IndeterminateBeam Reference

Main module that contains the main class for Beam and auxillary class for Support.

Example

>>> beam = Beam(6)
>>> a = Support()
>>> c = Support(6,(0,1,0))
>>> beam.add_supports(a,c)
>>> beam.add_loads(PointLoadV(-1500,3))
>>> beam.analyse()
>>> beam.plot_beam_external()
>>> beam.plot_beam_internal()

Support

class indeterminatebeam.Support(coord=0, fixed=(1, 1, 1), kx=None, ky=None)

A class to represent a support.

Attributes:

_position: float

x coordinate of support on a beam (default 0)

_stiffness: tuple of 3 floats or infinity

stiffness K (default units N/m) for movement in x, y and bending. oo represents infinity in sympy and means a completely fixed conventional support, and 0 means free to move.

_DOFtuple of 3 booleans

Degrees of freedom that are restraint on a beam for movement in x, y and bending. 1 represents that a reaction force exists and 0 represents free (default (1,1,1))

_fixed: tuple of 3 booleans

Degrees of freedom that are completely fixed on a beam for movement in x, y and bending. 1 represents fixed and 0 represents free or spring (default (1,1,1))

Examples

>>> # Creates a fixed suppot at location 0
>>> Support(0, (1,1,1))
>>> # Creates a pinned support at location 5 m
>>> Support(5, (1,1,0))
>>> # Creates a roller support at location 5.54 m
>>> Support(5.54, (0,1,0))
>>> # Creates a y direction spring support at location 7.5 m
>>> Support(7.5, (0,1,0), ky = 5)
indeterminatebeam.Support.__init__(self, coord=0, fixed=(1, 1, 1), kx=None, ky=None)

Constructs all the necessary attributes for the Support object.

Parameters:

coord: float

x coordinate of support on a beam (default unit m) (default 0)

fixed: tuple of 3 booleans

Degrees of freedom that are fixed on a beam for movement in x, y and bending. 1 represents fixed and 0 represents free (default (1,1,1))

kx :

stiffness of x support (default unit N/m), if set will overide the value placed in the fixed tuple. (default = None)

ky(positive number)

stiffness of y support (default unit N/m), if set will overide the value placed in the fixed tuple. (default = None)

Beam

class indeterminatebeam.Beam(span: float = 5, E=200000000000, I=9.05e-06, A=0.23)

Represents a one-dimensional beam that can take axial and tangential loads.

_x0

Left end coordinate of beam (always defined as 0).

Type:

float

_x1

Right end coordinate of beam (default unit m).

Type:

float

_E

Young’s Modulus of the beam (default unit N/m2 or Pa)

Type:

float

_I

Second Moment of Area of the beam (default unit m4)

Type:

float

_A

Cross-sectional area of the beam (default unit m2)

Type:

float

_loads

list of load objects associated with the beam

Type:

list

_supports

A list of support objects associated with the beam.

Type:

list

_query

A list containing x coordinates that are to have values explicitly written on graphs.

Type:

list

_normal_forces

A sympy function representing the internal axial force (default unit N) as a function of x (m).

Type:

sympy piecewise function

_shear_forces

A sympy function representing the internal shear force (default unit N) as a function of x (m).

Type:

sympy piecewise function

_bending_moments

A sympy function representing the internal bending moments (default unit N.m) as a function of x (m).

Type:

sympy piecewise function

_deflection_equation

A sympy function representing the tangential deflection (default unit m) as a function of x (default unit m).

Type:

sympy piecewise function

_reactions

A dictionary with keys for support positions. Each key is associated with a list of forces of the form [‘x’,’y’,’m’]

Type:

dictionary of lists

_DATA_POINTS

Number of data points generated for plotting (default 200).

