Here you can find a comprehensive but by no means exhaustive list of examples exploring the capabilities of SymBeam. In each example, you will find a hyperlink to the associated file in the repository, the respective source code and output: both console and plot.
- Symbolic length
- Roller
- Pin
- Symbolic distributed linear load
- Symbolic distributed constant load
from symbeam import beam
test_beam = beam("l", x0=0)
test_beam.add_support(0, "roller")
test_beam.add_support("l", "pin")
test_beam.add_distributed_load(0, "l/2", "-2 * q / l * x")
test_beam.add_distributed_load("l/2", "l", "-q")
test_beam.solve()
fig, ax = test_beam.plot()
Beam points
===================================================================================
Coordinate Type Load Moment
-----------------------------------------------------------------------------------
0 Roller 0 0
l/2 Continuity point 0 0
l Pinned Support 0 0
===================================================================================
Beam segments
===================================================================================
Span Young modulus Inertia Distributed load
-----------------------------------------------------------------------------------
[ 0 - l/2 ] E I -2*q*x/l
[ l/2 - l ] E I -q
===================================================================================
Exterior Reactions
===================================================================================
Point Type Value
-----------------------------------------------------------------------------------
0 Force 7*l*q/24
l Force 11*l*q/24
===================================================================================
Internal Loads
===================================================================================
Span Diagram Expression
-----------------------------------------------------------------------------------
[ 0 - l/2 ] V(x) -7*l*q/24 + q*x**2/l
[ 0 - l/2 ] M(x) 7*l*q*x/24 - q*x**3/(3*l)
-----------------------------------------------------------------------------------
[ l/2 - l ] V(x) -13*l*q/24 + q*x
[ l/2 - l ] M(x) -l**2*q/24 + 13*l*q*x/24 - q*x**2/2
===================================================================================
Rotation and deflection
===================================================================================
Span Variable Expression
-----------------------------------------------------------------------------------
[ 0 - l/2 ] v(x) -187*l**3*q*x/(5760*E*I) + 7*l*q*x**3/(144*E*I) - q*x**5/(60*E*I*l)
[ 0 - l/2 ] dv/dx(x) -187*l**3*q/(5760*E*I) + 7*l*q*x**2/(48*E*I) - q*x**4/(12*E*I*l)
-----------------------------------------------------------------------------------
[ l/2 - l ] v(x) -l**4*q/(1920*E*I) - 157*l**3*q*x/(5760*E*I) - l**2*q*x**2/(48*E*I) + 13*l*q*x**3/(144*E*I) - q*x**4/(24*E*I)
[ l/2 - l ] dv/dx(x) -157*l**3*q/(5760*E*I) - l**2*q*x/(24*E*I) + 13*l*q*x**2/(48*E*I) - q*x**3/(6*E*I)
===================================================================================
- Symbolic length
- Roller
- Pin
- Symbolic distributed linear load
- Symbolic distributed constant load
- User-specified symbolic substitutions
from symbeam import beam
test_beam = beam("l", x0=0)
test_beam.add_support(0, "roller")
test_beam.add_support("l", "pin")
test_beam.add_distributed_load(0, "l/2", "-2 * q / l * x")
test_beam.add_distributed_load("l/2", "l", "-q")
test_beam.solve()
fig, ax = test_beam.plot(subs={"q": 2, "l": 2, "x": 10}) # 'x' is not substituted
Beam points
===================================================================================
Coordinate Type Load Moment
-----------------------------------------------------------------------------------
0 Roller 0 0
l/2 Continuity point 0 0
l Pinned Support 0 0
===================================================================================
Beam segments
===================================================================================
Span Young modulus Inertia Distributed load
-----------------------------------------------------------------------------------
[ 0 - l/2 ] E I -2*q*x/l
[ l/2 - l ] E I -q
===================================================================================
Exterior Reactions
===================================================================================
Point Type Value
-----------------------------------------------------------------------------------
0 Force 7*l*q/24
l Force 11*l*q/24
===================================================================================
Internal Loads
===================================================================================
Span Diagram Expression
-----------------------------------------------------------------------------------
[ 0 - l/2 ] V(x) -7*l*q/24 + q*x**2/l
[ 0 - l/2 ] M(x) 7*l*q*x/24 - q*x**3/(3*l)
-----------------------------------------------------------------------------------
[ l/2 - l ] V(x) -13*l*q/24 + q*x
[ l/2 - l ] M(x) -l**2*q/24 + 13*l*q*x/24 - q*x**2/2
===================================================================================
Rotation and deflection
===================================================================================
Span Variable Expression
-----------------------------------------------------------------------------------
[ 0 - l/2 ] v(x) -187*l**3*q*x/(5760*E*I) + 7*l*q*x**3/(144*E*I) - q*x**5/(60*E*I*l)
[ 0 - l/2 ] dv/dx(x) -187*l**3*q/(5760*E*I) + 7*l*q*x**2/(48*E*I) - q*x**4/(12*E*I*l)
-----------------------------------------------------------------------------------
[ l/2 - l ] v(x) -l**4*q/(1920*E*I) - 157*l**3*q*x/(5760*E*I) - l**2*q*x**2/(48*E*I) + 13*l*q*x**3/(144*E*I) - q*x**4/(24*E*I)
[ l/2 - l ] dv/dx(x) -157*l**3*q/(5760*E*I) - l**2*q*x/(24*E*I) + 13*l*q*x**2/(48*E*I) - q*x**3/(6*E*I)
===================================================================================
- Symbolic length
- Fixed
- Hinge
- Symbolic distributed constant load
- Symbolic point load
from symbeam import beam
test_beam = beam("l", x0=0)
test_beam.add_support(0, "fixed")
test_beam.add_support("l/2", "hinge")
test_beam.add_support("l", "roller")
test_beam.add_distributed_load("l/2", "l", "-q")
test_beam.add_point_load("l/4", "-q*l")
test_beam.solve()
fig, ax = test_beam.plot()
Beam points
===================================================================================
