Engineering mechanics for diploma-Trusses.pptx

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1. 1 Trusses Learning outcomes: Introduction to Trusses Types of Trusses Assumptions for a Perfect Truss Method of Joints Analysis of Truss

2. 2 Introduction to trusses A truss is a structure that is made of straight slender bars that are joined together at their ends by frictionless pins to form a pattern of triangle. The loads act only at joints and not on the members. Thus, every member of truss is identified as two-force member. Applications : Trusses are usually designed to transmit forces over relatively long spans, common examples being bridge trusses, roof trusses, transmission towers, etc.

3. 3 Types of trusses Perfect Truss: A pin jointed truss which has got just sufficient number of members to resist the load without undergoing any deformation in shape is called a perfect truss. Triangular frame is the simplest perfect truss and has three joints and three members. Hence, the following expression may be written down as the relationship between the number of members m, number of joints j and number of support reaction components r. A truss which satisfies the relation m = 2j - r is called a perfect truss.

4. 4 Types of trusses Imperfect Truss: A truss which does not satisfies the relation m = 2j - r is called an imperfect truss. Following are two subimperfect trusses. Imperfect Deficient Truss : A truss which satisfies the relation m < 2j - r is called a deficient truss. It is unstable and may collapse under external forces.

5. 5 Types of trusses Imperfect Truss: A truss which does not satisfies the relation m = 2j - r is called an imperfect truss. Following are two subimperfect trusses. 2. Imperfect Redundant Truss : A truss which satisfies the relation m > 2j - r is called a redundant truss. It is over rigid truss. It cannot be completely analysed by static equilibrium condition. Therefore, it is an indeterminate structure.

6. 6 1. All the members of truss are straight and connected to each other at their ends by frictionless pins. 2. All loading (external forces) on truss are acting only at pins. 3. All the members are assumed to be weightless. 4. All the members of truss and external forces acting at pins lies in same plane. 5. Static equilibrium condition is applicable for analysis of perfect truss (i.e., Σ F x = 0, Σ F y = 0 and Σ M = 0). Assumptions for a Perfect Truss

7. 7 Procedure for Method of Joints: For simply supported truss, consider the FBD of the entire truss. Applying condition of equilibrium (i.e., Σ F x = 0, Σ F y = 0 and Σ M = 0) find x y support reactions. 2. Consider the FBD of joint (pin) from the truss at which not more than two members with unknown force exists. 3. Assume the member to be in tension or compression by simple inspection and applying condition of equilibrium (i.e., Σ F x = 0, Σ F y = 0 ) to find the answers. 4. The assumed sense can be verified from the obtained numerical results. A positive answer indicate that the sense is correct, whereas a negative answer indicates that the sense shown on the FBD must be changed. 5. Select the new FBD of joint with not more than two unknowns in a member and repeat points 3, 4 and 5 for complete analysis. 6. Tabulate the answer representing the member, magnitude of force and their nature. Method of Joints

8. 8 Analysis of Truss Truss Analysis External equilibrium Internal equilibrium To find the reaction forces To find the force in each member Method of joints Method of sections External Equilibrium : to find the reaction forces , follow the below steps: Draw the FBD for the entire truss system. Determine the reactions . Using the equations of (2 D) which states:

9. 9 Analysis of Truss Method of Joints : to find the forces in any member , choose a joint , to which that member is connected, and follow the below steps: Draw the FBD for the entire truss system. Determine the reactions . Using the equations of (2 D) which states : Choose the joint, and draw FBD of a joint with at least one known force and at most two unknown forces . Using the equation of ( 2 D ) which states : The internal forces are determined . Choose another joint .

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