CV2101 Chapt 5 Structural Analysis

CV2101 Chapt 5 Structural Analysis - Chapter 5 Structural...

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Chapter 5 tructural Analysis Structural Analysis
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bjectives Objectives ± To show how to determine the forces in the members of a truss using the method of joints and the method of sections. ± To analyze the forces acting on the members of frames and machines composed of pin-connected member. 5-2
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tructures Structures Trusses, Frames and Machines: ± A truss is a fully constrained structure with 2-force members ± A frame is a fully constrained structure containing one or more multi-force members. ± A machine or mechanism is a structure with moving parts. achines are designed to transmit or modify forces. Machines are designed to transmit or modify forces. 5-3
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1 Simple Trusses 5.1 Simple Trusses A truss consists of straight, slender members joining at their ends. Typically, trusses are used to support roofs & bridges. Design assumptions: 1. All loading are applied at the joints. The weight of the members is neglected. 2. The members are joined together by smooth pins. Where bolted or welded joints are used, then the centre-lines of the joining members are to be j, jg concurrent. 5-4
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1 Simple Trusses 5.1 Simple Trusses cont. The simplest form of truss is a single triangle (3 members and 3 joints). A simple truss is formed by adding 2 members and a joint to py g j the basic triangle. Examples of simple truss, except one. 5-5
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1 Simple Trusses 5.1 Simple Trusses cont. Simple truss = Triangle + N × (2 members + 1 joint) Total number of joints: J = 3 + N Total no. of members: m = 3 + 2N where N is an integer. Eliminating N , we have The equation gives the no. of members sufficient to build a statically determinate truss, if they are arranged in a suitable way. If m > 2J -3 —> statically indeterminate truss If m < 2J -3 —> unstable truss (not rigid) 5-6
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1 Simple Trusses 5.1 Simple Trusses cont. Each truss member is subjected to an axial force, either in tension (T) or compression (C). These internal forces in the members can be determined using the method of joints and the method of sections. 5-7
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2 Analysis by ethod f Joints onsider a simple truss which is properly constrained by 3 reactions the 5.2 Analysis by Method of Joints Consider a simple truss which is properly constrained by 3 reactions, the unknowns are m member forces plus the 3 reactions, i.e. (m+3) in all. If a truss is in equilibrium, then each joint provides 2 equations, Σ F x = 0 and Σ F y = 0, i.e., a total of 2J equations . For a simple truss, we know that m = 2J – 3 the unknowns equal the number of equations. Hence all member forces and reactions can be completely determined. Steps for analysis: Begin at a joint with 2 unknown member forces and solve for the unknowns from the 2 equilibrium eqns. Then use the results on the adjacent joints until all the unknown quantities are determined.
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This note was uploaded on 09/06/2009 for the course CEE CV2101 taught by Professor Soh during the Spring '09 term at Nanyang Technological University.

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CV2101 Chapt 5 Structural Analysis - Chapter 5 Structural...

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