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Calculation Example - Calculate the member diagrams.
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Calculate the member diagrams for the uniform loading q for the pinned beam at two ends.

### Calculation Example – Buckling of Column (EC3).

Check the column for buckling according to EC3. HEB300/S275 and axial force NEd=1000KN. The column (L=15m) is pinned at the two far ends (strong axis y-y). The column is pinned every 5m at the weak axis z-z.

### Calculation Example – Shear bolt connection EC3.

Check the shear connection for the IPE450-S275 for the design shear VEd=200KN. Bolts M20-8.8, plate thickness t=10mm.

### Calculation Example – Angular acceleration, angular velocity.

The column A moves to the right with variable speed V(t)=2*Vo*t+c. Calculate the angular velocity and the angular acceleration of the beam B. The beam is pinned at one end. (c is constant).

### Calculation Example – Evaluation of Structural Property Matrices.

Calculate the stiffness matrix for the frame structure. It is assumed that the members do not distort axially. The frame has three joint degrees of freedom. At end A, B is rigidly fixed to the ground.

### Calculation Example – Undamped free Vibration (Part B).

Calculate the modal frequencies for the shear frame at the previous exercise Undamped free Vibration (Part A). The story weight of the first floor is W1=60 KN end at the second floor W2=50 KN. The cross section of the columns is circular with radius r1=0.5m at the first floor and r2=0.2m at the second floor. The columns are considered to have no mass. (Modulus of elasticity E=2.1*107 KN/m2, Story height h1=5m, h2=3m.)

### Calculation Example – Undamped free Vibration (Part A).

Calculate the Mass and the Stiffness matrix for the shear frame below. The mass is lumped at each level. The supports at end A,B are fixed . The columns are considered to have no mass. (Modulus of elasticity E, Storey masses m1,m2, Column moment of inertia I_{1},I_{2}. )