examples

Examples

Example 1

Problem¹

• l₁ = 1500 mm
• α = 30 deg
• EA = 1 x 10⁶ N
• u_app = 7 mm
• v_app = 2 mm

Solution

The problem is modelled as follow:

Figure 1. Modelled problem.

From the structure properties the nodal displacements can be recovered:

u2 = 1.948 mm
u3 = 7 mm
v3 = 2 mm

Example 2

Problem¹

• l₁ = 1000 mm
• α = 30 deg
• EJ₁ = 1 x 10¹² Nmm²
• EA₁ = 1 x 10⁶ N
• EA₂ = 1 x 10⁸ N
• q = 10 N/mm

Solution

The problem is modelled as follow:

Figure 2. Modelled problem.

From the structure properties the nodal displacements can be recovered:

u2 = -0.1136 mm
v2 =  0.2029 mm
t2 = -0.0001042 deg

To recover the axial force in the middle of beam #1, the command [N, ~] = str.get_internal_actions(1, 0.5) can be used:

N = -113.626 N

Example 3

Problem¹

• EA₁ = 5 x 10⁶ N
• EA₂ = 2 x 10⁶ N
• EA₃ = 3 x 10⁶ N
• l = 750 mm
• k₁ = 8 x 10³ N/mm
• k₂ = 4 x 10³ N/mm
• u_app = 5 mm

Solution

The problem is modelled as follow:

Figure 3. Modelled problem.

From the structure properties the nodal displacements can be recovered:

u1 = 1.842 mm
u2 = 5 mm
u3 = 2.5 mm

To recover the axial force in the middle of beam #2, the command [N, ~] = str.get_internal_actions(2, 0.5) can be used:

N = -10000 N

Example 4

Problem¹

• l₁ = 1000 mm
• l₂ = 1500 mm
• EJ₁ = 1 x 10¹² Nmm²
• EJ₂ = 1 x 10¹¹ Nmm²
• w = 3 mm
• q = 10 N/mm

Solution

The problem is modelled as follow:

Figure 4. Modelled problem.

From the structure properties the nodal displacements can be recovered:

v2 =  3 mm
t2 = -0.00627 deg
v3 =  28.8 mm

Similary, the reaction force associated to the prescribed displacements is stored in str.R_num:

Rv2 = -16622.95 N

Example 5

Problem¹

• l₁ = 1000 mm
• l₂ = 200 mm
• a = 100 mmm
• b = 10 mm
• E = 72 GPa
• P = 5 x 10⁴ N

Solution

The problem is modelled as follow:

Figure 5. Modelled problem.

From the structure properties the nodal displacements can be recovered:

u2 =  0 mm
v2 =  3.513 mm
t2 = -0.005269 deg
u3 =  0 mm
v3 =  1.693 mm
t3 = -0.002539 deg

Similary, the vertical reaction force in node #5 is stored in str.R_num:

Rv5 = -40629.76 N

Footnotes

1. Credits to prof. Riccardo Vescovini, course of Space Structures at Politecnico di Milano. ↩ ↩² ↩³ ↩⁴ ↩⁵