bending_response

Description :

The bending_response function computes the deflection and stress at the extremity of the beam under a specified bending load. Users can define the frequency segment within which the response will be analyzed. This function is crucial for understanding how the beam behaves when subjected to bending moments, helping engineers assess its performance under various loading conditions.

Syntax :

>>> import beamas as bm
>>> material = bm.isotropic_material(E, G, P, D)
>>> beam = bm.isotropic_beam(L,b,h,a,J,material)
>>> beam.bending_response(Fmin, Fmax)
>>>

Note :

Fmin : Minimum frequency domain
Fmax : Maximum frequency domain

torsion_response

Description :

The torsion_response function evaluates the response of the beam when subjected to torsional loading. Similar to the bending response, it provides results for deflection and stress at the extremity of the beam within a user-defined frequency range. This function is essential for applications where twisting forces are present, ensuring that the beam can withstand the associated stresses.

Syntax :

>>> import beamas as bm
>>> material = bm.isotropic_material(E, G, P, D)
>>> beam = bm.isotropic_beam(L,b,h,a,J,material)
>>> beam.torsion_response(Fmin, Fmax)
>>>

Note :

Fmin : Minimum frequency domain
Fmax : Maximum frequency domain

tension_response

Description :

The tension_response function calculates the response of the beam under axial tensile loading. Users can specify the frequency segment for analysis, allowing them to understand how the beam reacts to stretching forces at its extremity. This is particularly important for beams that are subject to pulling forces, aiding in the design and evaluation of structural integrity.

Syntax :

>>> import beamas as bm
>>> material = bm.isotropic_material(E, G, P, D)
>>> beam = bm.isotropic_beam(L,b,h,a,J,material)
>>> beam.tension_response(Fmin, Fmax)
>>>

Note :

Fmin : Minimum frequency domain
Fmax : Maximum frequency domain

compression_response

Description :

The compression_response function determines the beam's deflection and stress when subjected to axial compressive loads. By allowing users to define a specific frequency range, this function assists in analyzing how the beam performs under pushing forces, which is vital for applications involving compression, ensuring safety and reliability in structural designs.

Syntax :

>>> import beamas as bm
>>> material = bm.isotropic_material(E, G, P, D)
>>> beam = bm.isotropic_beam(L,b,h,a,J,material)
>>> beam.compression_response(Fmin, Fmax)
>>>

Note :

Fmin : Minimum frequency domain
Fmax : Maximum frequency domain

loading_response

Description :

The loading_response function provides a versatile method for calculating the beam's response to user-defined loading conditions. Users can specify their own load vector, which allows for a more tailored analysis compared to predetermined loading scenarios. This function is invaluable for complex loading cases, enabling detailed investigations into the beam's behavior under unique conditions.

Syntax :

>>> import beamas as bm
>>> material = bm.isotropic_material(E, G, P, D)
>>> beam = bm.isotropic_beam(L,b,h,a,J,material)
>>> beam.loading_response(Fmin, Fmax, F, n)
>>>

Note :

Fmin : Minimum frequency domain
Fmax : Maximum frequency domain
F : Loading vector
n : Visualized displacement vector element
Loading and Displacement vectors are twelve-element vectors exploiting the six possible deformations in both beam ends.

stack

Description :

The stack function enables users to define the thickness of individual layers in a multilayer beam. This function is essential and necessary for creating a multilayer_beam, as it allows for customization of layer properties. Users can specify the thickness of each layer as needed, facilitating detailed analyses of multilayered structures and their performance under various loading conditions. Without this function, accurately modeling and analyzing multilayer beams would not be possible.

Syntax :

>>> import beamas as bm
>>> s = bm.stack([h1,...,hn])
>>>

Note :

h : Height of each individual layer
The stack function is a crucial step to define the successivity of layers and their heights before creating a multi-layer beam.

Example : isotropic_beam bending

Description :

this example demonstrates the application of the BeamAS library to analyze the bending behavior of a single-layer isotropic beam. It guides users through defining the material and geometric properties, creating an instance of the isotropic_beam class, and applying a bending load. The example highlights the necessary parameters and functions to observe the beam's bending response, providing a straightforward walkthrough for understanding the behavior of isotropic beams under bending loads.

Syntax :

>>> import beamas as bm
>>> steel = bm.isotropic_material(2e11, 8e10, 0.3, 7850)
>>> beam = bm.isotropic_beam(0.7,0.05,0.02,0,3.33e-8,steel)
>>> beam.bending_response(1, 10000)
>>>

Note :

E : Young's modulus (200 GPa)
G : Shear modulus (80 GPa)
P : Poisson's ratio (0.3)
D : Density (7850 kg/m³)
L : Lenght (0.7 m)
b : Widht (0.05 m)
h : Height (0.02 m)
a : Orientation angle (0°)
J : Moment of inertia (3.33 × 10^-8 m⁴)
Fmin : Minimum frequency domain (1 Hz)
Fmax : Maximum frequency domain (10000 Hz)