Type:

integer,

Notes

  • Default units are SI units all using N and m, this can however be changed using the update_units() method

  • The default units for length, force and bending moment (torque) are in N and m (m, N, N·m)

  • The default units for beam properties (E, I, A) are in N and m (N/m2, m4, m2)

  • The default unit for spring support stiffness is N/m

indeterminatebeam.Beam.__init__(self, span: float = 5, E=200000000000, I=9.05e-06, A=0.23)

Initializes a Beam object of a given length.

Parameters:

  • span (float) – Length of the beam span (default unit m). Must be positive, and the pinned and rolling supports can only be placed within this span. The default value is 5 m.

  • E (float) – Youngs modulus for the beam (default unit Pa). The default value is 200 GPa, which is the youngs modulus for steel.

  • I (float) – Second moment of area for the beam about the z axis (default unit m4). The default value is 9.05*10**-6 m4.

  • A (float) – Cross-sectional area for the beam about the z axis (default unit m2). The default value is 0.23 m4.

Notes

  • Default properties are for a 150UB18.0 steel beam.

indeterminatebeam.Beam.update_units(self, key='length', unit='m', reset=False)

Change units used for inputs and outputs.

Parameters:

  • key (string, default 'length') – Identifying property with unit to be changed. One of the following: ‘length’, ‘force’, ‘moment’, ‘distributed’, ‘stiffness’, ‘A’, ‘E’, ‘I’, ‘deflection’

  • unit (string, default 'm') – unit to assign should contain a unit balanced representation consisting of the following units: ‘mm’, ‘cm’, ‘m’, ‘N’, ‘kN’, ‘Pa’, ‘kPa’, ‘MPa’, ‘in’, ‘ft’, ‘lbf’, ‘kip’. Unit combinations are written in the following formats: ‘mm2’, ‘mm4’, ‘N/m’, ‘N.m’, ‘kip/ft2’.

  • reset (boolean, default False) – If True then all units reset to default SI units.

indeterminatebeam.Beam.add_loads(self, *loads)

Associate load objects with the beam object.

Parameters:

*loads (iterable) – An iterable containing load objects to be applied to the Beam object. Note that the load application point (or segment) must be within the Beam span.

indeterminatebeam.Beam.remove_loads(self, *loads, remove_all=False)

Unassociate load objects with the beam object.

Parameters:

  • *loads (iterable) – An iterable containing load objects to be removed from the Beam object. If load not on beam then does nothing.

  • remove_all (boolean) – If true all loads associated with beam will be removed, by default False.

indeterminatebeam.Beam.add_supports(self, *supports)

Associate support objects with the beam object.

Parameters:

*supports (iterable) – An iterable containing Support objects to be applied to the Beam object. Note that the load application point (or segment) must be within the Beam span.

indeterminatebeam.Beam.remove_supports(self, *supports, remove_all=False)

Unassociate support objects with the beam object.

Parameters:

  • *supports (iterable) – An iterable containing Support objects to be removed from the Beam object. If support not on beam then does nothing.

  • remove_all (boolean) – If true all supports associated with beam will be removed, by default False.

indeterminatebeam.Beam.analyse(self)

Solve the beam structure for reaction and internal forces

indeterminatebeam.Beam.get_reaction(self, x_coord, direction=None)

Find the reactions of a support at position x.

Parameters:

  • x_coord (float) – The x_coordinates on the beam to be substituted into the equation. List returned (if bools all false)

  • direction (str ('x','y' or 'm')) – The direction of the reaction force to be returned. If not specified all are returned in a list.

Returns:

  • int – If direction is ‘x’, ‘y’, or ‘m’ will return an integer representing the reaction force of the support in that direction at location x_coord.

  • list of ints – If direction = None, will return a list of 3 integers, representing the reaction forces of the support [‘x’,’y’,’m’] at location x_coord.

  • None – If there is no support at the x coordinate specified.

indeterminatebeam.Beam.get_bending_moment(self, *x_coord, return_max=False, return_min=False, return_absmax=False)

Find the bending moment(s) on the beam object.

