Consider the cantilever beam shown in Figure 2, which is subjected to a linearly distributedtransverse load with intensity qo at the tip. Using a single cubic beam finite element and thecorresponding consistent load vector obtain:(a) The deflection and slope at the tip (free end) of the beam.(b) The reactions at the fixed boundary.(c) Comment on how the above finite element results would compare with the "exact" resultsfor the beam obtained from the solution of the governing differential equation. Withoutperforming the calculations, comment on how the exact and finite element predicted (i)deflection profiles and (ii) strain energies would compare?EILFigure 2

Slope and deflection at free end Deflection δδ=WL430EISlope θθ=WL324EISubstituteDeflection at free…

Consider the cantilever beam shown in Figure 2, which is subjected to a linearly distributed transverse load with intensity qo at the tip. Using a single cubic beam finite element and the corresponding consistent load vector obtain: (a) The deflection and slope at the tip (free end) of the beam. (b) The reactions at the fixed boundary.

Consider the cantilever beam shown in Figure 2, which is subjected to a linearly distributed transverse load with intensity qo at the tip. Using a single cubic beam finite element and the corresponding consistent load vector obtain: (a) The deflection and slope at the tip (free end) of the beam. (b) The reactions at the fixed boundary.

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Concept explainers

Beams

In structural engineering, a beam is a component made of a variety of materials (including steel alloys, and wood) that can resist loads applied laterally to the beam axis. Members, elements, rafters, shafts, and purlins are all terms used to describe beams.

Question

Consider the cantilever beam shown in Figure 2, which is subjected to a linearly distributed
transverse load with intensity qo at the tip. Using a single cubic beam finite element and the
corresponding consistent load vector obtain:
(a) The deflection and slope at the tip (free end) of the beam.
(b) The reactions at the fixed boundary.
(c) Comment on how the above finite element results would compare with the "exact" results
for the beam obtained from the solution of the governing differential equation. Without
performing the calculations, comment on how the exact and finite element predicted (i)
deflection profiles and (ii) strain energies would compare?
EI
L
Figure 2

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