Coordinate Type Load Moment
-----------------------------------------------------------------------------------
0 Fixed 0 0
l/4 Continuity point -l*q 0
l/2 Hinge 0 0
l Roller 0 0
===================================================================================
Beam segments
===================================================================================
Span Young modulus Inertia Distributed load
-----------------------------------------------------------------------------------
[ 0 - l/4 ] E I 0
[ l/4 - l/2 ] E I 0
[ l/2 - l ] E I -q
===================================================================================
Exterior Reactions
===================================================================================
Point Type Value
-----------------------------------------------------------------------------------
0 Force 5*l*q/4
0 Moment 3*l**2*q/8
l Force l*q/4
===================================================================================
Internal Loads
===================================================================================
Span Diagram Expression
-----------------------------------------------------------------------------------
[ 0 - l/4 ] V(x) -5*l*q/4
[ 0 - l/4 ] M(x) -3*l**2*q/8 + 5*l*q*x/4
-----------------------------------------------------------------------------------
[ l/4 - l/2 ] V(x) -l*q/4
[ l/4 - l/2 ] M(x) -l**2*q/8 + l*q*x/4
-----------------------------------------------------------------------------------
[ l/2 - l ] V(x) -3*l*q/4 + q*x
[ l/2 - l ] M(x) -l**2*q/4 + 3*l*q*x/4 - q*x**2/2
===================================================================================
Rotation and deflection
===================================================================================
Span Variable Expression
-----------------------------------------------------------------------------------
[ 0 - l/4 ] v(x) -3*l**2*q*x**2/(16*E*I) + 5*l*q*x**3/(24*E*I)
[ 0 - l/4 ] dv/dx(x) -3*l**2*q*x/(8*E*I) + 5*l*q*x**2/(8*E*I)
-----------------------------------------------------------------------------------
[ l/4 - l/2 ] v(x) l**4*q/(384*E*I) - l**3*q*x/(32*E*I) - l**2*q*x**2/(16*E*I) + l*q*x**3/(24*E*I)
[ l/4 - l/2 ] dv/dx(x) -l**3*q/(32*E*I) - l**2*q*x/(8*E*I) + l*q*x**2/(8*E*I)
-----------------------------------------------------------------------------------
[ l/2 - l ] v(x) -5*l**4*q/(96*E*I) + 3*l**3*q*x/(32*E*I) - l**2*q*x**2/(8*E*I) + l*q*x**3/(8*E*I) - q*x**4/(24*E*I)
[ l/2 - l ] dv/dx(x) 3*l**3*q/(32*E*I) - l**2*q*x/(4*E*I) + 3*l*q*x**2/(8*E*I) - q*x**3/(6*E*I)
===================================================================================
- Numeric length
- Fixed
- Hinge
- Numeric distributed linear load
- Numeric distributed contstant load
- Numeric point moment
from symbeam import beam
test_beam = beam(6, x0=0)
test_beam.add_support(0, "fixed")
test_beam.add_support(2, "hinge")
test_beam.add_support(4, "roller")
test_beam.add_distributed_load(0, 4, "-5/4 * x")
test_beam.add_distributed_load(4, 6, -5)
test_beam.add_point_moment(4, 20)
test_beam.solve()
fig, ax = test_beam.plot()
Beam points
===================================================================================
Coordinate Type Load Moment
-----------------------------------------------------------------------------------
0 Fixed 0 0
2 Hinge 0 0
4 Roller 0 20
6 Continuity point 0 0
===================================================================================
Beam segments
===================================================================================
Span Young modulus Inertia Distributed load
-----------------------------------------------------------------------------------
[ 0 - 2 ] E I -5*x/4
[ 2 - 4 ] E I -5*x/4
[ 4 - 6 ] E I -5
===================================================================================
Exterior Reactions
===================================================================================
Point Type Value
-----------------------------------------------------------------------------------
0 Force 65/6
0 Moment 20
4 Force 55/6
===================================================================================
Internal Loads
===================================================================================
Span Diagram Expression
-----------------------------------------------------------------------------------
[ 0 - 2 ] V(x) 5*x**2/8 - 65/6
[ 0 - 2 ] M(x) -5*x**3/24 + 65*x/6 - 20
-----------------------------------------------------------------------------------
[ 2 - 4 ] V(x) 5*x**2/8 - 65/6
[ 2 - 4 ] M(x) -5*x**3/24 + 65*x/6 - 20
-----------------------------------------------------------------------------------
[ 4 - 6 ] V(x) 5*x - 30
[ 4 - 6 ] M(x) -5*x**2/2 + 30*x - 90
===================================================================================
Rotation and deflection
===================================================================================
Span Variable Expression
-----------------------------------------------------------------------------------
[ 0 - 2 ] v(x) -x**5/(96*E*I) + 65*x**3/(36*E*I) - 10*x**2/(E*I)
[ 0 - 2 ] dv/dx(x) -5*x**4/(96*E*I) + 65*x**2/(12*E*I) - 20*x/(E*I)
-----------------------------------------------------------------------------------
[ 2 - 4 ] v(x) -x**5/(96*E*I) + 65*x**3/(36*E*I) - 10*x**2/(E*I) + 248*x/(9*E*I) - 496/(9*E*I)
[ 2 - 4 ] dv/dx(x) -5*x**4/(96*E*I) + 65*x**2/(12*E*I) - 20*x/(E*I) + 248/(9*E*I)
-----------------------------------------------------------------------------------
[ 4 - 6 ] v(x) -5*x**4/(24*E*I) + 5*x**3/(E*I) - 45*x**2/(E*I) + 1748*x/(9*E*I) - 2912/(9*E*I)
[ 4 - 6 ] dv/dx(x) -5*x**3/(6*E*I) + 15*x**2/(E*I) - 90*x/(E*I) + 1748/(9*E*I)
===================================================================================
- Numeric length
- Pin
- Two rollers
- Numeric distributed constant load
- Numeric distributed quadratic load
from symbeam import beam
test_beam = beam(6, x0=0)
test_beam.add_support(0, "roller")
test_beam.add_support(2, "roller")
test_beam.add_support(6, "pin")
test_beam.add_support(4, "hinge")
test_beam.add_distributed_load(0, 4, -5)
test_beam.add_distributed_load(4, 6, "-(-3*(x-5)**2 + 8)")
test_beam.solve()
fig, ax = test_beam.plot()
Beam points
===================================================================================
Coordinate Type Load Moment