Parameters:

  • x_coord (list) – The x_coordinates on the beam to be substituted into the equation. List returned (if bools all false)

  • return_max (bool) – return max value of function if true

  • return_min (bool) – return minx value of function if true

  • return_absmax (bool) – return absolute max value of function if true

Returns:

  • int – Max, min or absmax value of the bending moment depending on which parameters are set. If single x-coordinate set then also returns int.

  • list of ints – If x-coordinates are specfied value at x-coordinates for func.

Notes

  • Priority of query parameters is return_max, return_min, return_absmax, x_coord (if more than 1 of the parameters are specified).

indeterminatebeam.Beam.get_shear_force(self, *x_coord, return_max=False, return_min=False, return_absmax=False)

Find the shear force(s) on the beam object.

Parameters:

  • x_coord (list) – The x_coordinates on the beam to be substituted into the equation. List returned (if bools all false)

  • return_max (bool) – return max value of function if true

  • return_min (bool) – return minx value of function if true

  • return_absmax (bool) – return absolute max value of function if true

Returns:

  • int – Max, min or absmax value of the shear force depending on which parameters are set. If single x-coordinate set then also returns int.

  • list of ints – If x-coordinates are specfied value at x-coordinates for func.

Notes

  • Priority of query parameters is return_max, return_min, return_absmax, x_coord (if more than 1 of the parameters are specified).

indeterminatebeam.Beam.get_normal_force(self, *x_coord, return_max=False, return_min=False, return_absmax=False)

Find the normal force(s) on the beam object.

Parameters:

  • x_coord (list) – The x_coordinates on the beam to be substituted into the equation. List returned (if bools all false)

  • return_max (bool) – return max value of function if true

  • return_min (bool) – return minx value of function if true

  • return_absmax (bool) – return absolute max value of function if true

Returns:

  • int – Max, min or absmax value of the normal force depending on which parameters are set. If single x-coordinate set then also returns int.

  • list of ints – If x-coordinates are specfied value at x-coordinates for func.

Notes

  • Priority of query parameters is return_max, return_min, return_absmax, x_coord (if more than 1 of the parameters are specified).

indeterminatebeam.Beam.get_deflection(self, *x_coord, return_max=False, return_min=False, return_absmax=False)

Find the deflection(s) on the beam object.

Parameters:

  • x_coord (list) – The x_coordinates on the beam to be substituted into the equation. List returned (if bools all false)

  • return_max (bool) – return max value of function if true

  • return_min (bool) – return minx value of function if true

  • return_absmax (bool) – return absolute max value of function if true

Returns:

  • int – Max, min or absmax value of the deflection depending on which parameters are set. If single x-coordinate set then also returns int.

  • list of ints – If x-coordinates are specfied value at x-coordinates for func.

Notes

  • Priority of query parameters is return_max, return_min, return_absmax, x_coord (if more than 1 of the parameters are specified).

indeterminatebeam.Beam.add_query_points(self, *x_coords)

Document the forces on a beam at position x_coord when plotting.

Parameters:

x_coord (list) – The x_coordinates on the beam to be queried on plot.

indeterminatebeam.Beam.remove_query_points(self, *x_coords, remove_all=False)

Remove a query point added by add_query_points function.

Parameters:

  • x_coord (list) – The x_coordinates on the beam to be removed from query on plot.

  • remove_all (boolean) – If true all query points will be removed.

indeterminatebeam.Beam.plot_beam_external(self)

Generates a single figure with 2 plots corresponding respectively to:

  • a schematic of the loaded beam

  • reaction force diagram

Returns:

figure – Returns a handle to a figure with the 2 subplots.

Return type:

plotly.graph_objs._figure.Figure

indeterminatebeam.Beam.plot_beam_internal(self, reverse_x=False, reverse_y=False)

Generates a single figure with 4 plots corresponding respectively to:

  • normal force diagram,

  • shear force diagram,

  • bending moment diagram, and

  • deflection diagram

Parameters:

  • reverse_x (bool, optional) – reverse the x axes, by default False

  • reverse_y (bool, optional) – reverse the y axes, by default False

Returns:

figure – Returns a handle to a figure with the 4 subplots.

