Structural Analysis - Cont-Beam, Study notes of Structural Analysis

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Stiffness Method

Single Beam with

Concentrated Loads

3 m 4 m 5 m 5 m 50 kN 100 kN 150 kN A B C D E Deflected Shape

K =

D =

Similarly, by formulating stiffness matrices for all the segments and appending them gives the composite stiffness matrix. i.e., stiffness matrix for the entire beam. By applying unit displacements on every segment the corresponding stiffnesses are obtained. The matrices for a single segment have been formulated below. KAB = K = Stiffness Matrix D = Matrix of unknown Displacements

K = The stiffness matrix for the entire structure is as below: The useful portion of the matrix has been demarcated. The portion left in white will be used for calculation of unknown displacements.

Solving the above in MATLAB gives the following results: ΔB = 1619.9/EI ΔC = 4761.3/EI ΔD = 3738/EI θB = 869.3/EI θC = 460.9/EI θD = -829.4/EI Calculating final reactions and moments at fixed ends: For End A: = For End E : =

After substituting the respective values for the displacements in the above equations, the values of moments and reactions at A and E are obtained as follows: RA = -139.412 RE = -159. MA = -501.519 ME = 565. Shear Force Diagram: 0 -139. -89.