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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 c a b 2 2 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 Ifangle I know θ2 what would I use to find side b? B B Csinθ 2 C A A Ccosθ 2 C Worksheet needed • Using sine and cosine find the sizes of the sides of different triangles