Return type:

plotly.graph_objs._figure.Figure

indeterminatebeam.Beam.plot_beam_diagram(self, fig=None, row=None, col=None)

Returns a schematic of the beam and all the loads applied on it

Parameters:

  • fig (bool, optional) – Figure to append subplot diagram too. If creating standalone figure then None, by default None

  • row (int, optional) – row number if subplot, by default None

  • col (int, optional) – column number if subplot, by default None

Returns:

figure – Returns a handle to a figure with the beam schematic.

Return type:

plotly.graph_objs._figure.Figure

indeterminatebeam.Beam.plot_reaction_force(self, fig=None, row=None, col=None)

Returns a plot of the beam with reaction forces.

Parameters:

  • fig (bool, optional) – Figure to append subplot diagram too. If creating standalone figure then None, by default None

  • row (int, optional) – row number if subplot, by default None

  • col (int, optional) – column number if subplot, by default None

Returns:

figure – Returns a handle to a figure with reaction forces.

Return type:

plotly.graph_objs._figure.Figure

indeterminatebeam.Beam.plot_normal_force(self, reverse_x=False, reverse_y=False, switch_axes=False, fig=None, row=None, col=None)

Returns a plot of the normal force as a function of the x-coordinate.

Parameters:

  • reverse_x (bool, optional) – reverse the x axes, by default False

  • reverse_y (bool, optional) – reverse the y axes, by default False

  • switch_axes (bool, optional) – switch the x and y axis, by default False

  • fig (bool, optional) – Figure to append subplot diagram too. If creating standalone figure then None, by default None

  • row (int, optional) – row number if subplot, by default None

  • col (int, optional) – column number if subplot, by default None

Returns:

figure – Returns a handle to a figure with the normal force diagram.

Return type:

plotly.graph_objs._figure.Figure

indeterminatebeam.Beam.plot_shear_force(self, reverse_x=False, reverse_y=False, switch_axes=False, fig=None, row=None, col=None)

Returns a plot of the shear force as a function of the x-coordinate.

Parameters:

  • reverse_x (bool, optional) – reverse the x axes, by default False

  • reverse_y (bool, optional) – reverse the y axes, by default False

  • switch_axes (bool, optional) – switch the x and y axis, by default False

  • fig (bool, optional) – Figure to append subplot diagram too. If creating standalone figure then None, by default None

  • row (int, optional) – row number if subplot, by default None

  • col (int, optional) – column number if subplot, by default None

Returns:

figure – Returns a handle to a figure with the shear force diagram.

Return type:

plotly.graph_objs._figure.Figure

indeterminatebeam.Beam.plot_bending_moment(self, reverse_x=False, reverse_y=False, switch_axes=False, fig=None, row=None, col=None)

Returns a plot of the bending moment as a function of the x-coordinate.

Parameters:

  • reverse_x (bool, optional) – reverse the x axes, by default False

  • reverse_y (bool, optional) – reverse the y axes, by default False

  • switch_axes (bool, optional) – switch the x and y axis, by default False

  • fig (bool, optional) – Figure to append subplot diagram too. If creating standalone figure then None, by default None

  • row (int, optional) – row number if subplot, by default None

  • col (int, optional) – column number if subplot, by default None

Returns:

figure – Returns a handle to a figure with the bending moment diagram.

Return type:

plotly.graph_objs._figure.Figure

indeterminatebeam.Beam.plot_deflection(self, reverse_x=False, reverse_y=False, switch_axes=False, fig=None, row=None, col=None)

Returns a plot of the beam deflection as a function of the x-coordinate.

