T R U S S A truss is a structure that consists of All straight members connected together with pin joints connected only at the ends of the members and All external forces (loads & reactions) must be applied only at the joints. A truss is a structure composed of slender members joined together at their end points. Each member only takes axial forces. Truss Assumptions There are four main assumptions made in the analysis of truss. Truss members are connected together at their ends only. Trusses are connected together by frictionless pins. The truss structure is loaded only at the joints. The weights of the members may be neglected. Types of Trusses Simple Trusses: 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. Other Types: Priodeep Chowdhury;Lecturer;Dept. of CEE;Uttara University//TRUSS Page 1
METHODS OF SOLVING TRUSS Method of Joints Principle If a truss is in equilibrium, then each of its joints must also be in equilibrium. The truss is made up of single bars, which are either in compression, tension or no-load. The means of solving force inside of the truss use equilibrium equations at a joint. This method is known as the method of joints. Procedure Tips starts with a joint that has no more than two unknown forces Establish the x and y axis; At this joint, F x = 0 and F y = 0; After finding the unknown forces applied on this joint, these forces become the given values in the analysis of the next joints. - The joints with external supports always connect with two truss members. Thus many times, the analysis starts from analyzing the supports. Therefore very often the analysis begins with finding the reaction forces applied at the supports. - Pay attention to symmetric systems and zero-force members. Identification of these special cases sometimes will make the whole analysis WAY EASIER!! Priodeep Chowdhury;Lecturer;Dept. of CEE;Uttara University//TRUSS Page 2
Zero Force Members: (a) If only two no collinear members are connected to a joint that has no external loads or reactions applied to it, then the force in both members is zero. (b) If three members, two of which are collinear, are connected to a joint that has no external loads or reactions applied to it, then the force in the member that is not collinear is zero. Zero Member Force Calculations Priodeep Chowdhury;Lecturer;Dept. of CEE;Uttara University//TRUSS Page 3
Problem: Solution: Finding the reaction forces Σ F x = 0; Σ F y = R(F y ) + R(J y ) 40k 20k 20k 10k 10k = 0; Σ M (F) = 0; R(J y ) x 40 20k x 10 40k x 20 20k x 30 10k x 40 = 0 R(F y ) = R(J y ) = 50 Start off with joint A Σ F x = F(FG) = 0 Σ F y = 50k F(AF) = 0 F(AF) = 50k (in compression) Σ F x = F(AG) *sin45 F(AB) = 0 Σ F y = 50k F(AG) *cos45 10k = 0 F(AG) = 56.6k (in tension) F(AB) = 40k (in compression) By using the same method, analyze joint B, C, G, H; Since the truss is symmetric, the forces on the members are symmetric as well. Thus we only need to analyze half of the truss and then mirror the forces onto the rest half. The result is shown in the following: Priodeep Chowdhury;Lecturer;Dept. of CEE;Uttara University//TRUSS Page 4
Method of Sections Principle If a truss is in equilibrium, then whichever section of the truss being considered must also be in equilibrium. Procedure - Finding the reaction forces; - Make a cut through the members where the unknown forces are applied; - Establish equilibriums for one of the sections: F x = 0; F y = 0; M = 0; - If your result comes out to be negative, then it means you assumed a wrong direction of the force. Application - The method of sections is commonly used when the forces in only a few particular members of a truss are to be determined; - The method of sections is always used together with the method of joints to analyze trusses. Problem: Solution: Finding the reaction forces Σ F x = 0; Σ F y = R(F y ) + R(J y ) 40k 20k 20k 10k 10k = 0; Σ M (F) = 0; R(J y ) x 40 20k x 10 40k x 20 20k x 30 10k x 40 = 0 R(F y ) = R(J y ) = 50 Since the forces of particular members laying in the middle of the truss are asked, we use the method of section. Cut the truss through the members with the unknown forces: Write the equation of equilibrium for the section: Σ F x = F(BC) + F(BG) x sin45 + F(GH) = 0 Σ F y = 50k 10k 20k F(BG) x cos45 = 0 Σ M (B) = F(GH) x 10 + 10k x 10 50k x 10 = 0 Solve the equilibrium, we find: F(GH) = 40k (in tension) F(BG) = 28.3k (in tension) F(BC) = -60k (the negative sign means we assumed the wrong direction. BC is in compression) Priodeep Chowdhury;Lecturer;Dept. of CEE;Uttara University//TRUSS Page 5
Solved Problems on Truss Problem: Using the method of joints, indicate all the members of the truss shown in the figure below that have zero force. Solution: Joint D ΣF y = 0: F DC sinθ = 0, F DC = 0 ΣF x = 0: F DE + 0 = 0, F DE = 0 Joint E ΣF x = 0: F EF = 0 Joint H ΣF y = 0: F HB = 0 ΣF y = 0: F GA = 0 Joint G Priodeep Chowdhury;Lecturer;Dept. of CEE;Uttara University//TRUSS Page 6
Problem: Determine all the member forces Identify zero-force members Solution: Priodeep Chowdhury;Lecturer;Dept. of CEE;Uttara University//TRUSS Page 7
Problem: Determine the force in members GF and GD of the truss shown in the figure below. State whether the members are in tension or compression. The reactions at the supports have been calculated. Priodeep Chowdhury;Lecturer;Dept. of CEE;Uttara University//TRUSS Page 8
Solution: Problem: Determine the force in members BC and MC of the K-truss shown in the figure below. State whether the members are in tension or compression. The reactions at the supports have been calculated. Priodeep Chowdhury;Lecturer;Dept. of CEE;Uttara University//TRUSS Page 9
Solution: Compound Trusses Procedure for Analysis Step 1. Identify the simple trusses Step 2. Obtain external loading Step 3. Solve for simple trusses separately Priodeep Chowdhury;Lecturer;Dept. of CEE;Uttara University//TRUSS Page 10
Problem: Determine the force in members of the truss shown in the figure below. State whether the members are in tension or compression. The reactions at the supports have been calculated. Solution: Priodeep Chowdhury;Lecturer;Dept. of CEE;Uttara University//TRUSS Page 11
Priodeep Chowdhury;Lecturer;Dept. of CEE;Uttara University//TRUSS Page 12