Truss and Frame Analysis Chapter 4 Truss and Frame Analysis

Trusses Account for the majority of the structures constructed in the world today A pin connected truss has all of its members ideally in pure axial tension or pure axial compression All members are considered to be two-force members

Trusses (Cont’d)

Truss Behavior A truss is typically a network of triangles that all lie in the same plane It is a stable shape that prevents “racking” when lateral forces are applied Trusses are connected by frictionless pins

Truss Behavior (Cont’d) All the forces on a truss are applied at the joints The selfweight of the members are negligible and is either neglected or applied equally at the joints as a concentrated load

Truss Behavior (Cont’d)

Truss Behavior (Cont’d)

Truss Behavior (Cont’d)

Method of Joints This method constructs a free-body diagram of each joint The principles of equilibrium are used to solve for the unknown joint forces Fx = 0 Fy = 0 Because all of the forces at a joint act through the joint, it is considered to be a concurrent system

Steps for Using the Method of Joints Solve the external support reactions of the truss Draw free-body diagrams of each joint in the truss Begin at a joint that does not have many potential unknown forces

Steps for Using the Method of Joints (Cont’d) Flip-flop the joint forces that act at one end of a member to the opposite end of that member Go on to another joint until the truss is completed

Method of Joints Example

Method of Joints Example

Method of Sections Involves cutting the truss through the members whose forces are to be determined The equations for equilibrium are used to determine the forces that act on the members that have been cut

Steps for Using the Method of Sections Solve the support reactions of the complete truss Section the truss through the members that are to be found

Steps for Using the Methods of Sections (Cont’d) Work with only one piece of the truss as the new free-body diagram Write and solve the appropriate equilibrium equations

Method of Sections Example

Method of Sections Example

Method of Sections Example

Method of Sections Example

Method of Sections Example

Frames Assumed to be pin-connected Considered to have the ability to develop reactions forces while being free to rotate Key concept to frame analysis is Newton's concept of action and reaction

Newton’s First Law of Motion If the algebraic sum of all forces in a system is equal to zero, then the system will retain its present state

Newton’s Second Law of Motion If the algebraic sum of the forces in a system is not equal to zero, then the net result will be that the system will accelerate or decelerate The acceleration or deceleration of the system will be directly proportional to the force that is applied and inversely proportional to the mass of the system

Newton’s Second Law of Motion (Cont’d) The system will accelerate in a straight line to the force (in the same direction)

Newton’s Third Law of Motion When an object transmits a force to another object, the net result is the receiving object will transmit a force of equal magnitude in the opposite direction

Frame Analysis The analysis of pin-connected frames is based on the concepts of isolating a free-body and writing algebraic equations

Steps for Performing Frame Analysis Determine the external support (pins, rollers, etc.) for complete structure Explode the frame into separate free-body diagrams of each member

Steps for Performing Frame Analysis (Cont’d) Use the three equilibrium equations to solve for unknown pin reactions Continue until all pin reactions are solved