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Transcript Document

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 Ccos θ 2
C
Worksheet needed
• Using sine and cosine find the sizes of the
sides of different triangles