Typical formula for beam deflection is not usable when we encounter a non-prismatic beam. The cross-sectional area of a non-prismatic beam changes along the beam span. This violates the condition to use such formula i.e. the cross-sectional properties of beam remain constant.
The reaction and internal moment function of a non-prismatic beam is determined as usual, regardless its cross-sectional properties. To calculate the beam deflection, conjugate beam method may be used.
Unlike prismatic beam, the beam needs to be segmentized prior to analysis, and the subsequent analysis will be conducted based on the segmentation. The cross-sectional properties and eventually M/EI for segmentation points are determined.
Conjugate beam is developed based on the real beam condition. Then, M/EI is superimposed to the beam as loading. The magnitude at segment ends is marked for easy reference during analysis. By determine the bending moment at interested point, we calculate the deflection of actual beam.
The following introduces the calculation of non-prismatic beam deflection using conjugate beam method. Watch the video above for full details.
Non-prismatic beam overview
Support reaction
Internal moment function
Segmentization of non-prismatic beam
Conjugate beam
Bending moment calculation at fixed end for conjugate beam
Final result
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