# analysis of truss by strain energy method

In addition to axial strain (like the bar), a frame element can also store strain energy as bending strain and shear strain. The stresses ˙ ij are not considered to be constant because they are related to the variable strains. Objective(s) Familiarisation with strain energy and complimentary energy 3 … In the above equation the surface traction are given and considered to be constant. 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 Consider Computing Displacements There are 4 nodes and 4 elements making up the truss. Figure 8.4: Equivalence of the strain energy and complementary strain energy. B Y D R . 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. 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. TRUSSES David Roylance Department of Materials Science and Engineering Massachusetts Institute of Technology Cambridge, MA 02139 June 8, 2000 Introduction 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. Energy Methods in Structural Analysis . When the complementary strain energy is equal to the strain energy (i.e. This chapter discusses the strain energy method. ... Work is done by a moment acting through and in-line rotation. A frame element, unlike the truss bar element that we discussed previously, has multiple different ways to store strain energy. Suggested Readings Reference 1 Reference 2 Reference 3 2 3. Although the practical application of the ﬂexibility and stiffness methods is generally computer based, they are fundamental to ‘hand’ methods of analysis … Complimentary Energy Method in structural analysis 1. The stiffness method, on the other hand, requires no such judgement to be made and is therefore particularly suitable for automatic computation. Version 2 CE IIT, Kharagpur Lesson 6 Engesser’s Theorem and ... Compute deflections in trusses using unit-load method due to fabrication errors. Method of Virtual Work for Trusses Steven Vukazich San Jose State University. +Now we have the external virtual work, we also need the internal virtual work. Perform a truss analysis to find all truss member virtual axial forces, F Qi 1 Strain Energy in Linear Elastic Solids 5 Bending Strain Energy, σ xx= −M zy/I z, xx≈−v00by A short section of a beam subjected to a bending moment M z about the z-axis bends by an angle dθ. UNIT – V THREE-DIMENSIONAL OSCILLATION ANALYSIS OF TRUSS GIRDERS BY THE THIN-WALLED ELASTIC BEAM THEORY CONSIDERING CROSS-SECTIONAL DEFORMATIONS. 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. We are going to do a two dimensional analysis so each node is constrained to move in only the X or Y direction. 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