Structural Analysis by Anthony E. Armenakas

By Anthony E. Armenakas

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Find the vertical displacement of point A on the curved beam. Version 2 CE IIT, Kharagpur The bending moment at any section θ of the curved beam (see Fig. 3 Find horizontal displacement at D of the frame shown in Fig. 4. Assume the flexural rigidity of the beam EI to be constant through out the member. Neglect strain energy due to axial deformations. Version 2 CE IIT, Kharagpur The deflection D may be obtained via. Castigliano’s theorem. The beam segments BA and DC are subjected to bending moment Px ( 0 < x < L ) and the beam element BC is subjected to a constant bending moment of magnitude PL .

State and prove Maxwell-Betti’s Reciprocal theorem. 1 Introduction In the last chapter the Castigliano’s theorems were discussed. In this chapter theorem of least work and reciprocal theorems are presented along with few selected problems. We know that for the statically determinate structure, the partial derivative of strain energy with respect to external force is equal to the displacement in the direction of that load at the point of application of load. This theorem when applied to the statically indeterminate structure results in the theorem of least work.

7. If the force P is removed then the spring shortens. When the elastic limit of the spring is not exceeded, then on removal of load, the spring regains its original shape. If the elastic limit of the material is exceeded, a permanent set will remain on removal of load. In the present case, load the spring beyond its elastic limit. Then we obtain the load-displacement curve OABCDO as shown in Fig. 7. Now if at B, the load is removed, the spring gradually shortens. However, a permanent set of OD is till retained.

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