how is trigonometry used and applied to the constuction of a bridge? 2

[mcdiva]

I need some info on how trig is used in the construction of a bridge for a math project. How are the different sin,cos,tan etc. laws applied?

 

[Qshake]

First let me assume that your task involves a truss type bridge, one which most laypeople are familiar with even though there fewer of them and more of the slab and girder bridges on our interstates.

Truss bridges are bridges that are made up of steel members that are connected together to form a triangle (a most stable configuration for loading). It is then of interest to determine the loads in all members of the trusses (triangles) so we may size the members appropriately. If we have four members joining together, two horizontal and two at some angle to the horizontal such as


M M
M M
M M
MMMMMMMMMMOMMMMMMMMMMM
|
|
V Load

Where M represents the members and O is the point where they all come together.

We can determine the forces in the diagonal members which result from the vertical load using trigonometry. The loads to the diagonal members may be broken in to vertical and horizontal components, because joint is not moving we can assume equilibrium thus the sum of all the vertical compoents (including the applied vertical load) and the sum of the horizontal compoents must equal zero. This will tell us what the vertical component is for each diagonal and so on. Once we know the vertical component, we can use trigonometry to determine the resultant force (force along the diagonal) which is equal to (0.5V/sin(angle)) where the angle is measured from the horizontal to the diagonal. We also apply Pythagorus theorem to determine the horizontal compoent as we now know the hypotenuse and side opposite and we can find the side adjacent. To find additional angles, we also use the fact that all of the angles within a triangle must add to 180 degrees. We also use the law of cosines and law of sines and make use of proportional triangles as well to help us learn more information.

I hope this helps, it's rather difficult to visualize without the proper illustrations.