Characteristic Equation for a 4*4 Matrix (Eigenvalues)

Whenever a 4*4 matrix is given, and it is to find the characteristic equation. Always expand along the column or row, which has the maximum number of zeroes. Look for the solved example given below.
Given Matrix A is a 4*4 matrix, with 9, 7, 5 and 9 as the diagonal elements. First column contains the maximum zeroes, so expand along it. The final equation is the characteristic equation. Soling it gives 9, 5 and 7 as the eigenvalues.

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Solved - Virtual Work Method - Deflection of Beam - Propped Cantilever with Internal hinge

Hi

Consider the compound beam shown in fig. EI is constant. Use the principle of Virtual Work. Determine the displacement at point D.
Please refer the image below for the solution.

Virtual Work Method - Deflection of beam - Propped cantilever with internal hinge

Virtual Work Method - Deflection of Beam - Propped Cantilever with Internal Hinge

Solved - Moment Distribution Method -Frame with pinned and fixed ends)

hi,
The given frame has two roller supports and one fixed, support. One must know the stiffness and distribution factors to distribute the unbalanced moments. Take the following example. Solution is handwritten below.