-----------------------------------------------------------------------------------
0 Roller 0 0
2 Roller 0 0
4 Hinge 0 0
6 Pinned Support 0 0
===================================================================================
Beam segments
===================================================================================
Span Young modulus Inertia Distributed load
-----------------------------------------------------------------------------------
[ 0 - 2 ] E I -5
[ 2 - 4 ] E I -5
[ 4 - 6 ] E I 3*(x - 5)**2 - 8
===================================================================================
Exterior Reactions
===================================================================================
Point Type Value
-----------------------------------------------------------------------------------
0 Force -7
2 Force 34
6 Force 7
===================================================================================
Internal Loads
===================================================================================
Span Diagram Expression
-----------------------------------------------------------------------------------
[ 0 - 2 ] V(x) 5*x + 7
[ 0 - 2 ] M(x) -5*x**2/2 - 7*x
-----------------------------------------------------------------------------------
[ 2 - 4 ] V(x) 5*x - 27
[ 2 - 4 ] M(x) -5*x**2/2 + 27*x - 68
-----------------------------------------------------------------------------------
[ 4 - 6 ] V(x) -x**3 + 15*x**2 - 67*x + 85
[ 4 - 6 ] M(x) x**4/4 - 5*x**3 + 67*x**2/2 - 85*x + 60
===================================================================================
Rotation and deflection
===================================================================================
Span Variable Expression
-----------------------------------------------------------------------------------
[ 0 - 2 ] v(x) -5*x**4/(24*E*I) - 7*x**3/(6*E*I) + 19*x/(3*E*I)
[ 0 - 2 ] dv/dx(x) -5*x**3/(6*E*I) - 7*x**2/(2*E*I) + 19/(3*E*I)
-----------------------------------------------------------------------------------
[ 2 - 4 ] v(x) -5*x**4/(24*E*I) + 9*x**3/(2*E*I) - 34*x**2/(E*I) + 223*x/(3*E*I) - 136/(3*E*I)
[ 2 - 4 ] dv/dx(x) -5*x**3/(6*E*I) + 27*x**2/(2*E*I) - 68*x/(E*I) + 223/(3*E*I)
-----------------------------------------------------------------------------------
[ 4 - 6 ] v(x) x**6/(120*E*I) - x**5/(4*E*I) + 67*x**4/(24*E*I) - 85*x**3/(6*E*I) + 30*x**2/(E*I) + 61*x/(3*E*I) - 1024/(5*E*I)
[ 4 - 6 ] dv/dx(x) x**5/(20*E*I) - 5*x**4/(4*E*I) + 67*x**3/(6*E*I) - 85*x**2/(2*E*I) + 60*x/(E*I) + 61/(3*E*I)
===================================================================================
- Numeric length
- Pin
- Roller
- Symbolic point load
from symbeam import beam
test_beam = beam(3, x0=0)
test_beam.add_support(0.5, "pin")
test_beam.add_support(2.5, "roller")
test_beam.add_point_load(0, "-P")
test_beam.add_point_load(3, "-P")
test_beam.solve()
fig, ax = test_beam.plot()
Beam points
===================================================================================
Coordinate Type Load Moment
-----------------------------------------------------------------------------------
0 Continuity point -P 0
0.5 Pinned Support 0 0
2.5 Roller 0 0
3 Continuity point -P 0
===================================================================================
Beam segments
===================================================================================
Span Young modulus Inertia Distributed load
-----------------------------------------------------------------------------------
[ 0 - 0.5 ] E I 0
[ 0.5 - 2.5 ] E I 0
[ 2.5 - 3 ] E I 0
===================================================================================
Exterior Reactions
===================================================================================
Point Type Value
-----------------------------------------------------------------------------------
0.5 Force P
2.5 Force P
===================================================================================
Internal Loads
===================================================================================
Span Diagram Expression
-----------------------------------------------------------------------------------
[ 0 - 0.5 ] V(x) P
[ 0 - 0.5 ] M(x) -P*x
-----------------------------------------------------------------------------------
[ 0.5 - 2.5 ] V(x) 0
[ 0.5 - 2.5 ] M(x) -0.5*P
-----------------------------------------------------------------------------------
[ 2.5 - 3 ] V(x) -P
[ 2.5 - 3 ] M(x) P*x - 3.0*P
===================================================================================
Rotation and deflection
===================================================================================
Span Variable Expression
-----------------------------------------------------------------------------------
[ 0 - 0.5 ] v(x) -P*x**3/(6*E*I) + 0.625*P*x/(E*I) - 0.291666666666667*P/(E*I)
[ 0 - 0.5 ] dv/dx(x) -P*x**2/(2*E*I) + 0.625*P/(E*I)
-----------------------------------------------------------------------------------
[ 0.5 - 2.5 ] v(x) -0.25*P*x**2/(E*I) + 0.75*P*x/(E*I) - 0.3125*P/(E*I)
[ 0.5 - 2.5 ] dv/dx(x) -0.5*P*x/(E*I) + 0.75*P/(E*I)
-----------------------------------------------------------------------------------
[ 2.5 - 3 ] v(x) 0.166666666666667*P*x**3/(E*I) - 1.5*P*x**2/(E*I) + 3.875*P*x/(E*I) - 2.91666666666667*P/(E*I)
[ 2.5 - 3 ] dv/dx(x) 0.5*P*x**2/(E*I) - 3.0*P*x/(E*I) + 3.875*P/(E*I)
===================================================================================
- Numeric length
- Pin
- Rollers
- Symbolic point load
- Discontinuous distribution of Young modulus
- Discontinuous distribution of second moment of area
EandIsymbols created with SymPy- User-speficied substitution
from symbeam import beam
Beam points
===================================================================================
Coordinate Type Load Moment
-----------------------------------------------------------------------------------
0 Continuity point -P 0
0.5 Pinned Support 0 0
1 Continuity point 0 0
1.5 Continuity point 0 0
2.5 Roller 0 0
3 Continuity point -P 0
===================================================================================
Beam segments
===================================================================================
Span Young modulus Inertia Distributed load
-----------------------------------------------------------------------------------
