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... Work is done by a moment acting through and in-line rotation. UNIT – V Potential Energy Approach to Derive Bar Element Equations where N1 and N2 are the interpolation functions gives as: Using the stress-strain relationships, the axial strain is: x du dx 1 2 11 x u LLu 11 B LL The axial stress-strain relationship is: xx []D x []{}Bd 121 2 dN dN u dx dx u CIVL 7/8117 Chapter 3 - Truss Equations - Part 2 11/44 Plane Truss :: Analysis Methods Zero Force Members: Conditions •if only two noncollinear members form a truss joint and no external load or support reaction is applied to the joint, the two members must be zero force members •if three members form a truss joint for which two of the members are collinear, the third member is a zero-force We are going to do a two dimensional analysis so each node is constrained to move in only the X or Y direction. Perform a truss analysis to find all truss member virtual axial forces, F Qi 1 B Y D R . THREE-DIMENSIONAL OSCILLATION ANALYSIS OF TRUSS GIRDERS BY THE THIN-WALLED ELASTIC BEAM THEORY CONSIDERING CROSS-SECTIONAL DEFORMATIONS. Objective(s) Familiarisation with strain energy and complimentary energy 3 … +Now we have the external virtual work, we also need the internal virtual work. Figure 8.4: Equivalence of the strain energy and complementary strain energy. TRUSSES David Roylance Department of Materials Science and Engineering Massachusetts Institute of Technology Cambridge, MA 02139 June 8, 2000 Introduction Version 2 CE IIT, Kharagpur Lesson 6 Engesser’s Theorem and ... Compute deflections in trusses using unit-load method due to fabrication errors. This chapter discusses the strain energy method. Complimentary Energy Method in structural analysis 1. Method of Virtual Work for Trusses Steven Vukazich San Jose State University. Suggested Readings Reference 1 Reference 2 Reference 3 2 3. Energy Methods in Structural Analysis . M A H D I D A M G H A N I 2 0 1 6 - 2 0 1 7 Structural Design and Inspection-Energy method 1 2. In addition to axial strain (like the bar), a frame element can also store strain energy as bending strain and shear strain. Chapter 3 - Finite Element Trusses Page 7 of 15 3.4 Truss Example We can now use the techniques we have developed to compute the stresses in a truss. A frame element, unlike the truss bar element that we discussed previously, has multiple different ways to store strain energy. ENERGY THEOREMS: Introduction-Strain energy in linear elastic system, expression of strain energy due to axial load, bending moment and shear forces – Castigliands ﬁrst theorem-Deﬂections of simple beams and pin jointed trusses. M The incremental internal strain energy, d d q /2 M x s xx dx y z z d = (d /dx) dx q q = k dx dx+ dx = dx- y dx e k q /2 Figure 5. The stresses ˙ ij are not considered to be constant because they are related to the variable strains. 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