Direct Integration Of A Beam
Direct integration is a structural analysis method for measuring internal shear, internal moment, rotation, and deflection of a beam.
For a beam with an applied weight, taking downward to be positive, the internal shear force is given by taking the negative integral of the weight:
The internal moment M(x) is the integral of the internal shear:
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The angle of rotation from the horizontal, is the integral of the internal moment divided by the product of the Young's modulus and the area moment of inertia:
Integrating the angle of rotation obtains the vertical displacement :
Read more about Direct Integration Of A Beam: Integrating, Sample Calculations
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