[ 0 - 0.5 ] E/1000 I 0
[ 0.5 - 1 ] E/1000 I 0
[ 1 - 1.5 ] E/1000 100*I 0
[ 1.5 - 2.5 ] E 100*I 0
[ 2.5 - 3 ] E 100*I 0
===================================================================================
Exterior Reactions
===================================================================================
Point Type Value
-----------------------------------------------------------------------------------
0.5 Force P
2.5 Force P
===================================================================================
Internal Loads
===================================================================================
Span Diagram Expression
-----------------------------------------------------------------------------------
[ 0 - 0.5 ] V(x) P
[ 0 - 0.5 ] M(x) -P*x
-----------------------------------------------------------------------------------
[ 0.5 - 1 ] V(x) 0
[ 0.5 - 1 ] M(x) -0.5*P
-----------------------------------------------------------------------------------
[ 1 - 1.5 ] V(x) 0
[ 1 - 1.5 ] M(x) -0.5*P
-----------------------------------------------------------------------------------
[ 1.5 - 2.5 ] V(x) 0
[ 1.5 - 2.5 ] M(x) -0.5*P
-----------------------------------------------------------------------------------
[ 2.5 - 3 ] V(x) -P
[ 2.5 - 3 ] M(x) P*x - 3.0*P
===================================================================================
Rotation and deflection
===================================================================================
Span Variable Expression
-----------------------------------------------------------------------------------
[ 0 - 0.5 ] v(x) -500*P*x**3/(3*E*I) + 345.31375*P*x/(E*I) - 151.823541666667*P/(E*I)
[ 0 - 0.5 ] dv/dx(x) -500*P*x**2/(E*I) + 345.31375*P/(E*I)
-----------------------------------------------------------------------------------
[ 0.5 - 1 ] v(x) -250.0*P*x**2/(E*I) + 470.31375*P*x/(E*I) - 172.656875*P/(E*I)
[ 0.5 - 1 ] dv/dx(x) -500.0*P*x/(E*I) + 470.31375*P/(E*I)
-----------------------------------------------------------------------------------
[ 1 - 1.5 ] v(x) -2.5*P*x**2/(E*I) - 24.68625*P*x/(E*I) + 74.843125*P/(E*I)
[ 1 - 1.5 ] dv/dx(x) -5.0*P*x/(E*I) - 24.68625*P/(E*I)
-----------------------------------------------------------------------------------
[ 1.5 - 2.5 ] v(x) -0.0025*P*x**2/(E*I) - 32.17875*P*x/(E*I) + 80.4625*P/(E*I)
[ 1.5 - 2.5 ] dv/dx(x) -0.005*P*x/(E*I) - 32.17875*P/(E*I)
-----------------------------------------------------------------------------------
[ 2.5 - 3 ] v(x) 0.00166666666666667*P*x**3/(E*I) - 0.015*P*x**2/(E*I) - 32.1475*P*x/(E*I) + 80.4364583333333*P/(E*I)
[ 2.5 - 3 ] dv/dx(x) 0.005*P*x**2/(E*I) - 0.03*P*x/(E*I) - 32.1475*P/(E*I)
===================================================================================
- Numeric length
- Pin
- Rollers
- Symbolic point load
- Discontinuous distribution of Young modulus
- Discontinuous distribution of second moment of area
EandIimported directly from SymPy library- User-speficied substitution
from sympy.abc import E, I
from symbeam import beam
Beam points
===================================================================================
Coordinate Type Load Moment
-----------------------------------------------------------------------------------
0 Continuity point -P 0
0.5 Pinned Support 0 0
1 Continuity point 0 0
1.5 Continuity point 0 0
2.5 Roller 0 0
3 Continuity point -P 0
===================================================================================
Beam segments
===================================================================================
Span Young modulus Inertia Distributed load
-----------------------------------------------------------------------------------
[ 0 - 0.5 ] E/1000 I 0
[ 0.5 - 1 ] E/1000 I 0
[ 1 - 1.5 ] E/1000 100*I 0
[ 1.5 - 2.5 ] E 100*I 0
[ 2.5 - 3 ] E 100*I 0
===================================================================================
Exterior Reactions
===================================================================================
Point Type Value
-----------------------------------------------------------------------------------
0.5 Force P
2.5 Force P
===================================================================================
Internal Loads
===================================================================================
Span Diagram Expression
-----------------------------------------------------------------------------------
[ 0 - 0.5 ] V(x) P
[ 0 - 0.5 ] M(x) -P*x
-----------------------------------------------------------------------------------
[ 0.5 - 1 ] V(x) 0
[ 0.5 - 1 ] M(x) -0.5*P
-----------------------------------------------------------------------------------
[ 1 - 1.5 ] V(x) 0
[ 1 - 1.5 ] M(x) -0.5*P
-----------------------------------------------------------------------------------
[ 1.5 - 2.5 ] V(x) 0
[ 1.5 - 2.5 ] M(x) -0.5*P
-----------------------------------------------------------------------------------
[ 2.5 - 3 ] V(x) -P
[ 2.5 - 3 ] M(x) P*x - 3.0*P
===================================================================================
Rotation and deflection
===================================================================================
Span Variable Expression
-----------------------------------------------------------------------------------
[ 0 - 0.5 ] v(x) -500*P*x**3/(3*E*I) + 345.31375*P*x/(E*I) - 151.823541666667*P/(E*I)
[ 0 - 0.5 ] dv/dx(x) -500*P*x**2/(E*I) + 345.31375*P/(E*I)
-----------------------------------------------------------------------------------
[ 0.5 - 1 ] v(x) -250.0*P*x**2/(E*I) + 470.31375*P*x/(E*I) - 172.656875*P/(E*I)
[ 0.5 - 1 ] dv/dx(x) -500.0*P*x/(E*I) + 470.31375*P/(E*I)
-----------------------------------------------------------------------------------
[ 1 - 1.5 ] v(x) -2.5*P*x**2/(E*I) - 24.68625*P*x/(E*I) + 74.843125*P/(E*I)
[ 1 - 1.5 ] dv/dx(x) -5.0*P*x/(E*I) - 24.68625*P/(E*I)
-----------------------------------------------------------------------------------
[ 1.5 - 2.5 ] v(x) -0.0025*P*x**2/(E*I) - 32.17875*P*x/(E*I) + 80.4625*P/(E*I)
[ 1.5 - 2.5 ] dv/dx(x) -0.005*P*x/(E*I) - 32.17875*P/(E*I)
-----------------------------------------------------------------------------------
[ 2.5 - 3 ] v(x) 0.00166666666666667*P*x**3/(E*I) - 0.015*P*x**2/(E*I) - 32.1475*P*x/(E*I) + 80.4364583333333*P/(E*I)
[ 2.5 - 3 ] dv/dx(x) 0.005*P*x**2/(E*I) - 0.03*P*x/(E*I) - 32.1475*P/(E*I)
