Structural Analysis I Truss Bridge Definitions Static Determinancy and Stability Structural Analysis Trigonometry Concepts Vectors Equilibrium Reactions Free Body Diagrams Calculating Bridge Member Forces

Your Truss Bridge Drawing

Determinancy and Stability Stable trusses can be analyzed by the Method of Joints Statically indeterminant bridges require more complex analysis techniques Unstable truss does not have enough members to form a rigid structure

Determinancy and Stability Stable truss: 2j = m + 3 Statically indeterminate truss: 2j < m + 3 Unstable truss: 2j > m + 3

Structural Analysis Structural analysis is a mathematical examination of a complex structure Analysis breaks a complex system down to individual component parts Uses geometry, trigonometry, algebra, and basic physics

How Much Weight Can This Truss Bridge Support?

Pythagorean Theorem In a right triangle, the length of the sides are related by the equation: a 2 + b 2 = c 2 a b c

Sine (sin) of an Angle In a right triangle, the angles are related to the lengths of the sides by the equations: sinθ 1 = = Opposite a Hypotenuse c sinθ 2 = = Opposite b Hypotenuse c a b c θ1θ1 θ2θ2

Cosine (cos) of an Angle In a right triangle, the angles are related to the lengths of the sides by the equations: cosθ 1 = = Adjacent b Hypotenuse c cosθ 2 = = Adjacent a Hypotenuse c a b c θ1θ1 θ2θ2

This Truss Bridge is Built from Right Triangles a b c θ1θ1 θ2θ2

Trigonometry Tips for Structural Analysis A truss bridge is constructed from members arranged in right triangles Sin and cos relate both lengths AND magnitude of internal forces Sin and cos are ratios