m2l10

# m2l10 - Module 2 Analysis of Statically Indeterminate...

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Module 2 Analysis of Statically Indeterminate Structures by the Matrix Force Method Version 2 CE IIT, Kharagpur

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Lesson 10 The Force Method of Analysis: Trusses Version 2 CE IIT, Kharagpur
Instructional Objectives After reading this chapter the student will be able to 1. Calculate degree of statical indeterminacy of a planar truss 2. Analyse the indeterminate planar truss for external loads 3. Analyse the planar truss for temperature loads 4. Analyse the planar truss for camber and lack of fit of a member. 10.1 Introduction The truss is said to be statically indeterminate when the total number of reactions and member axial forces exceed the total number of static equilibrium equations. In the simple planar truss structures, the degree of indeterminacy can be determined from inspection. Whenever, this becomes tedious, one could use the following formula to evaluate the static indeterminacy of static planar truss (see also section 1.3). j r m i 2 ) ( + = (10.1) where j m , and r are number of members, joints and unknown reaction components respectively. The indeterminacy in the truss may be external, internal or both. A planar truss is said to be externally indeterminate if the number of reactions exceeds the number of static equilibrium equations available (three in the present case) and has exactly ( ) 3 2 j members. A truss is said to be internally indeterminate if it has exactly three reaction components and more than members. Finally a truss is both internally and externally indeterminate if it has more than three reaction components and also has more than members. ( 3 2 j ) ) ( 3 2 j The basic method for the analysis of indeterminate truss by force method is similar to the indeterminate beam analysis discussed in the previous lessons. Determine the degree of static indeterminacy of the structure. Identify the number of redundant reactions equal to the degree of indeterminacy. The redundants must be so selected that when the restraint corresponding to the redundants are removed, the resulting truss is statically determinate and stable. Select redundant as the reaction component in excess of three and the rest from the member forces. However, one could choose redundant actions completely from member forces. Following examples illustrate the analysis procedure. Example 10.1 Determine the forces in the truss shown in Fig.10.1a by force method. All the members have same axial rigidity.

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## This note was uploaded on 06/30/2009 for the course CE 358 taught by Professor Trifunac during the Fall '07 term at USC.

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m2l10 - Module 2 Analysis of Statically Indeterminate...

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