===================================================================================
- Numeric length
- Fixed
- Hinge
- Roller
- Numeric point moment
- Two numeric distributed linear loads
from symbeam import beam
test_beam = beam(6, x0=0)
test_beam.add_support(0, "fixed")
test_beam.add_support(4, "hinge")
test_beam.add_support(6, "roller")
test_beam.add_point_moment(6, 20)
test_beam.add_distributed_load(0, 2, "-5*x")
test_beam.add_distributed_load(2, 4, "-(20-5*x)")
test_beam.solve()
fig, ax = test_beam.plot()
Beam points
===================================================================================
Coordinate Type Load Moment
-----------------------------------------------------------------------------------
0 Fixed 0 0
2 Continuity point 0 0
4 Hinge 0 0
6 Roller 0 20
===================================================================================
Beam segments
===================================================================================
Span Young modulus Inertia Distributed load
-----------------------------------------------------------------------------------
[ 0 - 2 ] E I -5*x
[ 2 - 4 ] E I 5*x - 20
[ 4 - 6 ] E I 0
===================================================================================
Exterior Reactions
===================================================================================
Point Type Value
-----------------------------------------------------------------------------------
0 Force 30
0 Moment 80
6 Force -10
===================================================================================
Internal Loads
===================================================================================
Span Diagram Expression
-----------------------------------------------------------------------------------
[ 0 - 2 ] V(x) 5*x**2/2 - 30
[ 0 - 2 ] M(x) -5*x**3/6 + 30*x - 80
-----------------------------------------------------------------------------------
[ 2 - 4 ] V(x) -5*x**2/2 + 20*x - 50
[ 2 - 4 ] M(x) 5*x**3/6 - 10*x**2 + 50*x - 280/3
-----------------------------------------------------------------------------------
[ 4 - 6 ] V(x) -10
[ 4 - 6 ] M(x) 10*x - 40
===================================================================================
Rotation and deflection
===================================================================================
Span Variable Expression
-----------------------------------------------------------------------------------
[ 0 - 2 ] v(x) -x**5/(24*E*I) + 5*x**3/(E*I) - 40*x**2/(E*I)
[ 0 - 2 ] dv/dx(x) -5*x**4/(24*E*I) + 15*x**2/(E*I) - 80*x/(E*I)
-----------------------------------------------------------------------------------
[ 2 - 4 ] v(x) x**5/(24*E*I) - 5*x**4/(6*E*I) + 25*x**3/(3*E*I) - 140*x**2/(3*E*I) + 20*x/(3*E*I) - 8/(3*E*I)
[ 2 - 4 ] dv/dx(x) 5*x**4/(24*E*I) - 10*x**3/(3*E*I) + 25*x**2/(E*I) - 280*x/(3*E*I) + 20/(3*E*I)
-----------------------------------------------------------------------------------
[ 4 - 6 ] v(x) 5*x**3/(3*E*I) - 20*x**2/(E*I) + 760*x/(3*E*I) - 1160/(E*I)
[ 4 - 6 ] dv/dx(x) 5*x**2/(E*I) - 40*x/(E*I) + 760/(3*E*I)
===================================================================================
- Numeric length
- Roller
- Pin
- Numeric distriuted linear load
- Numeric distriuted quadratic load
- Two numeric distributed linear loads
from symbeam import beam
test_beam = beam(4, x0=0)
test_beam.add_support(2, "roller")
test_beam.add_support(4, "pin")
test_beam.add_distributed_load(0, 2, "-5*x")
test_beam.add_distributed_load(2, 4, "-(4*x**2-24*x+42)")
test_beam.set_inertia(0, 4, 2.051e-5)
test_beam.set_young(0, 4, 210e9)
test_beam.solve()
fig, ax = test_beam.plot()
Beam points
===================================================================================
Coordinate Type Load Moment
-----------------------------------------------------------------------------------
0 Continuity point 0 0
2 Roller 0 0
4 Pinned Support 0 0
===================================================================================
Beam segments
===================================================================================
Span Young modulus Inertia Distributed load
-----------------------------------------------------------------------------------
[ 0 - 2 ] 210000000000.000 2.05100000000000e-5 -5*x
[ 2 - 4 ] 210000000000.000 2.05100000000000e-5 -4*x**2 + 24*x - 42
===================================================================================
Exterior Reactions
===================================================================================
Point Type Value
-----------------------------------------------------------------------------------
2 Force 62/3
4 Force 4
===================================================================================
Internal Loads
===================================================================================
Span Diagram Expression
-----------------------------------------------------------------------------------
[ 0 - 2 ] V(x) 5*x**2/2
[ 0 - 2 ] M(x) -5*x**3/6
-----------------------------------------------------------------------------------
[ 2 - 4 ] V(x) 4*x**3/3 - 12*x**2 + 42*x - 172/3
[ 2 - 4 ] M(x) -x**4/3 + 4*x**3 - 21*x**2 + 172*x/3 - 64
===================================================================================
Rotation and deflection
===================================================================================
Span Variable Expression
-----------------------------------------------------------------------------------
[ 0 - 2 ] v(x) -9.6739492156362e-9*x**5 + 1.27954101625482e-6*x - 2.24951565760928e-6
[ 0 - 2 ] dv/dx(x) 1.27954101625482e-6 - 4.8369746078181e-8*x**4
-----------------------------------------------------------------------------------
[ 2 - 4 ] v(x) -2.57971979083632e-9*x**6 + 4.64349562350538e-8*x**5 - 4.0630586705672e-7*x**4 + 2.21855902011923e-6*x**3 - 7.4295929976086e-6*x**2 + 1.33835862748588e-5*x - 9.61719538023778e-6
[ 2 - 4 ] dv/dx(x) -1.54783187450179e-8*x**5 + 2.32174781175269e-7*x**4 - 1.62522346822688e-6*x**3 + 6.6556770603577e-6*x**2 - 1.48591859952172e-5*x + 1.33835862748588e-5
===================================================================================
- Numeric length
- Roller
- Hinge
- Fixed
- Numeric distributed constant load
- Numeric distributed quadratic load
from symbeam import beam
