This post explains the first theorem of the conjugate beam method.
Theorem 1: Conjugate Shear is Real Rotation
The first theorem deals with finding rotation
This post explains the first theorem of the conjugate beam method.
The first theorem deals with finding rotation
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Let's focus on the figure shown to verify this theorem. We have a simple beam with length
Suppose that we are interested in finding the rotation at
Equation 1:
Below the actual beam is the fictional loading
Let's compute for the shear at the left end
This result is the expression we use to solve for the reaction at
Equation 2:
Equations 1 and 2 are equal - it shows the validity of the first theorem. To stress out again, if you take the shear
Let's summarize:
The fictional shear of the conjugate beam at any point is the rotation (slope) of the actual beam at said point.
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