Parameters:

  • reverse_x (bool, optional) – reverse the x axes, by default False

  • reverse_y (bool, optional) – reverse the y axes, by default False

  • switch_axes (bool, optional) – switch the x and y axis, by default False

  • fig (bool, optional) – Figure to append subplot diagram too. If creating standalone figure then None, by default None

  • row (int, optional) – row number if subplot, by default None

  • col (int, optional) – column number if subplot, by default None

Returns:

figure – Returns a handle to a figure with the deflection diagram.

Return type:

plotly.graph_objs._figure.Figure

PointLoads

class indeterminatebeam.PointTorque(force=0, coord=0)

Point clockwise torque.

Parameters:

force: float

Torque load (default units N.m), (named force for consistency with other load types)

coord: float

x coordinate of torque on beam (default units m)

Examples

>>> # 30 N·m (anti-clockwise) torque at x = 4 m
>>> motor_torque = PointTorque(30, 4)

Note: Anti-clockwise is positive

class indeterminatebeam.PointLoad(force=0, coord=0, angle=0)

Point load.

Parameters:

Force: float

Force load (default units m)

coord: float

x coordinate of load on beam (default units m)

angle: float

angle of point load where: - 0 degrees is purely horizontal +ve - 90 degrees is purely vertical +ve - 180 degrees is purely horizontal -ve of force sign specified.

Examples

>>> # 100 N towards the right at x = 9 m
>>> external_force = PointLoad(100, 9, 90)
>>> # 300 N downwards at x = 3 m
>>> external_force = PointLoad(-300, 3, 0)
>>> external_force
    PointLoad(force=-300, coord=3, angle=0)
class indeterminatebeam.PointLoadV(force=0, coord=0)

Vertical Point Load.

Parameters:

Force: float

Force load (default units N)

coord: float

x coordinate of load on beam (default units m)

Examples

>>> # 100 N towards the right at x = 9 m
>>> external_force = PointLoad(100, 9)

Note: Positive force acts up.

class indeterminatebeam.PointLoadH(force=0, coord=0)

Horizontal Point Load.

Parameters:

Force: float

Force load (default units m)

coord: float

x coordinate of load on beam (default units m)

Examples

>>> # 100 N up at x = 9 m
>>> external_force = PointLoad(100, 9)

Note: Positive force acts right.

DistributedLoads

class indeterminatebeam.UDL(force=0, span=(0, 0), angle=0)

Uniformly Distributed Load (UDL).

Parameters:

  • force (int, optional) – UDL load (default units N/m), by default 0

  • span (tuple of floats) – A tuple containing the starting and ending coordinate that the UDL is applied to (default units m).

  • angle (float) – angle of point load where: - 0 degrees is purely horizontal +ve - 90 degrees is purely vertical +ve - 180 degrees is purely horizontal -ve of force sign specified.

Examples

>>> # load of 1000 N/m from 1 m <= x <= 4 m (vertical)
>>> self_weight = UDL(1000, (1, 4), 90)
class indeterminatebeam.UDLV(force=0, span=(0, 0))

Vertical Uniformly Distributed Load.

Parameters:

  • Force (float) – Force load (default units N/m)

  • span (tuple of floats) – A tuple containing the starting and ending coordinate that the UDL is applied to (default units m).

Examples

>>> # load of 1000 N/m (acting down) from 1 <= x <= 4 m
>>> self_weight = UDL(-1000, (1, 4))

Note: Positive force acts up.

class indeterminatebeam.UDLH(force=0, span=(0, 0))

Horizontal Uniformly Distributed Load.

Parameters:

  • Force (float) – Force load (default units N/m)

  • span (tuple of floats) – A tuple containing the starting and ending coordinate that the UDL is applied to (default units m).

Examples

>>> # load of 1000 N/m (acting right) from 1 <= x <= 4 m
>>> self_weight = UDL(-1000, (1, 4))

Note: Positive force acts right.

class indeterminatebeam.TrapezoidalLoad(force=(0, 0), span=(0, 0), angle=0)

Trapezoidal Distributed Load.