test_beam = beam(4, x0=0)
test_beam.add_support(0, "roller")
test_beam.add_support(1, "hinge")
test_beam.add_support(4, "fixed")
test_beam.add_distributed_load(0, 2, "-5")
test_beam.add_distributed_load(2, 4, "-(4*x**2 - 24 *x + 37)")
test_beam.solve()
fig, ax = test_beam.plot()
Beam points
===================================================================================
Coordinate Type Load Moment
-----------------------------------------------------------------------------------
0 Roller 0 0
1 Hinge 0 0
2 Continuity point 0 0
4 Fixed 0 0
===================================================================================
Beam segments
===================================================================================
Span Young modulus Inertia Distributed load
-----------------------------------------------------------------------------------
[ 0 - 1 ] E I -5
[ 1 - 2 ] E I -5
[ 2 - 4 ] E I -4*x**2 + 24*x - 37
===================================================================================
Exterior Reactions
===================================================================================
Point Type Value
-----------------------------------------------------------------------------------
0 Force 5/2
4 Force 73/6
4 Moment -74/3
===================================================================================
Internal Loads
===================================================================================
Span Diagram Expression
-----------------------------------------------------------------------------------
[ 0 - 1 ] V(x) 5*x - 5/2
[ 0 - 1 ] M(x) -5*x**2/2 + 5*x/2
-----------------------------------------------------------------------------------
[ 1 - 2 ] V(x) 5*x - 5/2
[ 1 - 2 ] M(x) -5*x**2/2 + 5*x/2
-----------------------------------------------------------------------------------
[ 2 - 4 ] V(x) 4*x**3/3 - 12*x**2 + 37*x - 175/6
[ 2 - 4 ] M(x) -x**4/3 + 4*x**3 - 37*x**2/2 + 175*x/6 - 16
===================================================================================
Rotation and deflection
===================================================================================
Span Variable Expression
-----------------------------------------------------------------------------------
[ 0 - 1 ] v(x) -5*x**4/(24*E*I) + 5*x**3/(12*E*I) - 2932*x/(45*E*I)
[ 0 - 1 ] dv/dx(x) -5*x**3/(6*E*I) + 5*x**2/(4*E*I) - 2932/(45*E*I)
-----------------------------------------------------------------------------------
[ 1 - 2 ] v(x) -5*x**4/(24*E*I) + 5*x**3/(12*E*I) + 452*x/(15*E*I) - 4288/(45*E*I)
[ 1 - 2 ] dv/dx(x) -5*x**3/(6*E*I) + 5*x**2/(4*E*I) + 452/(15*E*I)
-----------------------------------------------------------------------------------
[ 2 - 4 ] v(x) -x**6/(90*E*I) + x**5/(5*E*I) - 37*x**4/(24*E*I) + 175*x**3/(36*E*I) - 8*x**2/(E*I) + 188*x/(5*E*I) - 1472/(15*E*I)
[ 2 - 4 ] dv/dx(x) -x**5/(15*E*I) + x**4/(E*I) - 37*x**3/(6*E*I) + 175*x**2/(12*E*I) - 16*x/(E*I) + 188/(5*E*I)
===================================================================================
- Symbolic length
- Fixed
- Symbolic point force
- Classical clamped beam problem
from symbeam import beam
test_beam = beam("L", x0=0)
test_beam.add_support(0, "fixed")
test_beam.add_point_load("L", "-P")
test_beam.solve()
fig, ax = test_beam.plot()
Beam points
===================================================================================
Coordinate Type Load Moment
-----------------------------------------------------------------------------------
0 Fixed 0 0
L Continuity point -P 0
===================================================================================
Beam segments
===================================================================================
Span Young modulus Inertia Distributed load
-----------------------------------------------------------------------------------
[ 0 - L ] E I 0
===================================================================================
Exterior Reactions
===================================================================================
Point Type Value
-----------------------------------------------------------------------------------
0 Force P
0 Moment L*P
===================================================================================
Internal Loads
===================================================================================
Span Diagram Expression
-----------------------------------------------------------------------------------
[ 0 - L ] V(x) -P
[ 0 - L ] M(x) -L*P + P*x
===================================================================================
Rotation and deflection
===================================================================================
Span Variable Expression
-----------------------------------------------------------------------------------
[ 0 - L ] v(x) -L*P*x**2/(2*E*I) + P*x**3/(6*E*I)
[ 0 - L ] dv/dx(x) -L*P*x/(E*I) + P*x**2/(2*E*I)
===================================================================================
- Symbolic length
- Fixed
- Symbolic point moment
- Classical clamped beam problem
from symbeam import beam
test_beam = beam("L", x0=0)
test_beam.add_support(0, "fixed")
test_beam.add_point_moment("L", "M")
test_beam.solve()
fig, ax = test_beam.plot()
Beam points
===================================================================================
Coordinate Type Load Moment
-----------------------------------------------------------------------------------
0 Fixed 0 0
L Continuity point 0 M
===================================================================================
Beam segments
===================================================================================
Span Young modulus Inertia Distributed load
-----------------------------------------------------------------------------------
[ 0 - L ] E I 0
===================================================================================
Exterior Reactions
===================================================================================
Point Type Value
-----------------------------------------------------------------------------------
0 Force 0
0 Moment -M
===================================================================================
Internal Loads
===================================================================================
Span Diagram Expression
