Deflections of Beams and Frames (EHCS0001)

Deflections of Beams and Frames, CONTENTS:

INTRODUCTION : When a structure is loaded, its stressed elementsdeform. In a truss, bars in tension elongate and bars in compression shorten.Beams bend. As this deformation occur, the structure changes shape and points on the structure displace. Although these deflections are normally small, as a part of the total design the engineer must verify that these deflections are within the limits specified by the governing design code to ensure that the structure is serviceable. Large deflections cause cracking of non structuralelements such as plaster ceiling, tile walls or brittle pipes. Since the magnitude of deflections is also a measure of a member’s stiffness, limiting deflections also ensures that excessive vibrations of building floors.

In this chapter we consider several methods of computing deflections and slopes at points along the axis of beams and frames. These methods are based on the differential equation of the elastic curve of a beam. This equation relates curvature at a point along beam’s longitudinal axis to the bending moment at that point and the properties of the cross section and the material. If the elastic curve seems difficult to establish, it is suggested that the moment diagram for the beam or frame be drawn first. A positive moment tends to bend a beam concave upward. Likewise a negative moment bend the beam concave downward.

Double integration method

Moment-area method

Conjugate beam method

External work and strain energy

Castigliano’s theorem for beams and frames

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