# Statics - Finite Elements Methods : Beams and Springs

Problem 1: (Please see the attached file for the fully formatted problems.)

The figure shows a beam element with the following properties:

E=200 GNm2,I = 5-l0m4, L = 4m, A=250 mm2

and a bar element with:

A = 500 mm2, E 200 GNm2.

Find:

1. The stiffness matrix of each clement in the local (element) coordinate system.

2. The rotated element stiffness matrix (where needed).

3. Thc global stiffness matrix.

4. The constrained (reduced) stifihess matrix.

5. The displacement components of node 2.

Problem 2:

Eindige Element Metodes 414 / Finite Element Methods 414

....

The beam has a roller (or hinge) support al node 2 and a spring support at node 3. Use two beam elements and one spring element to solve the problem.

Given: P 50 kN. k=200kNIm, L 3m, E=210 GN/m2, i2l0m4

Beam element I

...

Bar element 2

...

Find: Deflections and rotations of node 2 and 3. Assume there is zero axial (X) deformation.

Please see the attached file for the fully formatted problems.

You must use finite element methods to solve these 2 problems. Principle of Superposition is not correct.

Do calculations with MATLAB & provide code.

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#### Solution Summary

Beam and spring elements are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.