-----------------------------------------------------------------------------------
[ 0 - L ] V(x) 0
[ 0 - L ] M(x) M
===================================================================================
Rotation and deflection
===================================================================================
Span Variable Expression
-----------------------------------------------------------------------------------
[ 0 - L ] v(x) M*x**2/(2*E*I)
[ 0 - L ] dv/dx(x) M*x/(E*I)
===================================================================================
- Numeric length
- Pin
- Roller
- Numeric point force
- Classical pinned beam problem with half-span force
from symbeam import beam
test_beam = beam("l", x0=0)
test_beam.add_support(0, "pin")
test_beam.add_support("l", "roller")
test_beam.add_point_load("l/2", "-P")
test_beam.solve()
fig, ax = test_beam.plot()
Beam points
===================================================================================
Coordinate Type Load Moment
-----------------------------------------------------------------------------------
0 Pinned Support 0 0
l/2 Continuity point -P 0
l Roller 0 0
===================================================================================
Beam segments
===================================================================================
Span Young modulus Inertia Distributed load
-----------------------------------------------------------------------------------
[ 0 - l/2 ] E I 0
[ l/2 - l ] E I 0
===================================================================================
Exterior Reactions
===================================================================================
Point Type Value
-----------------------------------------------------------------------------------
0 Force P/2
l Force P/2
===================================================================================
Internal Loads
===================================================================================
Span Diagram Expression
-----------------------------------------------------------------------------------
[ 0 - l/2 ] V(x) -P/2
[ 0 - l/2 ] M(x) P*x/2
-----------------------------------------------------------------------------------
[ l/2 - l ] V(x) P/2
[ l/2 - l ] M(x) P*l/2 - P*x/2
===================================================================================
Rotation and deflection
===================================================================================
Span Variable Expression
-----------------------------------------------------------------------------------
[ 0 - l/2 ] v(x) -P*l**2*x/(16*E*I) + P*x**3/(12*E*I)
[ 0 - l/2 ] dv/dx(x) -P*l**2/(16*E*I) + P*x**2/(4*E*I)
-----------------------------------------------------------------------------------
[ l/2 - l ] v(x) P*l**3/(48*E*I) - 3*P*l**2*x/(16*E*I) + P*l*x**2/(4*E*I) - P*x**3/(12*E*I)
[ l/2 - l ] dv/dx(x) -3*P*l**2/(16*E*I) + P*l*x/(2*E*I) - P*x**2/(4*E*I)
===================================================================================
- Numeric length
- Pin
- Roller
- Set of numeric point forces and moments
from symbeam import beam
test_beam = beam("l", x0=0)
test_beam.add_support(0, "pin")
test_beam.add_support("l", "roller")
test_beam.add_point_load("l/4", "P")
test_beam.add_point_moment("l/4", "P*l / 2")
test_beam.add_point_load("l/2", "-2*P")
test_beam.add_point_moment("7*l/8", "-P*l")
test_beam.add_point_load("3*l/4", "-3*P")
test_beam.solve()
fig, ax = test_beam.plot()
Beam points
===================================================================================
Coordinate Type Load Moment
-----------------------------------------------------------------------------------
0 Pinned Support 0 0
l/4 Continuity point P P*l/2
l/2 Continuity point -2*P 0
3*l/4 Continuity point -3*P 0
7*l/8 Continuity point 0 -P*l
l Roller 0 0
===================================================================================
Beam segments
===================================================================================
Span Young modulus Inertia Distributed load
-----------------------------------------------------------------------------------
[ 0 - l/4 ] E I 0
[ l/4 - l/2 ] E I 0
[ l/2 - 3*l/4 ] E I 0
[ 3*l/4 - 7*l/8 ] E I 0
[ 7*l/8 - l ] E I 0
===================================================================================
Exterior Reactions
===================================================================================
Point Type Value
-----------------------------------------------------------------------------------
0 Force P/2
l Force 7*P/2
===================================================================================
Internal Loads
===================================================================================
Span Diagram Expression
-----------------------------------------------------------------------------------
[ 0 - l/4 ] V(x) -P/2
[ 0 - l/4 ] M(x) P*x/2
-----------------------------------------------------------------------------------
[ l/4 - l/2 ] V(x) -3*P/2
[ l/4 - l/2 ] M(x) -3*P*l/4 + 3*P*x/2
-----------------------------------------------------------------------------------
[ l/2 - 3*l/4 ] V(x) P/2
[ l/2 - 3*l/4 ] M(x) P*l/4 - P*x/2
-----------------------------------------------------------------------------------
[ 3*l/4 - 7*l/8 ] V(x) 7*P/2
[ 3*l/4 - 7*l/8 ] M(x) 5*P*l/2 - 7*P*x/2
-----------------------------------------------------------------------------------
[ 7*l/8 - l ] V(x) 7*P/2
[ 7*l/8 - l ] M(x) 7*P*l/2 - 7*P*x/2
===================================================================================
Rotation and deflection
===================================================================================
Span Variable Expression
-----------------------------------------------------------------------------------
[ 0 - l/4 ] v(x) 11*P*l**2*x/(384*E*I) + P*x**3/(12*E*I)
[ 0 - l/4 ] dv/dx(x) 11*P*l**2/(384*E*I) + P*x**2/(4*E*I)
-----------------------------------------------------------------------------------
[ l/4 - l/2 ] v(x) -7*P*l**3/(384*E*I) + 71*P*l**2*x/(384*E*I) - 3*P*l*x**2/(8*E*I) + P*x**3/(4*E*I)
[ l/4 - l/2 ] dv/dx(x) 71*P*l**2/(384*E*I) - 3*P*l*x/(4*E*I) + 3*P*x**2/(4*E*I)
-----------------------------------------------------------------------------------
[ l/2 - 3*l/4 ] v(x) 3*P*l**3/(128*E*I) - 25*P*l**2*x/(384*E*I) + P*l*x**2/(8*E*I) - P*x**3/(12*E*I)
