BYVISHAL SHARMARB4803A22B.TECH(ME) : BYVISHAL SHARMARB4803A22B.TECH(ME) POWERPOINT PERSENTATION
TRUSSES 6 - 1 Contents : Contents Introduction
Definition of a Truss
Analysis of Trusses by the Method of Joints
Joints Under Special Loading Conditions
Sample Problem 6.1
Analysis of Trusses by the Method of Sections Trusses Made of Several Simple Trusses
Analysis of Frames
Frames Which Cease to be Rigid When Detached From Their Supports
Machines Introduction : Introduction 6 - 3 For the equilibrium of structures made of several connected parts, the internal forces as well the external forces are considered. In the interaction between connected parts, Newton’s 3rd Law states that the forces of action and reaction between bodies in contact have the same magnitude, same line of action, and opposite sense. Three categories of engineering structures are considered:
Frames: contain at least one one multi-force member, i.e., member acted upon by 3 or more forces.
Trusses: formed from two-force members, i.e., straight members with end point connections
Machines: structures containing moving parts designed to transmit and modify forces. Truss : Truss Space Trusses - are structures that are not contained in a single plane and/or are loaded out of the plane of the structure. Truss : Truss Planar Trusses - lie in a single plane and all applied loads must lie in the same plane. Truss : Truss Space Trusses - are structures that are not contained in a single plane and/or are loaded out of the plane of the structure. Truss : Truss There are four main assumptions made in the analysis of truss Plane Trusses : Plane Trusses Plane trusses: lie in a single plane.
Space trusses: not contained in a single plane and/or loaded out of the structure plane. Simple Truss : Simple Truss The basic building block of a truss is a triangle. Large truss are constructed by attaching several triangles together A new triangle can be added truss by adding two members and a joint. A truss constructed in this fashion is known as a simple truss. Simple Truss : Simple Truss A truss is analysis by using m=2*j-3, where m is number of members, j represents the number of joints and 3 represents the external support reactions. Trusses Made of Several Simple Trusses : Trusses Made of Several Simple Trusses 6 - 11 Method of Joints -Truss : Method of Joints -Truss Simple Truss : Simple Truss If m< 2j-3, then the truss is unstable and will collapse under load. If m> 2j-3, then the truss has more unknowns than know equations and is an indeterminate structure. If m= 2j-3, ensures that a simple plane truss is rigid and solvable, it is neither sufficient nor necessary to ensure that a non-simple plane truss is rigid and solvable. Slide 14: Assumptions 1) Truss members are connected together at their ends only.
2) Truss members are connected together by frictionless pins.
3) The truss structure is loaded only at the joints.
4) The weight of the member may be neglected. Slide 15: The Four Assumptions Truss members are two-force members F F Truss member F F Slide 16: Straight Members Forces act along the axis of the member Slide 17: “Rigid” trusses “Rigid”- the truss will retain its shape when removed from its support Simple truss- constructed by attaching several triangles together.
Allows a simple way to check rigidity. Slide 18: What are we looking for? The support reaction .
The force in each member. How many equations are available? How many unknowns? Each joint- 2 equations
Unknowns- number of members+ support reaction. Slide 19: Stability Criteria m=2j-3
2j- number of equations to be solved.
m- number of members.
3- number of support reaction m<2j-3 Truss unstable m>2j-3 Statically indeterminate Slide 20: Example m (Number of members) = 13 j (Number of joints) = Number of supports= 8 3 Slide 21: Method of Joints Separate free-body diagrams for:
each pin Equilibrium equations for each pin:
no moment equation Slide 22: Zero Force Members SFy=0 Slide 23: SFy=0 Machines : Machines 6 - 24 Given the magnitude of P, determine the magnitude of Q. CONCLUSION : CONCLUSION SO AT LAST WE HAVE CONCLUDED THAT TRUSSES ARE VERY IMPORTANT IN OUR LIFE.IN OUR MAXIMUM WORKS ARE DEPENDING UPON TRUSSES LIKE IN BRIDGES,MECHANICS,ETC .AS ALREADY WE HAVE DISCUSSED ABOUT THE TRUSSES IN MECHANICS .