends or sways when it is loaded. Structural analysis is used to see if the system is working as planed and, if it is not, to correct the problem.

Vectors To find if a truss bridge can hold a load we use vectors to determine what forces are being applied where. We will need to use some concepts from Trigonometry but instead of measuring the size of the parts of a triangle we will measure the forces a load places on different parts of a triangle.

Some Basic Concepts from Trigonometry This diagram shows a right triangle—a triangle with one of its three angles measuring exactly 90°. Sides a and b form the 90° angle. The other two angles, identified as 1 and  2, are always less than 90°. Side c, the side opposite the 90° angle, is always the longest of the three sides. It is called the hypotenuse of the right triangle.

The Pythagorean Theorem Thanks to an ancient Greek mathematician named Pythagoras, we can easily calculate the length of the hypotenuse of a right triangle. The Pythagorean Theorem tells us that

Triangle sides Two terms from trigonometry—sine and cosine are used to find the sides of a right triangle. Both definitions are based on the geometry of a right triangle. We use sin to find the size of the side opposite of a known angle and cosine the find the side next to the known angle If I know θ2 what would I use to find side b?

Worksheet needed Using sine and cosine find the sizes of the sides of different triangles