[ l/2 - 3*l/4 ] dv/dx(x) -25*P*l**2/(384*E*I) + P*l*x/(4*E*I) - P*x**2/(4*E*I)
-----------------------------------------------------------------------------------
[ 3*l/4 - 7*l/8 ] v(x) 15*P*l**3/(64*E*I) - 349*P*l**2*x/(384*E*I) + 5*P*l*x**2/(4*E*I) - 7*P*x**3/(12*E*I)
[ 3*l/4 - 7*l/8 ] dv/dx(x) -349*P*l**2/(384*E*I) + 5*P*l*x/(2*E*I) - 7*P*x**2/(4*E*I)
-----------------------------------------------------------------------------------
[ 7*l/8 - l ] v(x) 79*P*l**3/(128*E*I) - 685*P*l**2*x/(384*E*I) + 7*P*l*x**2/(4*E*I) - 7*P*x**3/(12*E*I)
[ 7*l/8 - l ] dv/dx(x) -685*P*l**2/(384*E*I) + 7*P*l*x/(2*E*I) - 7*P*x**2/(4*E*I)
===================================================================================
- Numeric
- Pin
- Roller
- Numeric sinusoidal distributed force
from symbeam import beam
test_beam = beam(1, x0=0)
test_beam.add_support(0, "pin")
test_beam.add_support(1, "roller")
test_beam.add_distributed_load(0, 1, "sin(20 * x)")
test_beam.solve()
fig, ax = test_beam.plot()
Beam points
===================================================================================
Coordinate Type Load Moment
-----------------------------------------------------------------------------------
0 Pinned Support 0 0
1 Roller 0 0
===================================================================================
Beam segments
===================================================================================
Span Young modulus Inertia Distributed load
-----------------------------------------------------------------------------------
[ 0 - 1 ] E I sin(20*x)
===================================================================================
Exterior Reactions
===================================================================================
Point Type Value
-----------------------------------------------------------------------------------
0 Force -1/20 + sin(20)/400
1 Force -sin(20)/400 + cos(20)/20
===================================================================================
Internal Loads
===================================================================================
Span Diagram Expression
-----------------------------------------------------------------------------------
[ 0 - 1 ] V(x) cos(20*x)/20 - sin(20)/400
[ 0 - 1 ] M(x) x*sin(20)/400 - sin(20*x)/400
===================================================================================
Rotation and deflection
===================================================================================
Span Variable Expression
-----------------------------------------------------------------------------------
[ 0 - 1 ] v(x) -203*x*sin(20)/(480000*E*I) + (x**3*sin(20)/2400 + sin(20*x)/160000)/(E*I)
[ 0 - 1 ] dv/dx(x) (x**2*sin(20)/800 + cos(20*x)/8000)/(E*I) - 203*sin(20)/(480000*E*I)
===================================================================================
- Symbolic length scaled by number
- Roller
- Hinge
- Fixed
- Symbolic distributed linear load
- Symbolic distributed quadratic load
from symbeam import beam
test_beam = beam("3*l", x0=0)
test_beam.add_support("l", "roller")
test_beam.add_support("2*l", "hinge")
test_beam.add_support("3*l", "fixed")
test_beam.add_distributed_load(0, "l", "- q / l * x")
test_beam.add_distributed_load("2*l", "3*l", "q / l**2 * x**2 - 6*q*x/l + 9*q")
test_beam.solve()
fig, ax = test_beam.plot()
plt.savefig(__file__.split(".py")[0] + ".svg")
Beam points
===================================================================================
Coordinate Type Load Moment
-----------------------------------------------------------------------------------
0 Continuity point 0 0
l Roller 0 0
2*l Hinge 0 0
3*l Fixed 0 0
===================================================================================
Beam segments
===================================================================================
Span Young modulus Inertia Distributed load
-----------------------------------------------------------------------------------
[ 0 - l ] E I -q*x/l
[ l - 2*l ] E I 0
[ 2*l - 3*l ] E I 9*q - 6*q*x/l + q*x**2/l**2
===================================================================================
Exterior Reactions
===================================================================================
Point Type Value
-----------------------------------------------------------------------------------
l Force 2*l*q/3
3*l Force -l*q/2
3*l Moment 5*l**2*q/12
===================================================================================
Internal Loads
===================================================================================
Span Diagram Expression
-----------------------------------------------------------------------------------
[ 0 - l ] V(x) q*x**2/(2*l)
[ 0 - l ] M(x) -q*x**3/(6*l)
-----------------------------------------------------------------------------------
[ l - 2*l ] V(x) -l*q/6
[ l - 2*l ] M(x) -l**2*q/3 + l*q*x/6
-----------------------------------------------------------------------------------
[ 2*l - 3*l ] V(x) 17*l*q/2 - 9*q*x + 3*q*x**2/l - q*x**3/(3*l**2)
[ 2*l - 3*l ] M(x) 17*l**2*q/3 - 17*l*q*x/2 + 9*q*x**2/2 - q*x**3/l + q*x**4/(12*l**2)
===================================================================================
Rotation and deflection
===================================================================================
Span Variable Expression
-----------------------------------------------------------------------------------
[ 0 - l ] v(x) -13*l**4*q/(60*E*I) + 9*l**3*q*x/(40*E*I) - q*x**5/(120*E*I*l)
[ 0 - l ] dv/dx(x) 9*l**3*q/(40*E*I) - q*x**4/(24*E*I*l)
-----------------------------------------------------------------------------------
[ l - 2*l ] v(x) -53*l**4*q/(180*E*I) + 13*l**3*q*x/(30*E*I) - l**2*q*x**2/(6*E*I) + l*q*x**3/(36*E*I)
[ l - 2*l ] dv/dx(x) 13*l**3*q/(30*E*I) - l**2*q*x/(3*E*I) + l*q*x**2/(12*E*I)
-----------------------------------------------------------------------------------
[ 2*l - 3*l ] v(x) 33*l**4*q/(20*E*I) - 61*l**3*q*x/(20*E*I) + 17*l**2*q*x**2/(6*E*I) - 17*l*q*x**3/(12*E*I) + 3*q*x**4/(8*E*I) - q*x**5/(20*E*I*l) + q*x**6/(360*E*I*l**2)
[ 2*l - 3*l ] dv/dx(x) -61*l**3*q/(20*E*I) + 17*l**2*q*x/(3*E*I) - 17*l*q*x**2/(4*E*I) + 3*q*x**3/(2*E*I) - q*x**4/(4*E*I*l) + q*x**5/(60*E*I*l**2)
===================================================================================