Parameters:

  • force (tuple of floats) – A tuple containing the starting and ending loads of the trapezoidal load (default units N/m).

  • span (tuple of floats) – A tuple containing the starting and ending coordinate that the trapezoidal load is applied to (default units m).

  • angle (float) – angle of point load where: - 0 degrees is purely horizontal +ve - 90 degrees is purely vertical +ve - 180 degrees is purely horizontal -ve of force sign specified.

Examples

>>> # trapezoidal load starting at 2000 N/m at 1 m and ending at 3000 N/m
>>> # at 4 m (vertical)
>>> self_weight = UDL((2000, 3000), (1, 4), 90)
class indeterminatebeam.TrapezoidalLoadV(force=(0, 0), span=(0, 0))

Vertical Trapezoidal Distributed Load.

Parameters:

  • force (tuple of floats) – A tuple containing the starting and ending loads of the trapezoidal load (default units N/m).

  • span (tuple of floats) – A tuple containing the starting and ending coordinate that the trapezoidal load is applied to (default units m).

Examples

>>> # trapezoidal load starting at 2000 N/m at 1 m and ending at 3000 N/m
>>> # at 4 m (acting down)
>>> self_weight = UDL((-2000,-3000), (1, 4))

Note: Positive force acts up.

class indeterminatebeam.TrapezoidalLoadH(force=(0, 0), span=(0, 0))

Horizontal Trapezoidal Distributed Load.

Parameters:

  • force (tuple of floats) – A tuple containing the starting and ending loads of the trapezoidal load (default units N/m).

  • span (tuple of floats) – A tuple containing the starting and ending coordinate that the trapezoidal load is applied to (default units m).

Examples

>>> # trapezoidal load starting at 2000 N/m at 1 m and ending at 3 N/m
>>> # at 4 m (acting right)
>>> self_weight = UDL((2000, 3000), (1, 4))

Note: Positive force acts right.

class indeterminatebeam.DistributedLoad(expr, span=(0, 0), angle=0)

Distributed load, described by its functional form, application interval and the angle of the load relative to the beam.

Parameters:

expr: sympy expression

Sympy expression of the distributed load function expressed using variable x which represents the beam x-coordinate. Requires quotation marks around expression (default units in N/m).

span: tuple of floats
A tuple containing the starting and ending coordinate that

the function is applied to (default units m).

angle: float

angle of point load where: - 0 degrees is purely horizontal +ve - 90 degrees is purely vertical +ve - 180 degrees is purely horizontal -ve of force sign specified.

Examples

>>> # Linearly growing load for 0 < x < 2 m
>>> snow_load = DistributedLoad("10 * x + 5", (0, 2), 90)
class indeterminatebeam.DistributedLoadV(expr=0, span=(0, 0))

Vertical distributed load, described by its functional form, application interval and the angle of the load relative to the beam.

Parameters:

expr: sympy expression

Sympy expression of the distributed load function expressed using variable x which represents the beam x-coordinate (default units N/m).Requires quotation marks around expression.

span: tuple of floats
A tuple containing the starting and ending coordinate that

the function is applied to (default units m).

Examples

>>> # Linearly growing load (acting down) for 0 < x < 2 m
>>> snow_load = DistributedLoad("-10*x-5", (0, 2))

Note: Positive force acts up.

class indeterminatebeam.DistributedLoadH(expr=0, span=(0, 0))

Horizontal distributed load, described by its functional form, application interval and the angle of the load relative to the beam.

Parameters:

expr: sympy expression

Sympy expression of the distributed load function expressed using variable x which represents the beam x-coordinate (default units N/m). Requires quotation marks around expression.

span: tuple of floats
A tuple containing the starting and ending coordinate that

the function is applied to (default units m).

Examples

>>> # Linearly growing load (acting right) for 0 < x < 2 m
>>> snow_load = DistributedLoad("10*x+5", (0, 2))

Note: Positive force acts right.