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Stiffness Matrices and Global Assembly for Three Identical Structural Elements, Exercises of Mathematical Methods for Numerical Analysis and Optimization

Aligarh Muslim UniversityMathematical Methods for Numerical Analysis and Optimization

The stiffness matrices in local coordinates for three identical structural elements, along with their lengths and young's modulus. The transformation matrix is also given. Using these values, the global stiffness matrices are derived and then assembled to obtain the final stiffness matrix for the system.

Typology: Exercises

2011/2012

Uploaded on 07/08/2012

ramu
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Problem 6.12
From problem 6.7 we get the stiffness matrices in local coordinates as follows:
For Element 1:
A=6 in2 L=36 in E=30×106 psi I= 2 in4
For Element 2:
A=6 in2 L=60 in E=30×106 psi I= 2 in4
For Element 3:
A=6 in2 L=36 in E=30×106 psi I= 2 in4
From Problem 6.8 we have the transformation matrix as follows:
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Problem 6. From problem 6.7 we get the stiffness matrices in local coordinates as follows: For Element 1: A=6 in^2 L=36 in E=30×10^6 psi I= 2 in^4 For Element 2: A=6 in^2 L=60 in E=30×10^6 psi I= 2 in^4 For Element 3: A=6 in^2 L=36 in E=30×10^6 psi I= 2 in^4

From Problem 6.8 we have the transformation matrix as follows:

Now we have the formulae for global matrix as follows

By applying this formulae we have the global stiffness matrices as follows: