Some of these displacements may be equal to zero or May Similar equations are written down for elements BC, CD, in a continuous beamįor convenience, the deflections can but substituted by chord rotations. These are mental equations relating the unknown end moments (MM) of any prismatic beam AB to the known fixed-end moments (MM ) and the slopes (0,0) and s e ctions ( A, A ,) at the two ends.įor convenience, the deflections can substitute by chord rotations. The approach in the Slope-deflection slope deflection is to consider each beam element separately and to write down the so-called slope deflection equations for each element, in a somewhat mechanical fashion. Consider a simply a supported straight beam subjected to transverse loading.Deflection of beam controls the powerful duration to intensity ratio of beam.The slope is the attitude of beam axis between preliminary function and very last function after deflection.
However, dx/dy is very small is square is still smaller compared to unityĭeflection equation where c1 and c2 are the constant in integration which can be evaluate by using support boundary equation
Is above equation is known as differential equation of the elastic curve of a beam. Where EI – is the flexural rigidity of the beam Where R is radius of curvature for arc length ds The elastic curve is very flat and its slope at any point is very small the deflected axis of beam is called elastic curve which bends into an arc of a circle with radius of curvature R It will deflect about its original axis as shown in fig. Th e slope is the attitude of beam axis between preliminary function and very last function after deflection.ĭeflection of beam controls the powerful duration to intensity ratio of beam.Ĭonsider a simply a supported straight beam subjected to transverse loading. The reason of calculating deflection in beam is to decide the vertical intensity of its sag from preliminary horizontal (longitudinal) axis of beam. 6.1 Slope and deflection - Relation between moments