• Primary objective of the force method is to determine the chosen set of excess unknown forces and/or couples – redundants. Chapter 2 : Part 2 – Unit Load Method • Aims – Determine the slope and deflection by using Unit Load Method • Expected Outcomes : – Able to analyze determinate beam – deflection and slope by Unit Load Method • References – Mechanics of Materials, R.C. Figure 1 - Truss structure to analyze.
5. Answer: The deformations or movements of a structure and its components, such as beam ends, truss joints etc., from their original positions/location. approach –aside: this method is also known as “dummy load” method or “unit load” method. METHOD … Introduction • Statically indeterminate structures are the ones where the independent reaction components, and/or internal forces cannot be obtained by using the equations of equilibrium only. Using the method of consistent deformations, determine the vertical and horizontal reactions at A and E and the resulting member loads for the truss in the accompanying figure. truss. Indeterminate Analysis Force Method1 • The force (flexibility) method expresses the relationships between displacements and forces that exist in a structure. Deflection is caused by many sources, such as, loads, temperature, Statically Indeterminate Truss •cannot be analysed using equations of equilibrium alone! The virtual work method can be used to determine the deflection of trusses. • The method of sections consists of cutting through the truss into two parts, provided that the unknown values are not more than three • The unknown forces will be assumed to be either in tension or compression • Three equilibriums ( F x = 0, F y = 0, M = 0) will be used to solve the problems. The existing force method has some advantages about analysis of truss structures such as it is easier basic concept than finite element method, which apply to analyze truss structures. • The number of redundants is equal to the degree of static indeterminacy of the structure. The truss systems are mainly used in the construction of bridge and roof construction. P a g e | 172 Prepared by R.Vijayakumar, B.Tech (CIVIL), CCET, Puducherry STRUCTURAL ANALYSIS – 1 UNIT – 1 1.
We know from the principle of virtual work for trusses that the deflection can be calculated by the equation with n equal to the virtual force in the member and equal to the change in length of the member.
Force Method for Analysis of Indeterminate Structures Number of unknown Reactions or Internal forces > Number of equilibrium equations Note: Most structures in the real world are statically indeterminate. A triangular formed out of 3 members will form the basic unit of a simple truss.