pycba.beam.Beam#

class Beam(L=None, EI=None, R=None, LM=None, eletype=None)[source]#

Bases: object

Class definition

Constructs a beam object

Parameters:

L (np.ndarray) – A vector of span lengths.
EI (np.ndarray) – A vector of member flexural rigidities.
R (np.ndarray) – A vector describing the support conditions at each member end.
LM (Optional[list[list[Union[int, float]]]]) – The load matrix: a list of loads on the beam; each load with several parameters.
eletype (Optional[np.ndarray]) – A vector of the member types. Defaults to a fixed-fixed element.

Return type:

None.

Methods

`add_load`	Adds a new load to the beam's load matrix
`add_span`	Add a span to the continuous beam
`get_local_span_coords`	Returns the span index and position in span for a position given in global coordinates on the beam
`get_ref`	Returns Released End Forces for the member; that is, the Consistent Nodal Loads modified for the element type (i.e.
`get_span_k`	Returns the stiffness matrix for the ith span
`k_FF`	Stiffness matrix for a fixed-fixed element
`k_FP`	Stiffness matrix for a fixed-pinned element
`k_PF`	Stiffness matrix for a pinned-fixed element
`k_PP`	Stiffness matrix for a pinned-pinned element

Attributes

`length`	returns: length -- The total length of the beam :rtype: float
`loads`	Returns the load matrix for the beam
`no_fixed_restraints`	Returns the number of fixed restraints of the beam (fully-supported DOFs)
`no_restraints`	Returns the number of restraints of the beam
`no_spans`	Returns the no.
`restraints`	Returns the restraints vector for the beam

add_span(L, EI, eletype)[source]#

Add a span to the continuous beam

Parameters:

L (float) – The length of the member.
EI (np.ndarray) – The flexural rigidity of the member.
eletype (int) – The element type for the member

Return type:

None.

property loads: List[List[int | float]]#

Returns the load matrix for the beam

Returns:: LM – The load matrix for the beam
Return type:: LoadMatrix

add_load(load)[source]#

Adds a new load to the beam’s load matrix

Parameters:: load (List[Union[int,float]]) – A list describing the load to be added
Return type:: None

property restraints: ndarray#

Returns the restraints vector for the beam

Returns:: _restraints – The restraints vector for the beam
Return type:: np.ndarray

property no_spans#

Returns the no. of spans in the beam

Returns:: no_spans – The number of spans in the beam
Return type:: int

property no_restraints#

Returns the number of restraints of the beam

Returns:: no_restraints – The number of restraints in the beam
Return type:: int

property no_fixed_restraints#

Returns the number of fixed restraints of the beam (fully-supported DOFs)

Returns:: no_fixed_restraints – The number of fixed restraints in the beam
Return type:: int

property length#: returns: length – The total length of the beam :rtype: float

get_local_span_coords(pos)[source]#

Returns the span index and position in span for a position given in global coordinates on the beam

Parameters:

pos (float) – The position of interest in global coordinates along the length of the beam

Return type:

(int, float)

Returns:

ispan (int) – The index (1-based) of the span in which the point of interest falls
pos_in_span (float) – The local coordinate along the member of the point of interest

get_ref(i_span)[source]#

Returns Released End Forces for the member; that is, the Consistent Nodal Loads modified for the element type (i.e. releases)

Parameters:: ispan (int) – The index (1-based) of the span in which the point of interest falls
Returns:: ref – The totalled CNL object for the member, considering all loads.
Return type:: LoadCNL

get_span_k(i_span)[source]#

Returns the stiffness matrix for the ith span

Parameters:: ispan (int) – The index (1-based) of the span in which the point of interest falls
Returns:: kb – The stiffness matrix for the member
Return type:: np.ndarray

k_FF(EI, L)[source]#

Stiffness matrix for a fixed-fixed element

Parameters:

EI (float) – The flexural rigidity for the member (assumed prismatic)
L (float) – The length of the member

Returns:

k – The stiffness matrix for the member

Return type:

np.ndarray

k_FP(EI, L)[source]#

Stiffness matrix for a fixed-pinned element

Parameters:

EI (float) – The flexural rigidity for the member (assumed prismatic)
L (float) – The length of the member

Returns:

k – The stiffness matrix for the member

Return type:

np.ndarray

k_PF(EI, L)[source]#

Stiffness matrix for a pinned-fixed element

Parameters:

EI (float) – The flexural rigidity for the member (assumed prismatic)
L (float) – The length of the member

Returns:

k – The stiffness matrix for the member

Return type:

np.ndarray

k_PP(EI, L)[source]#

Stiffness matrix for a pinned-pinned element

Parameters:

EI (float) – The flexural rigidity for the member (assumed prismatic)
L (float) – The length of the member

Returns:

k – The stiffness matrix for the member

Return type:

np.ndarray