Section Properties of Closed Shape

Determine the section properties of closed shapes

Supply coordinate pairs of a planar closed polygon and the section properties are calculated

Example Rectangular Section

We provide the coordinates of a 1.2m deep by 0.6m wide rectangular section and use closed form solutions to compare the results

from ge_lib.general.section_props.SectionProperties import SectionProperties 

    data = {"coords":[
                [0,0],
                [0,1.2],
                [0.6,1.2],
                [0.6,0],
                [0,0]
                ],
                "units":"m"
                }
    sp =  SectionProperties()
    values, symbols, description, units = sp.calc_props(data)
    result = { "symbols":symbols,
               "description":description,
               "units": units,
               "values":values} 
    print (result)

result:

{
    "symbols": [
        "Area",
        "AX",
        "AY",
        "IX",
        "IY",
        "IXY",
        "Xc",
        "Yc",
        "IXC",
        "IYC",
        "IXYC",
        "IU",
        "IV",
        "Theta"
    ],
    "description": [
        "Section area",
        "First moment of area about the X axis",
        "First moment of area about the Y axis",
        "Second Moment of Area about the X axis",
        "Second Moment of Area about the Y axis",
        "Product of Inertia about origin",
        "Centroid X coordinate",
        "Centroid Y coordinate",
        "2nd Moment of Area about axis through the centroid parallel to X",
        "2nd Moment of Area about axis through the centroid parallel to Y",
        "Product of Inertia about centroid",
        "2nd moment of area about principal axis 1 through centroid",
        "2nd moment of area about principal axis 2 through centroid",
        "Angle of principal axes to X,Y axes"
    ],
    "units": [
        "m2",
        "m3",
        "m3",
        "m4",
        "m4",
        "m4",
        "m",
        "m",
        "m4",
        "m4",
        "m4",
        "m4",
        "m4",
        "degrees"
    ],
    "values": [
        0.72,
        0.432,
        0.216,
        0.34559999999999996,
        0.08639999999999999,
        0.12960000000000002,
        0.3,
        0.6,
        0.08639999999999998,
        0.021599999999999994,
        2.7755575615628914e-17,
        0.08639999999999998,
        0.021599999999999994,
        0
    ]
}

Comparison with section properties calculated from formulae for rectangular section

Property	Units	From formulae	From function	Error (%)
Area (AX)	bd	1.2*0.6 = 0.72	0.72	0
Second Moment of Area (IX)	bd3/12	0.6*1.2^3/12 = 0.864	0.8639999	0
Second Moment of Area (IY)	db3/12	1.2*0.6^3/12 = 0.0216	0.2159999	0

Example UC Section

We provide the coordinates of a structural a structural steel section in mm (356 x 406 x 634 x 633.9kg/m UC) and use the published geometry of to compare the results

from ge_lib.general.section_props.SectionProperties import SectionProperties 

 # 356 x 406 x 634 x 633.9kg/m UC
    data = {"name":"356x406x634x633.9kg/m",
            "coords":[
                        [0,0],
                        [0,77],
                        [188.2,77],
                        [188.2,397.6],
                        [0,397.6],
                        [0,474.6],
                        [424,474.6],
                        [424,397.6],
                        [235.8,397.6],
                        [235.8,77],
                        [424,77],
                        [424,0],
                        [0,0]],
            "units":"mm"}


    sp =  SectionProperties()

    values, symbols, description, units = sp.calc_props(data)
    result = {"symbols":symbols,
                "description":description,
                "units": units,
                "values":values} 
    print (result)

result:

{
 "symbols": [
        "Area",
        "AX",
        "AY",
        "IX",
        "IY",
        "IXY",
        "Xc",
        "Yc",
        "IXC",
        "IYC",
        "IXYC",
        "IU",
        "IV",
        "Theta"
    ],
    "description": [
        "Section area",
        "First moment of area about the X axis",
        "First moment of area about the Y axis",
        "Second Moment of Area about the X axis",
        "Second Moment of Area about the Y axis",
        "Product of Inertia about origin",
        "Centroid X coordinate",
        "Centroid Y coordinate",
        "2nd Moment of Area about axis through the centroid parallel to X",
        "2nd Moment of Area about axis through the centroid parallel to Y",
        "Product of Inertia about centroid",
        "2nd moment of area about principal axis 1 through centroid",
        "2nd moment of area about principal axis 2 through centroid",
        "Angle of principal axes to X,Y axes"
    ],
    "units": [
        "mm2",
        "mm3",
        "mm3",
        "mm4",
        "mm4",
        "mm4",
        "mm",
        "mm",
        "mm4",
        "mm4",
        "mm4",
        "mm4",
        "mm4",
        "degrees"
    ],
    "values": [
        80556.56,
        19116071.688000005,
        17077990.720000003,
        7279809664.205869,
        4601636571.1754675,
        4052607197.8560004,
        212.00000000000003,
        237.30000000000007,
        2743565852.643466,
        981102538.5354662,
        -0.000001430511474609375,
        2743565852.643466,
        981102538.5354662,
        -4.6504383599970096e-14
    ]
}

Comparison with published section properties

Property	Units	Published	Calculated	Error (%)
Area (AX)	mm2	80800	80557	-0.301
Second Moment of Area (IX)	mm4	2748000000	2743565853	-0.161
Second Moment of Area (IY)	mm4	981300000	981102539	-0.020