What is a Truss? A structure composed of members connected together to form a rigid framework. Usually composed of interconnected triangles. Members carry load in tension or compression.

Component Parts Support (Abutment)

Standard Truss Configurations

Types of Structural Members These shapes are called cross-sections.

Types of Truss Connections Pinned Connection Gusset Plate Connection Most modern bridges use gusset plate connections

Forces, Loads, & Reactions Force – A push or pull. Load – A force applied to a structure. Reaction – A force developed at the support of a structure to keep that structure in equilibrium. Self-weight of structure, weight of vehicles, pedestrians, snow, wind, etc. Forces are represented mathematically as VECTORS.

Equilibrium A Load... ...and Reactions Newton’s First Law: An object at rest will remain at rest, provided it is not acted upon by an unbalanced force. A Load... ...and Reactions

Tension and Compression An unloaded member experiences no deformation Tension causes a member to get longer Compression causes a member to shorten

Tension and Compression EXTERNAL FORCES and INTERNAL FORCES Must be in equilibrium with each other.

Structural Analysis For a given load, find the internal forces (tension and compression) in all members. Why? Procedure: Model the structure: Define supports Define loads Draw a free body diagram. Calculate reactions. Calculate internal forces using “Method of Joints.”

Model the Structure 15 cm D A B C mass=5 kg =2.5 kg per truss

Draw a Free Body Diagram 15 cm D A B C x y RA RC 24.5N mass=2.5 kg

Calculate Reactions Total downward force is 24.5 N. Total upward force must be 24.5 N. Loads, structure, and reactions are all symmetrical. RA and RC must be equal.

Calculate Reactions 15 cm 15 cm D 15 cm A B C y 12.25 N RA RC 24.5 N x

Method of Joints Isolate a Joint. 15 cm C B D RC 24.5 N 12.25 N A y x

Method of Joints Isolate a Joint. Draw a free body diagram of the joint. Include any external loads of reactions applied at the joint. Include unknown internal forces at every point where a member was cut. Assume unknown forces in tension. Solve the Equations of Equilibrium for the Joint. FAD A x y FAB 12.25 N EXTERNAL FORCES and INTERNAL FORCES Must be in equilibrium with each other.

Equations of Equilibrium The sum of all forces acting in the x-direction must equal zero. The sum of all forces acting in the y-direction must equal zero. For forces that act in a diagonal direction, we must consider both the x-component and the y-component of the force. 12.25 N A x y FAD FAB

Components of Force A (FAD)y (FAD)x q FAD q A If magnitude of FAD is represented as the hypotenuse of a right triangle... Then the magnitudes of (FAD)x and (FAD)y are represented by the lengths of the sides.

Trigonometry Review x y q Definitions: H Therefore:

Components of Force y (FAD)y FAD q=? q=? 45o x A A (FAD)x Therefore:

Equations of Equilibrium 0.707 FAD FAD A x y FAB 12.3 N ? FAB=12.25 N (tension) FAD=17.3 N (compression)

Method of Joints...Again Isolate another Joint. 12.25 N A 15 cm C D RC B 24.5 N y x

Equations of Equilibrium FBD FBC=12.25 N (tension) FAB FBC B x y 24.5 N FBD=24.5 N (tension)

Results of Structural Analysis D B 24.5 N 12.25 N (T) 24.5 N (T) 17.3 N (C) Do these results make sense?

Results of Structural Analysis D B 24.5 N 12.25 N (T) 24.5 N (T) 17.3 N (C) In our model, what kind of members are used for tension? for compression?